Infrared Absorption and its Sources of CdZnTe at Cryogenic Temperature

Cadmium zinc telluride (CdZnTe) is a compound semiconductor of the II-VI type, commonly used as X-ray detectors Eisen1998 or substrates for the growth of epitaxial layers of mercury cadmium telluride (MCT) for infrared detector arrays Norton2002 . Large-size single-crystal CdZnTe growth techniques have been developed for such applications. Single-crystal ingots of CdZnTe with 5-inch diameter are now commercially available, with 6-inch crystals in the experimental stage Noda2011 .

CdZnTe is also promising as an infrared optical material with wavelengths between 5–20 $\mu$m. In general, the electronic and lattice absorptions characterize intrinsic absorption, which is the immutable absorption even for pure semiconductors Deutsch1975 . CdZnTe has little intrinsic absorption in the infrared wavelength range. Also, CdZnTe has extrinsic absorption, such as free-carrier absorption due to impurities and attenuation due to Te precipitates Noda2011 ; Sarugaku2017 . As a result, we anticipate that CdZnTe can be used as an infrared optical material by controlling its extrinsic properties (e.g., impurity or Te precipitates).

In addition, these infrared materials are frequently used in low-temperature environments to reduce thermal background radiation, particularly in astronomical observation optics (e.g., SPICA Mid-Infrared Instrument Wada2020 on board the SPICA mission^aaaSPICA had been one of the candidates for the fifth M-class mission in the ESA Cosmic Vision but was canceled on financial grounds in October 2020. Nakagawa2020 ; Roelfsema2018 ). As a result, the ability of infrared materials to transmit light at low temperatures is essential for astronomical applications.

An immersion grating is an optical material application of CdZnTe ikeda2015a . Immersion gratings are diffraction gratings with a grooved surface immersed in a high-refractive-index material Leitner1975 ; Marsh2007 . CdZnTe is an attractive material for immersion grating at wavelengths of $\lambda=$10–20 $\mu$m due to its high-refractive index ($n\sim 2.7$) and transparency Sukegawa2012 ; Kaji2014 . Owing to its high-refractive index $n$, an immersion grating can be downsized $1/n$-sized in length compared to conventional gratings. In size-constrained situations, the $1/n$-downsizing of a grating has a significant impact on the design of a compact optical system (e.g., astronomical satellites, systems in cryostat dewars). CdZnTe-immersion grating is expected to be applied in space telescopes Sarugaku2012 .

The room-temperature absorption coefficient in infrared wavelengths is known to be resistivity dependent. Kaji et al. Kaji2014 investigated the absorption coefficient of CdZnTe crystals with resistivities of $\rho=3.5\times 10^{10}~{}{\rm\Omega cm}$ and $\rho\sim 1\times 10^{2}~{}{\rm\Omega cm}$ at room temperature. They discovered that the absorption coefficient of low-resistivity CdZnTe was higher than that of high-resistivity CdZnTe and increased with wavelength at $\lambda=$ 5–20 $\mu$m. This high absorption is considered to be caused by free-carrier absorption Deutsch1975 ; Kaji2014 . When low-resistivity CdZnTe is cooled down to cryogenic temperature, the free-carrier absorption coefficient becomes smaller than the coefficient at room temperature due to free-carriers freeze-out. Therefore, low-resistivity CdZnTe, which is more readily available than high-resistivity CdZnTe, is expected to be suitable for cryogenic infrared materials. However, because few previous studies on the optical performance of CdZnTe at low temperatures, absorption causes in CdZnTe at cryogenic temperature are unknown. The optical performance of low-resistivity CdZnTe must be studied in order to develop cryogenic infrared materials (e.g., immersion gratings ikeda2015a ).

In this paper, we investigate the process for mid-infrared photon absorption by measuring the temperature dependence of the absorption coefficient of CdZnTe in the temperature range of $T=8.6$–300 K. We expect cryogenic absorption coefficients of CdZnTe crystals to be predictable from room-temperature physical properties after revealing the possible processes for the mid-infrared photon absorption.

