Investigation of transport properties of doped GaAs epitaxial layer using open photoacoustic cell Sajan.D.George*, Dilna. S., P.Suresh Kumar, P. Radhakrishnan, V. P. N. Nampoori and C. P. G. Vallabhan International School of Photonics ABSTRACT An open photoacoustic cell under heat transmission configuration has been employed to evaluate the thermal and transport properties of n-type Si doped GaAs epitaxial layer and p-type Be doped GaAs epitaxial layer grown on GaAs substrate by molecular beam epitaxial method. The variation of the characteristics of the photoacoustic signal with chopping frequency clearly indicate the different heat generation mechanisms occurring in the sample under optical excitation at 2.54eV with laser beam. The values of thermal diffusivity, diffusion coefficient, surface recombination velocity and nonradiative recombination time have been evaluated for the sample by fitting the experimentally obtained phase of the photoacoustic signal with the theoretical model. It has been observed that the nature of dopant influences the values of thermal and transport properties of the semiconductor samples.
Keywords: photoacoustic, compound semiconductors, transport properties. INTRODUCTION In recent years, the non-contact and non-invasive methods based on photothermal effect have been widely used in the characterization of thermal, transport and optical parameters of a variety of materials like liquid crystals, ceramics, semiconductors etc. [1-5]. All of these photothermal methods depend essentially on the detection by one means or other of a transient temperature change, which characterizes the thermal waves generated in the specimen due to the absorption of a periodically modulated optical radiation. The nonradiative deexcitation processes occurring in the specimen following the optical excitation, give rise to heat generation in the surface and bulk of the sample. The laser induced photoacoustic (PA) effect is a very convenient and elegant experimental set up that is very effectively employed to evaluate the thermal and optical properties of matter in all its different states [3-7]. In the PA technique, the features of the detected PA signal depends on how heat diffuses through the specimen and this aspect allows us to gather information regarding thermal parameters, structural formations, structural inhomogenities etc. associated with the sample. During the last decade, PA technique, that directly monitors the nonradiative relaxation processes has emerged as an effective spectroscopic tool, which can complement conventional absorption and photoluminescence spectroscopic methods, especially in the case of semiconductors [8-11]. Both piezoelectric transducer based method and the microphone version of photoacoustic technique are being employed to evaluate transport and optical properties of direct and indirect band gap semiconductors [8-12]. Depending on the position of microphone in the PA cell, the microphone version of PA technique can be used in two distinct configurations i.e., either in the reflection detection configuration (RDC) or in the transmission detection configuration (RDC). The transmission detection configuration which is the basis of open photoacoustic cell (OPC) is found to be more convenient and useful in evaluating the transport properties of semiconductors, especially in the low chopping frequency range [12]. OPC technique has been effectively used to evaluate the thermal and transport properties of semiconductors such as GaAs, InP, PbTe, CdTe, CdInGeS4 as well as solar cells [11-15]. In the case of semiconductors, the thermal source resulting from the absorption of light depends not only on the optical properties of the sample but also its transport properties (carrier lifetime, diffusion length, recombination velocity etc.). *
[email protected], International School of Photonics, Cochin University of Science and Technology, Kochi, India –682 022
