CdTe epitaxial films with graded band gap

Infrared Physics & Technology 42 (2001) 61±67

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Optical and photoelectrical properties of Hg1 x Cdx Te/CdTe epitaxial ®lms with graded band gap Z.F. Ivasiv, V.V. Tetyorkin *, F.F. Sizov Institute of Semiconductor Physics, Ukrainian Academy of Sciences, Nauki Avenue 45, Kiev 03028, Ukraine Received 15 March 1999

Abstract The infrared transmission and photoconductivity spectra of HgCdTe epitaxial ®lms with graded band gap were investigated both theoretically and experimentally. Theoretical calculations were performed in the framework of the WKB approximation. The composition pro®le has been obtained from a ®tting procedure. In order to reduce the total number of ®tting parameters as well as to improve accuracy of this procedure the di€erential of the transmission versus photon energy curves was used. The best ®t was obtained for an exponential composition gradient. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Epitaxial ®lm; Graded band gap; Optical transmission

1. Introduction Most modern IR photodetectors based on Hg1 x Cdx Te narrow-gap semiconductors are manufactured from LPE ®lms grown on CdTe or CdZnTe substrates. Grading of the alloy composition seems to be an inherent feature of Hg1 x Cdx Te LPE ®lms grown both on lattice matched CdZnTe and lattice unmatched CdTe substrates. The grading a€ects the physical properties of the ®lms as well as the performance of the IR devices based on them [1±6]. Despite the fact that e€ect of composition grading on the optical, photoelectrical and electrical properties of Hg1 x Cdx Te LPE

*

Corresponding author. E-mail address: [email protected] (V.V. Tetyorkin).

®lms has been investigated in several papers [7±12], some problems still exist. In LPE ®lms with graded band gap optical absorption increases with frequency above the fundamental edge due to depth dependence of the energy gap Eg (z). If the spatial variation of Eg on a distance scale of the light wavelength is weak enough, the WKB approximation can be used for theoretical calculations. The spectral dependence of the optical density is [13±15] Z d D…hx† ˆ a…hx; z†dz 0

Z ˆ

Eg

Eg

max

min

a…hx; Eg †

oz dEg ; oEg

…1†

where d is the thickness of a ®lm, a…hx; z† is the local absorption coecient, Eg min and Eg max is minimum and maximum energy gap at z ˆ 0 and z ˆ d, accordingly. It follows from Eq. (1) that the

1350-4495/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights revserved. PII: S 1 3 5 0 - 4 4 9 5 ( 0 1 ) 0 0 0 6 4 - 0

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Z.F. Ivasiv et al. / Infrared Physics & Technology 42 (2001) 61±67

dependence Eg (z) can be established if Eg min , Eg max and a… hx; Eg † are known. Choosing a gradient rEg =rz as the ®tting parameter, it is possible to calculate D… hx† as well as the spectral dependence of the optical transmission (see Appendix A). In application to LPE Hg1 x Cdx Te ®lms a similar problem was investigated in several papers [11, 12,16±18]. In Ref. [12] the value of Eg min and the thickness of the ®lm are considered to be known, and rEg =rz is assumed to be constant. In Ref. [11] an attempt to determine the parameters from the transmission spectra T … hx† was made. The composition pro®le x…z† was represented by an expression with three ®tting parameters. However, these parameters seem to be not independent. As was shown in Ref. [16], one can ®nd several groups of parameters to ®t experimental data rather well. In order to eliminate uncertainties in calculations the total number of ®tting parameters should be decreased. In the papers mentioned above simpli®ed model for the local absorption coecient have been used. One should note that, as a rule, a… hx; Eg † in nonuniform ®lms is assumed to be the same as in the uniform bulk crystals [15]. Despite the fact that the band nonparabolicity can in¯uence optical absorption in Hg1 x Cdx Te [19], it has not been taken into account in studies carried out previously. However, even assuming exact knowledge of the local absorption coecient on the composition and frequency, one may not know how well the transmission spectrum is represented by the WKB approximation. The aim of this work is to clarify of IR transmission measurements for determination the band gap gradient as well as the precise form of the band gap pro®le in Hg1 x Cdx Te LPE ®lms.

