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Temperature dependence of the energy bandgap of HgInTe
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Infrared Physics & Technology 51 (2008) 256–258 www.elsevier.com/locate/infrared
Temperature dependence of the energy bandgap of HgInTe X.L. Zhang a
a,b,*
, W.G. Sun
a,b
, L.A. Kosyachenko c, L. Zhang
b
Northwestern Polytechnical University, 710072 Xi’an, Shanxi, People’s Republic of China Luoyang Optoelectronic Institute, 471009 Luoyang, Henan, People’s Republic of China c Chernivtsi National University, 058012 Chernivtsi, Ukraine
b
Received 24 April 2007 Available online 23 May 2007
Abstract Infrared transmission spectroscopy was employed to study the temperature dependence of the bandgap of mercury indium tellurium (MIT) alloys in the temperature range from 12 K to 300 K. Band-edge absorption curves in Hg(33x)In2xTe3 (x = 0.5) were fitted to the absorption equation to obtain absorption coefficients. Based on the experimental data, the relation between temperature and the energy bandgap of Hg3In2Te6 was experimentally determined and an analytical dependence was found. 2007 Elsevier B.V. All rights reserved.
Single-crystal Hg3In2Te6 (MIT) is a novel material for NIR photovoltaic detectors. The stoichiometric compound Hg(33x)In2xTe3 (x = 0.5) is an alloy of Hg3Te3 and In2Te3 that crystallizes in a defected zinc-blend structure [1,2]. In it the anion sites are occupied by Te ions, and the cation sites are occupied by Hg ions, In ions, and structural vacancies. The number of structural vacancies is proportional to the In2Te3 content, which strongly affects the properties of the crystals. Since the concentration of stoichiometric vacancies is high (about 1021 cm3), MIT crystal is electrically inactive to the introduced impurities. Other important properties of this material are also related to the special features of its structure. These properties include a high resistance of Hg3In2Te6 to ionizing radiation and the inertness of the surface to adsorption of atoms from atmospheric air. Finally, Hg3In2Te6-based photodiodes have a high quantum efficiency over a wide range of photon energies (0.74–3 eV) [3]. As a result, this material can be used in a wide range of applications [3,4]. In this letter, we report the temperature dependence of the bandgap of Hg3In2Te6 alloy. The relation between tempera* Corresponding author. Address: Luoyang Optoelectronic Institute, 471009 Luoyang, Henan, People’s Republic of China. Tel.: +86 379 63385422; fax: +86 379 63937441. E-mail address: [email protected] (X.L. Zhang).
1350-4495/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.infrared.2007.05.003
ture and the energy bandgap of Hg3In2Te6 was experimentally determined, and analytical dependences were found. The crystals were grown by the vertical Bridgman method. For testing the transmission spectra, the samples were affixed onto the substrate before rubbing, polishing, and etching. Direct mechanical polishing of the MIT wafers was not possible because MIT wafers easily break under mechanical deformation. A good result was obtained by affixing the MIT wafers onto suitable durable and conducting substrate using transparent glue and then performing mechanical and chemical polishing until the necessary wafer thickness was reached (0.3 mm). The transmission spectrum was obtained by taking the ratio of the power spectrum as measured with a sample in place to the background power spectrum as measured with no sample in place. A Hofman helium research Dewar with multiple windows was modified for use in this investigation. The spectrum of each sample and the background spectrum were calculated using the averaged results of 100 interferometer scans. The reported results are the averaged results of 50 such spectra. Fig. 1 shows the transmittance spectra of single-crystal Hg3In2Te6 taken at 300, 260, 220, 180, 140, 100, 60, 30 and 12 K. As can be seen, the 0.3 mm thick sample demonstrates quite good transmittance in the range from 1.7 to 5.6 lm.
