Peering Down the Quantum Well: The Inner Workings of Diode Lasers Revealed Through Voltage Nanoscopy
by
Scott B. Kuntze
A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto
c 2004 by Scott B. Kuntze Copyright
Abstract Peering Down the Quantum Well: The Inner Workings of Diode Lasers Revealed Through Voltage Nanoscopy Scott B. Kuntze Master of Applied Science Graduate Department of The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto 2004 What can be learned of the inner workings of semiconductor lasers using properlyinterpreted voltage probing with nanometer resolution? To address this question, nanoscopic voltage probing is employed. Scanning voltage microscopy (SVM) reveals directly the potential profiles of actively-driven devices, combining high-impedance potentiometry with spatial profiling of atomic force microscopy. This work makes three contributions. (1) A model is developed to understand the measured quantity of a nanoscopic potential probe placed on a nonequilibrium semiconductor. Governing quantities deep within the device are revealed by voltage probing the surface. (2) The probe–sample interface is investigated experimentally and theoretically to optimize SVM measurements and ensure they are accurate and reproducible. Artifact-free voltage scans of semiconductor devices in operation are obtained at the spatial resolution limit. (3) SVM is applied to directly image parasitic power dissipation at the p-type contact in state-of-the-art quantum well lasers. Previously, such dissipation could only be inferred though experiments on test structures that do not represent actual diode lasers. This work quantifies both the measured potential and the method used to acquire it, peering directly into the inner workings of semiconductor lasers.
ii
Acknowledgements This work would simply not have occurred without the help and guidance of a number of incredible people. First and foremost, I must thank my supervisor Prof. Ted Sargent for constant encouragement, thoughtful support, and patient understanding. Typical discussions leave me with more answers than I had questions, but more more questions than I have answers— this I deem to be a very good thing. I could not ask for more in a supervisor. I thank Dr. Dayan Ban—who pioneered the experimental technique on semiconductor lasers on the way to his Ph. D.—for offering his great insight and interpretation. I feel fortunate to have spent a summer at Nortel Networks Optical Components—now Bookham Technology—during which this work started. Great thanks go to Dr. St. John Dixon-Warren for generously offering his lab, his diamond-coated tips, and his skill for days on-end as these experiments were performed, and for his enthusiasm at each stage. I thank Dr. J. Kenton White for physics lessons, theoretical insight, and vigorous agreement. Many thanks to Dr. Karin Hinzer for her tremendous enthusiasm and for pointing me in the right direction many times over. Prof. Peter Herman deserves a great thanks for the use of his atomic force microscope that worked flawlessly while gathering much of the data presented herein. I would like to thank Dr. Alex Shik for fruitful technical discussions and for reminding me about photocurrent. Thanks to Dr. Shiguo Zhang for ideas regarding InP contacts. In our research group I must thank Sam Cauchi for much help in getting a working scanning voltage microscopy lab at the university needed to complete the experimental work in this thesis. Many thanks to Emanuel Istrate and Andrew Stok for their patience in teaching me Linux and LATEX, and for great discussions of all sorts. I wish to thank the rest of the team for support and help and advice of all kinds during my first year here. Finally, I must thank my parents for their unending support and encouragement in uncountably many ways.
iii
Contents 1 Probing semiconductor devices electrically
1
1.1
Semiconductor devices and experimental challenges . . . . . . . . . . . .
1
1.2
Opening the black box: scanning voltage microscopy . . . . . . . . . . .
3
1.3
Goals and approach of this work . . . . . . . . . . . . . . . . . . . . . . .
7
1.4
Thesis organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.5
Notation, conventions and constants . . . . . . . . . . . . . . . . . . . . .
10
2 Prior art
11
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
2.2
Modern semiconductor diode lasers . . . . . . . . . . . . . . . . . . . . .
12
2.2.1
. . . . . . . . . . . . . . . . . .
12
Ridge waveguide lasers . . . . . . . . . . . . . . . . . . . . . . . .
14
Buried heterostructure lasers . . . . . . . . . . . . . . . . . . . . .
15
Nanoscopic scanning probe techniques . . . . . . . . . . . . . . . . . . .
15
2.3.1
Atomic force microscopy . . . . . . . . . . . . . . . . . . . . . . .
15
2.3.2
Conductive AFM tips . . . . . . . . . . . . . . . . . . . . . . . . .
17
2.3.3
Scanning resistance techniques . . . . . . . . . . . . . . . . . . . .
19
Nano-scanning resistance profiling . . . . . . . . . . . . . . . . . .
20
Scanning spreading resistance microscopy . . . . . . . . . . . . . .
22
2.3.4
Electrostatic/Kelvin force microscopy . . . . . . . . . . . . . . . .
23
2.3.5
Scanning capacitance microscopy . . . . . . . . . . . . . . . . . .
25
2.3.6
Scanning tunneling microscopy . . . . . . . . . . . . . . . . . . .
28
2.3.7
Direct voltage probing . . . . . . . . . . . . . . . . . . . . . . . .
28
Microscopic voltage probing . . . . . . . . . . . . . . . . . . . . .
28
Scanning voltage microscopy . . . . . . . . . . . . . . . . . . . . .
29
Conclusions and questions drawn from the prior art . . . . . . . . . . . .
31
2.3
2.4
Laser architecture and operation
iv
3 What a voltage probe measures on an active semiconductor
33
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
3.2
Modeling CVD boron-doped diamond probes . . . . . . . . . . . . . . . .
34
3.3
Thermodynamic picture of measured voltage . . . . . . . . . . . . . . . .
35
3.4
Carrier transport model of measured voltage . . . . . . . . . . . . . . . .
36
3.4.1
Drift-diffusion at the probe–sample interface . . . . . . . . . . . .
36
3.4.2
Model interpretation . . . . . . . . . . . . . . . . . . . . . . . . .
38
Modeling conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
3.5
4 Optimizing SVM spatial resolution
40
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
4.2
Interface characterization experiments
. . . . . . . . . . . . . . . . . . .
41
4.3
SVM hysteresis and impulse response . . . . . . . . . . . . . . . . . . . .
42
4.4
Transient interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
4.4.1
Transient equivalent circuit . . . . . . . . . . . . . . . . . . . . .
44
4.4.2
Tip–sample bandstructure . . . . . . . . . . . . . . . . . . . . . .
46
4.5
Limiting scan speed eliminates artifacts . . . . . . . . . . . . . . . . . . .
49
4.6
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
5 Investigating the p-type contact in coolerless lasers
54
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
5.2
InGaAs/InP heterojunction characterization . . . . . . . . . . . . . . . .
57
5.2.1
Experiment and results . . . . . . . . . . . . . . . . . . . . . . . .
57
5.2.2
Low-bias SVM artifact identification: photocurrent . . . . . . . .
60
5.2.3
p-type InGaAs/InP heterojunction parasitics . . . . . . . . . . . .
62
5.2.4
Heating effects from heterojunction power dissipation . . . . . . .
64
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
5.3
6 Conclusions and Future Work
67
6.1
Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . .
67
6.2
Original Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
6.3
Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
6.3.1
Improvements to the SVM (scanning voltage microscopy) Technique 69 Spatial resolution enhancement . . . . . . . . . . . . . . . . . . .
69
Noise analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
6.3.2
Semiconductor Diode Photodetectors . . . . . . . . . . . . . . . .
70
6.3.3
Quantum Cascade Diode Lasers . . . . . . . . . . . . . . . . . . .
71
v
6.4
6.3.4
SVM on Pulse-Biased Devices: The Analog Modulation Analogue
72
6.3.5
Nanocomposite Electroluminescent and Photodetection Devices .
74
Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
A Definition of Electrochemical Potential
78
B Tunneling at the SVM probe–sample interface
80
Bibliography
83
vi
List of Figures 1.1
Probing a semiconductor electroluminescent black box
. . . . . . . . . .
2
1.2
Generalized scanning voltage microscopy implementation. . . . . . . . . .
3
1.3
Logical schematic of SVM implementation . . . . . . . . . . . . . . . . .
4
1.4
Diode laser carrier and chip . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.5
Ridge waveguide laser in the AFM . . . . . . . . . . . . . . . . . . . . .
5
1.6
Voltage scanning a ridge waveguide laser . . . . . . . . . . . . . . . . . .
6
1.7
Two-dimensional voltage map of ridge waveguide laser . . . . . . . . . .
6
2.1
Diode laser architectures . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
2.2
Diode laser operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
2.3
Schematic of atomic force microscope . . . . . . . . . . . . . . . . . . . .
16
2.4
Band structure for H-terminated B-doped CVD diamond (100) and (111)
18
2.5
Schematic of spreading resistance profiling . . . . . . . . . . . . . . . . .
20
2.6
SRP current leakage correction . . . . . . . . . . . . . . . . . . . . . . .
21
2.7
Schematic of scanning spreading resistance microscopy . . . . . . . . . .
22
2.8
Generalized SVM experimental configuration . . . . . . . . . . . . . . . .
30
3.1
Sample–probe carrier concentrations . . . . . . . . . . . . . . . . . . . .
37
4.1
Time-resolved SVM setup . . . . . . . . . . . . . . . . . . . . . . . . . .
42
4.2
Electric potential cross-sections of the p–n–p–n blocking layers of a forwardbiased buried heterostructure laser . . . . . . . . . . . . . . . . . . . . .
4.3
43
Impulse response of the scanning voltage microscopy measurement circuit on buried heterostructure laser . . . . . . . . . . . . . . . . . . . . . . . .
45
4.4
SVM tip–sample equivalent circuits . . . . . . . . . . . . . . . . . . . . .
46
4.5
Energy band diagram of tip–sample interface for n-type and p-type InP
4.6
sample material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
Asymmetry in the tip–InP interface . . . . . . . . . . . . . . . . . . . . .
49
vii
4.7
Bandstructure comparison between CVD (chemical vapour deposition) diamond and common semiconductors . . . . . . . . . . . . . . . . . . . . .
51
4.8
Scan speed artifacts at high resolution . . . . . . . . . . . . . . . . . . .
51
4.9
High resolution SVM scan showing 4 nm quantum wells . . . . . . . . . .
52
5.1
Method of measuring specific contact resistance of p-InP contact . . . . .
56
5.2
Schematic of pVHT laser facet . . . . . . . . . . . . . . . . . . . . . . . .
57
5.3
SVM experimental implementation . . . . . . . . . . . . . . . . . . . . .
58
5.4
SVM scans of wide-MQW RWG laser, 0:10:190 mA . . . . . . . . . . . .
59
5.5
SVM scans of wide-MQW RWG laser, low bias voltage . . . . . . . . . .
60
5.6
Evidence of reverse photocurrent effects at low sample voltage . . . . . .
61
5.7
In0.53 Ga0.47 As/InP heterojunction bandstructure . . . . . . . . . . . . . .
62
5.8
Fractional parasitic voltage drop of p-InP/p-In0.53 Ga0.47 As heterojunction
63
5.9
Low-bias fractional parasitic voltage drop of p-InP/p-In0.53 Ga0.47 As heterojunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
5.10 Thermionic loss mechanism . . . . . . . . . . . . . . . . . . . . . . . . .
65
6.1
SVM on a photodiode . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
6.2
Quantum cascade laser phenomena . . . . . . . . . . . . . . . . . . . . .
72
6.3
Pulsed-bias SVM over p–n–p–n current blocking layers . . . . . . . . . .
74
6.4
Nanocrystal optoelectronic devices . . . . . . . . . . . . . . . . . . . . .
75
viii
List of Tables 1.1
Physical constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1
Summary of time constants on p-n-p-n scan time-resolved experiments and RC equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
10
44
Chapter 1 Probing semiconductor devices electrically 1.1
Semiconductor devices and experimental challenges
Electronic devices permeate the world: semiconductor microchips exist in everyday objects from cars to audio systems to personal computing and communication devices; photonic diode lasers connect electronic systems across the chassis of a car, between a compact disc player and an audio amplifier, between telephone and Internet central offices in cities across the globe. Since the invention of semiconductor devices and the stabilization of their fabrication processes in the middle of the Twentieth Century, these devices have been studied and modeled to improve both our understanding of the underlying physics and our ability to design the physics into the functionality that drives the computer and communications age. Semiconductor diode lasers are used extensively as the transmitters in fibre-optic communication systems at the electronic–optical interface [1]. Fibre-optic communication systems are pervasive—many telephone calls and nearly all internet data transfers take 1
2
1. Probing semiconductor devices electrically
Iapp(t)
+ V(t) -
L(λ,t)
Figure 1.1: A semiconductor electroluminescent device under input/output test. By setting the input current Iapp (t), one can learn about the output behavior of the device across the terminals and from the light-emitting facet. However, the internal governing processes generally remain hidden.
place over optical links driven by semiconductor lasers. Gone are the days of performance at any cost; lasers must be efficient, reliable, and relatively inexpensive.
From an experimental standpoint, semiconductor devices—in particular, lasers with nanometre-sized quantum well structures—are black boxes: one measures macroscopic input and output relationships quite easily but speculation, theory and simulation are required to query the microscopic (or nanoscopic) governing processes. For example, it is easy to measure the light–voltage–current relationships of an electroluminescent device, but it is rather more difficult to probe the inner electrical potential in operation. We measure the macroscopic behaviour as shown in Fig. 1.1, but what goes on at the nanoscopic level, where carriers are pushed and pulled according to local forces, is largely left to theory and indirect means of measurement that may or may not accurately represent the actual microscopic operation. As electronic devices shrink ever smaller into the nanoscopic [2, 3] and molecular realms [4, 5], peering inside the box becomes all the more difficult.
We are motivated to find an experimental method to open the black box and probe the active semiconductor device.
1. Probing semiconductor devices electrically
High-Z voltmeter Buffered output Data-capture circuit and software
3
Conductive AFM tip Sample
Bias Circuit
Figure 1.2: Generalized scanning voltage microscopy implementation.
