The refractive index dispersion of Hg1−xCdxTe by infrared spectroscopic ellipsometry

Infrared Physics & Technology 42 (2001) 77±80

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The refractive index dispersion of Hg1 xCdx Te by infrared spectroscopic ellipsometry Zhiming Huang *, Junhao Chu National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, 420 Zhong Shan Bei Yi Road, Shanghai 200083, People's Republic of China Received 20 February 2000

Abstract The refractive indices of Hg1 x Cdx Te (x ˆ 0:276, 0.309, and 0.378) bulk samples in the region below, in, and above the fundamental band gap have been measured by infrared spectroscopic ellipsometry at room temperature. A refractive index peak, in which the corresponding energy equals approximately the band gap energy, is observed for each refractive index spectrum with di€erent compositions. Above the band gap, the refractive index drops quickly near the gap, then decreases slowly as photon energy increases. The refractive index n above the band gap is found to follow the Sellmeier dispersion relationship n2 …k† ˆ A ‡ B=k2 ‡ C=k4 ‡ D=k6 as a function of the wavelength of light k. Ó 2001 Published by Elsevier Science B.V. PACS: 78.20.Ci; 07.60.Fs

1. Introduction Ternary compound mercury cadmium telluride Hg1 x Cdx Te (MCT), being an important quantum infrared detector and of interest also from a fundamental point of view, has brought about a lot of investigations. Its infrared optical constants in the region close to the fundamental band gap are signi®cant to design and analyze the MCT-based optoelectronic devices. However, most of the infrared optical studies have been limited to the analysis of the details of absorption mechanisms and consequently reported more about the absorption coecient, but less about the refractive index [1±5]. *

Corresponding author.

The refractive index of MCT in the infrared region can be derived from the spacing of measured interference fringes [1±3], or by means of the Kramers±Kronig (KK) relationship [5]. Unfortunately, only the refractive index below the band gap can be determined by using these techniques, due to the strong absorption coecient above the band gap region. To our knowledge, there is no report on the refractive index spectrum above the band gap energy for MCT materials. Spectroscopic ellipsometry is an accurate method and it is widely used to determine optical constants in near-ultraviolet, visible, and near-infrared range (6±1:5 eV) [6,7]. The complete optical constants (n and k) can be obtained synchronously by this technique without KK transformation. The purpose of this paper is to investigate the refractive indices of MCT bulk samples with x ˆ 0:276,

1350-4495/01/$ - see front matter Ó 2001 Published by Elsevier Science B.V. PII: S 1 3 5 0 - 4 4 9 5 ( 0 1 ) 0 0 0 5 9 - 7

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Z. Huang, J. Chu / Infrared Physics & Technology 42 (2001) 77±80

0.309, and 0.378 below, in, and above the fundamental band gap by infrared spectroscopic ellipsometry (IRSE).

2. Principle and experiments Spectroscopic ellipsometry measures the complex re¯ectance ratio q between the re¯ection coecients of r~p and r~s for the light polarized parallel and perpendicular, respectively, to the plane of incidence. By analyzing the state of the polarization of re¯ected light, one determines two parameters: tan w and cos D, which are related to q by qˆ

~rp ˆ tan w exp…iD†: r~s

…1†

The dielectric function  ˆ 1 ‡ i2 of a sample can be calculated by using an ideal two-phase model [8]: "  2 # 1 q 2 2 2  ˆ a sin /0 ‡ sin /0 tan /0 ; …2† 1‡q where a is the dielectric function of a transparent ambient without consideration of the possible presence of overlayers, and /0 is the angle of incidence. Then the refractive index and extinction coecient are obtained as follows: rq   1 n ˆ p 21 ‡ 22 ‡ 1 ; 2 …3† rq   1 k ˆ p 21 ‡ 22 1 : 2 The samples investigated were prepared by a modi®ed Bridgman method and the as-grown samples were afterwards annealed in Hg vapor to form n-type crystals. The surfaces of the MCT samples to be measured by the IRSE were mechanically polished, and the back sides were roughed using silicon carbide sandpaper to suppress the component of beam which was re¯ected from the back sides of the samples. Transmission spectra of the samples were recorded by a PE983 infrared spectrophotometer.

Spectroscopic ellipsometric measurements were carried out by an automatic infrared spectroscopic ellipsometer by synchronous rotation of the polarizer and analyzer with a speed ratio of 1:1 [9] at an angle of incidence 73°. A 1000 W water-cooled Globar lamp was used as the light source, and the spectroscopic ellipsometric measurements were carried out in air over a 0.1±0.5 eV energy range. The probe beam diameter size was / ' 4 mm. The absolute value of the measured refractive index was accurate to 1% in the measurements.

3. Results and discussion Alloy compositions of the samples are determined by ®tting the recorded transmission spectra. The transmission spectrum of one MCT bulk sample is shown, as an example, in Fig. 1. By ®tting the region near the absorption edge of transmission spectrum using the empirical formulas of MCT on energy gap and absorption rules in Refs. [10±12], the composition x ' 0:309 is obtained for this sample. Fig. 2 shows the measured refractive indices n of MCT bulk samples with x ˆ 0:276, 0.309, and 0.378 versus photon energy in the infrared region (top panel) by IRSE using a two-phase model (air/ MCT). Thin overlayers, such as oxides and microscopic roughness, on the sample surface are not

Fig. 1. The transmission spectrum of a MCT bulk sample at room temperature. The region near the absorption edge of transmission spectrum is ®tted to obtain sample composition.