X.L. Zhang et al. / Infrared Physics & Technology 51 (2008) 256–258 0.3
257
6 12 K
5 220K
12K
4 5
-2
α (10 cm )
300 k
3
2
Transmittance
300K
0.2
0.1
2 1
0.0 1
2
3 4 Wavelength (μm)
5
0 0.70
6
Fig. 1. Transmission spectrum for Hg3In2Te6 single-crystals at different temperatures (from bottom to top): 12, 60, 100, 180, 220, 260, 300 K.
The maximum transmittance of the sample approaches 0.3, suggesting very high quality and a low free-carrier concentration in the material. In terms of multiple reflections (with regard to interference), the optical transmittance of a sample with thickness d under normal incident light on a sample is given by [5] 2
T ¼
ð1 RÞ ead ; ð1 R2 Þe2ad
ð1Þ
where R is the reflection index from the crystal–air interface. The optical absorption curve for the given transmittance can be found by solving Eq. (1) for a: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 2 ð1 RÞ þ 4T 2 R2 þ ð1 RÞ 1 a ¼ ln : ð2Þ d 2T Here
0.71
0.72
0.73 0.74 h ν (eV)
0.75
0.76
0.77
Fig. 2. Absorption curves for MIT at different temperatures obtained using Eq. (2).
the temperature rises from 12 K to 300 K. Note that the room temperature value of Eg = 0.736 eV agrees with previously published data [6]. The temperature dependence of the bandgap of Hg3In2Te6 between 12 K and 300 K obtained from Fig. 2 is plotted in Fig. 3 with circles. The temperature dependence of the bandgap of different semiconductors has been described by different analytical expressions. Among them, Varshni’s equation is used most often to describe the nonlinear temperature dependence of the bandgap: Eg ðT Þ ¼ Eg ð0Þ
cT 2 : bþT
ð5Þ
The solid curve in Fig. 3 is the Eg(hv) dependence calculated using Eq. (5), which demonstrates the best fit with experimental data (the circles) when Eg(0) = 0.756 eV (the
2
ðn 1Þ þ j2 ðn þ 1Þ2 þ j2
;
ð3Þ
where n is the refractive index and j is the extinction coefficient. Although the reflection index depends on wavelength, our measurements show that the value of R within the narrow spectral range used for determining the value of the bandgap (hv Eg) can be assumed to be equal to 0.3 without introducing a large error. Since Hg3In2Te6 is a direct narrow-gap semiconductor [3], the dependence of the absorption coefficient on the photon energy at the bandgap edge follows the expression pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a ¼ a0 hv Eg ; ð4Þ where a0 is a value that can be assumed to be independent of the photon energy hv. Hence, to determine the Eg value, the dependence a(hv) should be plotted as a2 versus hv. In these coordinates, the curve a(hc) then takes the form of a straight line intersecting the x-axis at the point hv = Eg (Fig. 2). It follows from the figure that the energy bandgap Eg of Hg3In2Te6 decreases from 0.757 eV to 0.737 eV when
0.76
0.75
Eg (eV)
R¼
0.74
0.73
0.72 0
100
200
300
T (K)
Fig. 3. The bandgap Eg (eV) of Hg3In2Te6 at different temperatures. The circles are the experimental results; the solid and dashed lines are the dependences calculated using Eqs. (5) and (6), respectively.