1.2
Opening the black box: scanning voltage microscopy
Many sophisticated characterization techniques have been developed to open the black box. Photoluminescence (bandgap), secondary ion mass spectrometry (composition), Auger spectroscopy (composition), electron beam induced current (junction delineation), scanning electron microscopy (microscopic structure), are but a few examples. Advances in AFM (atomic force microscopy) techniques [6] have yielded electrical analysis methods [7–10] having spatial resolution commensurable to device features sizes [11]. While electrical characterization is possible with these techniques, interpretation is not straightforward, complicated by feedback loops and measurement of indirect, secondary effects. A simple, elegant technique has emerged. Scanning voltage microscopy places a nanoscopic voltage probe on an actively-biased sample [11–14] as illustrated in Fig. 1.2. Using a high-impedance voltmeter (input impedance ∼ 2 × 1014 Ω) ensures that negligible current is drawn from the sample and normal device operation is maintained. The voltmeter is simply used as a high-impedance buffer and its analog output is passed directly to data collection hardware and software. By rastering the probe over the sample surface, voltage maps and profiles are collected. Spatial resolution down to ∼ 5 nm is possible so that small features such as individual quantum wells can be resolved [14]. SVM is a diagnostic tool, capable of identifying sources of sub-optimal performance [15,16]. SVM is a failure analysis tool, able to pinpoint causes of device failure [17]. SVM
4
1. Probing semiconductor devices electrically AFM head
Dimension 3100 AFM
AFM tip
Voltmeter preamp
Sample
Signal access module
Power source
Nanoscope III controller
PC/software
data flow control
Figure 1.3: Logical schematic of SVM implementation.
is a reverse engineering tool, illuminating device structure and active behaviour [13, 14]. SVM is a development tool, used in conjunction with with other analysis techniques. Fig. 1.3 shows the logical system of SVM, implemented with a Veeco Metrology Dimension 3100 atomic force microscope. The AFM head holds the conductive tip and is accessed through the microscope base via the Nanoscope III controller, which is in turn controlled by a computer terminal. Feedback from the head is used to maintain precise and accurate motion of the tip. Experimental data flows from the powered sample, through the voltmeter’s preamplifier (buffer), and is passed to the controller and data collection software through the signal access module; the signal access module allows input of “external” data (i.e. that from the external voltmeter), and in particular, the lateral tip friction signal is replaced by the voltage signal. Similarly, topological data flows from the AFM head to the computer. In this work, semiconductor diode laser chips mounted on carriers (see Figs. 1.4 and 1.5) are oriented so that the conductive tip scans the light-emitting facet. The tip scans over the p–i–n layer structure at the exposed facet (illustrated in Fig. 1.6) and produces a voltage map such as the one in Fig. 1.7 (note that the measured voltage is inverted in this figure). Laser designers and devices physicist at the former Nortel Networks High Performance Optical Components division, now annexed to Bookham Technology, have expressed distinct interest in scanning voltage microscopy as a tool for confirming theoretical models
1. Probing semiconductor devices electrically
5
Figure 1.4: Diode laser carrier and chip. Left: Laser chip is at the centre, top, and is connected to the carrier via solder and bonding wires; the lines on the left are each 1 mm apart. Right: close-up of the laser chip; the light emitting facet lies into the page along the top of the edge.
Figure 1.5: Ridge waveguide laser chip in the AFM. Left: Laser facet glows under AFM illumination. The ridge is in the center of the left edge and the ridge bond wire can be seen at the top (out of focus). The carrier is on the right and the shadow of the tip points towards the ridge. Right: Zoom-in to the ridge that sits in an etched-out region.
6
1. Probing semiconductor devices electrically
n-substrate
SCH
MQW
SCH
V
p-ridge metal
Figure 1.6: Voltage scanning a ridge waveguide laser. The conductive tip is rastered over the cleaved facet and the voltage recorded at each position. A typical voltage map is shown in Fig. 1.7.
Figure 1.7: Two-dimensional voltage map of ridge waveguide laser (voltage inverted for clarity). The p-type ridge (lower left), multi-quantum wells (middle), and n-type substrate (upper right) are clearly visible. Also visible are the SCH regions and the etch-stop.
1. Probing semiconductor devices electrically
7
and for analyzing materials, growth processes and novel laser structures. Although SVM has many advantages, the forces between tip and sample required for good electrical contact tend to be destructive to fragile device structures such as ridge waveguides. Over time the tip can either scratch or even cleave the surface, particularly when the device structure juts out from a bulk as in a ridge waveguide. Debris can pile up around the tip and produce scanning artifacts. The tip itself is also susceptible to forces from the sample: at high bias points, the tip can lose its conductive diamond coating, either by heating or by large current draw across interfaces of drastically different voltage.1 Experimental evidence of another experimental disadvantage will be presented in this thesis, namely that SVM is an inherently slow process due to a time constant resulting from contact resistance and measurement circuit capacitance. It will be shown that much care is required to obtain artifact-free voltage profiles while pushing the nanometre spatial resolution.
1.3
Goals and approach of this work
This work aims to better understand a developing technique for studying operational semiconductor lasers. We pose the question: What can be learned of the inner workings of semiconductor lasers using properly-interpreted electrical potential probing with nanometer resolution? To address this question, prior research is expanded and extended by postulating three sub-questions: 1. What is the fundamental relationship between the voltage measured using a nanoscopic conductive tip at the surface of an actively-biased semiconductor and the fundamental governing quantities—carrier concentrations, Fermi levels, and potentials—deep 1
Presumably the tip blows like a fuse as it tries to come to steady-state with the sample.
1. Probing semiconductor devices electrically
8
in the device under study?
2. How do we ensure the most accurate scanning voltage measurements are captured at a desired spatial resolution, and what is the influence of probe–sample material parameters and nonequilibrium conditions?
3. How can we apply what we learn from 1 and 2 to elucidate device behaviours and limitations in state-of-the-art semiconductor lasers, informing future laser design by applying this direct measurement technique?
A model is developed to characterize what a nanoscopic voltmeter measures when placed on a nonequilibrium semiconductor surface, and furthermore, what underlying fundamental quantities (such as majority carrier concentration, quasi-Fermi level position, etc.) can be extracted. A theory of the tip–sample interface is proposed. This theory provides a rigorous and complete picture of what potential is acquired by the voltmeter. Interface theory is then applied to understand transient behaviour of the measurement process, the first investigation of its kind for SVM. Images captured in one direction are notably more smeared with heterojunctions more abrupt (and therefore correct) in the other scan direction. This transient asymmetry is predicted by the interface theory, and this prediction is demonstrated. Experimental characterization provides quantitative rules to acquire images with optimal spatial resolution and voltage sensitivity. Finally, the rules derived from transient characterization are applied to study a dissipative heterojunction in an uncooled multi-quantum well laser. SVM shows that over a third of the power delivered to the laser is lost well before entering the active region where light is produced. A further source of artifact from the AFM operation itself is also identified.
1. Probing semiconductor devices electrically
1.4
9
Thesis organization
SVM has been proposed as a means for characterizing the inner workings of semiconductor devices having nanometre features. Three key areas of investigation have been presented to resolve the question above. In Chapter 2, a survey is presented of the application of SVM to active semiconductor devices to gain a firm footing for the work that follows. This survey includes concise reviews of semiconductor lasers, atomic force microscopy techniques, voltage probing theory of semiconductors, the development of SVM, and the use of SVM to study activelybiased diode lasers. What a conductive voltage probe measures on an active semiconductor is modeled in Chapter 3, starting from a drift-diffusion interpretation of the probe–sample interface. The model is evaluated for several relevant cases and is shown to be consistent with a thermodynamic model. Equipped with the model of the SVM potential, Chapter 4 turns to examine how one obtains the highest spatial resolution while retaining full confidence in the measured potential. Hysteresis is shown to exist in the measured potential due to slow transient response of the probe–sample interface. The physical source of the slow response is traced to the contact bandstructure. Rules for eliminating hysteresis artifacts are presented. Chapter 5 applies what is learned in Chapters 3 and 4 to study high-temperature diode lasers used in telecommunications. In particular, the nonohmic p-type contact is examined and is shown by direct, accurate SVM to dissipate ∼ 35% of the terminal power and account for an equal portion of the series resistance. Along the way, photocurrent from the measurement process is identified as a source of artifact, albeit an insignificant one during normal device operation. This work is summarized in Chapter 6. Original contributions are noted, as are future directions of research.
1. Probing semiconductor devices electrically
10
Table 1.1: Physical constant values used in numerical calculations [18]. Constant Symbol Value Unit Elemental charge q 1.602 176 53 × 10−19 C −34 Planck’s constant h 6.626 069 3 × 10 J·s −23 Boltzmann’s constant kB 1.380 650 5 × 10 J·K−1 −12 Electric constant 0 8.854 187 817 × 10 F·m−1 Electron mass m0 9.109 382 6 × 10−31 kg
1.5
Notation, conventions and constants
MKS units are used throughout. Energy is denoted by curly E. Electric fields are represented by E (scalar) or E (vector). Potentials are denoted by φ, normally having units of volts; we write qφ for a corresponding potential energy in units of eV. “Room temperature” is taken to be 300 K. Unless otherwise noted, room temperature is assumed. Diode junctions will be represented from left-to-right as n–i–p in all diagrams and experimental plots unless otherwise indicated.
Chapter 2 Prior art
2.1
Introduction
From Chapter 1 we have seen that probing the inner workings of semiconductor devices poses experimental challenges. In particular, photonic diode lasers need ultrahigh resolution probe techniques to resolve the operation of quantum wells that may be ∼ 5 nm wide or smaller. SVM is a scanning probe technique that images the internal nonequilibrium electrical potential directly with nanometer-scale resolution commensurable with device feature sizes. A literature review of AFM techniques in presented in this chapter with an emphasis on semiconductor characterization techniques. We map the evolution of various highresolution experiments and end with a review of SVM, a relatively new but powerful experimental technique. Also examined is the doped-diamond conductive probe technology that enables SVM. We will see that SVM has identified and confirmed key limitations of semiconductor diode lasers. However, from examining other AFM-based techniques it will become clear that calibration and proper interpretation are necessary. This motivates the work that follows in subsequent chapters. 11
12
2. Prior art a)
b)
c)
d)
p
p
p
n
n
n
n p
p
n p
n
Figure 2.1: Plan view of the light-emitting facets of four different diode laser architectures. (a) Basic p–n junction. (b) Improved p–n junction design that includes confined “active” region (shaded). (c) Ridge waveguide laser, offering current confinement and optical mode guiding via an etched ridge structure. (d) Buried heterostructure offering excellent current confinement and optical mode guiding.
The emergence of SVM and its direct observations of a number of important phenomena in diode lasers will guide us to the question: what does a nanometer-sized voltage probe really measure on an active semiconductor? The collection of experimental results so far, results that already lend themselves to meaningful interpretation, guides us to the analysis and SVM modeling presented in the next chapter. We will also find the motivation to obtain the best resolution and the most accurate voltage data; this motivation will lead us to the transient measurement characterization presented in Chapter 4. However, we begin with a concise review of modern semiconductor lasers.
2.2 2.2.1
Modern semiconductor diode lasers Laser architecture and operation
In a semiconductor diode laser, electrons are injected from an n-type region and holes are injected from a p-type region into the active region [19]. Electron-hole pairs recombine in the active region and emit photons. Some photons result from spontaneous recombination of the electron-hole pair and propagate with random phase and direction. However, spontaneously emitted photons can trigger stimulated recombination in which the second photon is an exact copy in phase, wavelength, and direction. By providing feedback—
13
2. Prior art
a)
e-
Energy x h+
b)
Optical field x Index x
Figure 2.2: Diode laser operation. (a) Electrons an holes are injected from opposite ends into the active region where recombination occurs. (b) The refractive index profile supports the guiding of the optical mode. realized by reflecting photons back towards the active region from the cleaved facets1 — photons multiply by further stimulated emission and gain is achieved. When the gain is equal to the cavity loss, lasing is said to occur [21]; the lasing beam is coherent, focused, and intense. Lasing occurs in one of the supported optical resonator (Fabry-P´erot) modes.
The first semiconductor diode lasers [22–24] (1962) were broad-area p–n junctions made of a direct bandgap semiconductor such as GaAs. Recombination occurs over a large region so photon populations needed for lasing are slow to build and require high input currents. Confinement of carriers and the optical mode is poor. Nonradiative recombination is high. Radiative recombination can be enhanced by introduction of a double heterostructure between the hole and electron injectors [25–29] (see Figs. 2.1a and 2.2a). Threshold current is greatly reduced permitting continuous-wave operation at room temperature [25]. By reducing the thickness of the middle layer to the order of the de Broglie of the carriers and using a material of smaller bandgap, a quantum well is formed that 1
III-V semiconductors typically have n ≈ 3 and so there is roughly 25% reflection at the semiconductor–air interface; reflection can be enhanced to over 95% using periodic dielectric stacks [20].
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traps and quantizes carriers in the longitudinal direction [30]. Carriers exist in a twodimensional carrier gas confined in the third direction. In one-dimensional confinement, the density assumes a staircase series of step-functions constrained by the free electron dispersion relation [21, 30].2 The refractive index of the smaller-bandgap material is higher than that of the cladding materials for commonly used III-V material systems such as InGaAsP/InP and AlGaAs/GaAs, so that confinement and guiding are provided to the optical mode (see Fig. 2.2b). Active region media must be lattice-matched3 to the cladding layers; this is true for AlGaAs/GaAs and true for a range of InGaAsP compositions in InGaAsP/InP heterostructures. With the precision of MBE (molecular beam epitaxy) and MOCVD (metallic-organic chemical vapour deposition), one-dimensional superlattices can be grown in the growth direction [30] to form multiquantum well structures. Advantages of using multiple quantum wells include lower threshold current, reduced temperature dependence on bias current, emission wavelength tuning, and better dynamic behaviour [30–33].
Ridge waveguide lasers By confining current the lasing threshold is reduced because more photons from recombination are produced for stimulated emission in a small volume. In one method of current confinement a ridge structure is etched longitudinally along one carrier injector (illustrated in Fig. 2.1c), thus providing an closed circuit only through a small lateral region [34]. The ridge is achieved by the introduction of a thin layer through one cladding region that serves as an etch-stop during the etching process; a simple mask is used to define the lateral ridge structure. Often it is the p-type contact that is shaped into a ridge, although some broad-area p-type material is retained to keep the etch-stop layer away from the active region. The ridge additionally provides moderate refractive index 2
Broadening mechanisms smooth out the staircase so that the transitions from one step to the next are continuous [30]. 3 Slight strain is permissible for very thin layers [21].
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contrast to the optical mode and guiding occurs along the length of the ridge and laser cavity [35].
Buried heterostructure lasers BH (buried heterostructure) lasers offer low lasing threshold and strong guiding of the resulting optical mode [1,36,37]. The active region heterostructure is “buried” within the layer structure as illustrated in Fig. 2.1d. A relatively uniform refractive index contrast about the active region promotes the formation of a more circular transverse spatial mode which is better coupled into cylindrical fibre. Thyristor p–n–p–n layer structures on either side funnel current directly into the active region [38]. The feedback mechanism often employed in BH lasers is the distributed Bragg reflector, a periodic corrugation of the refractive index along the length of the laser cavity [39–41]. One can reinforce the operational (freespace) wavelength λ0 by setting the corrugation period to be Λ = λ0 /2¯ n for average refractive index n ¯ [1].
2.3
Nanoscopic scanning probe techniques
Here, AFM-based techniques for semiconductor characterization are presented with an emphasis on electrical methods. We begin by examining the atomic force microscope, the foundation from which all subsequent techniques are drawn.
2.3.1
Atomic force microscopy
With the invention of AFM in 1986 by Binnig,4 Quate and Geber [6] a means of probing devices was provided with spatial resolution commensurable with the ever-shrinking micron and sub-micron feature sizes. Two aspects make AFM ideally suited for electron and optoelectronic device characterization: firstly, AFM works well from atomic 4
Binnig won the Nobel prize in 1986 for the earlier invention of the scanning tunneling microscope.