This section describes the method used to measure the absorption coefficient. First, we describe the derivation method of the absorption coefficient from transmittance measurements. Taking into account the multiple reflections, we express the total transmittance $\tau$ as follows:

where $\alpha$ is the absorption coefficient, $R=(n-1)^{2}/(n+1)^{2}$ is the Fresnel surface reflectivity, and $t$ is the sample thickness Sarugaku2017 . We can estimate the absorption coefficient by measuring the transmittances ($\tau_{1},~{}\tau_{2}$) of samples made of the same material but with different thicknesses ($t_{1},~{}t_{2}$) as follows:

In this case, we assume the common surface reflectivity $R$. The term $X$ arises from the effect of the multiple reflections. In the case of the refractive index $n=2.7$, the $X/\alpha$ is less than 0.1 at any $\alpha$ value. If $X$ is included in the systematic error, $\alpha$ can be approximated as follows:

Therefore, $\alpha$ can be estimated without assuming the $R$ value. In this study, we use Eq. 4 to calculate $\alpha$ from the measured transmittance $\tau$.

Table I shows the specifications of the CdZnTe samples used in this study. JX Nippon Mining & Metals Corporation produced the ${\rm Cd_{0.96}Zn_{0.04}Te}$ single crystals used in the measurements. The vertical gradient freezing (VGF) method is used to make the CdZnTe ingot. In the main text, the conductivity is controlled to $p$-type for the ingot and $n$-type for Appendix A. The substrates were then cut from the ingot. To confirm whether the predicted change in absorption coefficient with temperature exists, we controlled the resistivity to the same order ($\rho\sim 10^{2}~{}{\rm\Omega cm}$) as the low-resistivity CdZnTe measured by Sarugaku et al. Sarugaku2017 . The ingot was then annealed to reduce scattering caused by Te precipitates by reducing precipitate size Noda2011 . The incident and exit surfaces are polished with a surface roughness of $Ra<$1 nm to reduce scattering loss on the surface, where $Ra$ is the calculated average roughness. To derive the absorption coefficient from the thickness dependence of the transmittance, samples with two types of thicknesses, lowR-t1 and lowR-t10, are taken from the same ingot.

Generally, infrared transmittance is measured using a Fourier transform spectrometer (FTS). However, commercial FTS products have numerous constraints, making it practically difficult to adjust the position of the sample cooling stage. In addition, for thick and high-refractive-index ($n$) substrates such as CdZnTe, transmittance measurement with a typical uncollimated FTS may result in significant systematic uncertainty due to the defocus effect Kaji2014 . Installing a thick and high-$n$ substrate in the sample compartment would lengthen the optical path and shift the detector’s focus position backward. Furthermore, the focal position is wavelength dependent due to the wavelength dependence of the refractive index $n$. Because of this, defocus large systematic errors in transmittance measurement would occur.

We built an original measurement system on an optical bench using a collimated beam and a cryostat to solve the adjustment difficulty and the defocus problem. We anticipate that the defocus effect will not be an issue by irradiating the collimated beam with the sample Kaji2014 . Figure 1 shows the originally developed measurement system and Table II summarizes the system’s specifications. To irradiate samples, we use a globar lamp (1 in Fig. 1; SLS303, Throlabs Japan Inc.) as an infrared light source. The lamp’s irradiated beam is guided by a polycrystalline infrared fiber (3) and is recollimated with a lens (4). We can change the wavelength of the collimated beam by mounting four bandpass filters ($\lambda=6.45,~{}10.6,~{}11.6,~{}15.1~{}\mu$m; listed in Table II) in the filter wheel. To pass through the sample-holder aperture ($\phi 5$ mm), the infrared light beam is adjusted to $\phi 2$ mm with an aperture (7). To monitor the time variation, we split the incident beam by the beam splitter (8), and the reflected beam B is focused on a Peltier-cooled MCT detector (13; PVMI-4TE-10.6-1x1-TO8-wZnSeAR-35; VIGO system S.A.). Beam A is transmitted to the sample (11) with the incident angle of $\sim 0^{\circ}$ and focused on another liquid-nitrogen (${\rm LN_{2}}$) cooled MCT detector (17: IOH-1064, Bomem inc.) to measure the transmitted-light power. We use an optical chopper (5; model 300 CD, Scitec instruments) with a frequency of $\sim 1$ kHz and lock-in amplifiers (SR830, Standard Research Systems) connected to the detectors because the incident beam to the sample is relatively faint ($\sim 10^{-5}~{}{\rm W~{}cm^{-2}}$ in the 10.6 $\mu$m band right after the aperture 7).

