Effects of electron doping level on minority carrier lifetimes in n-type mid-wave infrared InAs/InAs_1−xSb_x type-II superlattices

The minority-carrier lifetime (τ_MC) and the electron doping density (n₀) are crucial parameters that determine the performance of infrared (IR) photodetectors.^1,2 For a diffusion current-dominated photodetector, the dark current is inversely proportional to the product $n0τMC$⁠, and described as³ 

where n_i is the intrinsic carrier density, q is the electron charge, and W is either the absorber thickness or hole diffusion length, whichever is shorter. It can be seen from Eq. (1) that high doping levels and long minority carrier lifetimes would minimize diffusion current. However, since τ_MC is dependent on multiple carrier recombination mechanisms, all of which scale differently with n₀, there is a value of n₀ that minimizes dark diffusion current.

As HgCdTe (MCT) photodetector performance has shown limited progress in recent years,⁴ new materials become imperative for the continual growth of IR detection. Through recent advancements, type-II superlattices (T2SLs) have shown potential for use as photodetectors. Auger suppression in InAs/$Ga1−x$In_xSb superlattices has been theorized and shown experimentally to be significant enough to surpass the dark current performance of MCT.^5–7 However, this material system has been limited by parasitic Shockley-Read-Hall (SRH) defects resulting in short minority carrier lifetimes.^8–10 Due to the limitations of this native parasitic defect, other T2SL materials have been investigated, such as InAs/$InAs1−x$Sb_x. Long τ_MC values have been achieved in InAs/$InAs1−x$Sb_x T2SL structures^11–13 showing potential for use in IR detectors. A previous study by Höglund et al.¹⁴ has presented the $n0τMC$ product over the doping range of $1.2×1015$ cm⁻³–$4.5×1015$ cm⁻³ in InAs/$InAs1−x$Sb_x T2SLs. However, a systematic study over a much larger doping range is still lacking. The study presented in this Letter investigates carrier lifetimes in mid-wave infrared (MWIR) InAs/$InAs1−x$Sb_x T2SLs over the doping range $2×1014$ cm⁻³–$2×1016$ cm⁻³ to determine the optimum $n0τMC$ product. Dark current in two InAs/$InAs1−x$Sb_x photodetectors of different dopings (⁠$2×1014$ cm⁻³ and $7.5×1015$ cm⁻³) are shown, demonstrating a reduction in dark current by optimizing the doping level.

We first conduct a survey of not intentionally doped (nid) and intentionally doped MWIR InAs/$InAs1−x$Sb_x T2SL material grown at Sandia National Laboratories with 100 K bandgap energies between 215 meV (5.76 μm) and 250 meV (4.96 μm). From this list, samples are screened based on both τ_MC and n₀. The samples with the longest lifetimes at a particular doping level have been kept, as these present current limiting performance, resulting in the fourteen samples reported here. All samples are grown using molecular beam epitaxy on slightly n-type GaSb substrates. Absorber regions are approximately 4 μm thick. Appropriate cladding layers are present in all structures to ensure the measured minority carrier lifetimes are reflective of the narrow-bandgap T2SL region and not of carrier leakage into the substrate or surface recombination. In order to achieve doping above nid levels, either Si or Te is used as intentional n-type dopants. No significant effect on the resulting minority carrier lifetime is observed between the use of the two different dopants, and we do not differentiate between the samples with Si or Te doping in this Letter. Compositions for the $InAs1−x$Sb_x alloy layer of the T2SL structure range from approximately 30% to 50% Sb.

Minority carrier lifetimes and doping levels are measured using the time-resolved microwave reflectance (TMR) apparatus described by Olson et al.² This apparatus utilizes a 5 ns pulsed IR laser to optically inject charge carriers into the T2SL absorbing layer of the sample under test. For these measurements, substrate side illumination at the wavelength of 3.7 μm with a $e−1$ radius of 2.7 mm was used. The resulting carrier recombination decay is probed by 95 GHz continuous-wave microwave radiation reflected from the sample. The instantaneously excited carrier density is directly related to the reflected microwave power at a particular time through the change in sample conductivity that arises when the T2SL is perturbed from equilibrium. TMR data are collected and analyzed in the manner described previously in Ref. 2, 15, and 16, resulting in carrier lifetimes as a function of excited carrier density (⁠$Δn$⁠).

Representative lifetime data from three T2SL samples of different doping levels are shown in Fig. 1. All data presented are taken at 125 K and fit using an equation that takes into account SRH, radiative, and Auger recombination as² 

where τ_SRH is the SRH lifetime, B_r is the intrinsic radiative recombination coefficient, $ϕ$ is the photon recycling factor, and C_n is the electron Auger recombination coefficient. It is assumed that the Auger-1 recombination process dominates over the Auger-7 process.^2,15 For n-type doping, the SRH lifetime dependence on $Δn$ and n₀ is

where $τp0$ and $τn0$ are the characteristic hole and electron SRH lifetimes.¹⁷ Note the doping level is explicitly taken into account in the fitting of the carrier lifetime data. Using Eqs. (2) and (3) to fit the measured carrier lifetime data allows for accurate determination of τ_SRH, the ratio $Br/ϕ$⁠, C_n, and n₀. The minority carrier lifetime is found using Eq. (2) with $Δn≪n0$⁠.