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feedback to data capture
optical microscope piezo-electric driver
probe sample x,y translation stage
Figure 2.3: Schematic of the atomic force microscope.
resolution through to resolution of tens or hundreds of micrometers; secondly, AFM can be adapted in many different ways depending on the desired measured quantity as the following survey will show. AFM employs three-dimensional piezo-mechanical drivers to achieve precise subnanometer positioning in all directions. The drivers hold micromachined cantilevers with pyramidal probe tips at the very end, as illustrated schematically in Fig. 2.3. A laser beam is bounced off the end of the cantilever and is detected by a grid of photodetectors; by means of this “optical lever” small deflections of the probe tips are tracked by relatively large deflections of the laser on the detector array. A feedback loop allows accurate control of the tip, either by moving the sample or the probe (the latter is used throughout this work). Additionally, an optical microscope aids coarse positioning of the tip. Data is captured by onboard electronics and is sent to collection and processing software. Deflection of the tip can be caused by friction, surface interactions, non-contact electrostatic or electrodynamic interactions. In contact mode, the tip is simply dragged across the sample surface at a known and fixed tip–sample force. Alternatively, the tip may be bounced or floated across surface at a known oscillation frequency and deviations to this frequency interpreted as sample-induced interactions (less destructive, even non de-
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structive). Tip deflections as small as ∼ 10 pm or as large as ∼ 100 nm can be detected routinely, providing great dynamic range unobtainable by tunneling current methods [7]. AFM on its own can be used to characterize semiconductor devices beyond simple topographic mapping. For example, selective chemical etching can be used [10] to remove materials of certain composition or doping concentration and the resulting topography can be measured by AFM from which the doping and composition is inferred over the device surface.
2.3.2
Conductive AFM tips
Probe selection is important for electrical AFM techniques. Monocrystalline CVD diamond tips for STM (scanning tunneling microscopy) were first fabricated in 1992 [42]. Prior to that, thin platinum–iridium or tungsten wires were pulled and clipped to produce atomically sharp conductive needles.5 However, such a process produces a tip of random geometry (one hopes for an atomic point) that may contain extra protrusions that cause imaging artifacts.6 Polished diamonds of known shape could also be made conductive by ion-implantation doping. Diamond is ideal for electrical contact AFM because it is both very hard and chemically inert (it does not oxidize) [42]. In their first realization [42], CVD diamond tips were grown epitaxially on (110) diamond seed layers, grown to layer thicknesses of some 5 µm and doped with boron to impurity concentrations of 6 × 1020 cm−3 . The tips were then polished to fine points. Resistivity varied from ∼ 10−4 Ω · m at room temperature to ∼ 5 Ω · m at 4.2 K. Electronic transport properties of CVD diamond and boron-doped CVD diamond have been well characterized [43–48]. Electron and hole mobilities are each on the order of 103 cm2 /(V·s) [43]. CVD diamond may have a negative electron affinity depending on 5
Pt/Ir and W tips are still used in STM applications. For example, a tip with two protrusions of similar height will produce double images when scanning a small, singular object—one image for the pass of each tip. Other tip-induced artifacts may not be so easy to identify. 6
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CB Evac 5.5 eV
4 eV
EF VB 0.3 eV
Figure 2.4: Band structure for H-terminated B-doped CVD diamond (100) and (111) [45]. The electron affinity is negative, placing the conduction band above the vacuum level and giving rise to a work function that is less than the bandgap. orientation and surface termination, placing its conduction band above the vacuum energy level [44].7 Its bandgap is 5.5 eV [45]. Hydrogen-terminated (100) and (111) surfaces have a work function of ∼ 4 eV [45, 48]; a typical band structure is plotted in Fig. 2.4 for a boron concentration of 1016 cm−3 . Because the conduction band is energetically far from the valence band and Fermi level, heavily boron-doped CVD diamond films may be modeled as a metal [46]. CVD diamond is grown on silicon cantilevers [49] with spring constants ranging from 0.1 to 100 N/m [50], suitable for tip–sample forces on the order of micronewtons [49]. Cantilevers are produced en masse in wafers by a combination of anisotropic etching and micromachining [50]. Various tips have been characterized for use in electrical contact-mode operation [12, 13,49,51]. Trenkler and coworkers systematically evaluated nanoscopic boron-doped CVD diamond-coated silicon tips [12, 13, 49] for use in SSRM (scanning spreading resistance microscopy) and SVM; these tips consistently out-performed metallic, doped silicon, and ion-implanted solid diamond tips, both in terms of electrical and mechanical properties. For example, solid diamond tips were found to be too bulky mechanically [49], while metallic and silicon tips failed to track a simple square wave input [13]. Comparison of 7
CVD diamond could be used as a “cold cathode” owing to its negative electron affinity [44].
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triangular and rectangular cantilevers shows that rectangular cantilevers are mechanically more robust [52]. (Rectangular silicon cantilevers with boron-doped CVD diamond grown on etched pyramidal silicon points are used throughout this work.)
2.3.3
Scanning resistance techniques
Spreading resistance is measured by the application of a known voltage or current to a sample from a conductive tip and the resulting current or voltage measured. The resistivity at a tip–sample contact point is
Rsp =
ρ 4r
(2.1)
where ρ is resistivity and r is tip radius [53] or for hemispherical radius pressed into sample [54], Rsp =
ρ 2πr
(2.2)
The total resistance measured is [54]
RT = rc + Rsp + Rl
(2.3)
where rc is the contact resistance and Rl is a compound term accounting for any other sources of series resistance (such as from electrical connection leads). The contact resistance is in turn given by [54] rc =
Rc A
(2.4)
where Rc is specific contact resistance measured in Ω·cm2 and A is the contact area. For small tips, rc can become very large and dominant. Resistance is a function of tip radius, ρ, surface finish (e.g. polished), doping type, etc., so calibration must be performed on known structures [53]. Samples are often bevelled to gain better spatial resolution and reduce the affect of neighbouring interfaces.
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b)
V
AFM tips AFM tips
Sample
Sample
Figure 2.5: (a) Schematic of SRP circuit. (b) Beveled sample surface to elongate features and improve SRP resolution. There are two primary subdivisions of spreading resistance microscopy, multipoint SRP (scanning resistance profiling) and single point SSRM, each treated in the sections that follow.
Nano-scanning resistance profiling Two conductive probes with known separation are scanned across a sample surface and the resistance between them measured by applying small voltage across the tips. The measured resistance is sum of both contact resistances, both spreading resistances, and the semiconductor resistance [53]. SRP provides doping concentration profiles on inactive devices by measuring voltage response for a known test current. By cleaving through semiconductor layer stacks at shallow angles to expose the layers along the resulting beveled surfaces, improved spatial resolution is obtained beyond limitations imposed by the probe tips (see Fig. 2.5). However, the bevelled cleaves that facilitate the scanning process greatly disturb the true device structure and operation. Quantification and analysis were presented of sub-micron SRP (both single- and dualprobe) and spreading resistance in general for silicon MOS (metal–oxide–semiconductor) structures [55]. In particular, steps were taken to deconvolve actual carrier concentration from the total spreading resistance through simulation and modeling. Nanoscopic SRP data has been collected successfully on MOSFET (metal–oxide– semiconductor field-effect transistor) structures [56]. Measurable carrier concentration
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tip
sample
1
2
3
V
Figure 2.6: In spreading-resistance experiments, currents 1 and 3 may be drawn in addition to the desired current 2; the resistance (and thus the carrier concentration) calculated from the ammeter A and voltmeter V will not represent the isolated middle layer and so a correction factor must be incorporated into the calculation.
range was found to be 1014 –1020 cm−3 with a sensitivity of 1014 cm−3 . Spatial resolution was near 10 nm using doped CVD diamond tips. Spreading resistance measurements at a particular location can be influenced by lateral currents flowing from other regions of the sample as illustrated by Fig. 2.6. Calibration was performed [57] via epitaxially-grown staircase structures. Correction factors were derived for post data processing in order to account for neighbouring sources of resistance or current flow. Simulated and theoretical correction factors for nanometer-scale structures and scanning near interfaces have been calculated [58, 59]. Clarysse [59] used two probes (contact radius ∼ 1–2 µm) to scan resistance versus probe separation distance. The dopant profile was extracted by application of Schumann–Gardner multilayer correction factor making use of a Poisson solver. Surface states were thought to pinch off current between the probes for thin samples of less than 30 nm depth and increase the resistance by an order of magnitude. Further quantification and qualification of SRP (i.e. repeatability, experimental and software qualification) [60] and industrial qualification (including qualification samples) [61] have been pursued. Novel (multipoint) probe tips [62] and appropriate techniques for sub 70-nm resistance
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i
p
Sample
Figure 2.7: Schematic of SSRM circuit. profiling have been proposed and used [63]. Sub-10 nm techniques have been investigated including careful evaluation of tip and bevel geometries [64]. The effect of probe penetration into the sample on measured resistance resistance has also been studied [65].
Scanning spreading resistance microscopy For SSRM, a known current (or voltage) is placed across the grounded sample from probe tip to ground and the resulting voltage (or current) is measured—the ratio gives the spreading resistance. Using a single point probe and fixed current, the resistivity is [54] ρ=
A dV I dx
(2.5)
along a scan segment. Because the sample is grounded, the carrier concentration and doping level can be inferred. The schematic of SSRM is shown in Fig. 2.7. Because spreading resistance is a compound quantity, calibration is required. SSRMcollected data on InP was correlated to trusted SIMS (secondary ion mass spectrometry) data on identical structures [9]. Further calibration steps on InP (n–p)N step-like structures produced standardized calibration curves [66, 67]. Simulation confirmed that of SSRM can infer carrier concentrations [68]. Exhaustive calibration on InP and GaAs of typical optoelectronic device n- and ptype doping concentrations was performed to SIMS data [69, 70], along with interface analysis. A Schottky barrier model was fitted to the tip–sample interface with CVD
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SSRM was employed to find doping and carrier concentrations [71] in Si MOS structures and InP/InGaAsP BH lasers [72]. Sub-5-nm resolution was achieved using solid diamond tips on p-MOS fully-depleted silicon-on-insulator transistors [73] for next-generation transistor characterization; the solid diamond provided a smaller effective radius than with CVD the diamond coating as evident in scanning electron microscopy images.
2.3.4
Electrostatic/Kelvin force microscopy
EFM (electrical force microscopy) was first presented in 1987 by IBM researchers Martin, Williams, and Wickramasinghe [7]. They used optical heterodyne detection to measure frequency changes in a vibrating AFM probe cantilever caused by normal electric field components of surface charges and potentials. Knowing the spring constant and geometry of the cantilever, the gradient of the probe tip–sample force can be deduced as a function of the tip–sample distance, and the absolute force derived [7]. It is possible to derive capacitance and electric potential from the force gradient [8], thus expanding AFM into the realm of electronic measurement. Surface charge can also be recovered [74] with a sensitivity of tenths of an electronic charge [75]. In normal EFM operation, the AFM tip is driven at an AC frequency near its resonant frequency and electrostatic forces due to tip–sample interaction are considered to be second-order effects; the tip is hovered above the sample at a fixed distance z [76]. The electrostatic force between the AFM tip and the sample separated by a distance z is given by [76] F =
1 ∂C 2 V , 2 ∂z
(2.6)
where C is the tip–sample capacitance and V is the total voltage difference. This voltage can be decomposed into a sum of the contact potential Vcp , the induced voltage Vind
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related to the local sample potential, and the DC and AC voltages applied to the tip, Vdc and Vac sin ωt, respectively [76]. Writing Vstat = Vdc + Vind + Vdc as the total static potential, the force can be written
F =
1 ∂C 2 (V + 2Vstat Vac sin ωt + Vac2 sin2 ωt) 2 ∂z stat
(2.7)
from which one can easily extract the DC force component,
Fdc
1 ∂C = 2 ∂z
2 Vstat
1 2 + Vac , 2
(2.8)
the first harmonic, Fω =
∂C Vstat Vac sin ωt, ∂z
(2.9)
and the second harmonic, F2ω = −
1 ∂C Vac cos 2ωt. 4 ∂z
(2.10)
The first harmonic Fω is linear in the sample voltages Vcp and Vind and so sample voltage profiles can be obtained at a fixed scan distance z using a lock-in amplifier at ω [76]. Furthermore, a closed-loop controller can be incorporated to keep Fω = 0 by setting Vdc such that Vdc = −(Vcp + Vind ) and changes in Vcp or Vind can be detected in the error signal of the controller; this mode of operation is called Kelvin or nano-Kelvin operation [76]. The second harmonic F2ω given by Eq. (2.10) is linear in the capacitive coupling ∂C/∂z so variation in the sample dielectric constant can be imaged at a fixed scan distance [8, 75] using a lock-in amplifier at 2ω. Using the Kelvin operational mode, EFM was used to measure potential and field profiles of InP/InGaAsP lasers [77]. A laser was oriented with the light-emitting facet upwards for easy exposure to the tip. The actual laser structure studied was grown entirely by MOCVD and consisted of n- and p-type InP layers (nominal doping 10−18
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cm−3 ) cladding a single-layer InGaAsP active region 220 nm thick. A two-dimensional potential scan was captured over the light-emitting facet at constant tip height. The built-in potential from n to p was roughly half the theoretical drop from simulation; surface states of the native oxide were found to be the cause of disagreement and good agreement was obtained after updating the simulation with surface effect corrections [77]. The measured electric field profile exhibited a peak active region field of 2 MV/m which is quite reasonable in practice. Analysis of biased GaAlSbAs mid-infrared (2.36 µm) diode lasers featuring 7 nm-wide quantum wells employed a similar configuration [78]. A heavily-doped silicon tip 20 nm wide at the apex allowed ∼ 50 nm spatial resolution. The active region was imaged but due to the coarse spatial resolution the quantum wells remained invisible. The power of EFM as a diagnostic tool is evident from the analysis of failure conditions of a InAs/AlSb/GaSb quantum cascade laser [79].8 An otherwise healthy laser exhibited a sudden and drastic decrease in series resistance as the bias voltage was increased, leading to a current surge and loss of light emission. By scanning over the actively-biased laser, a sharp potential drop at the edge of an active region was observed above breakdown bias voltages, identifying the source of current surge and informing the next iteration of design. EFM measurement is susceptible to environment artifacts. During the imaging of p–n junctions and layered structures of GaAs and InAlAs/InGaAs [80], a change in contact potential between air and vacuum environments was noted. Hence, for absolute potential imaging, the Kelvin operational mode is preferred.
2.3.5
Scanning capacitance microscopy
SCM (scanning capacitance microscopy) is primarily used to quantify semiconductor 8
Quantum cascade lasers differ from normal diode lasers in that the optical transitions are intraband, not interband. Quantum wells are narrow (∼ 2 nm) and form superlattices, down which carriers “cascade” and emit mid-to-far infrared light [2].
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doping levels with ∼ 100 nm resolution, although it has been used to delineate depletion regions down to 20 nm. Typically, a semiconductor sample surface is polished oxidized, either in atmosphere or using wet oxidation.9 SCM (scanning capacitance microscopy) works by measuring the tip–sample capacitance at a fixed separation. Assuming a MOS structure, the capacitance is given by [81]
C=q
C0 1+
2K02 0 V qN Ks x20
,
(2.11)
where C0 , K0 , and x0 are oxide layer capacitance, dielectric constant, and thickness, respectively, Ks is the sample dielectric constant, V is the applied voltage, and N is sample carrier concentration which we wish to extract. The small tip implies very small capacitance (∼ 10−18 F). The shape of the triangular tip influences the measurement and so simulation and modeling are required [54] and the parallel plate assumption Eq. (2.11) must be modified accordingly. The tip can also be made to oscillate (tap) at its resonance frequency and instantaneous capacitance measured at 1 GHz (or greater) sampling rate [54] can provide dopant profiles. Alternatively, the sample can be driven at high frequency causing rapid change in carrier accumulation and depletion and giving rise to a modulated tip–sample capacitance that is similarly detected by the SCM circuit [72], ∂C =− ∂V
C03 h
qN 1 +
2V C02 qN
i3/2 .
