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GaSb Type II superlattices
ARTICLE IN PRESS
Materials Science in Semiconductor Processing 8 (2005) 463–466
Curvature of band overlap in InAs/GaSb Type II superlattices A.J. Ekpunobi Department of Physics and Industrial Physics, Nnamdi Azikiwe University, P.M.B. 5025, Awka, Nigeria Available online 8 October 2004
Abstract Tight binding calculations of the band alignment in InAs/GaSb type II broken-gap superlattices have been carried out with a valence band offset value of 0.57 eV obtained at root temperature 300 K, in good agreement with experiments. The valence band offset decreases with temperature, whereas the band overlap exhibits curvature with minimum at 550 K. It is inferred that there is no possibility of band alignment transition due to temperature. r 2004 Elsevier Ltd. All rights reserved.
1. Introduction The InAs/GaSb interface is characterized by a type II broken-gap band alignment. This band alignment has been exploited in the development of novel electrical devices and narrow-band-gap strained-layer superlattices for detection of infrared radiation and for numerous studies of fundamental physical interest [1]. Symons et al. [2] studied the temperature dependence of the band overlap in InAs/GaSb structures by performing magneto-transport measurements on both semiconducting and semimetallic superlattices at temperatures between 110 and 340 K and in fields up to 45T. Semiconducting samples had very few carriers at 4 K, but at these higher temperatures intrinsic carriers were thermally excited across the energy gap. By measuring the variation of the electron and hole densities with temperature it was possible to determine the energy gap between the electron and hole confinement energies and thus the band overlap between the InAs conduction band and the GaSb valence band. They noticed that this overlap was 30 meV larger at 300 K than at 4 K. Band offset dependence on temperature has been noticed by some other researchers [3–5]. Sai-Halasz et al. [6] measured optical absorption at low temperature in In1xGaAs/GaSb1yAsy superlattices, from which they deduced a valence-band offset for the InAs/GaSb heterojunction of 0.56 eV. Claessen et al. [7] confirmed
this result by measuring the pressure dependence of the InAs/GaSb band offset at 4.2 K obtaining a valence band offset of 0.56 eV at atmospheric pressure. In this paper, tight binding method is used to calculate the valence band offset at InAs/GaSb heterojunction. The variations of valence band offset and band overlap were studied using a model. The results of the calculations are compared with experiments.
2. Method The measured spectroscopic term values could be used for band offset calculations by applying a scaling factor to modify the values [8]. The spectroscopic term values in rydberg, electron volts and modified values in electron volts are listed in Table 1 for the positive ions In3+, Ga3+, As5+ and Sb5+. The valence band maxima is given by " #1=2 E cp þ E ap E cp E ap 2 2 þ þ V xx ð1Þ Ev ¼ 2 2 where Epc and Epa are p – eigenvalues of the cation and anion. The interatomic matrix element Vxx is V xx ¼
1369-8001/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.mssp.2004.05.006
1:88 _2 md 2
ð2Þ
ARTICLE IN PRESS A.J. Ekpunobi / Materials Science in Semiconductor Processing 8 (2005) 463–466
464
Table 1 Spectroscopic term values of Ga3+, In3+, As5+ and Sb5+
s(Ry) s(eV) s(eV) modified p(Ry) p(eV) p(eV) modified
Eg (T ) is the band gap at a temperature T, Eg(0) the band gap at absolute zero, a and b are constants. Using Eqs. (6) and (3) in the experimental results of ref [2] we deduce
Ga3+
In3+
As5+
Sb5+
2.25721 30.71115 12.80 1.65293 22.48943 4.69
2.06038 28.03312 11.68 1.51292 20.58449 4.29
6.68822 90.99858 22.74 4.88919 66.52134 8.32
6.05884 82.43537 20.60 4.46716 60.77929 7.60
dfVBOg ¼ 0:0003eV =K dT
ð7Þ
which is the model for variation of valence band offset with temperature which is used for further calculations in this work.