More conventional carrier density measurement methods do exist, such as capacitance-voltage (C-V) and Hall measurements.¹⁸ However, these require device fabrication steps in order to make electrical contact to the material. C-V measurements in particular, can also be highly dependent on the device architecture and geometry, and can be affected by parasitic capacitances. Extracting carrier concentrations from C-V data relies on accurate knowledge of the material's dielectric constant, which is not well known for T2SLs.^2,16 Here, since we measure carrier lifetimes with very high fidelity at excited carrier densities both greater than and much less than the net doping level, accurate extraction of the doping level can be made from fitting carrier lifetime data. Uncertainty in the extracted doping level using this technique is dependent on the calibration of the initial optically injected carrier densities, which rely on accurate measurements of the pump energy and spot size, the superlattice absorption coefficient, and the assumption that every photon absorbed by the T2SL creates an electron-hole pair. This technique also requires the Auger recombination rate to be within a range where doping density has enough influence to be measurable. For example, if the Auger rate is too small then the doping level will have little significance on the carrier lifetime leading to difficulty in extraction. The absorption coefficients in this work are calculated using 14-band k$·$p software (SLKdp, QuantCAD LLC). The estimated error in doping levels extracted from these high-fidelity lifetime data is approximately a factor of 2, which is similar to expected errors from such methods as C-V analysis. TMR also has the benefit of being completely non-contact and non-destructive, and does not require additional fabrication. For the three T2SL samples presented in Fig. 1, the extracted doping levels from lifetime fitting are $1.6×1015$ cm⁻³, $4.0×1015$ cm⁻³, and $8.4×1015$ cm⁻³ with corresponding minority carrier lifetimes of 5.73 μs, 1.69 μs, and 0.68 μs, respectively.

Repeating the described fitting procedure for the fourteen different T2SL samples in this study, a relationship between minority carrier lifetime and doping density is found, shown in Fig. 2 where the uncertainty in the minority carrier lifetime measurement is represented by the symbol size. In order to quantitatively investigate the dependence that τ_MC has with n₀, these data are analyzed using carrier recombination theory involving SRH, radiative, and Auger recombination. The minority carrier lifetime can be written as¹⁹ 

where $τSRHi$ is the SRH lifetime for the i-th defect level, τ_rad is the radiative lifetime, and τ_Auger is the Auger lifetime. Typically, when considering nid material, it is realistic to assume a single SRH defect level;² however, this may not necessarily be the case for intentionally doped T2SLs. Previous work by Olson et al.¹⁹ assumed a unique SRH defect level associated with the intentional dopant and found this SRH level to be approximately 70 ± 10 meV into the T2SL bandgap, compared to 130 ± 20 meV for the native SRH defect center. Thus, we assume that there are two unique SRH defect levels with associated SRH lifetimes for this analysis: one from the native defect that is independent of the doping level (⁠$τSRH1$⁠) and a second created by the intentional dopant atoms (⁠$τSRH2$⁠) that is dependent on the doping level.

The SRH lifetime is a complicated function of characteristic lifetimes and various carrier densities. However, at 125 K, the majority electron concentration is the largest carrier density and $τSRH=τp0$⁠, for the case of n-type material with low injection. With these considerations, Eq. (4) becomes

where $τp01$ corresponds to the SRH lifetime of the native defect and $τp02$ corresponds to the defect created by the intentional dopant. While $τp01$ is considered independent from the doping level (since the associated trap concentration is determined by factors other than the doping concentration), it is assumed $τp02$ scales with n₀. In general,

where σ_p is the hole defect capture cross-section, ν_p is the hole thermal velocity, and N_t is the trap density. The simplest case for $τp02$ is to assume uncompensated doping, and that every dopant atom creates an SRH recombination center, so that $Nt=n0$⁠. Prior to fitting the data in Fig. 2, the intrinsic radiative recombination coefficient is fixed based on results from Ref. 2, which calculates $Br=1.01×10−10$ cm³/s and provides experimental evidence that $ϕ=15$ for similar MWIR InAs/$InAs1−x$Sb_x T2SLs. The thermal hole velocity used is $2×107$ cm/s, determined using a k$·$p-calculated density-of-states heavy hole mass of 0.157m₀. With these parameters, the measured minority carrier lifetime data are best represented using $τp01$ = 10 μs, $σp2=1.7×10−18$ cm², and $Cn=1.6×10−26$ cm⁶/s. The Auger coefficient is consistent with those experimentally measured in MWIR InAs/$InAs1−x$Sb_x T2SLs of similar bandgap and composition.²⁰ The exact T2SL structure has been shown to slightly affect Auger resonances,²⁰ because this sample survey includes a range of alloy compositions; the Auger coefficient reported here can be considered an average.