(2.12)
Development of SCM at IBM ran parallel to that of EFM [7] and was employed for surface capacitance measurements [8]. Much more recently, Raineri [81] used the technique to measure transistor gate position and width and observe of depletion regions for unbiased devices. The need for highly-polished surface cleaves was noted to alleviate surface states that could interfere 9
SCM is very reproducible on silicon since SiO2 is easily grown and well understood [81].
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with nanoscopic feature delineation. SCM was extended to probe actively-biased devices with the observation of operational carrier distributions in MOS transistors [82]. Good qualitative agreement with theory was obtained but not quantitative agreement; quantitative discrepancy was attributed to a combination of perturbation from the tip and poor knowledge of the specific doping structure of the device. At the same time, SCM was performed on transistors at various bias points, not to characterize devices at different biases but rather to deconvolve carrier and dopant profiles from sample surface charge and thus calibrate the technique [83]. By taking ∂C/∂V –V curves on uniform samples, DC shifts due to surface preparation or tip shape were subtracted from different results for comparison. Application of SCM to InP/InGaAsP BH lasers [72] allowed calibration to wellaccepted SIMS dopant concentration profiles. p–n junctions, including depletion regions, were clearly observed between the many blocking layers. The active region was visible but not the individual quantum wells, limited by spatial resolution of the tip–sample interaction volume. Error in the doping profiles due to noise was estimated to be as high as 10%. Otherwise, good agreement between SCM and SIMS data was obtained. 5–20 nm In0.53 Ga0.47 As/InP quantum well structures have been imaged [84]. Depletion regions between the wells were observed at multiple device bias points. Although excellent spatial resolution was obtained, SCM-predicted carrier densities were considerably lower than expected from one-dimensional Poisson/Schr¨odinger simulation; such discrepancy was attributed to tip averaging over the tip–sample interaction volume [84]. A variation of SCM employing a charged tip was used [85] to delineate sub-micron features of a planar two-dimensional system at cryogenic temperatures: the charged tip caused local depletion in the sample which lowered the tip–sample capacitance, and the capacitance was detected by a low-temperature transistor right at the tip. This variation could likely be extended to carrier mapping of actively biased semiconductor devices.
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2.3.6
28
Scanning tunneling microscopy
STM operates by bringing a biased tip into close proximity with a sample, and measuring the resulting tunneling current across the tip–air–sample gap. The tunnel current depends exponentially on the the tip–sample separation, so that small changes in sample topology are easily detected in large changes of the tunnel current. STM potentiometry is extremely similar to EFM in that a modulated signal is applied to the tip [86]; the difference in the case of STM is that changes in tunnel currents are interpreted as the local potential, rather than vibrational deflections of the tip [86, 87]. Depletion widths of GaAs and Si p–n junctions have been delineated to within 10 nm using STM potentiometry [88]; Zn dopants were also located and quantified. Composition and growth details of quantum well intermixing have been identified [89] in InGaAsP/InP lasers, and similarly in InGaP/GaAs heterojunctions [90]. Novel cryogenic STM has been employed to measure potential profiles of a normal-superconducting junction [91].
2.3.7
Direct voltage probing
All the techniques reviewed thus far combine the fine spatial resolution of the AFM with complex control feedback loops to extract active carrier and potential profiles [92] of active devices, or equilibrium carrier concentrations and doping levels of passive devices. We turn now to review the simple technique of placing a voltage probe on an activelybiased semiconductor. Such experiments were performed long before the invention of the atomic force microscope, but modern SVM emerged only as late as 1998.
Microscopic voltage probing In 1952 Pearson, Read and Shockley probed [93] the space charge region of a germanium p–n junction with a sub-millimeter tungsten probe by measuring the potential zeroing current between the probe and sample, the first direct voltage observation of its kind
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[93]. By lightly dragging the tip across the device surface they found experimental measurements of the depletion width to be within 30% of theoretical values. Mayer et al. showed in 1965 [94] that potential probe measurements on semiconductors could be used to relate surface potentials to a weighted average of the bulk quasi-Fermi levels deep in the device. The derivation was most applicable to intrinsic or depleted material but could be applied more generally with calculable error. Mayer’s result, a mobility-weighted average of the electrochemical potentials in the intrinsic limit n ≈ p, φn and φp , φmeasured =
µn φn + µp φp , µn + µp
(2.13)
appears as a special case to the general model presented in Chapter 3. What is attractive about Mayer’s model is that the predicted measured potential of Eq. (2.13) is related to the potential deep within the device, far from interfacial effects at the probe–sample contact. Thus, we can uncover the electrochemical potentials (and hence the carrier concentrations and electrostatic potentials) at the heart of device operation. Further analysis of potential probe–semiconductor interfaces and associated built-in potentials was provided by Manifacier et al. in 1984 [95].
Scanning voltage microscopy Nanopotentiometry or scanning voltage microscopy (SVM) emerged in 1998, enabled by advances in CVD doped-diamond tip technology. By placing a conductive tip in full physical contact with an actively-biased sample and connecting the tip to a high-impedance voltmeter, potential maps of operational MOS transistors [12, 13] were obtained; the setup is shown schematically in Fig. 2.8. Cross-sectional voltage maps were taken and compared to simulation [13]; good qualitative agreement was obtained with a mobilityweighted average of the electrochemical potentials of the holes and electrons, Eq. (2.13). For the first time, acquiring direct potential measurements on the nanometer scale was possible.
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V
+ conductive probe sample
Figure 2.8: Generalized SVM experimental configuration, consisting of conductive tip in contact with biased sample and connected to high-impedance voltmeter and AFM sampling equipment; tip movement is controlled by the AFM.
Scanning voltage microscopy was really the first scanning probe technique to offer direct observation of the local sample electric potential because previous methods such as STM, SCM, KPFM, SSRM, and SRP all rely on indirect derivation of active quantities either through the extraction of secondary physical effects of the active device (as in the case of STM, SCM, EFM, and KPFM) or through hypothesis from inactive characteristics (SSRM, SRP). Choosing suitable probes for the study of semiconductors is important. For example, on silicon [13] only doped-diamond probes tracked square waves injected into the sample; doped-silicon and metal probes had poor tracking, were more susceptible to oscillatory noise from nearby electronics, and even gave rise to DC potential offsets. Starting with Ban’s work at the University of Toronto [96], SVM was used to characterize limiting mechanisms in actively-driven semiconductor lasers based on InP/InGaAsP material systems. For calibration, SVM on an InP p–n junction was performed with application of Mayer’s theory [94] to potential model of junction [11]. The potential drop across the device from the p to n contacts equaled the total applied voltage and there was no DC offset. Furthermore, excellent agreement between measured and calculated depletion region width was obtained. Hence, the use of CVD doped-diamond tips in conjunction with a high-impedance voltmeter produced accurate potential profiles on InP devices.
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31
Clear SVM images of BH lasers including resolution of individual quantum wells in the MQW (multi-quantum well) active region, the first images of their kind, were reported in 2002 [14]. SVM scans were taken across the p–n–p–n current blocking layers and motivated further study of current leakage. In a later report [17], buried heterostructure blocking layer breakdown, originally attributed to p–n–p–n thyristor turn-on, was in fact shown to be dominant through the diode leakage path.10 Such decisive results could not have been easily obtained by any other experimental method. SVM was applied to ridge waveguide lasers [15] and for the first time lateral current spreading below the ridge was directly observed. The potential difference between the position directly below the centre of ridge and the position below the edge of the ridge indicated that as much as 40% of the current was leaking laterally and thus not contributing to lasing. Finally, SVM was used as a diagnostic tool [16]. Two lasers, otherwise identical, exhibited notably different series resistances. SVM illustrated conclusively that the device of higher series resistance had a large voltage drop at the MBE–MOCVD grow interface, whereas the “healthy” laser did not. Hence, SVM easily found a growth process defect that would have remained elusive.
2.4
Conclusions and questions drawn from the prior art
We have seen numerous applications of scanning probe microscopy to study semiconductor devices, both in the passive and active states. Measurements of resistance, charge, topology, dopant concentration and type, and electric potential are possible. The focus now turns to SVM on actively-biased devices, and in particular, actively-biased semicon10
The diode leakage path is the small gap between the active region and the first n-type layer of the thyristor structure.
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32
ductor laser diodes. Nanometer spatial resolution of the desired quantity is not obtained in a trivial manner—calibration is required. We are motivate to determine conditions for optimal SVM spatial resolution; this will lead us to the transient measurement characterization presented in Chapter 4. The emergence of SVM and its direct observations of a number of important phenomena in diode lasers brings us to the question: what does a nanometer-sized voltage probe really measure on an active semiconductor? We proceed to the analysis modeling presented in the next chapter.
Chapter 3 What a voltage probe measures on an active semiconductor
3.1
Introduction
We have seen the capabilities of AFM-related techniques and the power of SVM specifically to image the voltage landscape of devices in operation. The goals of this chapter are to understand what SVM measures and decompose the resulting “potential” into fundamental carrier concentrations and energy levels deep inside the device, far from the measurement surface. Voltage meters measure the electrochemical potential difference across the terminals [97], so any deviation from simulated electrochemical potentials may reveal unmodeled processes We aim to calibrate these SVM measurements so that SVM becomes a fully quantitative measurement tool rather than remaining a qualitative imaging system. A voltage probe placed on an active semiconductor surface at (x, y) produces a voltage datum, φ(x, y). While collected voltage data are meaningful, for example, by taking SVM voltage differences to infer laterally outward spreading current below the ridge of a RWG (ridge waveguide) laser [15], the exact source of the SVM-acquired voltage needs to 33
3. What a voltage probe measures on an active semiconductor
34
be identified. Mayer et al. suggested [94] that the potential measured at a semiconductor surface is a weighted average of the non-equilibrium quasi-Fermi levels and that the levels deep within the bulk could be extracted. In this chapter, a carrier transport model is developed from the steady-state carrier dynamics between a conductive AFM tip and a semiconductor sample; this resulting model will agree with Mayer’s analysis [94]. For a semiconductor in equilibrium, the model predicts that the Fermi level should be measured, consistent with the thermodynamic treatment.
3.2
Modeling CVD boron-doped diamond probes
The band gap of diamond is 5.5 eV [45], a gap that is four or five times wider than that of a typical photonic or electronic semiconductor [98]. Furthermore, diamond can exhibit negative electron affinity [44]; that is, its conduction band can lie above the vacuum energy level. Because heavily boron-doped CVD diamond exhibits high mobility [98], wide band gap and negative electron affinity, it can be modeled as a metal [46] with a single metallic work function or Fermi level. The work function has been found to be approximately 4 eV below vacuum [45, 48], slightly less than the electron affinities and work functions of common semiconductors [98]. We adopt the metallic interpretation for the boron-doped CVD diamond-coated probes in the following analysis and use it further in Chapter 4 when we examine transient effects between the probe tip and sample. We assume there is complete recombination in the probe at steady-state since negligible current is drawn by the high-impedance voltmeter [11].
35
3. What a voltage probe measures on an active semiconductor
3.3
Thermodynamic picture of measured voltage
The measured voltage between any two points, say, between a voltage probe and a grounded reference point, is the difference in the local electrochemical potentials [97],
∆φ = φprobe − φreference ,
(3.1)
where the electrochemical potential is equivalent to the (quasi) Fermi level of a semiconductor [99], q∆φ = µe (x1 ) − µe (x2 ).
(3.2)
Electrochemical potentials can be easily be derived for electrons
nb = n0 eq(φb −φ0 −φn )/kB T ⇒
φn = (φb − φ0 ) −
nb kB T ln q n0
(3.3a) (3.3b)
and for holes
pb = p0 eq(−φb +φ0 +φp )/kB T ⇒
φp = (φb − φ0 ) +
pb kB T ln . q p0
(3.4a) (3.4b)
In the above equations, φn,p are the electron and hole electrochemical potentials (quasiFermi potentials), φb − φ0 is the electrostatic potential, and n0,b and p0,b are the electron and hole concentrations at equilibrium and under bias. Appendix A provides a background to the derivation. Although there is a built-in potential across the depletion region of a p–n junction at zero bias [100], this potential cannot be measured by a voltage probe because builtin potentials form at each probe point, exactly canceling the built-in potential at the junction. Hence, SVM must measure flat, zero potential across a device at equilibrium.
3. What a voltage probe measures on an active semiconductor
36
(In Section 5.2.2, this fact will lead us to the identification of low-bias voltage artifacts due to the architecture of AFM). If energy is provided to the junction, the measured electrochemical potential becomes [11, 101] kB T cb (r) φ(x, y) = φb (r) − φ0 (r) ± ln , q c0 (r)
(3.5)
where the first term is the electrostatic potential and the second term is the chemical potential containing bias and equilibrium carrier densities cb and c0 . In the next section we present a model based on the transport of carriers to and from the tip. We will find agreement between the thermodynamic and carrier transport views.
3.4
Carrier transport model of measured voltage
We now impose a carrier transport formalism on the carrier fluxes between probe and sample to derive an expression for the measured SVM potential of an nonequilibrium bipolar device.
3.4.1
Drift-diffusion at the probe–sample interface
Current flow between the conductive probe and semiconductor is restricted to one dimension normal to the interface. This assumption is supported by spreading resistance calculations of [55] and confirmed experimentally in nanometer-spatial resolution SSRM measurements [102]; two-dimensional current spreading effects are only relevant within one or two tip radii of an insulating barrier [102] such as the oxide layer of a MOSFET or the etched edge of a diode laser’s ridge waveguide. The voltmeter connected to the probe has an ultrahigh input impedance (∼ 2 × 1014 Ω) and draws negligible current, so there is no net electric field along the probe–semiconductor axis. Hence, the electron and hole fluxes to and from the semiconductor are equal and continuous, and the total
37
3. What a voltage probe measures on an active semiconductor
probe sample
+ nprb, pprb
-
V
n(r), p(r)
Figure 3.1: Sample–probe interface showing arbitrary sample concentrations n(r), p(r) and probe concentrations nprb , pprb . drift-diffusion current is zero
(−µn n∇φn + Dn ∇n) + (−µp p∇φp − Dp ∇p) = 0.
(3.6)
Rearranging and integrating Eq. (3.6) yields
µn n(φn − φ) + µp p(φp − φ) = Dn (n − nprb ) − Dp (p − pprb ).
(3.7)
In the probe, φ is the potential (registered at the voltmeter) and nprb and pprb are the carrier densities. In the semiconductor far from the interface, φn,p are the quasi-Fermi levels, µn,p are the mobilities, and n and p are the carrier densities. Isolating φ gives µn nφn + µp pφp +δ µn n + µp p
(3.8)
(Dn nprb − Dp pprb ) − (Dn n − Dp p) . µn n + µp p
(3.9)
φ=
where δ=
Therefore, the voltage probe measures a carrier-mobility weighted average of the quasiFermi levels plus an diffusivity-weighted error term. The error term δ contains the probe carrier concentrations nprb , pprb that we wish to eliminate so that the measured potential can be expressed in terms of the sample quan-
38
3. What a voltage probe measures on an active semiconductor
tities only. Using the Einstein relation D = µkB T /q and rewriting Eq. (3.10) suggests that kB T (µn nprb − µp pprb ) − (µn n − µp p) kB T |δ| = ∼ q , q µn n + µp p
(3.10)
which is only a small perturbation to the potential (3.8) and can be neglected in general. We may then make the reasonable approximation that the measured potential is
φ=
3.4.2
µn nφn + µp pφp . µn n + µp p
(3.11)
Model interpretation
The measured potential given by Eq. (3.11) is an average of the quasi-Fermi levels (electrochemical potentials), weighted by the carrier density–mobility products. When the semiconductor is at equilibrium, qφn = qφp , EF , yielding
qφ =
µn nEF + µp pEF , µn n + µp p
(3.12)
from which φ = EF /q clearly follows. Therefore, the probe measures the Fermi level of a semiconductor at equilibrium. At equilibrium, the Fermi level is flat across the entire device [100] and thus the measured potential is zero as dictated by thermodynamics. In unipolar regions where one carrier type dominates, the measured potential φ tends towards the dominant quasi-Fermi level,
φ → φn ,
µn n µp p
(3.13a)
φ → φp ,
µp p µn n.