3. Results and discussion
Fig. 1. Band lineup of InAs/GaSb.
d being the bond length. The details of tight binding method could be found in [9]. The band alignment of InAs/GaSb is such that the conduction band minimum in InAs is below the valence band maximum of GaSb. Fig. 1 shows the band lineup of this type II superlattice. The valence band offset VBO is related to the band overlap D by VBO ¼ E InAs þD g
ð3Þ
the conduction band offset CBO is related to the band overlap D by CBO ¼ E GaSb þD g
ð4Þ
Where EgInAs and EgGaSb are band gaps of InAs and GaSb respectively. The band gap difference is DE g ¼ E InAs E GaSb ¼ VBO CBO g g
ð5Þ
Which is the difference between the valence band offset and the conduction band offset. The temperature dependence of energy gap of a semiconducting material is [10]. E g ðTÞ ¼ E g ð0Þ
aT 2 T þb
ð6Þ
The properties of InAs and GaSb are listed in Table 2. The bond lengths were obtained from ref [9]. a and b used here were used in ref [2]. Eg(0) were obtained from ref [10]. The valence band maxima were calculated using Eq. (1). The modified values in Table 1 were used for the calculation. The valence band offset is the difference between the valence band maxima and is equal to 0.567 eV or approximately 0.57 eV obtained at root temperature 300 K. This is good agreement with experiments which yield valence band offset of 0.56 eV [6,7]. A similar method utilizing Herman and Skillman term values yield 0.52 eV [11]; a better agreement with experiment than dipole theory which utilizes HatreeFock term values giving 0.33 eV [12]. Because of the peculiar band lineup at this interface, the better theory of the band offset is direct substraction of the valence band maxima than inclusion of hybrid energy calculated in the tetrahedral configuration, used in some other systems [13–15]. The temperature dependence of band gap Eg, valence band offset VBO and band overlap are shown in Table 3. The band gaps were calculated using Eq. (6). The valence band offsets were calculated using Eq. (7) and the band overlaps were obtained from Eq. (3). The experimental values were deduced from ref [6]. The calculated valence band offset and band overlap variations with temperature are in good agreement with deductions from the experiments, for temperatures within the experimental range (below 350 K). The calculation is carried further up to 700 K and a curvature of the band overlap is observed. Table 4 shows the dependence on temperature of InAs band gap EInAs , g valence band offset VBO and band overlap D from 300 to 700 K. The band gap was calculated from Eq. (6), the VBO from Eq. (7) and D from Eq. (3). The band overlap decreases as temperature decreases from 700 K, it reaches a minimum at 550 K, then rises as temperature decreases to 150 K. This is depicted in Fig. 2. The physical implication of the curvature is that the band overlap cannot vanish with temperature variation as
ARTICLE IN PRESS A.J. Ekpunobi / Materials Science in Semiconductor Processing 8 (2005) 463–466
465
Table 2 Properties of InAs and GaSb
InAs GaSb
d(A˚)
a
b
Eg(0)(eV)
Ev(eV)
2.61 2.65
0.335 0.480
248 280
0.42 0.81
9.218 8.651
Table 3 Temperature dependence of Eg, VBO and D T (K)
(eV) EInAs g
EGaSb (eV) g
VBOexpt(eV)
VBOtheory(eV)
Dexpt(eV)
Dtheory(eV)
150 200 250 300 350
0.401 0.390 0.378 0.365 0.351
0.785 0.770 0.753 0.736 0.717
0.605 0.590 0.575 0.560 0.545
0.612 0.597 0.582 0.567 0.552
0.204 0.200 0.197 0.195 0.194
0.211 0.207 0.204 0.202 0.201
Table 4 Curvature of band overlap T (K)
(eV) EInAs g
VBOtheory(eV)
Dtheory(eV)
700 600 500 400 300
0.247 0.278 0.308 0.337 0.365
0.447 0.477 0.507 0.537 0.567
0.200 0.199 0.199 0.200 0.202
such there cannot be transition from type II broken-gap band alignment to another type of band alignment in the InAs/GaSb superlattice.
4. Conclusion Tight binding method has been used to calculate valence band offset at the InAs/GaSb interface. The valence band offset of 0.57 eV obtained at root temperature 300 K is in good agreement with experimental value of 0.56 eV. The valence band offset decreases with increasing temperature at the rate of 0.0003 eV/K. The band overlap shows curvature as the temperature increases from 150 to 700 K with a minimum at 550 K. The implication of the curvature is that there cannot be band alignment transition with temperature variation.
