Minority Carrier Lifetime and Interfacial Recombination 

Velocity in GaAs/AlGaAs Double Heterostructures

by P. A. Folkes, B. Connelly, and F. Towner

ARL-TR-6186 September 2012

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Army Research Laboratory

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ARL-TR-6186 September 2012

Minority Carrier Lifetime and Interfacial Recombination 

Velocity in GaAs/AlGaAs Double Heterostructures

P. A. Folkes and B. Connelly

Sensors and Electron Devices Directorate, ARL

F. Towner

Maxion, Inc.

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Minority Carrier Lifetime and Interfacial Recombination Velocity in 

GaAs/AlGaAs Double Heterostructures

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P. A. Folkes, B. Connelly, and F. Towner

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14. ABSTRACT

A novel technique is used to determine the minority carrier lifetimes, the interface recombination velocity, the internal 

radiative quantum efficiency, and the radiative recombination constant from PL decay measurements on a set of three samples 

and published theory. This technique is used to determine for the first time the minority carrier lifetimes of p-GaAs in double 

heterostructures that were grown by molecular beam epitaxy (MBE) at ARL. The results show the high quality of our bulk 

GaAs and the GaAs/AlGaAs interface in double heterostructure samples, and provide guidance for studies aimed at improving 

the quality of GaAs grown by MBE at the U.S. Army Research Laboratory (ARL).

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semiconductor

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P. A. Folkes

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iii

Contents

List of Figures iv

List of Tables iv

1. Introduction 1

2. Theory 1

3. Experimental Technique and Data 2

4. Data Analysis 6

5. Conclusion 6

6. References 7

List of Symbols, Abbreviations, and Acronyms 8

Distribution List 9
iv

List of Figures

Figure 1. TRPL of sample with a 2 μm GaAs layer and p0 = 3 × 1016 cm–3. ................................4

Figure 2. TRPL of sample with a 0.6 μm GaAs layer and p0 = 3 × 1016 cm–3. .............................4

Figure 3. TRPL of sample with a 0.3 μm GaAs layer and p0 = 3 × 1016 cm–3. .............................5

Figure 4. TRPL of sample with a 2 μm GaAs layer and p0 = 2 × 1017 cm–3. .................................5

List of Tables

Table 1. Sample data and PL decay times. .....................................................................................2
1

1. Introduction

Knowledge of minority carrier lifetimes is essential for the design and analysis of high-efficiency 

semiconductor solar cells (1) and other optoelectronic devices (2). Photoluminescence (PL) 

decay time measurements, which are typically used for the determination of the minority carrier 

lifetime in gallium arsenide (GaAs), are sensitive to surface recombination (3, 4), recombination 

at the active layer/substrate interface (5), and self-absorption of recombination radiation (6, 7). 

Due to the large surface recombination velocity (105–106cm/s) at the free GaAs interface (4, 8)

and the substrate/active layer interface (5), measurements of the PL decay time can be dominated 

by these effects depending on the carrier density, the sample thickness, and the bulk defect 

density in the GaAs sample. Consequently, the unambiguous determination of minority carrier 

lifetime typically requires measurement over a range of sample thicknesses and carrier densities. 

The surface and interface recombination velocity in GaAs was considerably reduced by the use 

of p-type GaAs/aluminum gallium arsenside (AlGaAs) double heterostructures that confine 

minority carriers in the GaAs quantum, well-defined by the potential barrier at the GaAs/AlGaAs 

interface due to the larger bandgap in AlGaAs (9). Theoretical analysis showed that selfabsorption of spontaneously emitted photons has significant effects on the lifetime of injected 

carriers in GaAs/AlGaAs double heterostructures (7). Minority carrier lifetimes and the radiative 

recombination constant were determined from PL decay time and internal radiative quantum 

efficiency measurements on GaAs samples, which were grown by liquid-phase epitaxy (LPE), 

and theory, which takes into account self-absorption and interface recombination (10). In this 

report we show that the minority carrier lifetimes, the interface recombination velocity, the 

internal radiative quantum efficiency, and the radiative recombination constant can be 

determined from PL decay measurements on a set of three samples and the theory developed by 

Nelson and Sobers (10). This technique is used to determine for the first time the minority carrier 

lifetimes of p-GaAs double heterostructures that were grown by molecular beam epitaxy (MBE) 

at the U.S. Army Research Laboratory (ARL).