(3.13b)
Hence, in heavily doped p-type regions we expect the voltage probe to follow φp . For example, if there is a heterojunction between p-type materials having different band gaps, we expect to observe a voltage drop under forward bias corresponding to the change in
39
3. What a voltage probe measures on an active semiconductor
φp across the heterojunction. It will be shown in Chapter 5 that such a voltage drop is indeed observed in experimental SVM data. In the case that there is quasi-space charge neutrality (for e.g. across a depletion or intrinsic region) n ≈ p and φ=
µn φn + µp φp , µn + µp
(3.14)
the mobility-weighted average of the electron and hole quasi-Fermi levels. Such a reduction has been well validated across the depletion region of a p–i–n junction [94]. Finally, in regions where φn,p , n, p, and µn,p change rapidly and simultaneously (for e.g. in a quantum well active region), φ may well become difficult to interpret. However, this in no way degrades the application of this model to bulk regions and heterojunctions.
3.5
Modeling conclusions
The general carrier dynamic model provided a basis from which the carrier densitymobility-weighted electrochemical potential Eq. (3.8) was derived. The probe was modeled as a metal and the carrier fluxes to and from the probe were considered in generating the potential at the probe. It must be emphasized that the quantities used in the model are those deep within the device, far from the measurement surface. At equilibrium, the voltage probe registers the Fermi level (chemical potential) which is consistent with the thermodynamic viewpoint. In strongly n-type (p-type) regions, the electron (hole) quasi-Fermi level is measured. Over intrinsic or space charge (depleted) regions, the carrier density dependence is removed and the measured potential is a mobility-weighting of the quasi-Fermi levels. Understanding what is measured ensures experimental scans of devices are interpreted properly. SVM scans can then be used to verify both theory and simulation. Theory and simulation can then be used in conjunction with properly interpreted scans to decompose the data into underlying components such as carrier densities and quasi-Fermi levels.
Chapter 4 Optimizing SVM spatial resolution 4.1
Introduction
We have seen that SVM measures a carrier density–mobility-weighted average of the hole and electron electrochemical potentials (quasi-Fermi levels). SVM, like all AFM and scanning probe techniques, is subject to measurement artifacts.1 If SVM is to be used to analyze nanometre-sized structures in a reliable, repeatable manner, it is critically important to identify and evaluate sources of artifact. Now that we know what SVM measures, we examine how SVM measures. It became apparent that SVM profiles exhibit discrepancies depending on scan direction and material doping type. During earlier work, qualitative differences in twodimensional SVM potential maps were noted. These differences depended on whether the probe was scanned in the direction of increasing or decreasing sample potential. In the direction that tracked increasing sample potential, abrupt interfaces between adjacent material layers were more clearly delineated than those in the decreasing-potential scan direction. Images taken in decreasing-potential direction were notably more smeared, particularly over p-type InP. 1
A common euphemism among AFM practitioners is that everything is an artifact until proven otherwise.
40
4. Optimizing SVM spatial resolution
41
In this chapter we examine the apparent differences in captured SVM images— whether captured in the increasing or decreasing potential direction on n- or p-type semiconductors—and identify the energy band alignment at the probe–sample interface as the source of the observed differences. We will see how spatial resolution is affected directly by the time needed for the measurement circuit to reach steady-state with the sample and we quantify the associated time constants. The measurement circuit system (including the probe–sample interface) is considered as an RC equivalent circuit with series resistance dependent on scan direction and material doping type due to the formation of a Schottky barrier at the interface. A limitation on the scan speed required for accurate SVM measurements is presented; the limit relationship is relevant to conductive scanning probe techniques having high series resistance.
4.2
Interface characterization experiments
Two experiments were conducted to investigate the material and directional dependencies so that the most accurate SVM data can be captured at the highest possible spatial resolution. An atomic force microscope (model Dimension 3100/Nanoscope III, Digital Instruments) was used in both experiments with conductive boron-doped diamond-coated tips (DDESP, Nanosensors, with tip radius ∼ 10 nm) connected electrically to an ultra-highimpedance voltmeter (model 6517A, Keithley). Tip–sample forces were sufficient to penetrate the native InP oxide layer and to provide good electrical contact at the interface (∼ µN). The samples studied were InGaAsP/InP buried heterostructure lasers with uncoated facets and metalized ohmic contacts [14]. Nominal doping concentration of the p–n–p–n current blocking layers was 1018 cm−3 . The lasers were mounted on heat-sinking carriers and were oriented to expose the facets to the AFM tip. Voltage–current characteristics
42
4. Optimizing SVM spatial resolution
Keithley 6517A high-Z voltmeter preamp out
Tektronix oscilloscope and software
AFM tip p
i
n
Sample Sig gen
Figure 4.1: SVM setup modified for time-resolved measurements: the current source is replaced with a square-pulse signal generator and the output of the voltmeter is directed to an oscilloscope to capture the impulse response of the SVM measurement circuit. of the lasers were recorded before and after the experiments to ensure normal device operation. In the first experiment, a conductive AFM tip was scanned over the alternating p– n–p–n current blocking layers2 of a DC-biased BH laser at various scan rates to observe hysteresis between the forward and reverse electric potential scans. In the second experiment, a BH laser was modulated with a square-wave to quantify the time constants of the SVM measurement circuit on n- and p-type InP. The output of the voltmeter’s initial preamplifier (voltage follower) was directed to an oscilloscope (see Fig. 4.1).
4.3
SVM hysteresis and impulse response
One-dimensional SVM cross-sectional potential profiles were measured across p–n–p–n current-blocking layers of the DC-biased BH laser. 512 samples were captured along 5 µm scans giving approximately 10 nm resolution limited ideally by the tip radius. Direct comparison of potential profiles in Fig. 4.2 reveals hysteresis between the different directional scans: the forward scan (left to right) tracks closely the abrupt increasing potential changes from layer to layer and is relatively invariant to scan speed whereas the 2
These layers form a thyristor structure that serves to funnel current into the active region [14].
43
4. Optimizing SVM spatial resolution 1
a) scan rate: 5 µm/s
b) 1 µm/s
0.8 0.6
Voltage [V]
0.4
p
p n
n c) 0.5 µm/s
d) 0.1 µm/s
0.8
p
p
0.6
n
0.4
p
p
0.2 0
p n
scan direction
0.2 0 1
p
n
n 0
n
n 1
2
3
4
50 1 Position [µm]
2
3
4
5
Figure 4.2: Electric potential cross-sections of the p–n–p–n blocking layers of a forwardbiased buried heterostructure laser (arrows show spatial scan direction of probe). Significant hysteresis is observed between increasing (left to right) and decreasing (right to left) electric potential scans on p-type material at faster scan rates (a) 0.5 Hz, (b) 0.1 Hz, and (c) 0.05 Hz. At the slowest scan rate of 0.01 Hz (d) steady-state has been reached and the hysteresis is reduced acceptably; shot noise is observed at this speed since otherwise dominant probe–sample steady-state-approaching currents have subsided. reverse scan (right to left) converges to abrupt decreasing potential changes only for the slowest scan speed shown (0.1 µm/s). Exponential time constants were estimated from these results and are summarized in Table 4.1 in the “p–n–p–n” column. Time constants on p-type InP are an order of magnitude slower than those on n-type InP; on p-type InP the average time constant for the decreasing potential scan direction is several times slower than that for the increasing potential scan direction. Noise becomes apparent only during the slowest scan (see Fig. 4.2d). To further examine the behaviour of the tip–sample interface and measurement circuit, the SVM setup was modified for the second experiment: a 50% duty-cycle squarewave bias was supplied to the BH laser and the potential output from the stationary AFM tip was captured on an oscilloscope via the voltmeter preamplifier output port. A similar set-up was used by Trenkler et al. [13] to characterize SVM probes. Fig. 4.3 shows
4. Optimizing SVM spatial resolution
44
Table 4.1: Summary of time constants measured for p-n-p-n scan and time-resolved experiments, and estimated from RC equivalent circuit for each doping type (nominal concentration 1018 cm−3 ) and potential change (potential increasing or decreasing). Doping Potential p-n-p-n Square Wave RC Model n-type increasing 4 × 10−2 s 10−2 s 10−2 s n-type decreasing 5 × 10−2 s 10−2 s 10−2 s p-type increasing 3 × 10−1 s 10−1 s 10−1 s −1 −1 p-type decreasing 9 × 10 s 9 × 10 s 1s the impulse response for n- and p-type InP of the BH laser for increasing bias frequency. The average time constants are summarized in Table 4.1 in the “Square Wave” column. Again, time constants for p-type InP are an order of magnitude slower than those on n-type InP and tracking decreasing potential is several times slower than tracking increasing potential. At 10 Hz input frequency (Fig. 4.3c), the p-type response shows the effects of severe low pass filtering. The voltmeter was isolated and found to have a frequency response many orders of magnitude higher than that of the tip–sample interface shown in Figs. 4.2 and 4.3.
4.4
Transient interpretation
4.4.1
Transient equivalent circuit
The response shown in Fig. 4.3 is characteristic of a low pass filter. There is no experimental evidence of high pass filtering caused by junction and diffusion capacitances (cj and cd ) in at the tip–sample interface so we neglect these small-signal series capacitances. Previous scanning spreading resistance microscopy measurements with identical tips have shown [70] that contact resistance rc dominates over the series resistance Rs of the diamond probes [51]; contact resistances are on the order of 108 Ω for n-type InP and 109 –1010 Ω for p-type InP near steady-state. The input impedance of the voltmeter consists of a very large resistance Rin shunted with parasitic capacitance Cin ; the recorded SVM potential quantity is measured across this input impedance. Voltmeter input ca-
45
4. Optimizing SVM spatial resolution
a) Input freq.: 0.1 Hz
Electric Potential [V] (arbitrary DC offset)
1
b) 1 Hz
c) 10 Hz
Input waveform
0.5
0 1
n-type InP response
0.5
0 1
p-type InP response
0.5
0
0
20
40
60
80
100 0
2
4
6
8
10 0
0.2
0.4
0.6
0.8
1
Time [s]
Figure 4.3: Impulse response of the scanning voltage microscopy measurement circuit on buried heterostructure laser: input waveform (above), n-type response (middle) and ptype response (below), InP material 1018 cm−3 nominal doping, biased with square waves at a) 0.1 Hz, b) 1 Hz, and c) 10 Hz. Faster impulse response of n-type InP is observed. Average time constants are summarized in Table 4.1.
46
4. Optimizing SVM spatial resolution a)
sample
sample-tip interface rc
Vsample
+ −
b)
voltmeter
rc
Rs
cj+cd Cp
Cin
Rin
VSVM
+ Vsample −
Cp+Cin
VSVM
Figure 4.4: SVM tip–sample interfacial equivalent circuits. (a) Complete circuit; (b) reduced RC circuit ignoring (cj + cd ) and taking Rin rc Rs . pacitance is fixed at 2 × 10−11 F and the input resistance is in excess of 2 × 1014 Ω [103]. Additional parasitic capacitance Cp appears in shunt due to the electrical cables and connectors between the AFM tip and voltmeter and simply adds to the input capacitance to yield a total shunt capacitance on the order of magnitude of 10−10 F. Since the input resistance of the voltmeter is several orders of magnitude greater than the series resistance of the interface, voltage division of the sample potential is insignificant and the input resistance can be considered infinite. The equivalent circuit model is reduced to a single-time-constant RC circuit with series incremental contact resistance that varies with material doping type and scan direction, and a fixed parasitic shunt capacitance (see Fig. 4.4). Calculated RC time constants from this model are summarized in Table 4.1 in the “RC Model” column and are consistent to the order of those measured in the experiments. It must be emphasized that this RC equivalent circuit represents the transient response of the SVM measurement circuit. At or near steady-state the voltmeter draws negligible current so no voltage falls across the contact resistance at the tip–sample interface and the true local electrochemical potential is registered at the voltmeter inputs.
4.4.2
Tip–sample bandstructure
The source of the high contact resistance can be traced to the formation of a Schottky barrier at the tip–sample interface. The diamond grain coating of the AFM tip is doped
47
4. Optimizing SVM spatial resolution
sufficiently heavily with boron that it is appropriate to model the tip material as a metal [46] with Fermi level EF m at the work function energy near 4 eV below vacuum [45, 71]. At the surface of the biased semiconductor laser, the quasi-Fermi levels φn and φp must converge as shown in Fig. 4.5a for both n- and p-type InP. The electron affinity of InP is 4.38 eV below vacuum; the band gap energy between conduction band edge Ec and valence band edge Ev is 1.34 eV [98]. The process of approaching steady-state at the tip– sample interface takes place as charge is transfered between tip and sample to align the Fermi level of the tip and the convergence point of the quasi-Fermi levels of the sample. A depletion region arises in the sample as the pinned energy bands bend, leading to the formation of a Schottky barrier [104] ΦB as shown in Fig. 4.5b. Two conduction mechanisms are possible for electrons to cross the Schottky barrier: thermionic emission and tunneling. For a semiconductor of light to moderate doping concentration, thermionic emission dominates [104] and the contact resistance rc is given by rc =
kB T q
exp
ΦB kB T
A∗ T 2
,
(4.1)
2 /h3 . where A∗ is the effective Richardson constant for thermionic emission, A∗ = 4πqm∗ kB
If the semiconductor is heavily doped, tunneling dominates, and the contact resistance is proportional to rc ∝ exp
2 ΦB ~
r
s m ∗ ~N
! ,
(4.2)
where s is the dielectric constant, m∗ is the appropriate effective mass, and N is the doping concentration. Typical doping concentrations for semiconductor lasers span the range from light to heavy, but regardless, contact resistance at the interface depends exponentially on the barrier height. Since the bandstructure of p-type InP gives rise to a larger barrier, its contact resistance must be substantially higher than that for n-type InP. Furthermore, the greater depletion of carriers across the interface in the p-type case further slows the approach to
48
4. Optimizing SVM spatial resolution a) Contact upon first probe tip placement or relocation n-type InP
~ 4 eV
4.38 eV
EFm
Evac
Ec EFn 1.34 eV
AFM tip
p-type InP
~ 4 eV
4.38 eV
EFm
Evac
Ec EFn 1.34 eV
EFp Ev
EFp Ev
b) Steady-state contact after sufficient steady-state approach time
AFM tip
n-type InP
Evac
Evac
AFM tip
~ 4 eV EFm
~ 4 eV ΦΒ
Ec EFn EFp Ev
EFm
Time to steady-state
AFM tip
p-type InP
ΦΒ
Ec EFn EFp Ev
Figure 4.5: Energy band diagram of tip–sample interface for n-type (left) and p-type (right) InP sample material: tip Fermi level EF m (work function near 4 eV), conduction band Ec , valence band Ev , quasi-Fermi levels φn and φp , and Schottky barrier height ΦB . a) Non-steady-state condition at first probe–sample contact or after probe relocation. b) Steady-state results when the Fermi levels align with charge redistribution, causing band bending and formation of space charge regions into the sample at the interface. Band bending is more severe for p-type InP and yields higher contact resistance. steady-state. Noise resulting from fluctuations in current at the interface3 appears at the slowest scan rate in Fig. 4.2d since the system has come to reasonable steady-state and charge transfer is no longer dominated by Fermi level alignment-induced current. With the parasitic capacitance of the measurement circuit fixed, the time-to-steady-state varies only with this contact resistance. Approaching steady-state for decreasing sample potential is notably slower (particularly on p-type InP) since the barrier ΦB and contact resistance increase for a lower convergence point of the quasi-Fermi levels, whereas approaching a higher steady-state 3
The dominant source of noise is random thermal generation of electron-hole pairs that are then swept to opposite sides [100]. Shot noise is generated across the depletion region width—the wider the depletion region, the greater the shot noise; hence, more noise appears on p-type material.