258
X.L. Zhang et al. / Infrared Physics & Technology 51 (2008) 256–258
energy bandgap at T = 0 K), c = 3 · 104 eV K1 (an empirical constant), and b = 1050 K (the value associated with the Debye temperature). In the high temperature region, the temperature dependence of a semiconductor can be approximated by the linear equation [7] Eg ðT Þ ¼ Eg ð0Þ þ c0 ðT Þ;
ð6Þ
where c0 is the temperature coefficient of the semiconductor bandgap. The dashed line in Fig. 3 is the Eg(T) linear dependence described by Eq. (6), which virtually coincides with the experimental data in the room temperature region if Eg(0) = 0.7757 eV and c0 = 1.3 · 104 eV/K. Note that for Ge, the bandgap of which (0.67 eV at 300 K) is close to that of Hg3In2Te6, the temperature coefficient of the bandgap is equal to 3.7 · 104 eV/K [8]. Thus the temperature stability of a Hg3In2Te6 photodiode is much higher than that of a Ge photodiode. In summary, we have measured the temperature dependence of the bandgap of Hg3In2Te6 alloy. The optical transmission curves were measured at different tempera-
tures from 12 K to 300 K. The absorption curves were calculated, from which an empirical analytical expression describing the temperature variations of the energy bandgap of the alloy was obtained for the first time. References [1] P.M. Spencer, B. Ray, Phase diagram of the alloy system Hg3Te3– In2Te3, Brit. J. Appl. Phys. (J. Phys. D) 1 (1968) 299. [2] D. Weitze, V. Leute, The phase diagram of the quasibinary systems HgTe/In2Te3 and CdTe/In2Te3, J. Alloys Compd. 236 (1996) 229. [3] A. Malik, Manuela Vieira, Miguel Fernandes, Filipe Macarico, Zinaida M. Grushka, Near-infrared photodetectors based on HgInTe semiconductor compound, SPIE, vol. 3629. [4] G.G. Grushka, Z.M. Grushka, A.P. Bakhtinov, The electrical properties of Hg3In2Te6 compound, Ukr. Phys. J. 30 (1985) 304. [5] J. Chu, Narrow gap semiconduction of physics, Science Press, 2005 (in Chinese). [6] P.N. Gorlei, O.G. Grushka, An impurity band in Hg3In2Te6 crystals doped with silicon, Semiconductors 37 (2) (2003) 168. [7] J.I. Pankov, Optical Processes in Semiconductors, Prentice-Hall Inc., New Jersey, 1996, 1971, p. 456. [8] E.L. Dereniak, G.D. Boreman, Infrared Detectors and Systems, John Wiley & Sons Inc., New York, 1996, P298.
Infrared Physics & Technology 51 (2008) 256–258 www.elsevier.com/locate/infrared
Temperature dependence of the energy bandgap of HgInTe X.L. Zhang a
a,b,*
, W.G. Sun
a,b
, L.A. Kosyachenko c, L. Zhang
b
Northwestern Polytechnical University, 710072 Xi’an, Shanxi, People’s Republic of China Luoyang Optoelectronic Institute, 471009 Luoyang, Henan, People’s Republic of China c Chernivtsi National University, 058012 Chernivtsi, Ukraine
b
Received 24 April 2007 Available online 23 May 2007
Abstract Infrared transmission spectroscopy was employed to study the temperature dependence of the bandgap of mercury indium tellurium (MIT) alloys in the temperature range from 12 K to 300 K. Band-edge absorption curves in Hg(33x)In2xTe3 (x = 0.5) were fitted to the absorption equation to obtain absorption coefficients. Based on the experimental data, the relation between temperature and the energy bandgap of Hg3In2Te6 was experimentally determined and an analytical dependence was found. 2007 Elsevier B.V. All rights reserved.
Single-crystal Hg3In2Te6 (MIT) is a novel material for NIR photovoltaic detectors. The stoichiometric compound Hg(33x)In2xTe3 (x = 0.5) is an alloy of Hg3Te3 and In2Te3 that crystallizes in a defected zinc-blend structure [1,2]. In it the anion sites are occupied by Te ions, and the cation sites are occupied by Hg ions, In ions, and structural vacancies. The number of structural vacancies is proportional to the In2Te3 content, which strongly affects the properties of the crystals. Since the concentration of stoichiometric vacancies is high (about 1021 cm3), MIT crystal is electrically inactive to the introduced impurities. Other important properties of this material are also related to the special features of its structure. These properties include a high resistance of Hg3In2Te6 to ionizing radiation and the inertness of the surface to adsorption of atoms from atmospheric air. Finally, Hg3In2Te6-based photodiodes have a high quantum efficiency over a wide range of photon energies (0.74–3 eV) [3]. As a result, this material can be used in a wide range of applications [3,4]. In this letter, we report the temperature dependence of the bandgap of Hg3In2Te6 alloy. The relation between tempera* Corresponding author. Address: Luoyang Optoelectronic Institute, 471009 Luoyang, Henan, People’s Republic of China. Tel.: +86 379 63385422; fax: +86 379 63937441. E-mail address: [email protected] (X.L. Zhang).
