APPLIED PHYSICS LETTERS 90, 161119 共2007兲

Enhancing the photomixing efficiency of optoelectronic devices in the terahertz regime Subrahmanyam Pillaa兲 Department of Physics, University of California, San Diego, California 92093

共Received 14 June 2006; accepted 19 March 2007; published online 18 April 2007兲 A method to enhance the photomixing efficiency by reducing the transit time of majority of carriers in photomixers and photodetectors to ⬍1 ps is proposed. Enhanced optical fields associated with surface plasmon polaritons coupled with velocity overshoot phenomenon results in net decrease of transit time of carriers. As an example, model calculations demonstrating ⬎280⫻ 共or ⬃2800 and 31.8 ␮W at 1 and 5 THz, respectively兲 improvement in terahertz power generation efficiency of a photomixer based on low temperature grown GaAs are presented. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2724924兴 Microwave to terahertz radiation sources in the 0.1– 10 THz are being extensively studied for their application in communications, medical imaging, and spectroscopy.1,2 For many applications, compact, narrowlinewidth, widely tunable continuous wave sources are necessary. In particular, to be used as a local oscillator in communications systems the terahertz source should produce stable output power ⬎10 ␮W.3 Among the various techniques being pursued,1,3,4 electrical down conversion of optical microwave sources in a suitable photomixer1,3,4 is appealing due to the easy availability of tunable, narrowlinewidth, and stable solid state lasers. However, until now the output power from these photomixers is limited to ⬍10 ␮W in the crucial terahertz range. In a conventional dc-biased metal-semiconductor-metal 共MSM兲 photomixer,5 optically thick 共⬃100 nm兲 interdigitated metal lines forming Schottky contacts are fabricated on a high resistivity semiconductor with subpicosecond recombination time of carriers 关␶e / ␶h for electrons 共e兲 holes 共h兲, respectively兴 and high breakdown field limit. So far, only a few materials such as low temperature 共LT兲-GaAs 共Refs. 1 and 5兲 and Fe implanted InGaAs 共Ref. 6兲 have been shown to meet these requirements. From the photomixer theory, when two lasers 关wavelengths ␭1, ␭2, ␭0 = 共␭1 + ␭2兲 / 2, and powers P1 = P2 = P0 / 2兴 with their differ−1 ence frequency f = c共␭−1 1 − ␭2 兲 in the terahertz range are in5 cident on a photomixer, the terahertz wave output power P f is given by Pf =

共1/2兲RLi2p , 关1 + 共2␲ f共RL + RS兲C兲2兴

共1兲

where i p is the photocurrent generated in the external circuit, c is velocity of light in free space, C is the capacitance, RS is small internal resistance of the metal structure, and RL is the load resistance in the 72–200 range.1,4,5 To accelerate carriers generated deep inside the semiconductor, high dc voltage 共Vb ⬇ 40 V兲 is applied across the electrodes. This results in fields quickly exceeding the breakdown limit near the electrodes leading to device failure. As the carrier transport is transit time 共ttr兲 limited, i.e., ttr ⬎ f −1, recombination time ␶ Ⰶ f −1 is required to recombine the carriers that do not cona兲

Electronic mail: [email protected]

