- Email: [email protected]
On the refractive index of InSbxAs1-X
Physica B xxx (xxxx) xxx
Contents lists available at ScienceDirect
Physica B: Physics of Condensed Matter journal homepage: http://www.elsevier.com/locate/physb
On the refractive index of InSbxAs1-X J.A.A. Engelbrecht a, *, J.R. Botha b, J.A.A. Engelbrecht Jr. c, S. Dobson b, E.G. Minnaar a, J. O’Connell a, W.E. Goosen a a
Centre for HRTEM, Nelson Mandela University, Port Elizabeth, South Africa Physics Department, Nelson Mandela University, Port Elizabeth, South Africa c Department of Electrical and Electronic Engineering, University of Stellenbosch, South Africa b
A R T I C L E I N F O
A B S T R A C T
Keywords: Refractive index InSbxAs1-x Overview Theoretical formula
InSbxAs1-x alloys are used in mid-infrared optoelectronic devices, requiring a knowledge of the refractive index of the material when designing new devices. Only a limited number of publications are available regarding the refractive index n of InSbxAs1-x. This article provides an overview of existing information. A formula for calculating the refractive index as a function of both Sb mole fraction x and wavenumber (or wavelength) is also proposed. The proposed formulation is assessed by comparison with earlier published research results.
1. Introduction The ternary alloy InSbxAs1-x finds application in mid-infrared opto electronic devices, including lasers [1,2], light emitting diodes [3,4] photodetectors [5,6] and quantum well heterostructures [7]. Conse quently, a knowledge of the optical parameters of the alloy, in particular the refractive index n, is a requirement for the design of the required optical devices. A literature survey revealed that very few references are available for the refractive index of InSbxAs1-x [7–9], which includes a theoretical model based on the Kramers-Kronig dispersion relation for calculating the refractive index [9]. This article provides a review of the refractive index of InSbxAs1-x and then proposes a semi-empirical formula to calculate the refractive index of InSbxAs1-x as a function of both Sb mole fraction x and the wavelength or wavenumber. The formula was assessed against previ ously published values of the refractive index. 2. Overview of current status Publications by Paskov [8,9] seem to be the first reported work on the refractive index of InSbAs. The detailed modelling of the optical properties using the Kramers-Kronig dispersion relation [9] included graphs for the refractive index of intrinsic, as well as n- and p-doped (both Nh and Ne ¼ 1 � 1018 cm 3) InAsxSb1-x. (It must be noted that the composition in the latter publication is indicated inverse to articles reference [8] where InSbxAs1-x was discussed).
Other publications of relevance are all related to the refractive indices of InSb and InAs [10–18]. The refractive index for InSb and InAs were investigated by Aspnes and Studna [14], and for InSb thin films by Qian et al. [19] in the range 0.5–6 eV (μm wavelength region). A compilation of the information is depicted in Figs. 1 and 2 for the infrared region, including the data of Paskov [9] for intrinsic material (where x ¼ 0 for InAs and x ¼ 1 for InSb). Clearly, there are notable differences between the values for the refractive indices of InSb and InAs obtained by the various researchers. Apart from the work by Paskov [9], the current information is limited to the refractive indices of InAs and InSb. The challenge is thus to determine the refractive index of InSbxAs1-x as function of Sb mole fraction x and wavelength/wavenumber of interest. 3. Results From the evidence presented in section 2, the equations of Sanderson [11] and Lorimar and Spitzer [12], as reported by Seraphin and Bennett [13] for the refractive indices of InSb and InAs, were used to obtain a formula for the refractive index of InSbxAs1-x; based on the formula proposed for the refractive index of AlxGa1-xN [20]. In the current investigation, a linear relationship was assumed between the indices of InAs and InSb at a chosen wavelength, in order to represent the increasing Sb mole fraction (Figs. 3 and 4). From the linear relations as depicted in Fig. 4, the slope m and intercept c of the relation y ¼ mx þ c was obtained for each wavenumber
* Corresponding author. HRTEM Facility, NMMU, PO Box 77000, Port Elizabeth, 6031, South Africa. E-mail address: [email protected] (J.A.A. Engelbrecht). https://doi.org/10.1016/j.physb.2019.411759 Received 17 May 2019; Received in revised form 30 September 2019; Accepted 6 October 2019 Available online 9 October 2019 0921-4526/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: J.A.A. Engelbrecht, Physica B, https://doi.org/10.1016/j.physb.2019.411759
J.A.A. Engelbrecht et al.
