Bulk HgCdTe samples were prepared by the Bridgman method. The p-type conductivity is due to intrinsic V_Hg, leading to a carrier density on the order of 10¹⁴ cm⁻³ at 77 K. The corresponding carrier mobility was on the order of 10⁴ cm²/V·s. The thickness of the samples was determined by a micrometer gauge with a standard thickness of less than 500 μm.

The LPE samples were V_Hg-doped by using a reflux vertical impregnation LPE system, which allows to grow big-area, compositional uniform, good surface profile epilayers with a controllable pressure of the solution. The substrates of the epilayers were (111) surfaces of CdTe or CdZnTe (∼ 4% of Zn), the latter was for the purpose of lattice match. The surface area was about 18 mm × 20 mm. The substrate was fixed by a clamp with a vertical inlet and outlet way. In a horizontal growth process, both the drop and pull-up of the sample were in vertical direction, while the growth direction was horizontal. The horizontal growth made the composition and thickness of the epitaxial layer uniform, while the vertical separation from the growth solution reduced the adhesion of any mother solution. After growth, the samples were annealed at different temperatures and times under Hg-rich condition. The p-type conductivity at 77 K was due to V_Hg, leading to a carrier density on the order of 10¹⁵ cm⁻³. The LPE samples L1–L6 were used for analysis. Among them, the main differences were the x value, the thickness, and, of course, the carrier density and mobility. The thickness of the HgCdTe layer was evaluated based on the Fabry–Pérot interference in the transmission spectra and was typically 10 μm.

The MBE-grown HgCdTe epilayers were grown in a Riber 32P MBE system on undoped semi-insulating GaAs (211)B substrates. A CdTe buffer layer 3 μm in thickness was grown prior to the HgCdTe nucleation. For comparison, As-doped and V_Hg-doped MBE samples were prepared. Except for the as-grown reference epilayer without any annealing, the other samples were annealed including a single- or two-stage annealing process, where the latter (e.g., 285 °C/0.5 h + 240 °C/48 h) was known to be beneficial to the As-activation without other residents. This happens because the first stage pushes the As from Hg sites to Te sites and the second stage, with a relatively low temperature, can remove the excess V_Hg and avoid forming the n-type As_Hg.^[17,18] The details of the samples are listed in Table 1, including composition and thickness, as well as the carrier concentration.

Table 1.

Table 1.

Table 1. Composition (x), thickness (d), carrier density (Nc), mobility (Mc), and nature of defects in MBE samples. . x d/μm /1015 /103 Defects Annealing/(°C/h) M0 0.300 6.0 12.30 0.26 VHg, AsHg as-grown M1 0.308 7.9 –9.50 –2.82 AsHg 240/48 M2 0.300 5.9 32.70 0.30 AsTe 285/0.5+240/48 M3 0.300 11.0 10.10 0.26 VHg 285/0.5+240/48 M4 0.305 6.1 36.40 0.29 AsTe, VHg 440/0.5+240/48 M5 0.225 10.7 32.00 0.31 VHg as-grown

Table 1. Composition (x), thickness (d), carrier density (Nc), mobility (Mc), and nature of defects in MBE samples. .

Characterization by optical absorption was performed by using a Bruker IFS 66v/S spectrometer, which was equipped with a KBr beam splitter and a liquid-nitrogen-cooled HgCdTe detector. The spectrometer was evacuated during the measurement to avoid any influence of infrared absorption lines in air.

PL spectra were recorded with this setup by using the step-scan option of the FTIR as described elsewhere in detail.^[15] The 514.5 nm line of a mechanically chopped (1.8 KHz) Ar⁺ laser was used to irradiate the sample with a beam diameter of ∼ 200 μm.

Before the experiment, the samples were treated with a quick etch in a 1% Br₂/methanol solution to avoid influencing the surface smear, and then mounted on the cold finger of an Oxford closed-cycle cryostat. The temperature was adjusted from ∼8 K to 300 K. The spectral resolution was set to be 6 cm⁻¹ or 0.7 meV.