tribute to i p before the beat cycle reverses.4,5 Even if the photomixer is placed in a suitable optical cavity, due to strong reflection from thick metal electrodes, no carriers are generated directly below the electrodes where ttr will be small. In addition, subwavelength features of the metal lines produce strong near field diffraction patterns that are not taken into account in conventional designs.1,4,5 In this letter we propose a device structure in which carrier generation and collection efficiencies5 are simultaneously enhanced for increasing P f . Surface plasmon polaritons 共SPPs兲 arising from optical fields alone are exploited for not only enhancing carrier generation efficiency but also for generating them close to subwavelength normal metal electrodes embedded in a photoconductor layer 共Fig. 1兲. When the metal’s real part of the dielectric constant is −ve or significantly lower than the surrounding material’s dielectric constant 共such as W or Pt in GaAs兲, the induced electron plasma in the normal metal will be ⬃180° out of phase with the incident field. The reradiated fields from this plasma will therefore be significantly out of phase with the incident field. As the plasma is mostly confined to the metal’s surface with the same polarization direction as the incident field, these excitations are referred to as surface plasmon polaritons. Under certain geometrical conditions, the incident, reradiated, and reflected fields can be made to form strong near field 共i.e., near the metal scatterer兲 interference patterns. Carrier collection efficiency is enhanced by maintaining strong dc electric fields throughout the active volume, well above the critical field required for achieving velocity overshoot,4,7–9 whereby ttr of majority of carriers is reduced to ⬍1 ps, i.e., ttr 艋 f −1. Geometry and distribution of metal fingers are optimized to accomplish this without significantly increasing C and RS. Recently, a planar photodetector design utilizing SPPs is proposed10 but it is not suitable for terahertz power generation due to high device capacitance 共⬎12 fF due to smaller line pitch兲, low active semiconductor volume, and lower external quantum efficiency 共⬃60% – 75% 兲. A three dimensional finite difference time domain 共3DFDTD兲 simulator with uniaxial perfectly matched layer11 surrounding the photomixer is developed for modeling the proposed device. The details of computation will be presented elsewhere. For a given D 共see Fig. 1兲, the refractive index and thickness of distributed Bragg reflector 共DBR兲 layers are first optimized by calculating the reflection and trans-

0003-6951/2007/90共16兲/161119/3/$23.00 90, 161119-1 © 2007 American Institute of Physics Downloaded 03 Jun 2007 to 132.239.1.232. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

161119-2

Subrahmanyam Pilla

FIG. 1. 共Color online兲 Schematic of Fabry-Pérot 共FP兲 cavity 共a兲 and a layer of interdigitated metal lines 共b兲. The FP cavity is formed by three or four dielectric layers constituting distributed Bragg reflector DBR1, N pairs of low/high refractive index dielectric layers constituting DBR2, and absorbing layer of thickness D. The lines parallel to the x axis 共width of 200 nm兲 are connected to either signal transmission lines or planar antenna fabricated on top of the absorbing layer 共not shown兲 through metal vias. The overall dimensions of the absorbing volume 共excluding DBRs and via leads兲 are given by Lx, Ly, D whereas number of interdigitated metal layers, their vertical positions, 共measured from the air-DBR1 interface兲, the metal line 共finger兲 thickness, pitch, width, and lengths of +ve and −ve electrodes are given by i, zi, d , p, w, l1, and l2 as shown, respectively. x = 0, y = 0 is located at the center of top half of the interdigitated pattern in 共b兲. The structures in 共b兲 connected in series can be excited by TEM01 mode lasers for doubling output power.

mission coefficients of the Fabry-Pe´rot 共FP兲 cavity using matrix methods.12 The FP cavity is excited by a linearly polarized, plane wave propagating along +z direction, with Gaussian 共elliptic兲 intensity profile in the x-y plane. Figure 2共a兲 shows the FDTD results of a three layer stack of interdigitated W lines embedded in 230 nm LT-GaAs absorbing layer of a photomixer design of Fig. 1 optimized for ␭0 = 850 nm. The plot clearly shows the near field enhancement resulting from the thin normal metal electrodes. In the

Appl. Phys. Lett. 90, 161119 共2007兲

FIG. 3. 共Color online兲 Carrier transit time distribution ntre共h兲共ttr兲 for e共h兲 共a兲 and calculated terahertz output power P f 共b兲 for the photomixer design of Fig. 1. The device is excited by an 850 nm source at P0 = 60 mW. In panel 共a兲 the parameters for ntre 关red 共solid兲兴 and ntrh 关blue 共dot兲兴 curves are same as in Fig. 2 whereas for ntre 关gray 共dash-dot兲兴 curve only the polarization is changed to Ey. For the ntre of green 共dash兲 and cyan 共short dash兲 curves 共Lx , p , w兲 are changed to 共7560, 300, 60兲 and 共7480, 320, 120兲 nm, respectively, while rest of the parameters remaining unaltered from those of Fig. 2. For clarity, the curves are shifted along the y axis and the relative shift can be easily obtained from the values at ttr = 0 fs. In panel 共b兲 ␶ = 4 ps for designs S1–S6 whereas for S7 ␶ = 1 ps. Parameters for S1 are the same as in Fig. 2 whereas for S2 z3 = 645 nm, for S3 z3 = 645 nm, and incident radiation is Ey polarized; for S4 共p , w兲 are 共320, 120兲 nm, respectively, for S5 共Lx , w兲 are 共7560, 60兲 nm, respectively, and for S6 共z1 , z3兲 are 共455, 655兲 nm, respectively.