We use a cryostat with a two-stage Gifford-Mcmahon cryocooler (PS24SS; Nagase & Co., Ltd) to cool a sample to cryogenic temperature. Furthermore, we attach anti-reflective-coated (AR-coated) ZnSe windows with thicknesses of 5 mm and 1 mm to the vacuum chamber and the radiation shield in the chamber, respectively, to transmit the mid-infrared beam. To avoid thermal conduction, we reduce the gas pressure inside the chamber to $<10^{-2}$ Pa. A built-in calibrated Si-diode sensor measures the temperature of the cold head. To stabilize the temperature during measurement, we install a heater near the cold head. We prepare two types of holders to cool samples: one for the thick sample and the other for the thin sample. The details of the holders are described in Appendix B.

Next, we describe the measurement procedure. A sample’s transmittance $\tau$ is calculated as

where $V_{x,{\rm smp}}~{}(x=A$ or $B)$ is the power detected on the detector of the beam $x$ side with the sample and $V_{x,{\rm ref}}$ is the power detected without the sample. To reduce the effect of time variation in incident light powers, we measure powers $V_{\rm A,smp}$ and $V_{\rm B,smp}$ simultaneously, as well as $V_{\rm A,ref}$ and $V_{\rm B,ref}$. We measure the $V_{\rm A,ref}(\lambda)/V_{\rm B,ref}(\lambda)$ at 300 K because the denominator $V_{\rm A,ref}/V_{\rm B,ref}$ is a constant value against temperature change. We measure the transmittance of two samples at the four bands described in Table II.

We cool the samples at a rate of $<6$ K min^-1 to reduce thermal stress on the sample. During the transmittance measurement, the temperature of the cold head is controlled within $\pm 0.1$ K by using a heater controller. Because thermal shrink affects the beam vignetting, it is necessary to optimize the beam alignment during the measurement. Also, because sample’s position shifts by $\sim 1$ mm due to thermal shrinkage of the cold-head shaft, the beam power measured at the aperture may be vignetted at $\sim 3\%$. Thus, at each measurement temperature, we adjust the stages $S_{1}$, $S_{2}$, and $S_{3}$ (see Fig. 1) in two vertical directions to the optical axis to allow the beam to pass through the center of the holder aperture. Subsequently, because the beam is collimated, the adjustment does not affect the focal length. As a result, we can adjust the beam position by adjusting the three stages. We measure the transmittance of thin and thick samples at various temperatures ranging from about $T=300$ K to the lowest temperature ($8.6$ K; see the following section).

Figure 2 shows the absorption coefficients $\alpha$ of the CdZnTe at $\lambda=6.45$, 10.6, 11.6, and 15.1 $\mu$m from room temperature to a cryogenic temperature at $T=8.6$ K.

We calibrate the systematic temperature error caused by the Seebeck effect by averaging the measured temperatures with the voltage polarity swapped. Based on the measurement system’s specification accuracy (model 218, Lakeshore inc.), we estimate the temperature uncertainty as $\Delta T=10,~{}5,~{}2,~{}1,~{}0.3,~{}0.05~{}$K at $T\sim 300,~{}200,~{}100,~{}50,~{}8.6$ K, respectively.

The uncertainty of the measured absorption coefficient is mainly caused by the reproducibility of optimizing the beam alignment described in the previous section. We hence assume that the reproducibility is the same for all cases of temperatures, wavelengths bands, and samples because we perform the stage adjustments following a similar approach. We measure the 1$\sigma$ reproducibility of the transmittance $\Delta\tau/\tau=0.011$ at 300 K and apply it to all the measured $\tau$. From the error propagation law using Eq. 4, the 1$\sigma$ uncertainty of $\alpha$ is estimated as $\Delta\alpha=0.016~{}{\rm cm^{-1}}$.

As shown in Fig. 2, the measured $\alpha$ ranges from 0.3–0.5 ${\rm cm^{-1}}$ at $T=300$ K and from 0.4–0.9 ${\rm cm^{-1}}$ at $T=8.6$ K. At each temperature, the absorption coefficient $\alpha$ at the longer wavelength is larger than the value at the shorter wavelength. At $T=100$–300 K, the $\alpha(\lambda=6.45~{}{\rm\mu m})$ decreases with cooling, whereas the $\alpha(\lambda=15.1~{}{\rm\mu m})$ increases. In the temperature range of $T=100$–300 K, the temperature dependences of $\alpha(\lambda=10.6~{}{\rm\mu m})$ and $\alpha(\lambda=11.6~{}{\rm\mu m})$ are small compared to the uncertainty. At all measured wavelengths, the absorption coefficient $\alpha$ increases by 16–40% from $T=100$ K to $T=50$ K. At $T<50$ K, the temperature dependence of the $\alpha$ becomes small. The dependence of the absorption coefficients on temperature is discussed in the next section.