References
Fig. 2. Curvature of band overlap in InAs/GaSb.
[1] Yu ET, McCaldin JO, McGill TC. In: Ehrenreich H, Turnbull D editors. Solid State Physics, Vol. 46. London: Academic Press; 1992. p. 52. [2] Symons DM, Lakrimi M, van der Burgt M, Vaughan TA, Nicholas RJ, Mason NJ, Walker PJ. Phys Rev B 1995;51:1729. [3] Frederiksen JT, Melcher PG, Veje E. Phys Rev 1998;B58:8020. [4] Ekpunobi AJ. Nonlinear Optics 2001;28:257. [5] Haase MA, Pan N, Stillman GE. Appl Phys Lett 1989;54:1457. [6] Sai-Halasz GA, Chang LL, Welter JM, Chang CA, Esaki L. Solid State Commun 1978;27:935. [7] Claessen LM, Maan JC, Altarelli M, Wydes P, Chang LL, Esaki L. Phys Rev Lett 1986;57:2556.
ARTICLE IN PRESS 466
A.J. Ekpunobi / Materials Science in Semiconductor Processing 8 (2005) 463–466
[8] Ekpunobi AJ, Okeke CE, Animalu AOE. Physica 1999;B271:364. [9] Harrison WA. Electronic Structure and Properties of Solids. San Francisco: W.H. Freeman and Company; 1980. p. 46. [10] Sze SM. Physics of Semiconductor Devices. New York: John Wiley and Sons; 1981. p. 15.
[11] [12] [13] [14]
Harrison WA. J Vac Sci Technol 1977;14:1016. Harrison WA, Tersoff J. J Vac Sci Technol 1986;B4:1068. Ekpunobi AJ. Nonlinear Optics 2001;28:129. Ekpunobi AJ, Animalu AOE. Superlattices and Microstructures 2002;31:247. [15] Ekpunobi AJ, Animalu AOE. Superlattices and Microstructures 2002;31:253.
Materials Science in Semiconductor Processing 8 (2005) 463–466
Curvature of band overlap in InAs/GaSb Type II superlattices A.J. Ekpunobi Department of Physics and Industrial Physics, Nnamdi Azikiwe University, P.M.B. 5025, Awka, Nigeria Available online 8 October 2004
Abstract Tight binding calculations of the band alignment in InAs/GaSb type II broken-gap superlattices have been carried out with a valence band offset value of 0.57 eV obtained at root temperature 300 K, in good agreement with experiments. The valence band offset decreases with temperature, whereas the band overlap exhibits curvature with minimum at 550 K. It is inferred that there is no possibility of band alignment transition due to temperature. r 2004 Elsevier Ltd. All rights reserved.
1. Introduction The InAs/GaSb interface is characterized by a type II broken-gap band alignment. This band alignment has been exploited in the development of novel electrical devices and narrow-band-gap strained-layer superlattices for detection of infrared radiation and for numerous studies of fundamental physical interest [1]. Symons et al. [2] studied the temperature dependence of the band overlap in InAs/GaSb structures by performing magneto-transport measurements on both semiconducting and semimetallic superlattices at temperatures between 110 and 340 K and in fields up to 45T. Semiconducting samples had very few carriers at 4 K, but at these higher temperatures intrinsic carriers were thermally excited across the energy gap. By measuring the variation of the electron and hole densities with temperature it was possible to determine the energy gap between the electron and hole confinement energies and thus the band overlap between the InAs conduction band and the GaSb valence band. They noticed that this overlap was 30 meV larger at 300 K than at 4 K. Band offset dependence on temperature has been noticed by some other researchers [3–5]. Sai-Halasz et al. [6] measured optical absorption at low temperature in In1xGaAs/GaSb1yAsy superlattices, from which they deduced a valence-band offset for the InAs/GaSb heterojunction of 0.56 eV. Claessen et al. [7] confirmed
this result by measuring the pressure dependence of the InAs/GaSb band offset at 4.2 K obtaining a valence band offset of 0.56 eV at atmospheric pressure. In this paper, tight binding method is used to calculate the valence band offset at InAs/GaSb heterojunction. The variations of valence band offset and band overlap were studied using a model. The results of the calculations are compared with experiments.
