Conduction band electron relaxation and spin relaxation dynamics in CdZnTe alloy

CdZnTe alloy have widespread applications in photovoltaic solar cells, x-ray detectors, and other electronic devices.^1–3 In these applications, the carrier lifetime is one of the most important parameters. Typically, for example, a sufficiently long carrier lifetime can greatly contribute to high power conversion efficiency in solar cells,^4,5 and efficient charge collection in x-ray detectors,⁶ while an ultrafast carrier relaxation process is required for electronic switching devices. However, the carrier relaxation process is very complex. On the one hand, Cd-based semiconductors exhibit a high density of point and extended defects,^7,8 which behave as defect levels and traps. On the other, Zn-related defects that act as acceptors are introduced into CdZnTe,^8,9 and the acceptor density increases with Zn composition. Thus, free carrier trapping and recombination lifetimes should strongly depend on the composition of Zn in CdZnTe. The characterization and understanding of carrier trapping and recombination processes become critical for the development of electronic devices. In Cd-based semiconductors, the effective carrier lifetime depends strongly on the recombination of electrons with holes in the valance band/accepter level, the capture of electrons and holes at the defects, and the emission of electrons from the point-trapping centers.⁶ Several groups have reported that the carrier lifetime in CdTe, depending on dopants and quality,⁵ lies in the range of 5 to 32 ns,^3,4,10 while the hole trapping time is only a few dozen picoseconds, much shorter than the carrier lifetime.¹¹ In CdZnTe, the carrier lifetime, depending on the Zn composition, is longer than 100 ns.¹² While the ultrafast relaxation of conduction band electrons dominated by electron trapping and recombination at the defect/impurity level has not been reported.

In addition, electron spin relaxation dynamics in semiconductor alloys have attracted much interest in recent years,^13–15 for example, it has been confirmed that the dilute incorporation of Bi into GaAs can lead to a strong reduction of the band gap and a strong enhancement of spin-orbit coupling, which can indicate a new way to modulate the spin relaxation time through Bi incorporation,^13–15 and hence suggest it is a useful application in spintronics. By contrast, when a small fraction of Cd is replaced by Zn in CdZnTe, the band gap increases by ≈6.07 meV when 1% of Cd is replaced by Zn.⁹ Meanwhile, Zn-related defects are introduced into CdZnTe, so that the spin relaxation dynamics should be affected by the Zn incorporation. However, only the electron spin relaxation in CdTe dominated by the D^’yakonov-Perel^’ (DP) mechanism has been reported.^16,17 The spin relaxation dynamics in CdZnTe have not yet been reported, therefore, investigating the effect of Zn incorporation on the spin relaxation dynamics would be significant. In this paper, the conduction band electron relaxation and spin relaxation dynamics in Cd_0.96Zn_0.04Te are investigated experimentally. Conduction band electron relaxation is found to undergo a fast process and a slow process. The incorporation of Zn can slow down the spin relaxation, and the DP mechanism dominates the spin relaxation.

The Te-rich Cd_0.96Zn_0.04Te crystal with a thickness of 500 μm is grown by the Bridgman method along the [111] direction. The measurements of the electron relaxation and spin relaxation are carried out using time-resolved pump-probe reflectivity spectroscopy. Laser pulses generated from a Ti:sapphire oscillator have a duration of 80 fs and a repetition rate of 82 MHz. The pulses are split into wavelength-degenerate pump and probe pulses with an intensity ratio of 6:1. Pump and probe pulses are focused on the sample with a spot size of 50 μm. The wavelengths of the laser pulses can be tuned from 750 to 850 nm. The reflected probe pulse is measured with a silicon photodiode, and the output signal is measured again with a lock-in amplifier.

At near-band edge wavelengths of 820nm, the differential reflection spectrum (DRS) obtained from orthogonal linearly polarization pump-probe beams, which exhibit the relaxation dynamics of conduction band electrons is shown in Fig. 1(a) by the black solid line. The measured profile demonstrates the presence of a fast process and a slow process. At near-band edge photon energy, the faint hot-electron effects can be neglected,¹⁸ thus, the electron cooling process is too weak to contribute, and the decay of the DRS is dominated only by the electron relaxation induced by electron trapping and recombination. We assume the electron density decreases with time according to a double exponential function of the form $A1⁡exp(−t/τ1)+A2⁡exp(−t/τ2)$⁠, where τ₁ and τ₂ are, respectively, the lifetimes of the fast and slow electron relaxation processes, and their corresponding intensities, respectively, are denoted by A₁ and A₂. Based on this assumption, the previously reported theoretical model of DRS is used to fit the experimental spectrum.^19–23 The fitting curve is also shown in Fig. 1(a) by the green line, and the fitting agrees well with the experimental spectrum. The experimentally deduced electron relaxation lifetimes are 6.2 ps for the faster decay part, and 25.4 ps for the slower component. The electron relaxation should be dominated by trapping and recombination at defect/impurity level, because the electron lifetime dominated by recombination of electrons with holes in the valance band is much longer than the lifetime we measured.¹² 