Figures 1(a)–1(c) show the transmission spectra of bulk, LPE, and MBE samples, respectively, which are recorded at low temperature of ∼ 8 K. The samples show high transmittance at the low energy side and relatively steep absorption feature when the photon energy is close to or become higher than the optical E_g. The epitaxial samples demonstrate that the strong interference fringes on the low energy side, i.e., the uniform (or single) pattern, for LPE are due to the interfacial reflectance between the HgCdTe layer and the substrate. The more complex patterns for the MBE sample are caused by the buffer layer between the HgCdTe layer and the substrate. Based on the interference energy distances, the HgCdTe epilayer thickness can be evaluated, as shown in Table 1.

Fig. 1.

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	Fig. 1. Transmission spectra of (a) bulk, (b) LPE, and (c) MBE samples at ∼8 K.

According to the transmission spectra at any temperature, one can obtain the optical E_g value of HgCdTe. However, when the sample is doped, it can be imagined that the defects can be activated thermally and the carrier density is determined by the doping level and the temperature. This suggests that the absorption process of the carriers in the doped samples should be different from that without doping, on which transmission measurements are often considered to provide the intrinsic absorption spectra.

Figure 2 shows the transmission spectra of the three samples at different temperatures. At first glance, the absorption edge seems to blue-shifted as the temperature increases. It is, however, important to mention that for the three samples, the absorption edge does not monotonically blue-shift but presents an S-shaped evolution in the low temperature range. First, it blue-shifts with the temperature increasing from the lowest value but then red-shifts as the temperature exceeds a certain value (e.g., ∼33 K for bulk, ∼50 K for LPE, and ∼30 K for MBE), and reaches the lowest energy point at ∼55 K, 67 K, and 70 K for the bulk, LPE, and MBE samples, respectively. Thereafter, the absorption edge moves monotonically up to 300 K. In other words, the evolution of the absorption edge is abnormal when the temperature is in a range of about 30–70 K. It is worthwhile emphasizing that the spectra of all of the other samples show similar temperature dependence with the exception of n-type MBE sample,^[19–21] which shows a monotonic temperature dependence of the absorption edge in the whole temperature range. Although the critical temperature points are different for different samples, the temperature is below 77 K.

Fig. 2.

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	Fig. 2. Transmission spectra of (a) bulk, (b) LPE, and (c) MBE samples at different temperatures.

From the transmission spectra given in Figs. 1 and 2, the corresponding absorption-coefficient α spectra can be deduced and are shown in Fig. 3.^[20] The x value can then be deduced from the spectra. Here, we first obtain the results at the lowest temperature of ∼8 K from the following absorption coefficient expression:^[22]

Fig. 3.

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	Fig. 3. Absorption coefficient spectra of (a) bulk, (b) LPE, and (c) MBE samples at different temperatures.

Because of the difference in α values between the bulk and epilayer due to the thickness difference of HgCdTe, different procedures should be undertaken for these two kinds of samples in order to determine the critical point on the absorption spectrum. For the bulk samples with a thickness on the order of submillimeters, the absorption coefficient is extrapolated to the α_Eg as the critical point (Fig. 3(a)). For the epilayers having a thickness on the order of μm, the energy point is determined as the critical value at the cross point between the plateau and exponential region (Figs. 3(b) and 3(c)). Note that the non-monotonic shift of the absorption edge on the low temperature side is still present.

Figure 4 summarizes the determined E_g values for all samples by referring to the α_Eg values at different temperatures.^[20] The E_g ∼ T evolution predicted by the CXT empirical expression is also shown for each sample to guide the eyes^[23]

Fig. 4.

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	Fig. 4. Representative temperature-dependent Eg values for (a) bulk, (b) LPE, and (c) MBE samples. Part of the data have been up- or down-shifted for clarity. The solid lines are predicted by CXT to guide the eyes.

The consistent x value can be calculated by referring to the absorption coefficient spectra at any temperature point and Eq. (2). However, due to the existence of the abnormal shift of the absorption edge, the referenced temperature point becomes a key issue for determining the exact x value. Here, we tentatively extract the value based on the result of the lowest temperature; e.g., ∼ 10 K. The reason and details will be discussed in the following.