Z. Huang, J. Chu / Infrared Physics & Technology 42 (2001) 77±80

Fig. 2. The refractive indices (top) of the MCT bulk samples with x ˆ 0:276, 0.309, and 0.378 measured by IRSE in the range below, in, and above the band gap at room temperature. The extinction coecients (bottom) are also presented above the band gap.

to be considered. We ®nd in the measurements ®nite overlayers mainly a€ected extinction coecient, therefore the optical constants are reported as observed without correction made for possible surface overlayers or damage e€ects. Below the band gap, due to the back sides of the samples were roughed, the re¯ection of light beam from back sides of the samples and its contribution to the refractive index are very small, reducing the refractive index 1% by estimation. There is no correction to the value of the refractive index below the band gap due to back re¯ection contribution. As shown in Fig. 2, we obtain the refractive index not only below the band gap, but also in and above the energy gap for di€erent compositions. A peak, whose energy position corresponding approximately to the band gap energy, is observed in the refractive index curve for each composition, which can be understood according to the following KK analysis:  0  Z c 1 da…m0 † m ‡m n…m† ˆ 1 ‡ log …4† dm0 ; p 0 dm0 m0 m where m0 , m are frequencies of light, c is the light velocity, and a…m0 † is the absorption coecient at

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frequency m0 . As it is well known, a complete intrinsic absorption spectrum includes not only the Urbach exponential-absorption edge, which results from interactions other than band-to-band transitions, such as electron hole, electron phonon, and electron impurity transitions, but also includes the Kane region that results from optical transitions of electrons from the valence band to the conduction band. They obey di€erent absorption rules [13]. In the energy region near the absorption edge, the value of da…m0 †=dm0 goes up and the refractive index increases as photon energy increases. However, when photon energy reaches the gap energy, the absorption curve changes its slope and becomes ¯atter, so the value of da…m0 †=dm0 decreases above the gap energy. Thus, a peak appears in the refractive index curve. In terms of the energy position of the refractive index peak shown in Fig. 2, the fundamental band gap is approximately 0.275, 0.317, and 0.414 eV, which is very near the approximate value 0.273, 0.318, and 0.413 eV by the empirical formula in Ref. [10] for the composition x ˆ 0:276, 0.309, and 0.378, respectively. Moreover, the refractive index above the band gap drops quickly near the gap then decreases slowly as energy increases. Extinction coecients k above the band gap are also presented in Fig. 2 (bottom panel) for x ˆ 0:276, 0.309, and 0.378. The extinction coecient k ' 0 is assumed in the region below the

Fig. 3. Measured and ®tted refractive index spectra above the band gap for MCT bulk samples with x ˆ 0:276, 0.309, and 0.378.

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Z. Huang, J. Chu / Infrared Physics & Technology 42 (2001) 77±80

Table 1 Fitting parameters for the refractive indices of MCT bulk samples above the band gap with Sellmeier form dispersion relationship: n2 …k† ˆ A ‡ B=k2 ‡ C=k4 ‡ D=k6 Composition x

A

0.276 0.309 0.378

13.219 14.193 18.728

B

C 33.208 57.099 134.941

143.517 338.827 759.160

band gap due to very small values in that region [14,15]. The extinction coecient k drops with energy decreasing approach to the band gap in the Kane region, which is in agreement with that from the intrinsic absorption spectroscopy [13]. The refractive index spectra of MCT above the band gap are plotted separately in Fig. 3 as a function of the wavelength of light. We analyze these experimental data using a Sellmeier type dispersion relationship: n2 …k† ˆ A ‡ B=k2 ‡ C=k4 ‡ D=k6 ;

…5†

where A, B, C, and D are the ®tting parameters, and k is the wavelength of light (in lm). The ®tted refractive index spectra, simulated with the best-®t model parameters, which are summarized in Table 1, are shown by solid lines in Fig. 3. The ®t was done by minimizing the mean-square error r2 . An excellent ®t is found between the simulation and the experimental data. 4. Summary In conclusion, we have measured the refractive index dispersion of MCT (x ˆ 0:276, 0.309, and 0.378) bulk samples by IRSE below, in, and above the band gap at room temperature. It shows a refractive index peak near the band gap energy for each composition, which can be accounted for based on KK relationship. The refractive index above the band gap drops quickly near the gap, then decreases slowly as energy increases. The energy of the band gap obtained from the refractive index peak is in good agreement with that from transmission spectrum. Above the band gap,

D 191.698 693.247 1506.012

r 0.012 0.010 0.006

the refractive index is ®tted to a Sellmeier form dispersion relationship.

Acknowledgements The authors would like to acknowledge Profs. Guoshen Xu, Guoliang Shi and Ms. Huamei Ji and Dr. Yong Chang for their helpful technique assistance. This work is supported by the National Natural Science Foundation of China (grant no. 69738020).

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