absence of the W electrodes, three amplitude maxima 共antinodes with maximum amplitude of 1.4 V / m兲 are observed. If W is replaced with perfect metal, no near field enhancement is observed and the electrodes behaved as shadow masks thereby reducing the absorption efficiency to ⬍60%. The 3D internal dc electric fields and C are computed using FD techniques. The data 关Fig. 2共b兲兴 show that unlike the traditional MSM structure, the dc field is well above the critical field 共⬃5 kV/ cm兲 throughout the device. Moreover, it is ⬃90 kV/ cm between neighboring electrodes, in particular, at the center of the device where most of the carriers are generated. In the rest of the volume it has a broad peak at 18 kV/ cm 共not shown兲. From FD calculations it is estimated that C ⯝ 4.9 fF. The contribution to RS from metal fingers is estimated to be ⬃2.4 ⍀ based on the resistivity of thin annealed or epitaxial W films 共⬃5 ␮⍀ cm兲.13 No band bending at the Schottky contacts is assumed in the transport calculations below consistent with the traditional modeling of these devices.5 The highest electric field inside the device is about four times lower than the breakdown field 共500 kV/ cm兲 thereby lowering chances of device failure at Vb = ± 1 V. Photocurrent i p is calculated by first computing the e共h兲 transit time distributions ntre 共ttr兲, ntrh 共ttr兲 shown in Fig. 3共a兲 for the entire absorbing volume. Based on the available data for LT-GaAs,4,7–9 for ttr 艋 tonset = 100 fs, the carrier motion can be approximated by ballistic transport with electron effective mass me = 0.088m0, where m0 is electron rest mass. This value is consistent with the slope of the linear portion of transient drift velocity curve.9 The corresponding effective mass for holes is mh = 0.106m0. Effective masses larger than the accepted values for GaAs 共0.063m0 and 0.076m0 for elec-

FIG. 2. 共Color online兲 Optical electric field amplitude 共a兲 and dc electric field strength 共b兲 inside the D = 230 nm LT-GaAs absorbing layer of the photomixer design of Fig. 1 optimized for ␭0 = 850 nm. Incident optical field amplitude Ex0 = 1 V / m and Vb = ± 1 V. For clarity, fields in only the x = ± 600 nm region along the y = 0 plane are plotted. The gray rectangular regions in the plots show the cross section of the interdigitated W lines with Lx = 7000, Ly = 2500, d = 10, z1 = 475, z2 = 555, z3 = 635, p = 300, w = 100, l1 = 1500, and l2 = 1400 nm, respectively. The FP cavity is formed by three layers of 共TiO2 , Si3Nx , CaF2兲 constituting DBR1 关refractive indices 共2.4, 2.0, 1.23 to 1.36兲 共Ref. 12兲 and thicknesses 共100, 150, 190兲 nm for each layer respectively兴, four pairs of 共Al2Ox, GaAs兲 layers forming DBR2 关refractive indices 共1.6, 3.53– 0.068i兲 and thicknesses 共130, 60兲 nm兴, and D ⬇ ␭ nm absorbing LT-GaAs layer with refractive index of 3.77i – 0.068i. Downloaded 03 Jun 2007 to 132.239.1.232. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