Physica B: Physics of Condensed Matter xxx (xxxx) xxx
used. i.e. as function of wavenumber. These relations were then plotted and best trend lines obtained from exponential fits and polynomial fits of order 6 (Figs. 5 and 6). Note that the intercept c relates physically to the refractive index of InAs, while the slope to the difference between the refractive indices of InSb and InAs at the specific wavenumber (wavelength). The polynomial and exponential fits enable the determination of the slope m and intercept c as function of the wavenumber ω of interest. For the polynomial fit (R2 ¼ 0.99): slope m ¼ 2.213 � 10 21 ω6 – 3.180 � 10 17 ω5 þ 1.825 � 10 13 ω4 – 5.336 � 10 10 ω3 þ 8.378 � 10 7 ω2 – 6.743 � 10 4 ω þ0.747
(1)
Intercept c ¼ 5.563 � 10 21 ω6 þ 8.045 � 10 17 ω5 -4.657 � 10 1.379 � 10 9 ω3 – 2.205 � 10 6 ω2 þ 1.826 � 10 3 ω þ 2.801
(2)
(Note that the above formulae 500–4000 cm 1). For the exponential fit (R2 ¼ 0.98): Fig. 1. Refractive index of InAs.
y ¼ A [1 – e (ω-ω0)/τ ] þ K
are
valid
in
13
the
ω4 þ
range
(3)
with ω0 ¼ 400 cm-1 Least squares fit yielded the following values for the parameters A, τ and K: For m: A ¼ 0.0843, τ ¼ 150 and K ¼ 0.6083 For c: A ¼ 0.1295, τ ¼ 270 and K ¼ 3.3040 Either of the above formulations are related to the form of a linear relation in order to calculate the refractive index at any wavenumber for any concentration x of Sb: Refractive index n(x,ω) ¼ m(ω)x þ c(ω)
(4)
Refractive index values calculated from the above equations (1)–(4) for InSb and InAs were then compared to those earlier found by other researchers for wavenumbers > 500 cm 1, as shown in Figs. 1 and 2. It is clear that the both the polynomial and exponential fits agree acceptably well with previously published research results for InAs and InSb. It should however be noted that the 6th order polynomial fit requires the
Fig. 2. Refractive index of InSb.
Fig. 3. Refractive indices of InSb and InAs from Refs. [11,12]. 2
J.A.A. Engelbrecht et al.
Physica B: Physics of Condensed Matter xxx (xxxx) xxx
use of expressions to the 3rd decimal. In comparison, the exponential function is much simpler. As an additional validation of the proposed analytical expressions, the thickness of the epilayer of sample InSb0.09As0.91 [23], grown by organometallic vapour phase epitaxy (OMVPE) on a GaAs substrate, was determined from infrared reflectance spectra. The interference spectrum of the sample is depicted in Fig. 7, while the cross-sectional transmission electron micrograph (TEM) of the sample is shown in Fig. 8. Results for the epilayer thicknesses obtained from the parallel plate interference formula, with relevant refractive indices calculated from the proposed formulae in this article, as compared to the measured value from TEM are presented in Table 1. Agreement is very good, with a difference of ~3% between measured and calculated values. However, it should be noted that the assumption of a linear rela tionship between die refractive indices of InSb and InAs is subjected to the following limitations:
Fig. 4. Linear relations between refractive indices InAs and InSb as function of the Sb mole fraction x at the indicated wavenumbers. Dotted lines are linear relationships, as indicated for 2500 cm 1 (top) and 500 cm 1 (bottom).
i) The assumption of a linear relationship between the refractive index and the mole fraction x is only valid over the
Fig. 5. Slope m of linear relations from Fig. 4 as function of wavenumber, with polynomial and exponential fit as indicated (for wavenumbers � 500 cm
1
Fig. 6. Intercept c of linear relations from Fig. 4 as function of wavenumber, with polynomial and exponential fit as indicated (for wavenumbers � 500 cm 3
).