Eq. (5) shows the dependence that minority carrier lifetime has with doping level, and highlights the importance of identifying not only the limiting carrier recombination mechanism but also the optimal doping level. For instance, combining Eq. (1) with an Auger-limited minority carrier lifetime (i.e., $τMC≈1/(Cnn02)$⁠) causes the diffusion current to increase with greater doping level, as shown in Fig. 3 by the decrease in $n0τMC$ associated with the Auger component. It is readily observed that the ideal doping density for minimizing dark diffusion current is $n0≃2.5×1015 cm−3$⁠, the doping level at which $n0τMC$ reaches a maximum. The individual recombination components identified in Fig. 2 have also been translated into Fig. 3 to highlight where each mechanism limits the $n0τMC$ product. This maximum in the experimental $n0τMC$ product coincides with the transition point from being limited by native defects (SRH₁) to Auger recombination. Clearly, the native defects are a hindrance to attaining larger $n0τMC$ products at doping levels lower than $n0=2.5×1015$ cm⁻³. Continued efforts to mitigate native defects in InAs/$InAs1−x$Sb_x T2SLs are therefore warranted. A secondary limitation arises from the intentional dopants and $τSRH2$⁠, which would begin to limit the $n0τMC$ product if the native defects are mitigated. However, little is known about how dopants are assimilated into the T2SL structures. Continued research is necessary to verify that intentional dopants do, indeed, create SRH recombination centers in the T2SL materials.

For doping levels greater than $n0=2.5×1015$ cm⁻³, Auger recombination is the limiting mechanism. Previous studies on the effects of layer thickness and alloy composition in MWIR InAs/$InAs1−x$Sb_x T2SLs indicate that only minor suppression of Auger recombination is possible while still attaining an approximate 5.2 μm bandgap and keeping strain balanced,²¹ suggesting that further improvement of $n0τMC$ at higher doping levels may prove difficult for this wavelength range. Improvements in the Auger recombination will likely require additional materials to be used in the formation of the T2SL structure, such as the recent demonstration of InGaAs/InAsSb superlattices,²² in order to provide greater versatility in manipulation of the electronic band structure to suppress Auger resonances.

Fig. 4(a) shows the dark current as a function of bias voltage at various temperatures for two MWIR InAs/$InAs1−x$Sb_x photodetectors. One has a nid absorber (⁠$2×1014$ cm⁻³) and the second is intentionally doped at a level of $7.5×1015$ cm⁻³. Both have 4 μm thick T2SL absorbing layers of similar bandgap energies, 231 meV for the nid sample and 219 meV for the doped sample at 100 K. The minority carrier lifetime was measured to be 9.93 μs for the nid sample and 0.97 μs for the higher doped sample at 125 K. Minimal variation in the minority carrier lifetime and doping level within the temperature range of 100–200 K has been shown previously.^2,19 The doping levels have been confirmed using the TMR analysis described here. All other device structure layers are nominally the same. Arrhenius plots are shown in Fig. 4(b) for a voltage of −0.2 V. Experimental data is compared to generalized temperature trends of diffusion current (⁠$Jdiff∝T3e−Eg/kBT$⁠).¹⁵ The nid sample shows slight differences with this temperature trend, which are most likely due to contributions of generation-recombination (G-R) current. An in-depth analysis of G-R current in InAs/$InAs1−x$Sb_x T2SLs can be found in Ref. 23.

The diffusion current component of the dark current, which is dominant at temperatures above 160 K for each sample, is shown to be suppressed in the higher doped T2SL. The $n0τMC$ product of the two presented samples is $7.27×109$ cm⁻³s for the higher doped sample and $2×109$ cm⁻³s for the nid sample. Taking into account the difference in n_i of the two samples due to differences in bandgap energy at 200 K, the calculated diffusion current ratio is 1.8 while the measured ratio is 2, demonstrating a close agreement.

In summary, time-resolved microwave reflectance was used to extract both minority carrier lifetimes and doping levels for MWIR InAs/$InAs1−x$Sb_x T2SLs over a range of doping levels. The minority carrier lifetime is found to be dominated by Auger recombination at high doping concentrations, $n0>2.5×1015$ cm⁻³, and Shockley-Read-Hall recombination through native defects at low doping concentrations, $n0<2.5×1015$ cm⁻³. We do not find that radiative recombination impacts the carrier lifetime significantly. For optimal reduction in dark diffusion current the $n0τMC$ product must be at a maximum, which was found at a doping level of $n0≃2.5×1015 cm−3$⁠. This maximum lies at the transition between SRH limited behavior from native defects at lower doping levels and Auger recombination at higher doping levels. Depending on the targeted doping level, further reduction in dark diffusion current (greater $n0τMC$ products) will require mitigation of native SRH defects or suppressing Auger recombination through engineering of the electronic band structure.

Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.