2. Method The measured spectroscopic term values could be used for band offset calculations by applying a scaling factor to modify the values [8]. The spectroscopic term values in rydberg, electron volts and modified values in electron volts are listed in Table 1 for the positive ions In3+, Ga3+, As5+ and Sb5+. The valence band maxima is given by " #1=2 E cp þ E ap E cp E ap 2 2 þ þ V xx ð1Þ Ev ¼ 2 2 where Epc and Epa are p – eigenvalues of the cation and anion. The interatomic matrix element Vxx is V xx ¼
1369-8001/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.mssp.2004.05.006
1:88 _2 md 2
ð2Þ
ARTICLE IN PRESS A.J. Ekpunobi / Materials Science in Semiconductor Processing 8 (2005) 463–466
464
Table 1 Spectroscopic term values of Ga3+, In3+, As5+ and Sb5+
s(Ry) s(eV) s(eV) modified p(Ry) p(eV) p(eV) modified
Eg (T ) is the band gap at a temperature T, Eg(0) the band gap at absolute zero, a and b are constants. Using Eqs. (6) and (3) in the experimental results of ref [2] we deduce
Ga3+
In3+
As5+
Sb5+
2.25721 30.71115 12.80 1.65293 22.48943 4.69
2.06038 28.03312 11.68 1.51292 20.58449 4.29
6.68822 90.99858 22.74 4.88919 66.52134 8.32
6.05884 82.43537 20.60 4.46716 60.77929 7.60
dfVBOg ¼ 0:0003eV =K dT
ð7Þ
which is the model for variation of valence band offset with temperature which is used for further calculations in this work.
3. Results and discussion
Fig. 1. Band lineup of InAs/GaSb.
d being the bond length. The details of tight binding method could be found in [9]. The band alignment of InAs/GaSb is such that the conduction band minimum in InAs is below the valence band maximum of GaSb. Fig. 1 shows the band lineup of this type II superlattice. The valence band offset VBO is related to the band overlap D by VBO ¼ E InAs þD g
ð3Þ
the conduction band offset CBO is related to the band overlap D by CBO ¼ E GaSb þD g
ð4Þ
Where EgInAs and EgGaSb are band gaps of InAs and GaSb respectively. The band gap difference is DE g ¼ E InAs E GaSb ¼ VBO CBO g g
ð5Þ
Which is the difference between the valence band offset and the conduction band offset. The temperature dependence of energy gap of a semiconducting material is [10]. E g ðTÞ ¼ E g ð0Þ
aT 2 T þb
ð6Þ
The properties of InAs and GaSb are listed in Table 2. The bond lengths were obtained from ref [9]. a and b used here were used in ref [2]. Eg(0) were obtained from ref [10]. The valence band maxima were calculated using Eq. (1). The modified values in Table 1 were used for the calculation. The valence band offset is the difference between the valence band maxima and is equal to 0.567 eV or approximately 0.57 eV obtained at root temperature 300 K. This is good agreement with experiments which yield valence band offset of 0.56 eV [6,7]. A similar method utilizing Herman and Skillman term values yield 0.52 eV [11]; a better agreement with experiment than dipole theory which utilizes HatreeFock term values giving 0.33 eV [12]. Because of the peculiar band lineup at this interface, the better theory of the band offset is direct substraction of the valence band maxima than inclusion of hybrid energy calculated in the tetrahedral configuration, used in some other systems [13–15]. The temperature dependence of band gap Eg, valence band offset VBO and band overlap are shown in Table 3. The band gaps were calculated using Eq. (6). The valence band offsets were calculated using Eq. (7) and the band overlaps were obtained from Eq. (3). The experimental values were deduced from ref [6]. The calculated valence band offset and band