The result is then compared to the free-carrier expectation Sarugaku2017 . The absorption rate caused by free carriers is proportional to the free carrier’s density. At low temperatures, the carrier density is proportional to $f(T)=\exp(-E_{a}/2k_{B}T)$, where $E_{a}$ is the energy separation of the donor or acceptor level from the conduction or valence band kittel1976 and $k_{B}$ is the Boltzmann constant. If we assume that $E_{a}$ of CdZnTe is consistent with that of CdTe ($E_{a}=60$ meV; Ahmad2015 ) for simplicity, cooling from $T=300$ K to $T<50$ K reduces the free-carrier density by less than $f(T=50~{}{\rm K})/f(T=300~{}{\rm K})\sim 0.003$. The proportional relationship would also reduce the free-carrier absorption coefficient by less than $\sim 0.003$ times. Even for the case of multi-impurity levels, free-carriers are estimated to be frozen out because the reported acceptor levels of CdTe are $\sim 60$ meV or $\sim 150$ meV Ahmad2015 ; molva1984 . In contrast to the free-carrier expectation, the measured $\alpha$ increases by about 1.3–1.8 times from $T=300$ K to $T=8.6$ K Sarugaku2017 . In the following section, we discuss this apparent inconsistency.

In this section, we discuss absorption causes in CdZnTe. As shown in the previous section, our result reveals that the $\alpha$ increases at the cryogenic temperature, contrary to the free-carrier expectation. This disparity suggests that, in addition to free-carrier absorption, other causes influence the absorption coefficient.

We measured the transmittance of CdZnTe substrates with two different thicknesses and estimated the absorption coefficient $\alpha$ in the $\lambda=6.45$, 10.6, 11.6, and 15.1 $\mu$m bands at $T=8.6$–300 K. At $T\sim 300$ K, the estimated $\alpha$ range is $\alpha=0.3$–0.5 ${\rm cm^{-1}}$ which increases to $\alpha=0.4$–0.9 ${\rm cm^{-1}}$ at cryogenic temperatures ($T=8.6\pm 0.1$ K). Based on the physical absorption model, we propose that the dominant absorption cause at $T=$ 150–300 K is attributed to free holes: the dominant absorption cause at cryogenic temperature is attributed to trapped holes. Moreover, we discuss a method to predict the CdZnTe absorption coefficient at cryogenic temperature based on the room-temperature resistivity.

The authors declare that they have no conflict of interest.

We thank Mr. A. Noda and Dr. R. Hirano of JX Nippon Mining & Metals Corporation for valuable comments. We appreciate members of the Laboratory of Infrared High-resolution spectroscopy (LIH) in Kyoto Sangyo University for informative advice on immersion grating and experiments for its material selections. This research is a part of conceptual design activity for the infrared astronomical space mission SPICA, which was a candidate for the ESA Cosmic Vision M5 and JAXA strategic L-class mission. We appreciate the production of the holders and technical support by the Instrument Development Center in Nagoya University. We are grateful for the technical assistance to construct the measurement system by Mr. R. Ito. We appreciate Dr. J. Kwon and Mr. R. Doi for their supports in preliminary experiments prior to this study. H.M. is supported by the Advanced Leading Graduate Course for Photon Science (ALPS) of the University of Tokyo.

As discussed in the main text, the absorption coefficient of a higher-resistivity CdZnTe is lower than that of a low-resistivity CdZnTe. We measure the absorption coefficient of a high-resistivity-type CdZnTe to see if it has low absorption at cryogenic temperatures.