1
).
J.A.A. Engelbrecht et al.
Physica B: Physics of Condensed Matter xxx (xxxx) xxx
Table 1 Comparison thickness.
of
measured
and
calculated
epilayer
Method
Thickness (μm)
TEM analysis Exponential fit Polynomial fit
4.45 � 0.22 4.59 � 0.08 4.60 � 0.09
impact of the band gap, and possible bowing of the band gap of InSbxAs1-x [21,22]. 4. Conclusions The current status of, and information available regarding the refractive index of InSbxAs1-x has been assessed, and while information is available for the refractive indices of InSb and InAs, there is limited information available for InSbxAs1-x. Using the information for InSb and InAs, a formula for the calculation of the refractive index for InSbxAs1-x as function of Sb mole fraction x and wavenumber ω (or wavelength λ) is proposed. Two different fitting expressions, viz. polynomial and expo nential were investigated to calculate the slope m and intercept c in the proposed linear relation for the refractive index n ¼ mx þ c, for any specific wavenumber and mole fraction concentration x. Results were compared to published values for InSb and InAs, and both functions yielded results comparable to known published values. It is envisaged that the simpler exponential function is most likely the more acceptable formulation. The proposed formulae were tested by using calculated values of the refractive index to determine epilayer thicknesses from interference fringe analysis of a InSbxAs1-x sample. Ellipsometry mea surements in the infrared region for the InSbxAs1-x samples are also envisaged, since the proposed formula to might be subject to correc tions. The assumption of the linear relationship between the refractive indices of InSb and InAs also require further investigation.
Fig. 7. Mid-infrared reflectance spectrum of InSb0.09As0.91.
range � 500 cm 1. The data from Paskov [9] for different mole fractions x do not comply with linearity below ~ 3000 cm 1. This aspect requires further investigation. ii) Data from some researchers [9,15–17] indicate that a nonlinear interpolation between the refractive indices of the binary end-materials may be more appropriate to obtain the refractive index of the ternary. iii) The refractive index of a semiconducting material is related to the band gap of the material through the mole fraction x. The current proposed analytical expressions do not take into account the
Acknowledgments The authors wish to thank M. van Greunen for technical assistance. Financial assistance of the National Research Foundation (NRF), South Africa, is gratefully acknowledged. Any opinion, findings and conclu sions or recommendations expressed in this article are those of the au thors, and therefore the NRF does not accept liability in regards thereto. References [1] H.Q. Le, G.W. Turner, S.J. Eglash, H.K. Choi, D.A. Coppeta, Appl. Phys. Lett. 62 (1984) 152. [2] S.R. Kurtz, R.M. Biefield, A.A. Allerman, A.J. Howard, M.H. Crawford, M. W. Pelczynski, Appl. Phys. Lett. 68 (1996) 1332. [3] W. Dobbelaere, J. Deboeck, C. Bruynserede, R. Mertens, G. Borghs, Electron. Lett. 29 (1993) 890. [4] P. Tang, M.J. Pullin, S.J. Chung, C.C. Phillips, R.A. Stradling, A.G. Norman, Y.B. Li, L. Hart, Semicond. Sci. Technol. 10 (1995) 1177. [5] H.H. Wieder, A.R. Clawson, Thin Solid Films 15 (1973) 217. [6] R. Hasegawa, A. Yoshikawa, T. Morishita, Y. Moriyasu, K. Nagase, N. Kuze, J. Cryst. Growth 464 (2017) 211. [7] N.V. Pavlov, G.G. Zegrya, J. Phys. Conf. Ser. 661 (2015), 012052. [8] P.P. Paskov, Solid State Commun. 82 (1992) 739. [9] P.P. Paskov, J. Appl. Phys. 81 (1997) 1890. [10] G. Dhaharaj, K. Byrappa, V. Prasad, M. Dudley (Eds.), Springer Handbook of Crystal Growth, Springer-Verlag, Berlin, 2010, p. 352. [11] R.B. Sanderson, J. Phys. Chem. Solids 26 (1965) 803. [12] O.G. Lorimor, W.G. Spitzer, J. Appl. Phys. 36 (1965) 1841. [13] B.O. Seraphin, H.E. Bennett, Semiconductors and semimetals, in: R.K. Willardson, A.C. Beer (Eds.), Optical Properties of III-V Compounds, vol. 3, Academic Press, NY, 1967, p. 499. [14] D.E. Aspnes, A.A. Studna, Phys. Rev. B 27 (1983) 985. [15] S. Adachi, J. Appl. Phys. 66 (1989) 6030. [16] R.T. Holm, in: E.D. Palik (Ed.), Handbook of Optical Constants of Solids, Academic Press, NY, 1977, p. 491. [17] E.D. Palik, R.T. Holm, in: E.D. Palik (Ed.), Handbook of Optical Constants of Solids, Academic Press, NY, 1977, p. 479.