As shown in Fig. 4, the absorption-edge energy is blue-shifted in the entire temperature range, but there exists a non-monotonic shift in the low temperature range, marked by the shadowed area. A red-shift can be observed except for the n-type epilayer sample. Since the x value is determined based on the result of ∼ 10 K, the predictions from the empirical expression match well with the experimental data from the low temperature side, but on the high temperature side they deviate evidently from each other. Note that although the n-type MBE sample does not show any redshift in the shadowed area, the evolution of the experimental data is slower than that of Eq. (2); i.e., with a smaller slope than the dE_g/dT value. In this case, extrapolating the linear region downwards the high temperature part, there should be an energy separation ΔE at 0 K (but not for the n-type samples).^[24] No doubt, based on one of the two evolution data, the determined x value should be inconsistent for a certain sample. Another important phenomenon should be pointed out that the deviation in V_Hg-doped samples (including the bulk, LPE, and MBE samples) gives a slightly bigger ΔE value than that of the As-doped MBE samples (including the p-type and, of course, n-type samples).

Figure 5(a) shows the PL spectra of several LPE samples at 8 K, which are unintentionally doped. The spectra show more than one PL peak. Curve fits demonstrate two separated peaks, the high energy peak named A₀ and the low energy peak B₀ with an energy separation of ∼ 14 meV (Fig. 5(b)). To reliably determine the peak positions, the second derivative procedure is adopted in Fig. 5(b), which gives an error of ∼ 1 meV as compared with that of the curve fit technique.^[25] This shows that the peak position can be accurately determined by both approaches. As for the sample at the bottom of Fig. 5(a), which shows that the PL peaks shift towards the long wavelengths up to ∼ 11 μm, the signal-to-noise ratio (SNR) of the spectrum is relatively poor, even under a high excitation power, which is possibly due to the poor quality of the sample with a relatively small x ∼ 0.235. However, two PL peaks are also evident. The curve fit procedure is done as shown in Fig. 5(c) for different temperatures. The energy separation between the two peaks is also close to that observed for the other samples. For high temperatures, at which a much higher excitation density is necessary, thermal effects induce the broadening of the spectra, particularly towards the high energy side.

Fig. 5.

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	Fig. 5. (a) PL spectra of LPE samples at ∼ 8 K, (b) curve fit and the second derivative procedures applied to the PL spectrum of sample L5, and (c) PL spectra and curve fit results of sample L6 at different temperatures.

PL measurements have been performed at different excitation power and temperatures. Figure 6 summarizes the results of the fit parameters including the peak energy and the integral intensity (I.I.). In Fig. 6(a), there is a blue-shift of both peak energies with the excitation power increasing, especially at high excitation power. This behavior can be interpreted by band filling in the narrow-gap HgCdTe, and on the high excitation power side by the thermal effect, which can make the peak energy blue-shifted due to the positive temperature coefficient of the bandgap (i.e., dE_g/dT) in HgCdTe with a small x. The thermal effect is also confirmed by the relationship between I.I. and excitation power in Fig. 6(b), where the I.I. almost linearly increases first, then becomes saturated (peak A₀) or even decreases (peak B₀) as the excitation power increases.

Fig. 6.

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	Fig. 6. (a), (b) Excitation power and (c) temperature dependence of the fit parameters obtained from the PL spectra.

Figure 6(c) further gives the temperature dependence of the peak energy. As a comparison, the predicted results of the CXT expression, i.e., Eq. (2), have been added to the figure. Considering the potential excitonic effects and band-tail states in narrow-gap HgCdTe, which frequently induce a redshift of the PL energy as compared with the intrinsic absorption results, the CXT results are given based on the PL energy at a high temperature (300 K). From the figure, we can see that in the entire temperature range, peak A₀ has always a nearly linear blue-shift with temperature increasing, while peak B₀ shows a similar blue-shift but only at low temperatures. Here it is not difficult to attribute the high energy peak A₀ to the band-to-band transition (i.e., ), since no higher energy peak is observed in the entire excitation and temperature range. The low energy peak B₀ represents a defect-related behavior. The V_Hg shallow defect could be responsible by taking into account the energy separation from peak A₀, and the facts that (i) the relative intensity of peak B₀ to peak A₀ decreases but does not change its spectral shape as the excitation power increases, and (ii) the V_Hg-doping of the samples. Thereafter, it can be estimated that the V_Hg has an activation energy of ∼ 14 meV, which is consistent with the results reported from electronic and optical experiments, as well as theoretical predictions. Note that the relation between the peak A₀ energy and temperature shows a steeper slope (i.e., dE_g/dT) than that of CXT, and that the defect activation energy related to V_Hg is close to the abnormal shift ΔE value in the absorption measurement.