First, we describe the high-resistivity CdZnTe sample and the measurement method. As listed in Table IV, the samples in this appendix are $n$-type high-resistivity ($\rho>10^{10}~{}{\rm\Omega cm}$) CdZnTe substrates, while those in the main text are $p$-type low-resistivity ($\rho\sim 10^{2}~{}{\rm\Omega cm}$) CdZnTe substrates. We prepare thin-type and thick-type samples, highR-t1 and highR-t10. The other conditions (surface roughness, Te-precipitate size, manufacturer) are the same as those described in the main text for samples. It is worth noting that the highR-t1 and highR-t10 are cut from different ingots. However, because they are manufactured in the same way, we assume that their absorption coefficients and reflectivities are similar. The measurement method is the same as that described in the main text.

Next, we describe the measurement result of the high-resistivity CdZnTe. Figure 5 shows the $\alpha$ of the high-resistivity CdZnTe at each temperature and wavelength. Also, because all the measured $\alpha$ are neither significantly above nor below zero, we set the 5$\sigma$ upper limits of the $\alpha<0.11~{}{\rm cm^{-1}}$. The $\alpha$ of the high-resistivity CdZnTe is lower than those of the low-resistivity one ($\alpha>0.35~{}{\rm cm^{-1}}$) in the main text at all the measured wavelengths and temperatures.

Following that, we compare our result with the previous result at room temperature. Kaji et al. Kaji2014 revealed that CdZnTe with lower resistivity absorbed more at room temperature. The room temperature $\alpha$ of the CdZnTe with a resistivity of $\rho=3.5\times 10^{10}~{}{\rm\Omega cm}$ measured by them is less than $0.01~{}{\rm cm^{-1}}$in the wavelength range of $\lambda=$ 6.45–15.1 $\mu$m. The room-temperature absorption coefficient measured by them and that measured by us are consistent, although we can only restrict the $\alpha$’s upper limit. In addition, our result reveals that CdZnTe with lower resistivity has higher absorption even in the temperature range of 8.6–300 K, whereas they revealed this relation only at room temperature ($T\sim 295$ K).

Next, we compare the high-resistivity CdZnTe with the $\alpha$ prediction based on room-temperature resistivity. As discussed in the main text, the trapped-carrier absorption coefficient is inversely proportional to resistivity and mobility. According to the model, the main absorption cause is trapped-carrier absorption. Because the low-resistivity CdZnTe is $p$-type and the high-resistivity CdZnTe is $n$-type, we consider the absorption due to electrons trapped at the donor level. We assume that electron mobility is the same as in CdTe ($\sim 700~{}{\rm cm^{2}V^{-1}sec^{-1}}$, wakaki2007 ). We also assume that trapped electron absorption follows the same order as trapped-hole absorption. Under these assumptions, the estimated absorption coefficient due to trapped electrons is negligible ($\alpha<10^{-9}~{}{\rm cm^{-1}}$). As a result, we consider the lattice absorption $\alpha_{\rm lattice}$ and Te-precipitates attenuation $\alpha_{\rm Te}$, as dominant causes, which are ignored in the main text. As discussed in the main text, the sum of $\alpha_{\rm lattice}$ and $\alpha_{\rm Te}$ at $T$=8.6 K is considered to be less than that at $T=$ 300 K ($\alpha<0.006~{}{\rm cm^{-1}}$ at $\lambda=6.45$–15.1 $\mu$m). Therefore, we can predict that the $\alpha$ of the high-resistivity CdZnTe at 8.6 K is $\alpha<0.006~{}{\rm cm^{-1}}$. Our result is consistent with this prediction, although the $\alpha$ has such a large uncertainty that we can only obtain the upper limit of the $\alpha$. A more precise measurement system is needed to reveal the temperature dependence of the $\alpha$ of high-resistivity CdZnTe because the $\alpha$ is lower than the uncertainty of our measurement system.

Figure 6 shows the sample holders for thick and thin samples. To secure thermal contact, we screw the top of the thick-sample holders to the cold head surface with screws and hold them from the side with a copper plate and indium sheets. To monitor the temperature of the sample, we place a calibrated Cernox temperature sensor (CX-1030-SD-HT-1.4L; Lakeshore inc.) on the side of the sample. A temperature monitor (model 218, Lakeshore inc.) is used to monitor the sensor signal. On the other hand, the thin sample is clamped between the thin-sample holder and the holding plate. We screw the thin-sample holder to the cold head and insert indium sheets between the sample and the thin-sample holder to secure thermal contact, To monitor the sample temperature, we use the same temperature sensor used in the thick-sample case on the holder.