Fig. 8. Cross-sectional TEM micrograph of InSb0.09As0.91. 4
J.A.A. Engelbrecht et al.
Physica B: Physics of Condensed Matter xxx (xxxx) xxx
[18] S. Adachi, The Handbook on Optical Constants of Semiconductors, World Scientific Publishing Co Pty. Ltd. Singapore, 2012, p. 181, 186. [19] Y. Qian, Y. Liang, X. Luo, K. He, W. Sun, H.-H. Lin, D.N. Talwar, T.-S. Chan, I. Fergason, L. Wan, Q. Yang, Z.C. Feng, Hindawi Adv. Mater. Sci. Eng. 2018 (2018). Article ID 5016435.
[20] J.A.A. Engelbrecht, B. Sephton, E.G. Minnaar, M.C. Wagener, Physica B 480 (2016) 181. [21] S.P. Svensson, W.L. Sarney, H. Hier, Y. Lin, D. Wang, D. Donetsky, L. Shterengas, G. Kipshidze, G. Belenky, Phys. Rev. B 86 (2012) 245205. [22] R.S. Indolia, Int. J. Pure Appl. Phys. 13 (2017) 185. [23] F. Reizman, J. Appl. Phys. 36 (1965) 3804.
5
Contents lists available at ScienceDirect
Physica B: Physics of Condensed Matter journal homepage: http://www.elsevier.com/locate/physb
On the refractive index of InSbxAs1-X J.A.A. Engelbrecht a, *, J.R. Botha b, J.A.A. Engelbrecht Jr. c, S. Dobson b, E.G. Minnaar a, J. O’Connell a, W.E. Goosen a a
Centre for HRTEM, Nelson Mandela University, Port Elizabeth, South Africa Physics Department, Nelson Mandela University, Port Elizabeth, South Africa c Department of Electrical and Electronic Engineering, University of Stellenbosch, South Africa b
A R T I C L E I N F O
A B S T R A C T
Keywords: Refractive index InSbxAs1-x Overview Theoretical formula
InSbxAs1-x alloys are used in mid-infrared optoelectronic devices, requiring a knowledge of the refractive index of the material when designing new devices. Only a limited number of publications are available regarding the refractive index n of InSbxAs1-x. This article provides an overview of existing information. A formula for calculating the refractive index as a function of both Sb mole fraction x and wavenumber (or wavelength) is also proposed. The proposed formulation is assessed by comparison with earlier published research results.
1. Introduction The ternary alloy InSbxAs1-x finds application in mid-infrared opto electronic devices, including lasers [1,2], light emitting diodes [3,4] photodetectors [5,6] and quantum well heterostructures [7]. Conse quently, a knowledge of the optical parameters of the alloy, in particular the refractive index n, is a requirement for the design of the required optical devices. A literature survey revealed that very few references are available for the refractive index of InSbxAs1-x [7–9], which includes a theoretical model based on the Kramers-Kronig dispersion relation for calculating the refractive index [9]. This article provides a review of the refractive index of InSbxAs1-x and then proposes a semi-empirical formula to calculate the refractive index of InSbxAs1-x as a function of both Sb mole fraction x and the wavelength or wavenumber. The formula was assessed against previ ously published values of the refractive index. 2. Overview of current status Publications by Paskov [8,9] seem to be the first reported work on the refractive index of InSbAs. The detailed modelling of the optical properties using the Kramers-Kronig dispersion relation [9] included graphs for the refractive index of intrinsic, as well as n- and p-doped (both Nh and Ne ¼ 1 � 1018 cm 3) InAsxSb1-x. (It must be noted that the composition in the latter publication is indicated inverse to articles reference [8] where InSbxAs1-x was discussed).