Now we come to the As-doped samples, which are grown by MBE. Figure 7(a) shows the PL spectrum of the as-grown sample at 8 K. It is an extremely complex PL spectrum with multiple peaks, including a pronounced part on the high energy side and the relatively weak part on the low energy side. Curve fits reveal more than seven peaks, which can be divided into two groups: one for peaks A–E and the other for peaks F and G. Between them exists an energy difference up to ∼ 90 meV. For comparison, figure 7(b) shows the PL spectrum of an annealed sample at the same temperature, to which an optimized two-stage process (see Table 1) is applied in order to fully activate the doped-As in HgCdTe.^[11] Indeed, this spectrum shows a relatively simple shape, similar to those of the V_Hg-doped samples in Fig. 5. Curve fits give two peaks separated by an energy difference of less than 12 meV. The band-to-band peak is increased at the cost of the defect-related transitions. It should be emphasized that comparing with the spectral shape of the as-grown sample, an annealing process can optimize the spectral shape, and at the same time also eliminate the PL signals on the low energy side.

Fig. 7.

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	Fig. 7. Representative PL spectra of (a) as-grown sample M0 and (b) As-activated annealed sample M2 at ∼ 8 K, and their line-shape fits. The samples are grown by MBE.

Figure 8 shows the excitation power and temperature dependent PL spectra and the corresponding results of a peak analysis of the annealed sample from Fig. 7(b). The slight blue-shift of the peak energy in Fig. 8(c) is due to band filling as the excitation power increases. In Fig. 8(d), the competition of the I.I. between the two peaks is clear, but beyond ∼ 40 mW both become saturated and even decrease, which is likely to be related to excitation-induced heating. Note that when peak B₁ first shows a near-linear increase with excitation power increasing, peak A₁ even presents a superlinear dependence (see the double-logarithmic scale). From the temperature-dependent peak energy (Fig. 8(e)) and I.I. (Fig. 8(f)), it is evident that the bandgap-related peak A ( ) shows a linear increase with temperature increasing and has an energy separation of ∼ 12 meV from the defect-related peak B₁. According to the doping and the p-type conductivity of the sample by As-activation annealing, as well as the previous discussion, the defect can be attributed to As_Te with an activation energy of ∼ 12 meV. It should be pointed out that for comparison, an MBE reference sample with unintentional doping is also annealed like the sample in Fig. 7(b). A similar two-peak structure can also be observed (not shown here) with an energy separation of ∼ 15 meV. It is related to the activation energy of V_Hg, which is close to the foregoing results in the LPE samples. Here, the smaller value of As_Te than that of V_Hg suggests that the former is shallower than the latter. This could be of benefit to the p-type material preparation and relevant device fabrications.^[26–28]

Fig. 8.

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	Fig. 8. PL spectra of sample M2 at different excitation powers and temperatures, and (c), (d) excitation power- and (b) temperature-dependent peak energy and peak integral intensity.

To find an optimized annealing process, different annealing procedures are tested. Figure 9 shows the PL spectra of an As-doped MBE sample, which is annealed at a higher annealing temperature (400 °C) during the first-stage as shown in Table 1. As is well known, the Hg–Te binding is extremely weak, and can be broken at a high temperature and therefore low temperature in the entire growth process is required.^[28,29] Therefore, a high activation temperature (e.g., ≥ 400 °C) in the first stage produces higher additional V_Hg than a low activation temperature (e.g., ≤ 300 °C). From Figs. 9(a) and 9(b), we can see that the PL spectra show four peaks A₂–D₂ compared with those in Fig. 8(a). The excitation power- and temperature-dependent peak energies (obtained by line-shape fitting) show that when A₂ can be ascribed to the E_g-related transition, B₂–D₂ should be defect-related, where the energy differences from A₂ are ∼ 9 meV, 23 meV, and 31 meV, respectively (Figs. 9(c) and 9(d)). Considering the annealing conditions and Berding’s theoretical reports,^[5,31] the n-type conductivity of this sample suggests not only a dominant As_Hg defect, but also the presence of V_Hg and complexes of As_Hg–V_Hg. According to the Sun’s theoretical predictions^[18,32] and the results obtained previously,^[9] peak B₂ can be attributed to an As_Hg-related transition with an activation energy of ∼ 9 meV and peak C₂ is related to a V_Hg-related transition with an activation energy of ∼ 14 meV. Thereafter, peak D₂ that only appears at low temperatures and low excitation densities can be ascribed to the transition related to the As_Hg–V_Hg complex, because the high temperature and strong excitation could simplify the complex. The energy distance of ∼ 8 meV of the complex from the As_Hg and V_Hg levels discloses its forming energy. Here, we should emphasize that the two-stage annealing process can be used to activate the As with a temperature as low as 285 °C. A higher temperature beyond 300 °C is undesirable from the point of view of defect creation.