2. Theory

In order to facilitate the discussion of the experimental results, we outline the essential features

of Nelson and Sobers’ theory (10). Including self-absorption and surface recombination, the 

effective minority carrier lifetime τ, is given by 
2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

, (1)

where τr is the minority carrier radiative recombination lifetime, F is the fraction of photons from 

radiative recombination that are self-absorbed, φ = 1/(1-F), τnr is the nonradiative recombination 

lifetime, S is the interfacial recombination velocity, and d is the sample thickness. For injected 

minority carrier densities that are small compared to the carrier concentration p0 (for p-GaAs), τr

= 1/(Bp0), where B is the radiative recombination constant (11). Note that in samples with no 

AlGaAs barrier at the GaAs/substrate interface, the factor 2S in equation 1 is replaced by the 

factor (S+Si), where Si is the recombination velocity at the GaAs/substrate interface. The factor φ 

in equation 1, which has been calculated for the GaAs/AlGaAs heterostructures (7, 10), depends 

on the sample’s carrier concentration and thickness. φ increases as d becomes large compared to 

the absorption length of luminescence. For sufficiently large d, equation 1 shows that τ is limited 

by τnr and interfacial recombination.

3. Experimental Technique and Data

The recombination parameters, τr, τnr, and S, can be determined from equation 1 using 

measurements of the effective minority carrier lifetimes on three GaAs/AlGaAs double 

heterostructures with different GaAs thicknesses and the calculated (7, 9) values for φ.

Calculated values of the parameter φ as a function of d for p0 = 2.6 × 1016 cm–3and for p0 = 1.2 × 

1018 cm–3have been published in references 10 and 7, respectively. The GaAs/AlGaAs double 

heterostructures used in the carrier lifetime measurements consist of the following layers: a semiinsulating GaAs substrate, 500 Å p-Al.5Ga.5As, the p-GaAs active region, 500 Å p-Al.5Ga.5As, 

and a 50 Å p-GaAs cap layer. The carrier concentration is the same in the GaAs and the AlGaAs 

regions. Carrier thickness and concentration were determined by MBE calibration procedures 

and electro-chemical capacitance-voltage measurements on calibration samples. The carrier 

density and thicknesses of the samples are given in table 1.

Table 1. Sample data and PL decay times.

Wafer p0 (cm–3) d (μm) φ τ (ns)

M1165 3 × 1016 2.0 4.83 131

M1167 3 × 1016 0.6 2.07 82

M1166 3 × 1016 0.3 1.54 61

M1168 2 × 1017 2.0 31

Carrier lifetimes in the GaAs/AlGaAs samples were measured using time-resolved 

photoluminescence (TRPL) at 300 K to obtain the PL decay time, which is the effective minority 
3

carrier lifetime. Samples were excited using a 250-kHz repetition rate, ultrafast 632-nm laser 

(~1.5 mm beam diameter) that was derived from frequency-doubling the output of a regenerative 

amplifier-pumped optical parametric amplifier. Excitation laser power was varied over the range 

0.27–29.9 mW, resulting in the initial excess carrier densities in the excited samples ranging 

between 6 × 1013 cm–3and 7 × 1015 cm–3. Photoluminescence was detected through a 700-nm 

long-pass filter, to minimize the laser scattering signal, with a fast 300-μm diameter Si 

photodiode. Data were acquired on a PCI averager card. The system response was measured to 

be ~2 ns.

Figure 1 shows the observed TRPL data for a sample, with d = 2 μm and p0 = 3 ×1016 cm–3for 

several excitation intensities. The PL decay is observed to be a single-mode exponential over 

roughly two decades with τ = 131 ns for excitation power ≤3.18 mW. For excitation power 

≤3.18 mW, the estimated initial photoexcited carrier density is ≤6 × 1014cm–3, indicating that 

the excited samples are in the weak-injection regime. Figure 1 shows that the PL decay cannot be 

fitted by a single-mode exponential for excitation power ≥12.4 mW, where the initial 

photoexcited carrier density is ≥3 ×1015 cm–3and the excited samples are entering the 

intermediate-injection regime. TRPL data for samples with p0 = 3 ×1016 cm–3and d = 0.6 μm 

and 0.3 μm, shown in figures 2 and 3, respectively, exhibit single-mode exponential decay over 

roughly two decades with τ = 82 ns and τ = 61 ns, respectively, for excitation power ≤1.13 mW. 