1350-4495/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.infrared.2007.05.003
ture and the energy bandgap of Hg3In2Te6 was experimentally determined, and analytical dependences were found. The crystals were grown by the vertical Bridgman method. For testing the transmission spectra, the samples were affixed onto the substrate before rubbing, polishing, and etching. Direct mechanical polishing of the MIT wafers was not possible because MIT wafers easily break under mechanical deformation. A good result was obtained by affixing the MIT wafers onto suitable durable and conducting substrate using transparent glue and then performing mechanical and chemical polishing until the necessary wafer thickness was reached (0.3 mm). The transmission spectrum was obtained by taking the ratio of the power spectrum as measured with a sample in place to the background power spectrum as measured with no sample in place. A Hofman helium research Dewar with multiple windows was modified for use in this investigation. The spectrum of each sample and the background spectrum were calculated using the averaged results of 100 interferometer scans. The reported results are the averaged results of 50 such spectra. Fig. 1 shows the transmittance spectra of single-crystal Hg3In2Te6 taken at 300, 260, 220, 180, 140, 100, 60, 30 and 12 K. As can be seen, the 0.3 mm thick sample demonstrates quite good transmittance in the range from 1.7 to 5.6 lm.
X.L. Zhang et al. / Infrared Physics & Technology 51 (2008) 256–258 0.3
257
6 12 K
5 220K
12K
4 5
-2
α (10 cm )
300 k
3
2
Transmittance
300K
0.2
0.1
2 1
0.0 1
2
3 4 Wavelength (μm)
5
0 0.70
6
Fig. 1. Transmission spectrum for Hg3In2Te6 single-crystals at different temperatures (from bottom to top): 12, 60, 100, 180, 220, 260, 300 K.
The maximum transmittance of the sample approaches 0.3, suggesting very high quality and a low free-carrier concentration in the material. In terms of multiple reflections (with regard to interference), the optical transmittance of a sample with thickness d under normal incident light on a sample is given by [5] 2
T ¼
ð1 RÞ ead ; ð1 R2 Þe2ad
ð1Þ
where R is the reflection index from the crystal–air interface. The optical absorption curve for the given transmittance can be found by solving Eq. (1) for a: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 2 ð1 RÞ þ 4T 2 R2 þ ð1 RÞ 1 a ¼ ln : ð2Þ d 2T Here
0.71
0.72
0.73 0.74 h ν (eV)
0.75
0.76
0.77
Fig. 2. Absorption curves for MIT at different temperatures obtained using Eq. (2).