Fig. 9.

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	Fig. 9. (a), (b) PL spectra of an As-doped MBE sample (M1) treated with a single-stage annealing process; (c), (d) the peak energies at different excitation powers and temperatures.

After obtaining the specific defect information, the discussion of the origin of abundant peaks in the as-grown sample becomes easier. Figure 10(a) shows the PL spectra of the sample already shown in Fig. 7(a) at different temperatures (up to 100 K).^[11] It is obvious that the SNRs of the spectra are relatively poor due to the quality of the epilayer before annealing, especially when the temperature increases. Besides the temperature-dependent evolution of the high energy part (i.e., evident blue-shift of peaks A–E with temperature), the low energy part (i.e., the deep levels F–H) shows unusual temperature dependence with competitive occurrence and disappearance of peaks with temperature increasing. For instance, both peaks G and F are visible at low temperatures, but with the temperature increasing, peak G disappears and peak F increases, accompanied with the appearance of an additional peak H.

Fig. 10.

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	Fig. 10. (a) PL spectra of sample M0 and (b) temperature dependence of the peak energy. For the sake of clarity, the values of F and G in panel (b) are upshifted by 35 meV.

Figure 10(b) summarizes the peak energies of up to eight peaks A–H as a function of temperature. For comparison, the results of the CXT formula are shown in the figure. Note that for the as-grown sample, the doped-As should be inactivated, i.e., without occupying the Te lattice sites. Due to the p-type conductivity, the intrinsic V_Hg should predominate, and the As is mainly expected to exist as As_Hg, which requires a suitable annealing process to transfer from the Hg site to the Te site.^[33,34] It needs to be pointed out that the peak number of the fit procedures on the high energy side is based on the previous results, where some values are used, including V_Hg ∼ 14 meV, As_Te ∼ 12 meV, As_Hg ∼ 9 meV, and the As_Hg–V_Hg complex ∼ 31 meV.

It is obvious that the high energy peaks A–D (maybe E, as well) show a parabolic evolution at low temperatures but as the temperature increases beyond 20 K, they evolve in a linear increase way. The deep-level-related peaks F–H shift linearly with temperature increasing. The peak positions of A–H can be determined by extrapolating to 0 K as ∼ 238 meV, 232 meV, 225 meV, 221 meV, 207 meV, 164 meV, 146 meV, and 180 meV, respectively. Obviously, peak A has the characteristics of band-to-band transitions, while peaks B–H are related to defect-related transitions. According to the energy separation of these peaks and the statements given above, the high energy peaks B–E can be attributed to As_Hg (∼ 6 meV), V_Hg (∼ 13 meV), Te_Hg (∼ 17 meV), and the As_Hg–V_Hg complex (∼ 31 meV) transitions, respectively. Note that (i) in the unintentionally-doped or the annealed As-doped samples, none of deep levels like peaks F–H is observed; and (ii) peak H only appears at high temperatures and almost overlaps the evolution of peak G in the temperature range after the upshift of 35 meV of peak G. These may suggest that (i) peaks F–H should be related to the As dopant, such as the As-related cluster (or perhaps its complex with V_Hg) due to the dopant source of As₄, which is prone to form As_i (i = 1, 2, and 4) clusters or interstitials in as-grown even by using a thermal cracker cell; and (ii) the deep levels are totally dependent on temperature, showing that the increase can first make the peak G-related defect state dissociate and strengthen the intensities of peaks F and H, and then make the peak F-related defect state de-complicated (to the H-related defect state) as the temperature increases further. However, obviously, the annealing process can annihilate all of them fully.^[11,19]