49
4. Optimizing SVM spatial resolution
V<0 n-type
a)
V=0 Ec EFn
b)
tip
c)
sample Ec EFn
EFm
EFm
V>0
EFm
Ec EFn
Ev Ev W
Ev
W
V<0
V=0
V>0
Ec
p-type
d)
EFp Ev
EFm
W
e)
tip
sample
EFm
Ec
EFp Ev
W
f)
Ec
EFm EFp Ev W
Figure 4.6: Asymmetry in the tip–InP interface. For each material type, the relative energetic position of the tip EF m (left side of interface, dashed line) and the positions of the conduction band Ec and valence bands Ev (right side of interface, solid lines) are pinned at the interface. Only the prevalent quasi-Fermi level EF n,p is shown in each case (right side, dashed line). potential decreases the barrier and contact resistance (see Fig. 4.6). More importantly, scanning from lower to higher potential shrinks the depletion region, allowing more carriers to be transported across the interface and accelerating the steady-state process; scanning from higher to lower potential has just the opposite effect—carriers become increasingly sparse as the depletion region expands. Therefore, there is a preferential scanning direction in terms of frequency response from lower to higher sample potential.
4.5
Limiting scan speed eliminates artifacts
To allow the probe–sample interface to reach steady-state for each electric potential location at a desired spatial resolution d, the scan speed of the tip v must be limited such
50
4. Optimizing SVM spatial resolution that v<
d , 5τ
(4.3)
where τ is the longest time constant encountered on a given scan (according to material type and whether potential is increasing or decreasing); after five time constants the tip is considered to be at steady-steady with the sample with less than 1% error.4 For example, at v = 0.5 µm/s, roughly 50 samples/s can be captured accurately at a resolution of 10 nm on n-type InP since each sample has 0.05 s to reach steady-state as shown in Fig. 4.2c. The time required to reach tip–sample steady-steady is shorter for scans in which increasing potential is measured so that v may be increased if scans in the direction of decreasing potential are discarded. These results apply generally to a wide variety of semiconductors. The band gaps for common semiconductors—including band gap ranges for ternary and quaternary materials—are plotted in Fig. 4.7. All have similar bandstructures relative to the CVD diamond tip workfunction and so p-type material will always form the greatest Schottky barrer and limit the scan speed. As a specific example, Fig. 4.8 illustrates artifacts resulting from scanning too fast that could have been overlooked. A lightly p-doped InGaAsP 12-multi-quantum-well structure was scanned at 50 nm/s and at 10 nm/s in the same direction of increasing potential. Arrows on Fig. 4.8 point to artifact locations where the faster scan “lags” the slower scan, producing incorrect features in the voltage profile. At such high resolution, careful selection of scan speed is required to avoid data misinterpretation. A counterexample is shown in Fig. 4.9: at a scan speed dictated by the limit (4.3) all 12 quantum wells are easily identified and artifacts are suppressed. Such accurate high resolution is unprecedented.
4 −5
e
= 0.007; it is common [105] to take five or six time constants in asymptotic approximation.
51
4. Optimizing SVM spatial resolution
CVD diamond
Si
GaAs
-4.0
cb In1-0.47yGa0.47yAsyP1-y
InP
In0.53Ga0.47As
cb
Energy [eV]
-4.5
-5.0 vb
-5.5 vb -6.0
Figure 4.7: Comparison between the metallic Fermi level of CVD diamond and the conduction (top solid line) and valence (bottom solid line) bands of common semiconductors; for InGaAsP, the range of conduction and valence band energies lattice-matched to InP is shown by upper and lower dashed lines. 1 n-InP
InGaAsP MQW
p-InP
etch-stop
0.9
SVM potential [V]
0.8
0.7
0.6
scan direction
0.5
0.4
80 mA 50 nm/s 80 mA 10 nm/s 0
100
200
300
400
500
Position [nm]
Figure 4.8: Scan speed artifacts at high resolution. Arrows point to artifacts attributed to the higher scan speed (both traces taken in the same direction).
52
4. Optimizing SVM spatial resolution 1.8 QW: 1
2
3
4
5
6
7
8
9
10
11
12
1.6 n-SCH
SVM potential [V] (arb. DC offsets)
1.4
p-SCH
1.2
50 mA
1 40 mA
0.8
30 mA
0.6 0.4
20 mA
0.2 1 0
0
2 50
3
4
5
6
7
8
100
9 150
10
11
12 200
10 mA
250
Position [nm]
Figure 4.9: High resolution SVM scan showing 4 nm quantum wells and illustrating spatial resolution limited by tip size, not scan speed.
4.6
Conclusions
Probing of the electric potential by scanning voltage microscopy has been shown experimentally to be an inherently slow process. Reaching steady-state between the semiconductor sample and measurement circuit must occur for accurate measurement of the local sample potential. First-order time constants of approaching steady-state are on the order of 10−2 s (tracking increasing and decreasing potentials) on n-type InP, and 10−1 s (tracking increasing potential) and 1 s (tracking decreasing potential) on p-type InP. For accurate measurements, the SVM scan speed must be limited by the ratio of spatial resolution to slowest time required to reach steady-state. There is a preferential scanning direction in terms of frequency response from lower to higher sample potential due to the asymmetry of the Schottky junction. Using diamond tips on InP and other common semiconductors, measuring n-doped regions will always be faster (and less noisy) than measuring p-doped, and measuring from low-to-high potential will be faster.
4. Optimizing SVM spatial resolution
53
We confirmed that the series resistance between probe and sample is dominated by the contact resistance resulting from the formation of a Schottky barrier at the interface; the resistance ranges from 108 –1010 Ω near steady-state depending on material doping type and potential gradient. Standard SVM was performed at different scan rates to qualify the nature of directional scan hysteresis. The standard SVM configuration was modified to quantify the frequency response of the SVM measurement circuit and elucidate the nature of the the probe–sample interface. By studying the bandstructure of the interface and inferring the barrier behaviour for different materials and relative potentials, we have formulated a necessary calibration step and scan speed restrictions to ensure accurate, reproducible, artifact-free SVM measurements at the desired spatial resolution.
Chapter 5 Investigating the p-type contact in coolerless ridge waveguide lasers It has been seen in Chapter 4 that care must be taken to acquire high-resolution SVM images free from transient-induced artifacts. Combining the scan rules we have developed with the interpretation that the measured potential is a weighted average of the quasiFermi levels, we now investigate an important heterojunction within a state-of-the-art semiconductor laser. We will see that this heterojunction is the source of considerable parasitic power loss.
5.1
Introduction
Digital subscriber loops (commonly known as DSL) serve as access links at edge of internet. They consist of relatively low capacity data paths compared to the wavelength division multiplexed core links, having a single wavelength channel per fibre (usually at 1310 nm to alleviate dispersion [1]) with data rates up to 10 Gb/s [106]. Fibre spans are typically short so the elevated fibre loss at 1310 nm is acceptable. The primary aim is to reduce the cost in bringing data to buildings, campuses, and local central offices. To reduce unit cost and improve reliability [107] lasers are implemented without a 54
5. Investigating the p-type contact in coolerless lasers
55
thermoelectric cooler.1 A cooler adds to the overall cost and complexity of the laser package and often employs costly feedback circuitry. Thermal management in laser design becomes critical: nonradiative carrier recombination may prevail if carriers bypass the active region by way of their thermal energy; this is “vertical” carrier leakage. Consequently, the active regions are usually exceptionally thick with many quantum wells to reduce thermionic over-barrier carrier leakage. Heating also causes threshold current to increase because more carriers on average will be able to surmount the energy barrier presented at the far side of the active region, leading to thermionic carrier leakage and lowering internal efficiency. A source of self-heating is the p-type InP/InGaAs electric contact, normally not addressed in studies of laser optimization [33,108,109]. In order to be classified as ohmic, a contact must have a linear current–voltage characteristic, which generally implies good energy band alignment from one material to the next [104]. Ideally, the specific contact resistance Rc = V /J should be 10−6 Ω·cm2 or less. Metal/p-InP contacts are primarily nonohmic because the energy barrier from the metallic work function to the InP Fermi level is ∼ 0.8 eV [110], leading to diode (Schottky) current–voltage behaviour. In particular, holes face a significant energy barrier from metal to p-InP and their scattering causes joule heating of the device. Minimizing both the specific contact resistance and the nonohmic tendencies of the contact improves device efficiency and frequency response while lowering the operating temperature [111]. Much research during the last two decades [111–114] has focused on bridging metal (specifically non-corrosive gold) and p-InP ohmically, employing combinations and alloys of Au, Zn, Ni, Pd, Pt, Mn, Sb, W, and Ti to achieve reasonably linear I–V characteristics with Rc ∼ 10−5 Ω·cm2 [110, 115].2 Beyond the metallurgy of the metal–semiconductor junction, a buffer layer of highly-doped InP-lattice-matched 1
Some spectral drift with temperature must be tolerated; this is tolerable in single-wavelength links. Using gold alone yields poor morphology of the contact; gold can also diffuse into the active region and serve as an undesirable nonradiative recombination centre [111]. 2
5. Investigating the p-type contact in coolerless lasers a)
b)
V
Itest
56
V
metal InGaAs InP
Itest
insulator
Figure 5.1: Method of measuring specific contact resistance of p-InP contact. (a) Measurement of the metal/p-InGaAs contact resistance. (b) The InGaAs between the electrodes is removed by etching, allowing the combined contact resistance to p-InP to be measured. In either case, the contact resistance for a single forward-biased metal/pInGaAs/p-InP cannot be isolated from the combined system and must be inferred.
In0.53 Ga0.47 As reduces the compound contact resistance [116, 117], although holes still must surmount an energy barrier at the p-InGaAs/p-InP heterojunction. Contact resistance can be measured by the test structure shown in Fig. 5.1. In the first instance, current is passed from one electrode to the other via the InGaAs layer, yielding the “resistance” of the metal/InGaAs contact; it must be noted that in fact, the resistance measured is influenced by both the forward and reverse contacts of the structure. The InGaAs layer is then etched between the electrodes and the “total resistance” is measured for the combined contact to p-InP; again, there are forward and reverse heterojunctions in the current path. Additionally, minority electrons from vertical current leakage may influence the total resistivity of the real diode laser [109]. The conclusion must be that this is an indirect method used to infer the actual resistance of the heterojunction in a real device. In this chapter, we use SVM to directly image the voltage division—and resulting contact resistance (and power loss)—at the p-In0.53 Ga0.47 As/p-InP heterojunction in a working, coolerless laser. This is the first direct study of this heterojunction. As an important digression, we evaluate the source of another potential SVM artifact, photopumping by the AFM optical lever laser. We investigate possible ramifications of the
5. Investigating the p-type contact in coolerless lasers
n-InP substrate
n-InP
QWs
etch-stop
n
57
p-InGaAs
p-InP ridge
p
~2 µm
SVM x-section
~120 µm
~3 µm
Figure 5.2: Schematic of pVHT laser facet. nonohmic characteristic of this heterojunction, particularly those associated to heating by the dissipative losses.
5.2 5.2.1
InGaAs/InP heterojunction characterization Experiment and results
InP/InGaAsP laser chip samples emitting in the 1310 nm range and having 12 quantum wells were studied. Threshold current is around 20 mA with a wallplug efficiency exceeding 0.24 mW/mA.3 A schematic of the light-emitting facet is shown in Fig. 5.2. The cavity length is 300 µm and is cleaved at each end. Each laser chip is mounted on a separate heat-sinking carrier and wire-bonded to large gold pads accessible to the sample holder. SVM was implemented for the first time at the University of Toronto. Unlike previous SVM experiments [11, 14, 15, 96] which had the p-type contact referenced to ground, the present configuration references the n-type contact to ground so that no inversion of the voltage data is necessary and there is no DC offset associated with the inversion. The grounds of the current source and and voltmeter are connected to eliminate ground loop noise; noise from the probe is reduced by connecting the shielding of its cable to the 3
With a highly reflective back coating the efficiency might increase to ∼ 0.5 mW/mA [107].
5. Investigating the p-type contact in coolerless lasers Keithley 6517A high-Z voltmeter
gnd + anlg out
Signal access Module
tip
n p
aux D
Nanoscope III controller and software
58
- current + source - voltage + source
PC controller and data-capture software
Figure 5.3: SVM experimental implementation with Dimension 3100 AFM. common star ground point. Buffered voltage data are directed into the Nanoscope III data collection system via the signal access module by replacing the lateral friction signal. The complete configuration is illustrated in Fig. 5.3. Rigorous testing and calibration steps were performed to ensure correct and optimal performance. 3 µm line scans with 512 samples per line were taken from the n-type substrate to the p-type metal, shown in Fig. 5.4. The tip velocity was 0.3 µm/s giving 15 nm resolution on n-type material and 150 nm resolution on p-type material, limited by scan speed4 according to the transient analysis of the previous chapter. An exceptional bias range was captured: 10–190 mA traces were obtained in increments of 10 mA (constant current); normally the tip fails catastrophically at 80–90 mA due to heating by the laser facet. From left to right in Fig. 5.4, we observe the
• n-InP layer; • n-SCH; • active region—low bias scans having distortion due to surface debris—high bias scans are excellent and individual quantum wells are visible; • p-SCH; • etch-stop (always visible as a 4 nm wide spike); 4
At 512 samples per line, the ideal resolution is 6 nm. Tip geometry likely limits resolution to 10 nm.
5. Investigating the p-type contact in coolerless lasers
n-InP 2.5
MQW ES n-SCH p-SCH
p-InP
59
p-InGaAs metal
SVM potential [V]
2
1.5
1
10:10:190 mA
0.5
0
0
0.5
1
1.5 Position [µm]
2
2.5
3
Figure 5.4: SVM scans of wide-MQW RWG laser, 0:10:190 mA. The layer structure is indicated. Rather exceptionally, SVM curves were obtained well above 80 mA bias. Shot noise increases on p-type material due to the wide depletion region at the tip–sample interface at high bias. • p-InP interface between regions of different doping, adjacent to the etch-stop; • p-InP ridge; • large voltage drop at the p-InP/p-InGaAs interface; and • transition from p-InGaAs to the metal contact, visible as a small bump in the maximum voltage plateau.