One basic problem requires attention. As we know, the DRS combines two contributions from electron filling (EF) and hole filling (HF),²⁴ however, the decay of the DRS is only assumed to be electron relaxation, because the contribution of HF can be ignored. On the assumption that electron and hole relaxations are synchronous, the individual contributions of EF and HF are calculated with the theoretical model of DRS, and they are plotted in Fig. 1(a) by the red and blue dashed lines, respectively. As the simulating calculation shows, compared with EF, HF hardly contributes to the DRS. In brief, the decay of DRS should mainly originate from electron relaxation instead of hole relaxation.

Fig. 1(b) shows the partial enlargement of DRS within the first 3 ps. The decay signal should be found during the thermalization process.²⁵ Surprisingly, however, the oscillating signal is observed instead of the decay signal. The signal can be broken down into three physical processes, positive peak A, negative peak B, and the end point of slow recovery C corresponding to the conditions shown in Figs. 2(a), (b) and (c), respectively. As Fig. 2(a) shows, the positive peak mainly reflects state filling of the non-thermalized photoexcited carriers,²⁵ when the pump and probe pulses overlap in time and space, because the pump and probe beams are perpendicularly polarized, the coherent effect can be ignored. Then, the electrons undergo an ultrafast thermalizing process via electron-electron, electron-impurity and electron-phonon interactions, which should be reflected by a decay signal.²⁵ However, the signal during the process from A to C decays first to a negative value and then increases, and this abnormal signal originates from the band gap renormalization effect.^19–23 As shown in Fig. 2(b), owing to the band gap shrinkage, the higher excess-energy states which may be empty and have a higher density of states in the conduction band, are probed, thus, the absorption of the probe pulse is enhanced near the negative peak B. As shown in Fig. 2(c), during the electron thermalization process, the electrons scatter out of their initial states and populated in the higher energy states, thus, the absorption of the probe pulse decreases with the thermalization of electrons, and the intensity of the reflection spectrum signal increases with the delay time until recover to the end-point C.

The normalized DRSs obtained from orthogonal linearly polarization pump-probe beams under different carrier densities and photon energies are shown in Fig. 3(a). At the photon energy of 1.515 eV, the DRS decays more quickly at the carrier density of 8.9×10¹¹cm^-2 than at 5.1×10¹¹cm^-2, meanwhile, at the carrier density of 8.9×10¹¹cm^-2, the DRS decays more quickly at the photon energy of 1.55 eV than at 1.515 eV. The decay profiles can be fit to the theoretical model of the DRS well, and the fittings are plotted in Fig. 3(a) by the green solid lines. The extracted excess energy and carrier density dependent electron relaxation lifetimes are shown in Figs. 3(b) and (c), respectively. Both measured relaxation lifetimes of fast and slow electron relaxation processes decrease with increasing excess energy, because additional channels such as electron intraband relaxation emerge, especially in high excess energy states. The probability of intraband relaxation increases with the excess energy, so that the measured relaxation lifetime decreases with increasing excess energy. On the other hand, the lifetimes of fast and slow relaxation processes also decrease with increasing carrier density, which is similar to the carrier density dependence of recombination lifetimes in GaAs,²⁶ but the mechanism can not be explained completely yet, further theoretical explorations are expected.

Fig. 4 shows the typical circularly polarized pump-probe DRSs at near-band edge photon energy. The profiles labeled as (σ⁺, σ⁺) and (σ⁺, σ⁻) are obtained from co-helicity and counter-helicity circularly polarized pump-probe beams, respectively. To eliminate the effect of electron relaxation and extract an accurate spin relaxation time, we process the experiment data in the following way. First of all, we extract the relative difference between the co-helicity and counter-helicity circularly polarized DRSs, which can be defined as $D=[(ΔR/R)+−(ΔR/R)−]/[(ΔR/R)++(ΔR/R)−]$⁠, where (ΔR/R)⁺ and (ΔR/R)⁻are, respectively, the reflectivity changes for the co-helicity and counter-helicity circularly polarized pump-probe, and the difference spectrum is shown in the inset of Fig. 4 by the black solid line. The difference spectrum can be fitted well by a single-exponential function described by $Ae−2t/τs$⁠, where A is the fitting coefficient, t and τ_s are, respectively, the delay time and spin relaxation time. The fitting is also shown in the inset of Fig. 4 by the red solid line. The spin relaxation time of 11.37±0.22 ps can be obtained.