The band-edge electronic structure in As-doped HgCdTe is schematically summarized in Fig. 11 for the different annealing conditions. In the as-grown samples, the As dopant is on the Hg site and the V_Hg–As_Hg complex is preferably formed due to the existence of V_Hg. At the same time, due to the excess V_Hg, the antisite of Te occupying Hg sites can be formed and causes n-type conductivity (or a reversion layer), in particular, at the surface, since the material can be of weakly p-type in conductivity. Obviously, the double deep levels are there, but the origination is pending even though a single deep level has been reported in a theoretical research relating to V_Hg,^[35] because none of the related levels is observed in unintentionally-doped HgCdTe. The n-type annealing process, e.g., at a temperature of 240 °C cannot be useful in removing the V_Hg if the As_Hg level exists in a certain density because they prefer to form a complex of V_Hg–As_Hg. It is, therefore, necessary to mention that the two-stage annealing process with a low temperature (down to 285 °C) can effectively activate the As as shallow acceptors with a lower activation energy than that of the intrinsic V_Hg.

Fig. 11.

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	Fig. 11. band-edge electronic structure including defect formation and levels in As-doped HgCdTe for different annealing conditions as determined from our measurements. Di (i = d1, d2, and d3) represent deep levels. Color arrows depict a dynamic process that Dd1 can be de-complicated to Dd2 and Dd3, and further from Dd2 to Dd3 with temperature increasing.

3.2.1. Stokes shift

As mentioned above, we observe that the absorption edge shifts abnormally with temperature increasing, and the determined E_g is inconsistent with the direct PL result , as shown in Fig. 12(a) for an LPE sample. However, it is necessary to point out that the Stokes shift E_s between the results obtained by the two techniques is quite interesting, namely, at 10 K with a normal E_s (about +27 meV) but at high temperatures up to 200 K with a negative E_s, and the absolute value should increase as the temperature increases. That is to say, the Stokes shift has a transition from positive to negative sign.^[36]

Fig. 12.

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	Fig. 12. (a) Comparison between PL and absorption spectra of a representative LPE sample, (b)–(e) plots of temperature-dependent optical bandgap value obtained from absorption and PL spectra, and experimental Stokes shifts.[36] For comparison, the Stokes shifts are also shown according to the CXT formula.

Details are shown in Figs. 12(b)–12(e), where the temperature-dependent band-edge-related energies and the corresponding E_s are compared. From the figures, we can see that as the PL gives the , the defect-related energy can be determined, which is close to the abnormal shift energy of the absorption edge with temperature increasing. Attention should be paid to the E_s as a function of temperature in Figs. 12(d) and 12(e). Here two conceptions about the Stokes shift are defined: the experimental E_s (corresponding to the value of E_g–E_PL) and corresponding to the value of E_CXT–E_PL. It is evident that both evolutions are dissimilar. While E_s decreases with the temperature increasing, decreases faster and changes the sign from positive (normal) to negative (abnormal) at a certain temperature point T_s, e.g., ∼ 150 K for the unintentionally doped LPE sample or ∼ 120 K for the As-activated MBE sample. Energetically, they (∼ 13 meV for the former and ∼ 10 meV for the latter) are relatively close to the activation energy of the corresponding defects; i.e., V_Hg and As_Te, respectively. This may further suggest that the abnormal shift of the Stokes energy is related to the defect levels as discussed in the abnormal shift of the absorption edge energy.

3.2.2. Comparison of the results obtained by different optical techniques

Based on this discussion, it can be imagined that to accurately determine the optical bandgap E_g (on which the x value depends in HgCdTe) is a key issue, because the measurement temperature point plays a vital role for different spectroscopic techniques including the transmission and PL. It involves that the reference temperature is intrinsically dependent on the selected optical method. Thus, to evaluate the accuracy of the determination of the optical E_g, figure 13 comparatively shows the PR and PC spectral results of an unintentionally-doped LPE sample at 77 K. This figure shows the line-shape fit results for PL and PR.^[10,37] Note that the fit to the PL spectrum has considered the asymmetry of the spectrum that is due to the thermal broadening.