Materials, Devices, and Systems for Display and Lighting, Fuxi Gan, Ming Hsien Wu, Lionel C. Kimerling, Editors, Proceedings of SPIE Vol. 4918 (2002) © 2002 SPIE · 0277-786X/02/$15.00
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A detailed discussion of the heat generation in semiconductors on the basis of thermal piston model of Rosencwaig and Gersho with the additional inclusion of the effect of photoexcited carriers is given by Pinto Neto etal.[13-14]. An analytical solution of contribution of the different factors such as thermalisation, bulk recombination and surface recombination are given by Dramicanin etal [16]. However, not much work has been done in the direction of the influence of type of dopant on the thermal and transport properties of the epitaxial layers. Some of the recent investigations using PA technique show that doping can influence the thermal diffusivity and surface recombination velocity of photoexcited carriers [10,15]. In this article, we present the result obtained from the PA experiment carried out under heat transmission configuration for both p and n-type GaAs epitaxial layer grown on GaAs substrate using molecular beam epitaxial (MBE) method. The three different processes of heat generation can be clearly distinguished from the amplitude of PA signal measured in these experiments. By fitting the experimentally obtained phase of the PA signal to that of the theoretical model of Pinto Neto etal., thermal diffusivity, diffusion coefficient, surface recombination velocity and nonradiative recombination time have been evaluated by taking them as adjustable parameters. GaAs is a compound semiconductor, which is widely used in high density electronic and optoelectronic industry. Hence the characterization of various heat generation mechanisms and the evaluation of thermal and transport properties of this material have great physical and practical significance
THEORY In order to explain the PA effect in our semiconducting samples, we resort to the thermal piston model of Rosencwaig and Gersho (RG), from which we get the pressure fluctuation δP in the PA cell due to periodic heating as
δP =
Po Θ jωt e To l gσ g
(1)
where P0 (To) is the ambient pressure (temperature), l g is the length of the gas chamber, σ g = (1 + j )a g where
a g = πf α g
1
= 1 and µ g is the thermal diffusion length in the gas with thermal diffusivity α g , and Θ is the µ g temperature fluctuation at the sample-gas interface (x=0) and ω = 2πf . Here f is the modulation frequency. The 2
geometrical view of PA cell used for present studies is given below
,QFLGHQW 5DGLDWLRQ *DV
x = lg
6DPSOH
x=0
*DV
x = −l s
)LJXUH *HRPHWULFDO YLHZ RI 2SHQ 3KRWRDFRXVWLF &HOO
If we excite a semiconductor sample with energy greater than bandgap energy, the heating is generated due to three processes namely thermalisation, bulk recombination and surface recombination. The thermalisation component is due to
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fast intraband transition (time scale ~ ps) of electron in the conduction band due to electron-phonon interaction. The bulk and surface recombination are due to nonradiative recombination of photoexcited carriers in the bulk and surface of the specimen respectively. Taking into account of all these processes, the expression for PA signal under heat transmission configuration is
δP =
2εI o Po To l gσ g k sσ s
ε − 1 −l σ Fσ s e s s+ Dγτ ε
1 vτ + 2 2 σ s σ s − γ
(2)
The first term represents the thermalisation component, which dominates in the low chopping frequency range
followed by bulk and surface recombination processes. In the expression (2) σ s = (1 + j )a s , a s = πf αs
1
2
= 1 µs
1