To reveal the effect of Zn incorporation on electron spin relaxation, the photon energy and carrier density dependence of spin relaxation in CdZnTe is studied systematically. Fig. 5(a) shows the DRSs with three selected photon energies at the excited carrier density of 9.1×10¹¹ cm⁻², and the measured carrier density dependence of DRSs at near-band edge photon energy is presented in Fig. 5(b). The red and black profiles are obtained from the co-helicity and counter-helicity circularly polarized pump-probe beams, respectively. The excess energy and carrier density dependent spin relaxation times extracted from the experimental data are shown in Figs. 5(e) and 5(f), respectively. The electron spin relaxation time decreases monotonously with increasing excess energy, which implies that the DP mechanism might dominate the spin relaxation process, because the electron spin relaxation time τ_s governed by the DP mechanism is inversely proportional to the excess energy.^16,27 The carrier density dependence of the spin relaxation time provides further evidence for the relaxation mechanism. As shown in Fig. 5(f), the spin relaxation time first increases with carrier density in the relatively low-density regime, then tends to decrease after a threshold value of the carrier density. The non-monotonic density dependence is similar to the ones in GaAs quantum wells and bulk CdTe dominated by the DP mechanism.^16,28 The spin relaxation time can be estimated as $1/τs∼Ω(k)2τp$⁠,^27,29 in the low-density (non-degenerate) regime, the inhomogeneous broadening $Ω(k)2$ changes little with carrier density because the energy distribution of electrons can be approximated as the Boltzmann distribution, whereas the electron-electron scattering can be enhanced with increasing carrier density. Thus the spin relaxation time increases with carrier density due to the decrease of momentum scattering time τ_p.^27,29 In the high-density (degenerate) regime, with increasing carrier density, the inhomogeneous broadening increases faster than electron-electron scattering, therefore, spin relaxation decreases due to the increase of inhomogeneous broadening.^27,29

For comparison, the excess energy and carrier density dependence of the spin relaxation time in CdTe is also measured. Fig. 5(c) shows the photon energy dependence of DRSs at the excited carrier density of 9.1×10¹¹ cm⁻², and the carrier density dependence of DRSs at near-band edge photon energy is also presented in Fig. 5(d). The excess energy and carrier density dependent spin relaxation times extracted from the experimental data are also shown in Figs. 5(e) and 5(f), respectively. Our CdTe and CdZnTe crystals are grown and measured under the same conditions, except that the carrier density dependence of the spin relaxation time in CdTe is measured at near-band edge photon energy of 1.489 eV. Obviously, the energy and density dependence of the spin relaxation time in CdTe resemble that in CdZnTe, because the DP mechanism also dominates the spin relaxation. Surprisingly, the incorporation of Zn can markedly prolong the spin relaxation time. This happens, for two reasons. First, because the Dresselhaus spin-orbit splitting energy is inversely proportional to the band gap,^15,27 when a small fraction of Cd is replaced by Zn in CdZnTe, the band gap increases and the spin-orbit splitting energy decreases, thus, the spin relaxation time is prolonged through the incorporation of Zn. Second, in comparison with CdTe, Zn-related impurity and defect in CdZnTe can result in a strong enhancement of electron-impurity scattering which can decrease the momentum scattering time, and then increase the spin relaxation time, because the spin relaxation time is inversely proportional to the momentum scattering time.^27,30,31

In summary, the conduction band electron relaxation dominated by trapping and recombination undergoes a fast process and a slow process. The time constants of the two processes decrease with the increasing excess energy and carrier density. The BGR effect can lead to an oscillating signal instead of a decaying signal during the ultrafast thermalization process. The excess energy and carrier density dependence of the spin relaxation time indicates that the DP mechanism dominates the spin relaxation process in CdZnTe. Because the decrease of spin-orbit splitting energy and enhancement of electron-impurity scattering can slow down the spin relaxation in CdZnTe, the spin relaxation times in CdZnTe are always longer than those in CdTe, which indicates a method of modulating the spin relaxation time through the incorporation of Zn.

This research is supported by National Natural Science Foundation of China under grant nos.11504194, 11874232.