Fig. 13.

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	Fig. 13. Determination of optical bandgap Eg in unintentionally-doped HgCdTe sample L2 by different spectroscopic techniques including transmission, PL, PR, and PC at 77 K. Fit results are shown in green. Marked stars refer to corresponding Eg. Eg(CXT) is obtained from the CXT expression. Dashed vertical line is used to guide the eyes to Eg obtained by PC.

From this figure, we can see that if the cutoff wavelength (or energy) of the PC spectrum is considered as the value of E_g for the material, the PR spectrum, which can give the fine electronic structure including the defect levels also gives a very consistent value. However, this value is a little blue-shifted as compared with the PL results but a little red-shifted as compared with the transmission results, and this value is used as a standard value to evaluate the optical E_g of semiconductors, where the Stokes shift has a positive coefficient. Note that the PL spectrum at 77 K does not show the defect-related (i.e., V_Hg) emission peak, while at a low temperature (10 K), the V_Hg-related peak is evident as shown by the first sample (Fig. 5(a)). It should be also mentioned that the evaluated E_g value from the transmission spectrum is smaller than the prediction of the CXT expression, probably due to the existence of the V_Hg. From the point of view of the determination of E_g, we can draw a preliminary conclusion that the transmission or absorption measurement can be regarded as a suitable way to evaluate the optical E_g of intrinsic HgCdTe, while for doped-HgCdTe, all of the methods show a red-shift due to the existence of either the defect levels or the band-tail states.

The Stokes shift E_s exists between the absorption and PL spectra, which are based on the reverse transition process of carriers. Thus, to explain the non-monotonic shift of the absorption edge and subsequently the abnormal shift of E_s as temperature increases, it is vital to determine the position of the Fermi level E_F, which influences the probability of transitions in a certain state. The electrical neutrality condition can be written as follows when considering p-type HgCdTe with only one single acceptor:

For comparison with the ionized defects, we calculate the intrinsic density of carriers n_i according to^[23]

In the temperature range of the non-monotonic shift of the absorption edge, equation (3) can be simplified in several specific temperature ranges (or points) including the low temperature zone (almost no ionization of defects), the middle ionization zone (low density of ionized defects), the strong ionization zone (high density of ionized defects), the transitional zone, and the high temperature intrinsic ionization zone (intrinsic carriers prevailing), based on which the E_F can be expressed by setting E_v = 0:

The E_F is a function of x, conductivity type, doping level, and ionization energy of defect. We mainly focus on the doping levels from 10¹⁴ to 10¹⁷ cm³ by considering the general density of extrinsic and intrinsic dopants in HgCdTe.^[38–40] Figure 14 gives the calculated temperature dependence of the band-edge electronic structure and E_F by taking p-doped Hg_0.7Cd_0.3Te for example.^[36] For comparison, the results of unintentionally-doped n-type HgCdTe are shown, since a similar phenomenon is also observed between the absorption edge energy and the empirical formula. From the figure, we can see that the material system shows a positive temperature coefficient of E_g, but CB and VB both decrease and E_F almost exponentially increases toward E_i with the increase of temperature. After the acceptors are fully ionized, E_F finally approaches to E_i. As mentioned previously, the range from ∼ T_d to T_e is the non-monotonic shift range of the absorption edge.

Fig. 14.

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	Fig. 14. The evolution of the EF in p- and n-type HgCdTe with temperature for different parameters (for n-type, ND = 1014–1016 cm−3; for p-type, NA = 1014–1017 cm−3). Triangles and dots represent the temperature points of Td and Te, respectively.