Other publications of relevance are all related to the refractive indices of InSb and InAs [10–18]. The refractive index for InSb and InAs were investigated by Aspnes and Studna [14], and for InSb thin films by Qian et al. [19] in the range 0.5–6 eV (μm wavelength region). A compilation of the information is depicted in Figs. 1 and 2 for the infrared region, including the data of Paskov [9] for intrinsic material (where x ¼ 0 for InAs and x ¼ 1 for InSb). Clearly, there are notable differences between the values for the refractive indices of InSb and InAs obtained by the various researchers. Apart from the work by Paskov [9], the current information is limited to the refractive indices of InAs and InSb. The challenge is thus to determine the refractive index of InSbxAs1-x as function of Sb mole fraction x and wavelength/wavenumber of interest. 3. Results From the evidence presented in section 2, the equations of Sanderson [11] and Lorimar and Spitzer [12], as reported by Seraphin and Bennett [13] for the refractive indices of InSb and InAs, were used to obtain a formula for the refractive index of InSbxAs1-x; based on the formula proposed for the refractive index of AlxGa1-xN [20]. In the current investigation, a linear relationship was assumed between the indices of InAs and InSb at a chosen wavelength, in order to represent the increasing Sb mole fraction (Figs. 3 and 4). From the linear relations as depicted in Fig. 4, the slope m and intercept c of the relation y ¼ mx þ c was obtained for each wavenumber
* Corresponding author. HRTEM Facility, NMMU, PO Box 77000, Port Elizabeth, 6031, South Africa. E-mail address: [email protected] (J.A.A. Engelbrecht). https://doi.org/10.1016/j.physb.2019.411759 Received 17 May 2019; Received in revised form 30 September 2019; Accepted 6 October 2019 Available online 9 October 2019 0921-4526/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: J.A.A. Engelbrecht, Physica B, https://doi.org/10.1016/j.physb.2019.411759
J.A.A. Engelbrecht et al.
Physica B: Physics of Condensed Matter xxx (xxxx) xxx
used. i.e. as function of wavenumber. These relations were then plotted and best trend lines obtained from exponential fits and polynomial fits of order 6 (Figs. 5 and 6). Note that the intercept c relates physically to the refractive index of InAs, while the slope to the difference between the refractive indices of InSb and InAs at the specific wavenumber (wavelength). The polynomial and exponential fits enable the determination of the slope m and intercept c as function of the wavenumber ω of interest. For the polynomial fit (R2 ¼ 0.99): slope m ¼ 2.213 � 10 21 ω6 – 3.180 � 10 17 ω5 þ 1.825 � 10 13 ω4 – 5.336 � 10 10 ω3 þ 8.378 � 10 7 ω2 – 6.743 � 10 4 ω þ0.747
(1)
Intercept c ¼ 5.563 � 10 21 ω6 þ 8.045 � 10 17 ω5 -4.657 � 10 1.379 � 10 9 ω3 – 2.205 � 10 6 ω2 þ 1.826 � 10 3 ω þ 2.801
(2)
(Note that the above formulae 500–4000 cm 1). For the exponential fit (R2 ¼ 0.98): Fig. 1. Refractive index of InAs.