161119-3

Appl. Phys. Lett. 90, 161119 共2007兲

Subrahmanyam Pilla

tron and light holes, respectively兲 are considered to obtain longer ttr, thereby lower estimate of i p. In the photomixer of Fig. 2, pure ballistic transport is applicable to electrons generated close to the +ve electrodes and holes generated close to −ve electrodes. These carriers generated predominantly in the near field enhancement region, transit through nonuniform dc fields in the 5 – 90 kV/ cm range. It should be noted that tonset = 100 fs is considerably lower than the theoretical limit of ballistic motion in GaAs for this field strength range.7 For ttr 艌 tonset, electron motion is approximated by qasiballistic transport with time dependent velocity distribution similar to Ref. 11 up to ttr = 3 ps, and equilibrium drift velocity 共⬃1 ⫻ 107 cm/ s兲 for ttr ⬎ 3 ps. Hole motion is approximated by one-third of the electron velocity5 at any given ttr 艌 tonset resulting in velocities lower than those reported for GaAs.8 The integral of curves in Fig. 3共a兲 give the carriers 关Ne共Nh兲 for e共h兲, respectively兴 generated per period 共T ⯝ 2.83 fs兲 of the 850 nm source with P0 = 60 mW. For the parameters of Fig. 2, ⬃98% of incident power is absorbed in LT-GaAs layer while ntr has peaks at ttr ⬇ 65共70兲 fs for e共h兲, respectively, resulting from intense near field regions in Fig. 2共a兲. Remaining satellite peaks result from periodicity of the electrode structure and specific choice of the velocity distribution. A sharp drop in ntr by a factor of 2共3兲 for e共h兲 at ttr ⬇ tonset is due to the lower estimate of carrier velocities for ttr ⬎ tonset resulting from the uniform field qasiballistic distribution function9 applied to a case where fields are inherently inhomogeneous. Although the above choice of velocity distribution for quasiballistic motion is consistent with the fact that over a large volume fraction of the absorbing layer the static field is ⬃18 kV/ cm 共not shown兲, a rigorous calculation should include quasiballistic velocity distribution appropriate for inhomogeneous fields. Such a calculation would probably produce a more uniform ntr共ttr兲 distribution around ttr ⬇ tonset without altering the distribution for ttr ⬍ tonset or the integral of ntr共ttr兲. This will further reduce the number of carriers in the long tail of the ntr distribution. The number of electrons captured in the metal electrodes at time t will be e ncap 共t兲 =



tc=t

e ngen 共tc兲ntre 共t − tc兲e−共t−tc兲/␶edtc ,

共2兲

tc=0

e 共t兲 = Nec / ␭0关1 + cos共2␲ ft兲兴 is the number of elecwhere ngen trons generated in LT-GaAs layer per second and tc is the carrier creation time. Similar expressions can be written for h 共t兲 and the e共h兲 available for number of holes captured ncap e h conduction in the photomixer navl 共t兲关navl 共t兲兴. In the calculae h tion of ncap, navl, i p共t兲 = e共ncap共t兲 + ncap共t兲兲 共e is electron charge兲, and P f , we set RL = 72 ⍀, ␶ = 2␶e = 2␶h / 3,5 and varied ␶ in the 0.5– 6 ps range. As ttr ⬍ 1 ps for majority of carriers in Fig. 3共a兲, ␶ is not a critical factor in determining the efficiency. For the parameters of Fig. 2, the steady state electron e 共t兲 for ␶ = 4 ps density ¯n obtained from the dc value of navl 15 −3 is ⬃6 ⫻ 10 cm 共at P0 = 60 mW兲 with holes 1.5 times more numerous than electrons. Dipole fields arising from this space charge are negligible 共⬍2.5% 兲 in comparison with strong fields 关Fig. 2共b兲兴 present in the photomixer. Figure 3共b兲 shows the P f values obtained from Eqs. 共1兲 and 共2兲 for some of the device configurations in the