overlap variations with temperature are in good agreement with deductions from the experiments, for temperatures within the experimental range (below 350 K). The calculation is carried further up to 700 K and a curvature of the band overlap is observed. Table 4 shows the dependence on temperature of InAs band gap EInAs , g valence band offset VBO and band overlap D from 300 to 700 K. The band gap was calculated from Eq. (6), the VBO from Eq. (7) and D from Eq. (3). The band overlap decreases as temperature decreases from 700 K, it reaches a minimum at 550 K, then rises as temperature decreases to 150 K. This is depicted in Fig. 2. The physical implication of the curvature is that the band overlap cannot vanish with temperature variation as
ARTICLE IN PRESS A.J. Ekpunobi / Materials Science in Semiconductor Processing 8 (2005) 463–466
465
Table 2 Properties of InAs and GaSb
InAs GaSb
d(A˚)
a
b
Eg(0)(eV)
Ev(eV)
2.61 2.65
0.335 0.480
248 280
0.42 0.81
9.218 8.651
Table 3 Temperature dependence of Eg, VBO and D T (K)
(eV) EInAs g
EGaSb (eV) g
VBOexpt(eV)
VBOtheory(eV)
Dexpt(eV)
Dtheory(eV)
150 200 250 300 350
0.401 0.390 0.378 0.365 0.351
0.785 0.770 0.753 0.736 0.717
0.605 0.590 0.575 0.560 0.545
0.612 0.597 0.582 0.567 0.552
0.204 0.200 0.197 0.195 0.194
0.211 0.207 0.204 0.202 0.201
Table 4 Curvature of band overlap T (K)
(eV) EInAs g
VBOtheory(eV)
Dtheory(eV)
700 600 500 400 300
0.247 0.278 0.308 0.337 0.365
0.447 0.477 0.507 0.537 0.567
0.200 0.199 0.199 0.200 0.202
such there cannot be transition from type II broken-gap band alignment to another type of band alignment in the InAs/GaSb superlattice.
4. Conclusion Tight binding method has been used to calculate valence band offset at the InAs/GaSb interface. The valence band offset of 0.57 eV obtained at root temperature 300 K is in good agreement with experimental value of 0.56 eV. The valence band offset decreases with increasing temperature at the rate of 0.0003 eV/K. The band overlap shows curvature as the temperature increases from 150 to 700 K with a minimum at 550 K. The implication of the curvature is that there cannot be band alignment transition with temperature variation.
References
Fig. 2. Curvature of band overlap in InAs/GaSb.
[1] Yu ET, McCaldin JO, McGill TC. In: Ehrenreich H, Turnbull D editors. Solid State Physics, Vol. 46. London: Academic Press; 1992. p. 52. [2] Symons DM, Lakrimi M, van der Burgt M, Vaughan TA, Nicholas RJ, Mason NJ, Walker PJ. Phys Rev B 1995;51:1729. [3] Frederiksen JT, Melcher PG, Veje E. Phys Rev 1998;B58:8020. [4] Ekpunobi AJ. Nonlinear Optics 2001;28:257. [5] Haase MA, Pan N, Stillman GE. Appl Phys Lett 1989;54:1457. [6] Sai-Halasz GA, Chang LL, Welter JM, Chang CA, Esaki L. Solid State Commun 1978;27:935. [7] Claessen LM, Maan JC, Altarelli M, Wydes P, Chang LL, Esaki L. Phys Rev Lett 1986;57:2556.
ARTICLE IN PRESS 466
A.J. Ekpunobi / Materials Science in Semiconductor Processing 8 (2005) 463–466
[8] Ekpunobi AJ, Okeke CE, Animalu AOE. Physica 1999;B271:364. [9] Harrison WA. Electronic Structure and Properties of Solids. San Francisco: W.H. Freeman and Company; 1980. p. 46. [10] Sze SM. Physics of Semiconductor Devices. New York: John Wiley and Sons; 1981. p. 15.
[11] [12] [13] [14]
Harrison WA. J Vac Sci Technol 1977;14:1016. Harrison WA, Tersoff J. J Vac Sci Technol 1986;B4:1068. Ekpunobi AJ. Nonlinear Optics 2001;28:129. Ekpunobi AJ, Animalu AOE. Superlattices and Microstructures 2002;31:247. [15] Ekpunobi AJ, Animalu AOE. Superlattices and Microstructures 2002;31:253.