At all bias points, the voltage measured at the metal on the p-type side by the SVM probe is identical to the voltage measured across the terminals during a separate V –I characterization. Noise increases dramatically along the p-type regions as the bias increases; as mentioned previously, this is shot noise elevated by the wide depletion region formed at the tip–sample interface on p-type material. A constant voltage source replaced the constant current source to reduce the bias
5. Investigating the p-type contact in coolerless lasers
60
2
SVM potential [V]
1.5
1
0.5
0
-0.5 0
0.5
1
1.5 Position [µm]
2
2.5
3
Figure 5.5: SVM scans of wide-MQW RWG laser, low bias voltage. Below a bias voltage of 0.49 V, the SVM potential dips below 0 V; this is due to reverse photocurrent induced by the AFM laser (i.e. of the optical lever), insignificant at higher bias points. voltage below the turn-on value.5 3 µm line scans with 512 samples per line were obtained as before. Hysteresis was significant in the decreasing-potential scan direction and all such curves were discarded. The traces are aligned manually at the p-InP/p-InGaAs interface; some thermal drift of the AFM piezo-electric drivers is noticeable as not all the etch-stops are perfectly aligned.
5.2.2
Low-bias SVM artifact identification: photocurrent
It is interesting to note that for bias voltages below 0.49 V, the p-type SVM voltage dips below 0 V. Even at a bias voltage of 0 V, the SVM voltage remains rooted firmly below zero, even after two hours of continuous scanning. In fact, the laser is not at equilibrium: the laser light from the AFM optical lever not reflected by the tip is absorbed by the sample laser which in turn produces a reverse 5
With a constant current source, the diode voltage immediately assumes a value of ∼ 0.5 V.
5. Investigating the p-type contact in coolerless lasers
61
25 0.014 0.012 0.01
20
0.008 0.006
Diode current [mA]
photocurrent
0.004
15
0.002 0 -0.002
10
0
0.1
0.2
0.3
0.4
0.5
5
0
-5
tip engaged, laser on tip disengaged, laser off 0
0.2
0.4
0.6
0.8 Voltage [V]
1
1.2
1.4
1.6
Figure 5.6: Evidence of reverse photocurrent effects at low sample voltage. Below 0.49 V bias, the photocurrent contends with the bias current (inset). When the AFM laser is deactivated, the photocurrent vanishes.
photocurrent, shown in the I–V characteristic of Fig. 5.6. Although SVM scans cannot be performed without the AFM laser activated (deflection feedback is necessary), the short-circuit photocurrent vanishes when the AFM laser is removed (see 5.6 inset). The wavelength of the AFM laser is 670 nm, well above the 1310 nm bandgap of the sample laser, and the output power is 1 mW before reflection off the tip, a significant portion of which is not reflected to the photodetector. At bias points above 0.49 V, the bias current (∼ mA) washes out the photocurrent (∼ µA) and all effects due to the AFM laser can be completely neglected. At bias points below 0.49 V where the SVM traces begin to dip below 0 V, the photocurrent is comparable to the external bias current as shown in the inset of Fig. 5.6 (both ∼ µA), and so it must be considered. Hence, when the bias is set to 0 V, the sample laser is not actually at equilibrium and is rather acting as a photovoltaic diode.
5. Investigating the p-type contact in coolerless lasers
62
0 In0.53Ga0.47As
Relative energy [eV]
InP
-0.5
-1
-1.5
Figure 5.7: In0.53 Ga0.47 As/InP heterojunction bandstructure.
5.2.3
p-type InGaAs/InP heterojunction parasitics
Dominating the voltage profiles—even at low voltage where the reverse photocurrent prevails—is the voltage drop across the p-type In0.53 Ga0.47 As/InP heterojunction interface. The bandstructure, calculated from first-principles [19, 98], is shown in Fig. 5.7 and illustrates the energy barrier presented to hole transport. Aligning the Fermi levels produces a valence band tunnel junction ∼ 0.25 eV tall and ∼ 10 nm wide. Thermionic emission is expected to dominate [116] over tunneling since the barrier is relatively wide. As holes scatter at this barrier, they contribute phonons to the lattice, thereby heating the ridge and surrounding regions. The voltage drop measured by the SVM circuit reveals the change of the hole quasi-Fermi level under forward bias as predicted by the model developed in Chapter 3. Dividing this voltage drop Vhet by the total voltage drop across the device yields the fractional voltage drop, power loss and series resistance at the heterojunction, Vhet Phet Rhet = = , Vtot Ptot Rtot
(5.1)
plotted in Fig. 5.8 for constant current bias and in Fig. 5.9 for constant low voltage
5. Investigating the p-type contact in coolerless lasers
63
% voltage drop, % power loss, % series resistance
50
45
40
35
30
25 operating range 20
0
10
20
30
40
50
60
70
80 90 100 110 120 130 140 150 160 170 180 190 Bias Current [mA]
Figure 5.8: Fractional parasitic voltage drop (power loss, series resistance) of p-InP/pIn0.53 Ga0.47 As heterojunction. The average value is 35% over the operating range. bias.6 It is striking that over the normal operating range of this laser (20–80 mA [118]), ∼ 35% of the wallplug power is lost before it ever reaches the active region. Clearly, from the SVM profiles the In0.53 Ga0.47 As layer yields a flat, relatively lossless contact with the metal. However, a highly nonohmic contact is formed subsequently with the InP ridge, degrading performance and wallplug efficiency. The specific contact resistance of this interface is a dismal ∼ 10(2 µm)(300 µm) = 6 × 10−5 Ω·cm2 , nearly two orders of magnitude greater than the metal/p-InGaAs contact. One novel approach to reducing the barrier is to use a reversed-biased tunnel junction [119], essentially a Zener diode in breakdown operation [100]. Instead of making metallic contact to p-type material, n-type material is used at both ends for good ohmic contact; at one end is a proper n-type region and at the other, a reversed-biased junction so heavily doped that carriers tunnel easily through. Total contact resistances of ∼ 10−6 Ω·cm2 6
Primary uncertainty in the data arises from estimating the actual voltage of the p-type InP which is subject to noise. There is less significant uncertainty in the bias current and the voltage level of the InGaAs.
5. Investigating the p-type contact in coolerless lasers
64
100
% voltage drop, % power loss, % series resistance
90 80 70 60 50 40 30 20 10 0
0
2
4
6
8
10 12 Bias Current [mA]
14
16
18
20
Figure 5.9: Low-bias fractional parasitic voltage drop of p-InP/p-In0.53 Ga0.47 As heterojunction. have been reported [119]. A more straightforward attempt to reduce the hole barrier is to grade the InGaAs/InP junction by MBE [116]; grading smoothes out the hole tunnel barrer and improves the specific contact resistance by an order of magnitude.
5.2.4
Heating effects from heterojunction power dissipation
The dissipation at the junction interally heats the laser. Heating of the active region causes carrier loss due thermionic over-barrier leakage [21] which dominates the threshold current at high temperatures (80◦ C) and limits the maximum lasing temperature [109] in ridge waveguide Fabry-P´erot architectures. As illustrated in Fig. 5.10, carriers possess enough energy to bypass the active region and recombine in the cladding regions either nonradiative, or radiatively at an undesired wavelength given by the bandgap of the cladding region. Thermal runaway occurs [120] where the increased temperature raises
5. Investigating the p-type contact in coolerless lasers e-
n-SCH
thermionic loss
65
thermionic loss
MQW
p-SCH
h+
Figure 5.10: Thermionic loss mechanism. Carriers have sufficient energy to bypass the active region and do not contribute to useful gain. the threshold current7 and lowers the differential quantum efficiency [21]; pumping the laser at a higher current to maintain threshold further heats the active region, completing the positive feedback loop. A parial remedy is to mount the laser chips “active-region down” so that the p-type ridge is soldered directly to a heatsinking electrode, cooling the dissipative regions of the chip as much as possible [120]. Thermal spread can be controlled by carefully optimizing the ridge width, balancing better thermal dissipation (with wider ridges) against better temperature independence of the threshold current (with thinner ridges) [120]. Ideally, forming a truly ohmic contact to the p-InP would alleviate much of the power loss and self-heating.
5.3
Conclusions
SVM was applied to study the p-type contact strategy of a state-of-the-art uncooled ridge waveguide laser. Although the metal/p-InGaAs contact was found to be ohmic and essentially lossless, the p-InGaAs/p-InP heterojunction was observed to dissipate ∼ 35% of the total power applied to the laser over the operating bias range, causing self-heating. Equivalently, ∼ 35% of the series resistance is due to this heterojunction, increasing the 7
Temperature dependence varies as Ith = I0 eT /T0 [21], where T0 is the characteristic temperature ∼ 70 K for InGaAsP lasers [21, 121].
5. Investigating the p-type contact in coolerless lasers
66
device RC time constant and limiting frequency response. This is the first direct study of the parasitic voltage division and resulting power loss and series contact resistance, illustrating the need for a good p-type contact strategy. This study also highlights the need for preceding characterization of the probe–sample interaction and corresponding measurement circuit time constants. Trends in the scans of the heterojunction could not have been quantified without carefully considering the time constants involved in the measurement process across the interface. Additionally, an important SVM-specific artifact was identified and evaluated. The artifact resulted from photocurrent generated in the sample by the AFM optical lever laser and is not significant beyond the initial turn-on range of the sample diode.
Chapter 6 Conclusions and Future Work
6.1
Summary and Conclusions
Scanning voltage microscopy elucidates the operation, limiting processes, and failures of fabrication in active semiconductor lasers, transistors, and hybrid nanocrystal/polymer devices. A model has been developed to account for the measured voltage of a nanoscopic voltage probe placed on a nonequilibrium semiconductor surface. Rules have been developed to ensure that scan-induced artifacts are eliminated while optimizing spatial resolution. The model and rules were then applied to study a parasitic heterojunction in state-of-the-art semiconductor lasers. In the first chapter, SVM was introduced as a direct method to open the black box of the modern microelectronic device. The key is that because the nanoscopic tip draws essentially zero current, electric potential maps can be obtained on devices in operation. Chapter 2 presented an overview of electrical scanning probe techniques. SVM arrived relatively late although it is perhaps the simplest of all the techniques. CVD dopeddiamond tip technology enabled SVM by combining suitable electrical and mechanical properties. The technique has been employed to study a variety of MOSFETs and diode lasers, but the question remained as to what exactly was measured. 67
6. Conclusions and Future Work
68
Chapter 3 confirmed through simulation that the mobility-weighted electrochemical potential is measured. This conclusion is supported by thermodynamics and carrier transport models. At equilibrium, the Fermi level is measured. On unipolar material, the measured potential is dominated by the appropriate quasi-Fermi level. Interpretation is straightforward and consistent. Equipped with a foundation of what SVM measures, the frequency response was examined in Chapter 4 and modeled with an equivalent RC circuit. SVM is an inherently slow process due to Schottky barrier formation at the tip–sample interface. The barrier is significantly greater for common p-type semiconductors and has a diode-like preferential transport direction. A scan speed limit was derived to ensure optimal spatial resolution and minimal transient-induced artifacts. Finally, Chapter 5 put all the previous work to use to characterize the p-type contact of a coolerless, high-performance laser. Through direct, accurate voltage measurement, we concluded that a third of the terminal power dissipates at the p-InGaAs/p-InP heterojunction; equivalently, a third of the series resistance results from this heterojunction. The contact resistance heats the device thereby lowering efficiency, and degrades RC frequency response.
6.2
Original Contributions
The five original contributions of this work to the prior art are summarized below. 1. Calculation of the measured potential using a drift-diffusion formalism; interpretation of the resulting model. 2. First quantitative examination of SVM transient frequency response and derivation of spatial resolution limitations due to frequency response [122]. 3. Technology transfer of SVM from industry to the University of Toronto: equipment
6. Conclusions and Future Work
69
acquisition, configuration, debugging, calibration, and extensive testing. 4. First application of SVM to study the contact to p-type InP; direct observation of voltage drop at the InGaAs/InP heterojunction causing 35% power loss and series resistance. 5. Identification of sample photocurrent generated by AFM optical lever laser as potential artifact for semiconductor characterization; evaluation of its impact to normal SVM scanning.
6.3
Future Research
The work completed to date opens up further lines of investigation, both into the SVM technique itself and its application to the analysis of novel devices.
6.3.1
Improvements to the SVM Technique
Spatial resolution enhancement Recently reported [102] was SSRM characterization of silicon with spatial resolution below 5 nm. Solid diamond tips [51] were used to offer better probe-size-limited resolution [102] than the diamond-coated tips used throughout the experimental work reported herein. Fresh diamond-coated tips resolve 3.5 nm structures with SVM (see for e.g. Fig. 4.9) but diamond grains at the very point can cleave away (particularly at high sample temperatures induced by high bias currents), leaving a blunt and often nonconducting silicon tip. With solid diamond tips it is reasonable to project ∼ 1 nm spatial resolution with far greater fine resolution and conduction lifetime. Another advantage of solid diamond tips is improved wear and lifetime [102] throughout a scan and over many scans. This ensures that the tip remains invariant through a series of scans as opposed to the diamond-coated tips currently used that degrade over a
6. Conclusions and Future Work
70
few series of scans depending on tip–sample pressure. Although solid diamond tips may be more durable, their unit cost may be a notable disadvantage. Methods of increasing scan speed while maintaining good spatial resolution need investigation. The critical path in the measurement circuit is the transmission line from from the AFM tip to high-impedance voltage buffer. Ideally, the buffering electronics could be implemented as a module (similar to commercial SSRM and EFM modules) as close to the tip as possible—the buffered signal can than be processed and captured downstream. The trade-off between high-impedance and reactance matching can be evaluated and further electronic circuitry added to the front-end of the voltage buffer; canceling the inductance–capacitance reactance in the transmission line, improve speed and spatial resolution;
Noise analysis Shot noise is prevalent when scanning on p-type material due to the large depletion region that forms between conductive probe and sample. It is likely enhanced by photopumping from the AFM laser that shines on the facet during scanning. The noise increases uncertainty in quantitative analysis, particularly at interfaces and transitions involving p-type material. Methods for reducing or filtering this noise need to be investigated. Other sources of noise—perhaps from the feedback loop of the voltmeter preamplifier that struggles to reach steady-state with the p-type voltage—need to be evaluated, quantified, and eliminated.
6.3.2
Semiconductor Diode Photodetectors
To date, photodetector diodes have not been studied with SVM. They present particular experimental challenges. For example, how does one supply a desired light source while removing the laser light of the optical lever? Diode lasers are biased at sufficiently high currents that photocurrent is negligible, but we are not so lucky with photodetectors that
71
6. Conclusions and Future Work light source optical lever fibre
+ −
n
+
i
V
-
p
Figure 6.1: SVM on a photodiode. The challenge is to couple desired light into the device while avoiding illumination by the AFM optical lever laser. The resistor can be replaced with an equivalent circuit of the front-end of a receiver circuit. will be susceptible to significant artifacts. A possible configuration is shown in Fig. 6.1 where the desired light source is supplied via fibre. However, it is unclear how to mask the AFM laser during scanning.