The observed PL decay time decreases to 31 ns for a sample with a 2 μm GaAs layer and p0 = 2 

× 1017 cm–3, as shown in figure 4. The observed structure in the PL intensity at times greater 

than 250 ns is more pronounced as τ decreases, suggesting that it is an experimental artifact that

is related to the detector/circuit frequency response. The sample characteristics, calculated values 

for φ, and the effective minority carrier lifetimes are summarized in table 1.
4

Figure 1. TRPL of sample with a 2 μm GaAs layer and p

0

= 3 × 1016 cm–3.

Figure 2. TRPL of sample with a 0.6 μm GaAs layer and p

0

= 3 × 1016 cm–3.
5

Figure 3. TRPL of sample with a 0.3 μm GaAs layer and p0= 3 × 1016 cm–3.

Figure 4. TRPL of sample with a 2 μm GaAs layer and p0= 2 × 1017 cm–3.
6

4. Data Analysis

The values for τ, d, and φ for the first three samples in table 1 are substituted into equation 1 to 

obtain three simultaneous equations, which are then solved to determine τr, τnr, and S. 

The results obtained from the analysis show that for GaAs with carrier concentration of 3 × 

1016 cm–3, τr = 97.9 ns, τnr = 208.9 ns, S = 74.8 cm/s, and the internal radiative quantum 

efficiency η = τnr/(τr + τnr) = 0.68. The low value of S obtained in our samples is comparable to 

the best values reported for MBE GaAs (12). We also determine that the radiative recombination 

constant, B = 1/τrp0 = 3.4 ×10–10 cm3/s, which is consistent with previous results (10, 13). 

Published results (7, 10) show η > 0.90 for the highest-quality GaAs, indicating that the τnr of our 

GaAs can be increased.

5. Conclusion

In this report we show that the minority carrier lifetimes, the interface recombination velocity, 

the internal radiative quantum efficiency, and the radiative recombination constant can be 

determined from PL decay measurements on a set of three samples and the theory developed by 

Nelson and Sobers (10). This technique is used to determine for the first time the minority carrier 

lifetimes of p-GaAs heterostructures that were grown by MBE at ARL. The results show the high 

quality of our bulk GaAs and the GaAs/AlGaAs interface in double heterostructure samples.
7

6. References

1. Kurtz, S. R.; Faine, P.; Olson, J. M. J. Appl. Phys. 1990, 68, 1890. 

2. Schnitzer, I.; Yablonovitch, E.; Caneau, C.; Gmitter, T. J. Appl. Phys. Lett. 1993, 62, 131. 

3. Keune, D. L. et al. J. of Appl. Phys. 1971, 42. 

4. Hwang, C. J. Phys. Rev. B 1972, 6, 1355. 

5. van Opdorp, C.; Werkhoven, C.; Vink, A. T. Appl. Phys. Lett. 1977, 30, 40. 

6. Dumke, W. P. Phys. Rev. 1957, 105, 139. 

7. Asbeck, P. J. of Appl. Phys. 1977, 48, 820. 

8. Panish, H. C.; Jayson, J. S. J. of Appl. Phys. 1971, 42, 2774.

9. Nelson, R. J.; Sobers, R. G. Appl. Phys. Lett. 1978, 32, 761. 

10. Nelson, R. J.; Sobers, R. G. J. Appl. Phys. 1978, 49, 6103. 

11. Sze, S. M. Physics of Semiconductor Devices; John Wiley & Sons: New York, 1981.

12. Dawson, P.; Woodbridge, K. Appl. Phys. Lett. 1984, 45, 1227. 

13. Casey, H. C.; Stern, F. J. Appl. Phys. 1976, 47, 631.
8

List of Symbols, Abbreviations, and Acronyms

AlGaAs aluminum gallium arsenide

ARL U.S. Army Research Laboratory

GaAs gallium arsenide

LPE liquid-phase epitaxy

MBE molecular beam epitaxy

PL photoluminescence

TRPL time resolved photoluminescence
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