the temperature rises from 12 K to 300 K. Note that the room temperature value of Eg = 0.736 eV agrees with previously published data [6]. The temperature dependence of the bandgap of Hg3In2Te6 between 12 K and 300 K obtained from Fig. 2 is plotted in Fig. 3 with circles. The temperature dependence of the bandgap of different semiconductors has been described by different analytical expressions. Among them, Varshni’s equation is used most often to describe the nonlinear temperature dependence of the bandgap: Eg ðT Þ ¼ Eg ð0Þ
cT 2 : bþT
ð5Þ
The solid curve in Fig. 3 is the Eg(hv) dependence calculated using Eq. (5), which demonstrates the best fit with experimental data (the circles) when Eg(0) = 0.756 eV (the
2
ðn 1Þ þ j2 ðn þ 1Þ2 þ j2
;
ð3Þ
where n is the refractive index and j is the extinction coefficient. Although the reflection index depends on wavelength, our measurements show that the value of R within the narrow spectral range used for determining the value of the bandgap (hv Eg) can be assumed to be equal to 0.3 without introducing a large error. Since Hg3In2Te6 is a direct narrow-gap semiconductor [3], the dependence of the absorption coefficient on the photon energy at the bandgap edge follows the expression pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a ¼ a0 hv Eg ; ð4Þ where a0 is a value that can be assumed to be independent of the photon energy hv. Hence, to determine the Eg value, the dependence a(hv) should be plotted as a2 versus hv. In these coordinates, the curve a(hc) then takes the form of a straight line intersecting the x-axis at the point hv = Eg (Fig. 2). It follows from the figure that the energy bandgap Eg of Hg3In2Te6 decreases from 0.757 eV to 0.737 eV when
0.76
0.75
Eg (eV)
R¼
0.74
0.73
0.72 0
100
200
300
T (K)
Fig. 3. The bandgap Eg (eV) of Hg3In2Te6 at different temperatures. The circles are the experimental results; the solid and dashed lines are the dependences calculated using Eqs. (5) and (6), respectively.
258
X.L. Zhang et al. / Infrared Physics & Technology 51 (2008) 256–258
energy bandgap at T = 0 K), c = 3 · 104 eV K1 (an empirical constant), and b = 1050 K (the value associated with the Debye temperature). In the high temperature region, the temperature dependence of a semiconductor can be approximated by the linear equation [7] Eg ðT Þ ¼ Eg ð0Þ þ c0 ðT Þ;
ð6Þ
where c0 is the temperature coefficient of the semiconductor bandgap. The dashed line in Fig. 3 is the Eg(T) linear dependence described by Eq. (6), which virtually coincides with the experimental data in the room temperature region if Eg(0) = 0.7757 eV and c0 = 1.3 · 104 eV/K. Note that for Ge, the bandgap of which (0.67 eV at 300 K) is close to that of Hg3In2Te6, the temperature coefficient of the bandgap is equal to 3.7 · 104 eV/K [8]. Thus the temperature stability of a Hg3In2Te6 photodiode is much higher than that of a Ge photodiode. In summary, we have measured the temperature dependence of the bandgap of Hg3In2Te6 alloy. The optical transmission curves were measured at different tempera-
tures from 12 K to 300 K. The absorption curves were calculated, from which an empirical analytical expression describing the temperature variations of the energy bandgap of the alloy was obtained for the first time. References [1] P.M. Spencer, B. Ray, Phase diagram of the alloy system Hg3Te3– In2Te3, Brit. J. Appl. Phys. (J. Phys. D) 1 (1968) 299. [2] D. Weitze, V. Leute, The phase diagram of the quasibinary systems HgTe/In2Te3 and CdTe/In2Te3, J. Alloys Compd. 236 (1996) 229. [3] A. Malik, Manuela Vieira, Miguel Fernandes, Filipe Macarico, Zinaida M. Grushka, Near-infrared photodetectors based on HgInTe semiconductor compound, SPIE, vol. 3629. [4] G.G. Grushka, Z.M. Grushka, A.P. Bakhtinov, The electrical properties of Hg3In2Te6 compound, Ukr. Phys. J. 30 (1985) 304. [5] J. Chu, Narrow gap semiconduction of physics, Science Press, 2005 (in Chinese). [6] P.N. Gorlei, O.G. Grushka, An impurity band in Hg3In2Te6 crystals doped with silicon, Semiconductors 37 (2) (2003) 168. [7] J.I. Pankov, Optical Processes in Semiconductors, Prentice-Hall Inc., New Jersey, 1996, 1971, p. 456. [8] E.L. Dereniak, G.D. Boreman, Infrared Detectors and Systems, John Wiley & Sons Inc., New York, 1996, P298.