Eg 1 + jwτ 2 where µ s is the thermal diffusion length of the sample, γ = is the carrier diffusion coefficient, ε = hυ Dτ 1 v v , ro = o and F = where Eg is the bandgap energy. v and v o are the r= γl Dγ Dγ (1 + ro )(1 + r )e − (1 − r )(1 − ro )e −γl recombination velocity of photoexcited carriers at x = −l s and x = 0 respectively. D is the diffusion coefficient and τ is the nonradiative recombination time It is reported in [14] that OPC signal for semiconductor samples in the thermally thick (l sσ s >> 1) region is essentially determined by nonradiative recombination processes. Thus the expression for pressure fluctuation is given by
δP =
2εf o Po F To l g k s Dγτσ s
1 vτ + 2 2 σs σ s − γ
(3)
and in the experimental frequency range for which ωτ << 1 , we can show that the phase of the OPC signal is given by
Φ=
π + ∆Φ 2
where tan ∆Φ =
(4)
(aD v )(ωτ
+ 1)
(aD v )(1 − ωτ )− 1 − (ωτ )
2
eff
eff
(5)
eff
with τ eff = τ D − 1 α s We had taken thermal diffusivity, diffusion coefficient, surface recombination velocity and relaxation time as adjustable parameters. We fitted the variable part of the equation (5) with experimentally obtained phase angle ∆Φ
EXPERIMENTAL SETUP The experimental setup used for the present studies is same as that used earlier by Sajan etal [15]. Optical radiation from an Argon ion laser at 488 nm (Liconix 5000) is used as the source of excitation, which is intensity modulated using a mechanical chopper (Stanford Research Systems SR 540) before it reaches the sample surface. Detection of the PA signal is made using a sensitive electret microphone (Knowles BT 1754). The phase of the photoacoustic signal is measured using a dual phase lock-in amplifier (Stanford Research Systems SR 830). The laser power used for the present studies is 50 mW with a stability of ± 0.5 %. The sample is fixed on the OPC using vacuum grease at the edges and the illumination by periodically modulated laser beam is done on the exposed portion of the sample without further focusing. The samples used for the present studies are Si doped n-type GaAs epitaxial and Be doped p-type GaAs epitaxial layer grown on GaAs substrate by molecular beam epitaxial (MBE) method. The epitaxial layers have a thickness of 2µm and a doping concentration of 2× 1018 cm-3
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exp
-af
log Amplitude(arbitrary units)
log Amplitude (arbitrary units)
RESULTS AND DISCUSSIONS
0.5
/f
1000
f
-1.55
100
f
-0.99
10
100
af05
exp /f 1000
f
-1.56
100
f
-0.98
10
100
1000
1000
log Frequency (Hz)
log Frequency (Hz)
Figure 2. log-log plot of amplitude of PA signal as a function of chopping frequency for n-type sample
Figure 3. log-log plot of amplitude of PA signal as a function of chopping frequency for p-type sample
Figure (2) and (3) show the log-log variation of the amplitude of the PA signal obtained under heat transmission configuration as a function of chopping frequency for n-type Si doped GaAs epitaxial layer and p-type Be doped GaAs epitaxial layer grown on GaAs substrate respectively. It is obvious from the graphs that the amplitude of the PA signal consists of three distinct regions. This feature can be explained on the basis of three different heat generation mechanisms in semiconductors namely thermalisation, bulk recombination and surface recombination. The thermalisation component
1 exp( −b f ) and when the dominant f
dominates in the low chopping frequency range for which PA signal varies as
heat generation is from bulk and surface recombination, the PA signal varies as f features are clearly visible in the above amplitude versus frequency plots.
−1.5
and f
-50.5
-53.0
theoretical fit experimental
-53.5
respectively and these
theoretical fit experimental
-51.0
-54.0
−1.0
-51.5
Phase (deg.)
Phase (deg.)
-54.5 -55.0 -55.5 -56.0 -56.5
-52.0 -52.5 -53.0 -53.5
-57.0
-54.0 -57.5 400
500
600
700
800
900
Frequecny (Hz)
Figure 4.Phase of PA signal as a function of chopping frequency for n-type sample. The solid line represents the best theoretical fit to the experiment
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400
500
600
700
800
900
Frequency (Hz)
Figure 5. Phase of the PA as a function of chopping frequency for p-type sample. The solid line represents the best theoretical fit to the experiment.