Table 2 gives the predicted results of T_d and T_e in p-type Hg_0.7Cd_0.3Te under different conditions including doping and activation energies. From the Table, we can see that T_d and T_e increase with doping level (N_A) and ionization energy of acceptors (ΔE_A) increasing,^[36] i.e., 13.6 K< T_d < 47.0 K and 27.3 K< T_e < 248.2 K. As discussed above, T_d with E_F ≈ E_A can be considered as the initial stage of the ionization of acceptors and T_e as the stage of full ionization of acceptors. In this case, for the As-activated (As_Te) Hg_0.7Cd_0.3Te, N_A = 5 × 10¹⁶ cm³ and ΔE_AsTe ≈ 10 meV, the key temperature points can be calculated to be T_d = 17.0 K and T_e = 70.0 K, which are consistent with the range of the non-monotonic shift of the absorption edge. For V_Hg-doped HgCdTe with x = 0.3, N_A is on the order of 10¹⁶ cm³ and ΔE_VHg ≈ 15 meV, the temperature ranges of T_d and T_e are ∼ 26–90 K, which are also close to the experimental observations. For the intrinsic n-type Hg_0.7Cd_0.3Te, N_D = 10¹⁴ cm³ and ΔE_D ≈ 3 meV, the temperature range of T_d and T_e can be deduced to be ∼ 15–90 K. Of course, as N_D increases, the range from T_d to T_e should be broadened, and even extended beyond 300 K for T_e. This is consistent with the experimental result, showing that it is difficult to observe the non-monotonic shift of the absorption edge at much higher donor densities due to the very small ΔE_D.

Table 2.

Table 2.

Table 2. Calculated values of the specified temperature points described in EF function. . Defect activation energy T/K @ NA/D ∈ 1014–1016 cm−3 and x = 0.3 Ea(AsTe) ∼ 10 meV Td 13.6–16.6 Te 27.3–68.2 Ea(VHg) ∼ 15 meV Td 19.3–26.1 Te 37.0–89.5 Ed ∼ 3 meV Td 12.2–45.1 Te 45.2–454.2

Table 2. Calculated values of the specified temperature points described in EF function. .

According to the E_F ∼ T expression and the experimental data, the temperature-dependent transitions can be explained when extrinsic/intrinsic shallow levels exist in HgCdTe, independent of growth methods and conductivity types, as well as dopant sources. As the experimental observation and the calculated result, the values of T_d and T_e represent the critical points of the non-monotonic shift of the absorption edge, the former corresponding to the occurrence of defect-related transition contribution and the latter for the full contribution of the defect-related transition.

Thus, a schematic evolution of the carrier transition can be presented by taking a p-type Hg_0.7Cd_.3Te for example as shown in Fig. 15. The temperature values in the figure refer to the specified parameters of the sample with E_a ∼ 11 meV at N_c∼ 1 × 10¹⁶ cm⁻³.^[24] This figure shows that at low temperature below 26 K (Fig. 15(a)), the carriers in the defect state (holes) are frozen. When the transmission measurement is conducted, only the electrons from the VB are excited to the CB but the states in E_a are localized without activity (i.e., holes are not activated). Here, the absorption edge follows the law of the intrinsic absorption. However, under the PL measurement conditions, the excited electrons in the CB from the VB by lasers can recombine with localized vacancies in the defect state together with holes in the VB. This is also the fact that for detecting defect-related shallow levels, low temperatures are frequently required for PL measurement. As the temperature increases (Fig. 15(b)), the frozen holes in the defect states begin to be thermally activated. In this case, the activated holes in E_a, the anions due to the capture of electrons, can join in the transition of transmission process, which provides a contribution to the absorption edge. Because the transition energy of the defect states is lower than the VB–CB transition energy, the absorption edge energy is red-shifted. As the temperature raises beyond 90 K (Fig. 15(c)), the holes in E_a are almost fully activated and the contribution of their transition to the absorption edge reaches the maximum, and even if the temperature increases further, the influence of the defect states on the absorption edge cannot be increased. As a result, the absorption edge energy follows again the law of the intrinsic absorption; i.e., it almost linearly increases with temperature increasing. It can also be pointed out that the full activation of E_a at high temperatures means that the defect states can always be occupied by electrons, which can participate in the absorption process to the CB but cannot find electrons from the CB to give rise to emission. This is also the reason why it is difficult to observe a PL signal of shallow defects at high temperatures.

Fig. 15.

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	Fig. 15. Schematics for temperature-dependent carrier transition in p-type Hg0.7Cd0.3Te with Ea ∼ 11 meV and Nc ∼ 1 × 1016 cm−3: (a) T < 26 K, (b) 26 K < T < 90 K, and (c) T > 90 K.