system for data measuring and processing which enables quadratic noise smoothing of the measured curves. Because optical transmission exponentially depends on thickness d, surface roughness and departure from the planar geometry can in¯uence measured spectra. In order to reduce surface roughness, prior to measurements the ®lms were etched in HBr‡Br2 solution for approximately one minute. After etching the ®lms with mirror-like surface were investigated. To examine the in¯uence of the surface tilt, optical transmission was measured at di€erent spots of the ®lms using IR beams with di€erent cross-sections. It has been found that only at the peripheral parts of the ®lms can it in¯uence IR transmission spectra. These data were not used. Calculated and measured D…hx† and T …hx† curves are shown in Figs. 1±4. The calculations were carried out in accordance with a technique early developed for GaAlAs ®lms with graded band gap [15]. The spectral region was divided on three parts: hx 6 Eg min , Eg min 6 hx 6 Eg max , hx P Eg max . At photon energies hx < Eg the absorption coecient in Hg1 x Cdx Te obeys the Urbach rule [20]:   hx E0 a ˆ a0 exp ; …2† D

2. Experimental results and discussion The ®lms investigated were grown by the LPE method on (1 1 1)CdTe and Cd1 y Zny Te (y ˆ 0:03±0:04) substrates. Their thickness was ranged from 15 to 35 lm. The ®lms were p-type conductivity with a hole concentration …6±20†  1015 cm 3 . IR transmission spectra were recorded on a grating spectrometer supplied with computerized

Fig. 1. Experimental ( ) and calculated (Ð) spectral dependencies of the optical density at T ˆ 300 K. Curves 1 and 2 are calculated using the formulas for the absorption coecient obtained by Blue [19] and in (A.3), respectively.

Z.F. Ivasiv et al. / Infrared Physics & Technology 42 (2001) 61±67

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Fig. 2. Optical transmission spectra in HgCdTe/CdZnTe epitaxial ®lm at 300 K. Theoretical curves are calculated for linear (1) and exponential (2) band gap gradient for Eg min ˆ 0:155 eV, Eg max ˆ 0:190 eV. The thickness of the ®lm is 35 lm.

where a0 , E0 and D are determined experimentally from the study of the spectral dependencies of the edge of the fundamental absorption. In the present work, E0 was taken to be equal to Eg (z). The parameter D was determined from the slope of the measured T … hx† curves at  hx < Eg min. The value a0 was derived from the ®tting procedure for each sample separately. The best ®t was obtained for a0 ranging from 800 to 1500 cm 1 . In bulk crystals the absorption coecient is known to obey the law (2) at a 6 1000 cm 1 and a0 may depend on composition x [20]. In calculations a0 was assumed to be independent of the composition. The in¯uence of a0 on calculated data is shown in Fig. 4. In the second spectral region direct transitions for the photons with the energy  hx > Eg are added, and on the third region absorption occurs only due to direct transitions from the valence bands into the conduction band. For calculations appropriate formulas for the local absorption coecient obtained by Blue [19] were used. Also, calculations were carried out for absorption coef®cient previously used by Herrmann et al. [12] (see expression (A.3) in Appendix A). As is seen from Fig. 1, the low-energy part of the experimental curve is well described by both theories. At higher energies experimental data coincide better with the calculated curve obtained for expression (A.3). Optical density in this spec-

tral region is caused mainly by optical transitions from the heavy-hole valence band to the conduction band. The value of the e€ective mass of the heavy holes was assumed to be equal to 0.55m0 . Below only expression (A.3) was used for theoretical analysis. Two types of Eg (z) dependencies ± linear and exponential ± were chosen for calculations. The exponential dependence Eg (z) was approximated by: Eg …z† ˆ E0 ‡ a exp …z=b†;

…3†

where constants E0 , a and b were determined for z ˆ 0 and z ˆ d, provided that Eg min and Eg max are known. It is seen from Fig. 2 that in the samples with small band gap gradient calculated data are not very sensitive to the choice of Eg (z) dependence. However, this seems not to be the case for the sample with rather high gradient, Fig. 3(a) and (b). The following approach was used to estimate Eg min and Eg max values. In accordance with theory developed in Ref. [14], the second derivative 2 d2 D…hx†=d…hx† should have extremes at energies where density of states has features. At least two peculiarities are to be observed if Eg (z) is represented by smooth curve (Fig. 5). Obviously, the ®rst one is located at z ˆ 0. In absence of the transition region at the interface the second