6.3.3
Quantum Cascade Diode Lasers
Quantum cascade diode lasers, first demonstrated at Bell Laboratories in 1994 [123], produce mid-IR (infrared) light exclusively through intraband electronic transitions. Quantum staircases are grown epitaxially with a nominal step width of 2 nm. The quantum cascade could be observed directly with SVM along with governing and limiting potential distributions. Three primary phenomena have been identified that are both important to quantum cascade laser designers and likely observable with current SVM spatial and voltage resolutions [124] (Fig. 6.2). Carriers are believed to “pool” between gain stages, causing band bending that could be detected. Gain stages having different lasing wavelength can be cascaded; the voltage distribution across each section could be easily measured to inform further design. Such lasers exhibit breakdown phenomena at certain elevated bias points, a behaviour thought to be linked to band misalignment between sections of the cascade; while pushing spatial resolution to the very limit, direct observation and
72
6. Conclusions and Future Work a)
b)
c)
no transition
energy position
λ = λ1
λ = λ2
Figure 6.2: Quantum cascade laser phenomena for anticipated scanning voltage microscopy study. a) Band bending (solid lines) due to interstage carrier pooling (grey regions); dotted lines show idealized band envelopes. b) Voltage distribution across sections of different emitted wavelength. c) V–L–I breakdown due to cascade energy level misalignment from one stage to the next. confirmation would aid improved designs. However, until recently [125] continuous-wave operation of theses lasers has required a cryogenic environment to dissipate the heat produced. These lasers can also be operated at room temperature but only with a < 1% duty cycle pulsed-wave bias. To perform SVM in the former cryogenic case, one requires a custom AFM designed for low-temperature measurements. In the latter pulsed-mode case, the slow transient response inherent to the SVM measurement process precludes the use of a lock-in amplifier or any other bias triggering mechanism.
6.3.4
SVM on Pulse-Biased Devices: The Analog Modulation Analogue
For some semiconductor devices, DC operation isn’t possible because heating either degrades performance severely or causes destruction. In practice these devices are biased with low-duty cycle square wave pulses so that heat can be dissipated during the offcycles; typical pulses may have 1% on-cycles of a 50 kHz pulse train. Is it possible to perform SVM on pulsed-bias devices, given that the response time of the SVM measuring circuit is so comparatively slow?
73
6. Conclusions and Future Work To attempt an answer, it is helpful to digress into communications theory.
Ideal suppressed-carrier signals consist of two frequency components: a fixed, singlevalued carrier of frequency fc , and a variable, finite-bandwidth message of instantaneous frequency fm . We shall take the AM (analog modulation) signals to have the form
vAM = Voffset + m(t) cos(2πfc t).
(6.1)
In this form, Voffset is a DC offset and the carrier is chosen such that fc max fm . Such AM signals can be decoded by a simple directional envelope detector; this circuit has the same form as the derived SVM measurement circuit, shown previously in Fig. 4.4. To follow the envelope of (6.1) we desire the RC time constant τ to satisfy the conditions [126] 1 (carrier suppression), 2πfc 1 τ (envelope tracking). 2πfm τ
(6.2a) (6.2b)
Returning to the problem of performing SVM on pulsed-bias devices, if we take the pulsed bias to be the carrier, the scan rate of the potential distribution across device features to be the message signal, and the SVM measurement circuit to be the envelope detector (since it is one naturally), we have an analogue AM system. In this case, fc is dictated by the heat dissipation of the device and τ is dictated by the probe–sample interface, but we are free to chose the scan speed and thus the frequence of feature change below the tip, fm , such that conditions (6.2a) and (6.2b) are satisfied. Pulsed-SVM was attempted for a 50% duty cycle, 1 V peak-to-peak square pulse train at various frequencies. The results, plotted in Fig. 6.3, are inconclusive. It is promising that some voltage profile is measured under square-wave bias, albeit not the correct one compared to DC bias; the measurement circuit appears to discharge too quickly.
74
6. Conclusions and Future Work 1 0.8
p
DC
metal
100 Hz
metal
0.6
p
SVM Voltage [V]
0.4 0.2
p
n n
p
n
n
0 -0.2 1 0.8
1 kHz
100 kHz
0.6
p
0.4
0
1
p
n
n
0 -0.2
p
metal
n
p
0.2
metal
2
3
4
5 0
1
n
2
3
4
5
Position [µm]
Figure 6.3: Pulsed-bias SVM over p–n–p–n current blocking layers, 50% duty cycle square-wave bias at frequency shown in each panel, 1 V peak-to-peak, 0.1 Hz scan rate. Eq. (6.2) is relevant for sinusoidal signals and the discrepancy may be correlated to the high frequency spectrum associated with step functions. Probe cantilevers are subject to forces from oscillating electrical sources [7, 8] (this is the principle on which EFM is founded), and the cantilever employed has resonant frequency in the kHz range so ringing over the n-type regions may be due to the tip bouncing across the surface. A bouncing tip may also explain why the measurement circuit discharges so quickly compared to expectation.
6.3.5
Nanocomposite Electroluminescent and Photodetection Devices
A new class of optoelectronic devices is emerging, a class that has wide spectral tunability, seamless integration with electronic and photonic circuits, and economic, scalable fabrication. Low-cost, easy-to-make optoelectronic devices will provide high-bandwidth data connections directly to users (e.g. fibre-to-the-desktop) for high-definition multime-
75
6. Conclusions and Future Work a)
cap
nanocrystal
z x
~ 5 nm y
b)
hole-rich polymer nanocrystal active region electron-rich polymer
y x
substrate light
c) electron
d) ∆E = hf
E
electron ∆E = hf
E x,y,z
hole
x,y,z
hole
Figure 6.4: Nanocrystal optoelectronic devices. (a) Spherical semiconductor colloidal nanocrystal, typical average size ∼ 5 nm (typical range 2–20 nm). (b) Typical nanocrystal–polymer composite device structure: metal electrodes address polymer functional layers with the central layer containing active semiconductor nanocrystals. (c) Energy transfer from polymer to nanocrystal for photogeneration. (d) Energy transfer from nanocrystal to polymer for photodetection.
dia on demand. Devices will be small enough (nanometers) and cheap enough (cents) to be used on circuit boards to eliminate data bottlenecks chip-to-chip and within chips to facilitate distribution of critical signals. Today’s optoelectronic components are grown by MBE and MOCVD, complex processes that require the cleanest and safest of conditions in highly specialized equipment. Current device structures limit spectral tunability; current materials limit electronic integration. The high performance of these devices comes at premium cost. Conversely, nanocrystals are easy to make in a regular chemistry lab, are widely tunable and highly integrable. The size of nanocrystal semiconductors gives rise to striking new properties. Luminescence and absorption are tuned over wide visible [127] and infrared [128] spectral ranges by nanocrystal size. Nanocrystals self-assemble in organometallic chemical reactions that take place in a flask of an ordinary fumehood [129] and their size is tuned by controlling the growth reaction. Electronic and mechanical properties are engineered by encapsulating the nanocrystal with semiconductor or organic ligands [130] (Fig. 6.4a). Encapsulation is also tuned by basic chemistry during or after growth. Nanocrystals are conveniently mixed into semiconducting polymers and the polymers are spun into layers to form devices (Fig. 6.4b). Optoelectronic luminescent (Fig. 6.4c) and photodetection (Fig. 6.4d) devices can be made to span the entire telecommunications spectral range and beyond with a single material system.
6. Conclusions and Future Work
76
Optoelectronic interaction between a host polymer and an active nanocrystal occurs via three processes: incoherent energy transfer (F¨orster transfer) [131], coherent energy transfer [132], and charge transfer [133]. While it is clear that coherent transfer dominates in nonlinear optical interactions [132], the nanocomposite research community remains agnostic as to whether F¨orster or charge transfer dominates in optoelectronic conversion (in either conversion direction) [134]. Scanning probe techniques could be used to resolve which energy transfer mechanism is dominant and identify specifics of the transfer such rate, pathway (whether mediated by intermediate nanocrystals), and so on. AFM has been used to characterize sizes of individual nanocrystals and ensembles [135], so spatial resolution is sufficient and addressing individual nanocrystals is possible. EFM1 was used to observe the charging and discharging of individual nanocrystals [75, 133], and to probe nanocomposite films [136]. Unlike EFM which is a non-contact technique, SVM requires good electrical contact with the sample and therefore a relatively smooth scan surface. The geometry of spincoated nanocomposite devices is unsuitable at present for SVM as the edges are uneven and uncleavable. Furthermore, nanocrystals are randomly distributed in the active layer and may not reach the scanning surface in a predictable manner; one must address how an edge-lying nanocrystal should differ in behaviour from a nanocrystal buried deep in the device. For these reasons, SVM has not been performed to date to the author’s knowledge. However, if these geometrical issues could be solved—perhaps by dye-casting devices in a cubic mold and ensuring smooth facets—potential distributions that are thought to govern charge capture [137] could be observed and confirmed. Proposed theoretical potential distributions [137] dictate current design rules and so direct observation is extremely valuable. 1
In EFM, a conductive AFM tip is oscillated a fixed frequency and at a and a known distance from the sample. Changes in the oscillation frequency due to electrostatic fields of the sample are detected by an ultrasensitive feedback circuit; the first and second harmonics of such frequency deviations yield [75] the charge and dielectric constant, respectively.
6. Conclusions and Future Work
6.4
77
Perspective
We have characterized the SVM measurement process and formulated requirements that ensure accurate measurements. We have modeled the SVM voltage and decomposed it into fundamental carrier and potential quantities. Hence, the sensitivity, reliability, repeatability, and accuracy of SVM are improved through this work. This work lays the foundation for SVM to join the portfolio of modern semiconductor device analysis techniques. With the characterization work presented herein, artifactfree voltage scans of semiconductor devices in operation can be obtained will pushing nanoscopic spatial resolution to the limit.
Appendix A
Definition of Electrochemical Potential
At thermal equilibrium, the carrier concentrations are Z
∞
n(T ) =
ρc (E)f (E, T )dE, Ec Z Ev
p(T ) =
(A.1) ρv (E) 1 − f (E, T ) dE
−∞
where f (E, T ) =
1 e(E−µ)/kB T
+1
(A.2)
and µ is the chemical potential that governs particle flow [101]. In a non-degenerate semiconductor the Boltzmann approximation can be employed and the Fermi probability (A.2) simplified such that f (E) ≈ e(E−µ)/kB T for E > Ec (A.3) (µ−E)/kB T
1 − f (E) ≈ e
78
for E < Ev .
79
A. Definition of Electrochemical Potential The carrier densities (A.1) can then be simplified to n(T ) = Nc (T )e−(Ec −µ)/kB T ,
(A.4) p(T ) = Pv (T )e−(µ−Ev )/kB T where the band-edge carrier concentrations are Z
∞
Nc (T ) =
ρc (E)e−(E−Ec )/kB T dE,
Ec Ev
Z
(A.5) −(Ev −E)/kB T
ρv (E)e
Pv (T ) =
dE.
−∞
Due to the exponentials in the above forms, the greatest contributions to (A.5) occur within kB T of the respective band edges where the parabolic band approximation can be used for the densities of states: 1 N c(T ) = 4
1 P v(T ) = 4
2mc kB T π~2
3/2
2mv kB T π~2
3/2
19
mc T m0 300
3/2
mv T m0 300
3/2
≈ 2.51 × 10
19
≈ 2.51 × 10
cm3 , (A.6) 3
cm .
Using the one-electron semiclassical framework, a local potential φ(r) simply shifts the levels Ec,v by −qφ(r) [99]. Define the electrochemical potential as
µe (r) , µ + qφ(r).
(A.7)
The carrier concentrations can then be written in terms of the electrochemical potential n(r) = Nc (T )e−[Ec −µe (r)]/kB T , (A.8) p(r) = Pv (T )e−[µe (r)−Ev ]/kB T .
Appendix B Tunneling at the SVM probe–sample interface
A simple model of what SVM measures is that we find the potential applied to the tip which zeroes the net current flow between sample and tip. A good and necessary assumption is that charge tunneling between tip and laser is lossless, hence we can apply energy conservation and the initial and final states are at the same energy. We need only consider transitions between states of the same energy [13]. We take the approximation that the tip is metallic [46] with a rectangular column of energetic states, with a single Fermi level that defines the transition between the sea of occupied states below the Fermi level to the sea of occupied states above. The current between the tip and sample is proportional to integral over all energies of the product of the density of states of the sample, the Fermi function of the sample (evaluated for the right band), the transition matrix element (assumed to be independent of energy in this first iteration), the tip density of states (which we let be fixed initially as in a metal), and the Fermi function for the tip (metal) which contains within it the 80
B. Tunneling at the SVM probe–sample interface
81
free parameter associated with the applied potential:
J1→2 net = J1→2 − J2→1 (B.1a) Z Z = ∂E ρ1 (E)f1 (E)T (E)ρ2 (E)(1 − f2 (E)) − ∂E ρ2 (E)f2 (E)T (E)ρ1 (E)(1 − f1 (E)) E
E
(B.1b) Z ∂E ρ1 ρ2 T (f1 − f2 ).
=
(B.1c)
E
What we measure in the experiment—the number that appears on the voltmeter for each position and bias—is this free potential associated with the potential applied to the tip which is needed for the above integration to be zero,
EF m = −qΦm − Vm ,
(B.2)
where the first term is the work function of the metal and the second term is the potential applied to the tip. Therefore the tip potential Vm measured is that which satisfies J1→2 net = 0. That is, the potential measured on the high-impedance voltmeter is that which equilibrates the potentials of the probe and sample, and hence no current should flow between the two.
In a bulk semiconductor and assuming parabolic band edges, we have that
p E − Ec p ∝ mv∗ 3/2 −(Ev − E).
ρ1 (E) ∝ m∗c 3/2
(B.3a) (B.3b)
Initially we assume that the density of states in the tip is constant. We also assume that the tip is at equilibrium such that
f2 (E) =
1 1 + exp
E−EF m kT
.
(B.4)
82
B. Tunneling at the SVM probe–sample interface
The semiconductor is under bias so we assign separate quasi-Fermi levels for the electrons and holes. Thus for T (E) = T (neglecting energy dependence of tunneling), Eq. (B.1c) evaluates to
Z ∂E
J1→2 net = ρ2 T E
∗ 3/2 √ mc E
− Ec
0 p m∗v 3/2 −(Ev − E)
fc − fm
fv − fm
.
(B.5)
Substituting the free potential (B.2) into the current (B.5) gives
m∗c 3/2
Z
∞
p
E − Ec
Ec
= m∗v 3/2
Z
Ev
p
1 1 + exp
−(E − Ev )
−∞
E−EF c kT
−
1 1 + exp
1 1 + exp
E−[qΦm +Vm ] kT
∂E
(B.6a)
E−EF v kT
−
1 1 + exp
E−[qΦm +Vm ] kT
∂E.
(B.6b)
If we assume m∗c ≈ m∗v (not always the case) and for quasi-charge neutrality in an undoped region we have n = p, then Ec − EF c = EF v − Ev . We can then simplify the expression above to get
Ec − [qΦm + Vm ] exp − kT
[qΦm + Vm ] − Ev = exp − kT
=⇒ Ec − (qΦm + Vm ) = (qΦm + Vm ) − Ev .
(B.7a) (B.7b)
So the final result for ρ2 and T constant, m∗c = m∗v , and n = p is
qΦm + Vm =
EF c + EF v . 2
(B.8)
If m∗c 6= m∗v but n = p then we can still isolate Vm for Jnet = 0 by finding a mirror point between EF c and EF v . Hence, the measured electric potential is a mobility-weighted average of the hole and electron electrochemical potentials.
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