Figure (4) and (5) shows the best fit plot of the PA signal phase to the equation (5) for n-type Si doped GaAs epitaxial layer and p-type Be doped GaAs epitaxial layer grown on 400 µm GaAs substrate respectively. Here the accuracy of fitting parameters as ± 2% for thermal diffusivity, ± 5% for diffusion coefficient, ± 3% for nonradiative recombination time and ± 8% for surface recombination velocity. The values obtained for the above four parameters corresponding to best correlation between experimental and theoretical curve is given in table I Sample Number Thickness of the epitaxial layer in µm Thickness of the substrate in µm Type of dopant (Concentration in cm-3) Thermal diffusivity in cm-2s-1 Diffusion coefficient in cm-2s-1 Surface recombination velocity cms-1 Nonradiative recombination time in µs
GaAs:Si (n-type) 2 400 Si (2 × 1018) 0.21 4.5 525 7
GaAs:Be (p-type) 2 400 Be (2 ×1018) 0.19 5.6 634 5
Table. I. Thermal and transport properties of n-type andp-type GaAs epitaxial layer from PA measurements Thermal diffusivity is an important thermophysical parameter and it is a measure of how heat diffuses through the material in which a transient temperature change has occurred. The reduction in thermal diffusivity value of our samples compared to intrinsic sample [17] can be explained in terms of phonon assisted heat conduction in semiconductors. For semiconductors having carrier concentration<1020cm-3, contribution to thermal conductivity from phonons is greater than that from electrons. Especially, in the case of thin films and epitaxial layers, phonon contribution to thermal conductivity is much greater than that from electrons. Introduction of a dopant creates scattering centers for these phonons, which in turn results in the reduction of phonon mean free path. A consequence of reduction in phonon mean free path is the lowering of lattice thermal conductivity and hence thermal diffusivity value. From the table I it is also seen that, p-type epitaxial layer has low thermal diffusivity value compared to n-type epitaxial layer. Lowered value of thermal diffusivity in p-type sample can be understood in terms of effective mass of photoexcited carriers. In the case of p-type epitaxial layer, scattering is more effective than in n-type epitaxial layer due to higher effective mass of holes. Here we have assumed isothermal contact between the samples, so that interface has negligible influence in our analysis Diffusion coefficient in any semiconductor has great practical significance because the value of the same with recombination time determines the distance traveled by photoexcited carriers before their recombination. Doping alters the mobility and hence the diffusion coefficient of carriers. Thus by analyzing the PA signal, which depends on the diffusion and recombination of the photoexcited carriers we get valuable information regarding the diffusion coefficient of the semiconductor. The diffusion coefficient is directly proportional to the mobility of carriers and hence inversely proportional to the effective mass of photoexcited carriers. This explains the lowered value for diffusion coefficient of n-type sample compared to p-type specimen. Surface recombination velocity has very significant impact on the behavior of the optoelectronic devices. There are dangling bonds at the surface of the sample which act as recombination centers for photoexcited carriers. Thus the value of surface recombination velocity depends greatly on growth mechanism under which the sample has been made. Introduction of dopant in the host lattice creates the recombination centers and hence influences the surface recombination velocity of the semiconductor. The surface recombination velocity is directly proportional to thermal velocity of photoexcited carriers. At constant temperature, thermal velocity is inversely proportional to the square root of effective mass of the carriers. Hence p-type sample have higher surface recombination velocity as seen in table I. The nonradiative recombination time has great physical and practical significance because it virtually determines the quantum efficiency of semiconductor light sources. For a doping concentration as in our present studies, both radiative and nonradiative life times are comparable. The nonradiative life time is inversely proportional to thermal velocity and hence proportional to the effective mass of photoexcited carriers. Since holes have higher effective mass, the corresponding recombination time for n-type sample is greater than that for p-type semiconductor which is evident from table I.
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CONCLUSION In this paper, we have made a PA study of thermal and transport properties of both n-type and p-type GaAs epitaxial layer grown on GaAs substrate by molecular beam epitaxial method. The amplitude of the PA signal obtained under heat transmission configuration gives an idea of various heat generating sources in the specimen. The values of thermal diffusivity, diffusion coefficient, surface recombination velocity and nonradiative recombination time are found by fitting the phase of the PA signal to theoretical model. Our present investigation show that nature of dopant influences the thermal and transport properties of semiconductors in a significant way. This paper also demonstrates that PA technique is a valuable tool to study the dynamics of photoexcited carriers.
ACKNOWLEGEMENTS This work is supported by Netherlands University Federation For International Collaboration (NUFFIC) under the MHO assistance to International School of Photonics. Authors acknowledge Prof. J. H. Wolter and Dr. J. E. M. Haverkort of Technical University of Eindhoven, The Netherlands, for providing semiconductor samples. Sajan D George acknowledge Council of Scientific and Industrial Research, India for his research fellowship. Dilna. S acknowledge Department of Science and Technology, India for a financial assistance. V P N Nampoori acknowledges Univesity Grant Commission for financial assistance through a research award project
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