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Z.F. Ivasiv et al. / Infrared Physics & Technology 42 (2001) 61±67

Fig. 3. Measured (1) and calculated (2,3) transmission spectra at 300 K (a) and 82 K (b) in HgCdTe/CdTe epitaxial ®lm. Curves 2 and 3 are calculated for exponential and linear band gap gradient, respectively, with parameters Eg min ˆ 0:162 eV, Eg max ˆ 0:268 eV (T ˆ 300 K) and Eg min ˆ 0:097 eV, Eg max ˆ 0:218 eV (T ˆ 82 K). Curves 4 are calculated for bulk crystal with Eg ˆ 0:162 and 0.097 eV at 300 and 82 K, respectively. The thickness of the ®lm is 15 lm.

peculiarity is located at z ˆ d, where density of states is signi®cantly changed. In the ®lms with the transition region the exact form of Eg (z) at the interface is unknown and its location can be de®ned within the accuracy of the thickness of this region. Typical spectral dependencies of the second derivatives of the optical density are shown in Fig. 6 for samples with di€erent values of the band gap gradient. It is seen that two extremes are observed for experimental curves. Their energies were identi®ed with minimum Eg min and maximum Eg max band gaps in the ®lm. It should be pointed out that Eg min and Eg max can be de®ned unam-

biguously for LPE ®lm without a transition region at the interface. In the opposite case Eg max means an e€ective band gap at the interface between the epitaxial layer and the substrate. If the band gap gradient increases the applicability of WKB approach becomes less obvious. Above all, in LPE ®lms the condition of applicability of WKB approach can be violated at the interface. However, the theory [14] predicts that the behavior of the second derivative is still preserved, except that its amplitude decreases. In order to analyze this situation, computer simulation for di€erent gradients was performed. If one compares data shown in Fig. 6(a) and (b), it is seen that in the sample with rather low band gap gradient experimental and calculated curves coincide well. The increase of the band gap gradient gives rise to disagreement between experimental and calculated data. For example, the best ®t between experimental and calculated curves T …hx† shown in Fig. 3(a) was achieved for the value Eg max ˆ 0:268 eV which exceeds Eg max ˆ 0:250 eV obtained from experimental dependence, Fig. 6(b). Also, the experimental curves have higher halfwidth values in comparison with calculated ones. Similar results were obtained previously [14] for LPE ®lms with linear band gap gradient. The disagreement between experimental and calculated spectra can arise from several reasons. A spread in transmission data may cause large ¯uctuations in second derivatives, some smoothing is required before di€erentiation. This may shift the position of the derivative peaks [14] as well as their halfwidth. The interface transition region may also a€ect both the amplitude and position of the derivative peak at energies close to Eg max . In theoretical calculation this region has not been taken into account. Using the data obtained at T ˆ 300 K and approximation (A.1) for Eg (x), x(z) dependencies were calculated, Fig. 7. Chemical composition was also determined independently on a cleaved samples using the local X-ray microanalyzer COMEBAX. Within the experimental errors the data measured agree with those obtained from the analysis of the T …hx† spectral dependencies. Gap pro®ling was also carried out by photoconductive spectra measurements combining with sequential removal of known thickness of a ®lm by

Z.F. Ivasiv et al. / Infrared Physics & Technology 42 (2001) 61±67

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Fig. 4. Optical transmission spectra in HgCdTe/CdTe epitaxial ®lm at 300 K. Theoretical spectra are calculated for the values of a0 ˆ 1500 (1), 1200 (2) and 800 (3) cm 1 , Eg min ˆ 0:177 eV and Eg max ˆ 0:350 eV, d ˆ 21 lm.