0.1– 10 THz range. The data show that P f ⬀ f −2.77 in the 0.5– 6.5 THz range in contrast to f −4 roll-off of P f for a conventional photomixer.5 A recent nip-nip photomixer concept is shown to have f −2 roll-off for f ⬍ 1.5 THz.4 Therefore, the design of Fig. 1 exploiting SPPs offers significant improvement over the existing photomixer designs. Based on 3D FD computation of steady state heat equation with appropriate thermal conductivity values14 for the device parameters of Fig. 2 共P0 = 60 mW, Vb = ± 1 V兲, internal temperature 共Ti兲 of the device is estimated to be ⬃200 K above the substrate temperature requiring substantial cooling 共to 77 K兲 when P0 is high. This internal heating therefore limits P0 to ⬃60 mW. If the structure of Fig. 1共b兲 is excited by TEM01 mode lasers with total power P0 = 120 mW as shown, the output can be increased to 2P f 关of Fig. 3共b兲兴 without worsening Ti or ¯n. In summary, model calculations for LT-GaAs photomixer with ttr ⬍ 1 ps and P f ⯝ 2800共31.8兲 ␮W at 1共5兲 THz, respectively, are presented. Similar calculations carried out for photomixers based on Be doped In1−xGaxAs and GaN optimized for operation at ␭0 = 1550 and 343 nm, respectively, show strong near field enhancement arising from SPPs similar to Fig. 2共a兲 and further work is underway to calculate their efficiencies as well as experimental demonstration. Due to minimal dependence on the carrier recombination time, it is anticipated that the proposed method paves the way for enhancing the speed and efficiency of photomixers and detectors covering UV to far infrared communications wavelengths. Author wishes to thank John Goodkind for introducing him to the fascinating subject of Auston switches. 1

J. E. Bjarnason, T. L. J. Chan, A. W. M. Lee, E. R. Brown, D. C. Driscoll, M. Hanson, A. C. Gossard, and R. E. Muller, Appl. Phys. Lett. 85, 3983 共2004兲. 2 D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, IEEE J. Sel. Top. Quantum Electron. 2, 679 共1996兲. 3 H. Ito, F. Nakajima, T. Furuta, and T. Ishibashi, Semicond. Sci. Technol. 20, S191 共2005兲. 4 G. H. Dohler, F. Renner, O. Klar, M. Eckardt, A. Schwanhauber, S. Malzer, D. Driscoll, M. Hanson, A. C. Gossard, G. Loata, T. Loffler, and H. Roskos, Semicond. Sci. Technol. 20, S178 共2005兲. 5 E. Brown, Appl. Phys. Lett. 75, 769 共1999兲. 6 M. Suzuki and M. F. Tonouchi, Appl. Phys. Lett. 86, 051104 共2005兲. 7 M. Betz, S. Trumm, F. Sotier, A. Leitenstorfer, A. Schwanhauber, M. Eckardt, O. Schmidt, S. Malzer, G. H. Dohler, M. Hanson, D. Driscoll, and A. C. Gossard, Semicond. Sci. Technol. 19, S167 共2004兲. 8 Y. Awano, Y. Tagawa, and M. Shima, Monte Carlo study of electron and hole transport for high speed and low-power sub-0.1 mum GaAs circuits. IEEE/Cornell Conference on Advanced Concepts in High Speed Semiconductor Devices and Circuits, 共Cat. No. 95CH35735兲, IEEE, New York, 1995, p. 408–414. 9 A. Reklaitis, A. Krotkus, and G. Grigaliunaite, Semicond. Sci. Technol. 14, 945 共1999兲. 10 S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, Appl. Phys. Lett. 85, 194 共2004兲. 11 A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time-Domain Method 共Artech House, Norwood, MA. 12 O. S. Heavens, Rep. Prog. Phys. 23, 1 共1960兲. 13 L. K. Elbaum, K. Ahn, J. H. Souk, C. Y. Ting, and L. A. Nesbit, J. Vac. Sci. Technol. A 4, 3106 共1986兲. 14 Thermal conductivity 共k兲 of DBR and LT-GaAs layers are approximated LT-GaAs DBR = 46 W m−1 K−1 and k⬜ = kDBR = k⬜ by assigning kLT-GaAs 储 储 = 10 W m−1 K−1, where k储 / k⬜ are in-plane/out-of-plane conductivities.