Fig. 5. Schematic energy diagram showing linear and exponential band gap grading in LPE Hg1 x Cdx Te ®lms without (a) and with (b) transition region at the interface.

chemical etching in Hbr‡Br2 solution. The gap was determined from the peak wavelength kp corresponding to the maximum of the normalized photoconductivity spectrum (Fig. 8). The data obtained from the photoconductivity and optical transmission spectra are not well correlated. The disagreement can originate from several causes. The value kp correlates well with the band gap value for bulk crystals without band gap grading [21]. But it is not the case for LPE ®lms with graded band gap. The disagreement is extremely pronounced for the ®lm thinned to approximately 3±4 lm. For this ®lm the in¯uence of the transition

region is more pronounced. Obviously, the transmission spectrum of a rather thick starting ®lm is less sensitive to the presence of the transition region. The composition x…z† dependencies found at room temperatures were used for calculation of T …hx† spectra at T ˆ 82 K, Fig. 3(b). As one can see, calculated and experimental curves agree well. Hence, by carrying out the analysis of T …hx† at room temperature it is possible to predict spectral dependence of the photoconductivity in Hg1 x Cdx Te ®lms with the band gap gradient at LN temperatures.

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Z.F. Ivasiv et al. / Infrared Physics & Technology 42 (2001) 61±67

Fig. 7. Composition pro®le obtained from the optical transmission (Ð), COMEBAX ( ) and photoconductivity ( ) measurements. The composition obtained from X-ray measurements are determined within experimental errors Dx ˆ 0:005.

Fig. 8. Photoconductivity spectra at 82 K measured for starting ®lm (1) and sequentially etched in HBr‡Br2 solution during 1 min (2) and 3 min (3). The thickness of the starting ®lm is 15 lm. Fig. 6. Experimental (1) and theoretical (2) spectra of the second derivative of the optical density at 300 K. Experimental data shown in (a) and (b) were derived from the optical transmission data shown in Figs. 2 and 3(a), respectively. Also shown is theoretical curve (3) for bulk crystal.

3. Conclusions From the investigation carried out one can conclude that the spectral dependencies of the optical transmission T … hx† in Hg1 x Cdx Te LPE ®lms with graded band gap are very sensitive to the absolute value of the band gap gradient as well

as to the form of the dependence Eg (z)-exponential or linear. It means that the investigation of the optical transmission allows one to make quantitative and qualitative analysis of the band grading in Hg1 x Cdx Te LPE ®lms. To a lesser degree optical transmission spectra are sensitive to the choice of the local absorption coecient. Experimental investigations of the spectral dependencies T …hx† performed at room temperatures allow one to calculate appropriate dependencies at LN temperatures with sucient accuracy. Additional theoretical and experimental investigations are

Z.F. Ivasiv et al. / Infrared Physics & Technology 42 (2001) 61±67

needed to clarify the in¯uence of the transition 2 region on T … hx† and d2 D…hx†=d… hx† spectra. Appendix A Dependence Eg …z; T † was taken from [22] Eg … z; T † ˆ

0:302 ‡ 1:93x

0:81x2

‡ 0:832x3 ‡ 5:32  10 4 …1   1822 ‡ T 3  : 255:2 ‡ T 2

2x† …A:1†

The transmission through the sample is given by [11]: T13 ˆ T2;3 ˆ

…1 1 …1

R1 †…1 H †T2;3 a1 ; R1 …1 H †R2;3 a21 R2 †…1 R3 †a2 ; 1 R 2 R3 … a 2 † 3

…A:2†

where a1 ˆ exp … D1 †, a2 ˆ exp … D2 †, D1 and D2 are the optical density for LPE and substrate accordingly. Subscripts 1±3 refer to interfaces air to LPE, LPE to substrate, and substrate to air, respectively. The re¯ection coecients R1 , R2 , R3
at three 2 interfaces are calculated from R ˆ ni nj =…ni ‡ 2 nj † . The local absorption coecient was taken from [12]: 8 h i1=2
2 i h 2 > 2 > a 1 ‡ 2 E = h x E … h  x † > 0 g g > > < 1 for a > 800 cm a…hx† ˆ 
 > > > 800 exp hx Eg1 =E0 > > : for a < 800 cm 1 …A:3† Parameters a0 , E0 , and Eg1 were assumed to be the same as in Ref. [12].

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