Downloaded 03 Jun 2007 to 132.239.1.232. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

Enhancing the photomixing efficiency of optoelectronic ...

c is velocity of light in free space, C is the capacitance, RS is ... A three dimensional finite difference time domain 3D- .... h blue dot curves are same as in Fig.

365KB Sizes 0 Downloads 215 Views

Recommend Documents

Enhancing billing system efficiency with cloud computing
architecture-based billing system—including computing performance, ... with Intel Xeon process E7 family and cloud computing technology enables a reliable.

Enhancing billing system efficiency with cloud computing
Adopt a cloud computing solution. Use Intel Xeon processor E7-8800/4800 product families to build an enhanced cloud computing platform that provides ...

ENHANCING THE ECONOMICS OF COMMUNICATIONS ...
ket studies and “best guess” extrapolations of current demand. The two quantities that have ..... S represents the current stock price, Γ is a random variable with a ...

Grating coupled vertical cavity optoelectronic devices
Feb 26, 2002 - This application is a continuation of application Ser. ... the expense of a larger threshold current. ..... matriX calculation for a slab Waveguide.

Semiconductor optoelectronic devices pallab bhattacharya solution ...
Semiconductor optoelectronic devices pallab bhattacharya solution manual. Semiconductor optoelectronic devices pallab bhattacharya solution manual. Open.

Enhancing the Explanatory Power of Usability Heuristics
status, match between system and the real world, user control and freedom ... direct commercial ... had graphical user interfaces, and 3 had telephone-operated.

Read PDF Semiconductor Optoelectronic Devices
... reader software Semiconductor Optoelectronic Devices (2nd Edition) ,google .... Devices (2nd Edition) ,epub creator Semiconductor Optoelectronic Devices ...

Enhancing the shopping process
products, making it easier to get the look at home while promoting their retail partners. Hanson used Amazon Web Services to build a powerful administrative.

Market Efficiency and Real Efficiency: The Connect ... - SSRN papers
We study a model to explore the (dis)connect between market efficiency and real ef- ficiency when real decision makers learn information from the market to ...

An empirical study of the efficiency of learning ... - Semantic Scholar
An empirical study of the efficiency of learning boolean functions using a Cartesian Genetic ... The nodes represent any operation on the data seen at its inputs.

Efficiency of Large Double Auctions
Similarly let ls(ф) be those sellers with values below Са − ф who do not sell, and let зs(ф) ≡ #ls(ф). Let slb(ф) ≡ Σ д∈lbHфI уд − Са[ sls(ф) ≡ Σ д∈ls HфI ...... RT т'. Z. For и SL, this contradicts υ ≥. Q и1^α

Efficiency of Large Double Auctions
Objects that trade automatically move from and to the right people, and so the only question is whether the .... We wish to relax independence conM siderably while still requiring 0some persistent independence1 as the population ...... librium in Lar

On the efficiency of the first price auction - Fabio Michelucci
Apr 20, 2017 - Group, Prague. ... Email: [email protected] URL: ... for a privatized service that gives profits π(D, Ci) > 0 after the firm incurs in a setup cost ki, and .... Hernando-Veciana, Angel and Fabio Michelucci, “Second best ...

advanced materials for optoelectronic packaging
INTRODUCTION (cont). • Microelectronic thermal problems well known. – Xbox 360 $1 billion “Red Ring of Death” failure widely cited as thermal issue. – Nvidia $150-200 million GPU thermal problem. – “Burned groin blamed on laptop” (BBC

Method for producing an optoelectronic semiconductor component
Oct 25, 2000 - cited by examiner. Primary Examiner—Wael Fahmy. Assistant Examiner—Neal BereZny. (74) Attorney, Agent, or Firm—Herbert L. Lerner;.

An empirical study of the efficiency of learning ... - Semantic Scholar
School of Computing. Napier University ... the sense that the method considers a grid of nodes that ... described. A very large amount of computer processing.

Use of Performance-Enhancing Substances - Pediatrics
Jun 27, 2016 - automatically expire 5 years after publication unless reaffirmed, revised ...... parent_ handbook. pdf). Table 4 summarizes guidance for parents.