y ¼ A [1 – e (ω-ω0)/τ ] þ K
are
valid
in
13
the
ω4 þ
range
(3)
with ω0 ¼ 400 cm-1 Least squares fit yielded the following values for the parameters A, τ and K: For m: A ¼ 0.0843, τ ¼ 150 and K ¼ 0.6083 For c: A ¼ 0.1295, τ ¼ 270 and K ¼ 3.3040 Either of the above formulations are related to the form of a linear relation in order to calculate the refractive index at any wavenumber for any concentration x of Sb: Refractive index n(x,ω) ¼ m(ω)x þ c(ω)
(4)
Refractive index values calculated from the above equations (1)–(4) for InSb and InAs were then compared to those earlier found by other researchers for wavenumbers > 500 cm 1, as shown in Figs. 1 and 2. It is clear that the both the polynomial and exponential fits agree acceptably well with previously published research results for InAs and InSb. It should however be noted that the 6th order polynomial fit requires the
Fig. 2. Refractive index of InSb.
Fig. 3. Refractive indices of InSb and InAs from Refs. [11,12]. 2
J.A.A. Engelbrecht et al.
Physica B: Physics of Condensed Matter xxx (xxxx) xxx
use of expressions to the 3rd decimal. In comparison, the exponential function is much simpler. As an additional validation of the proposed analytical expressions, the thickness of the epilayer of sample InSb0.09As0.91 [23], grown by organometallic vapour phase epitaxy (OMVPE) on a GaAs substrate, was determined from infrared reflectance spectra. The interference spectrum of the sample is depicted in Fig. 7, while the cross-sectional transmission electron micrograph (TEM) of the sample is shown in Fig. 8. Results for the epilayer thicknesses obtained from the parallel plate interference formula, with relevant refractive indices calculated from the proposed formulae in this article, as compared to the measured value from TEM are presented in Table 1. Agreement is very good, with a difference of ~3% between measured and calculated values. However, it should be noted that the assumption of a linear rela tionship between die refractive indices of InSb and InAs is subjected to the following limitations:
Fig. 4. Linear relations between refractive indices InAs and InSb as function of the Sb mole fraction x at the indicated wavenumbers. Dotted lines are linear relationships, as indicated for 2500 cm 1 (top) and 500 cm 1 (bottom).
i) The assumption of a linear relationship between the refractive index and the mole fraction x is only valid over the
Fig. 5. Slope m of linear relations from Fig. 4 as function of wavenumber, with polynomial and exponential fit as indicated (for wavenumbers � 500 cm
1
Fig. 6. Intercept c of linear relations from Fig. 4 as function of wavenumber, with polynomial and exponential fit as indicated (for wavenumbers � 500 cm 3
).
1
).
J.A.A. Engelbrecht et al.
Physica B: Physics of Condensed Matter xxx (xxxx) xxx
Table 1 Comparison thickness.
of
measured
and
calculated
epilayer
Method
Thickness (μm)
TEM analysis Exponential fit Polynomial fit
4.45 � 0.22 4.59 � 0.08 4.60 � 0.09
impact of the band gap, and possible bowing of the band gap of InSbxAs1-x [21,22]. 4. Conclusions The current status of, and information available regarding the refractive index of InSbxAs1-x has been assessed, and while information is available for the refractive indices of InSb and InAs, there is limited information available for InSbxAs1-x. Using the information for InSb and InAs, a formula for the calculation of the refractive index for InSbxAs1-x as function of Sb mole fraction x and wavenumber ω (or wavelength λ) is proposed. Two different fitting expressions, viz. polynomial and expo nential were investigated to calculate the slope m and intercept c in the proposed linear relation for the refractive index n ¼ mx þ c, for any specific wavenumber and mole fraction concentration x. Results were compared to published values for InSb and InAs, and both functions yielded results comparable to known published values. It is envisaged that the simpler exponential function is most likely the more acceptable formulation. The proposed formulae were tested by using calculated values of the refractive index to determine epilayer thicknesses from interference fringe analysis of a InSbxAs1-x sample. Ellipsometry mea surements in the infrared region for the InSbxAs1-x samples are also envisaged, since the proposed formula to might be subject to correc tions. The assumption of the linear relationship between the refractive indices of InSb and InAs also require further investigation.
Fig. 7. Mid-infrared reflectance spectrum of InSb0.09As0.91.
range � 500 cm 1. The data from Paskov [9] for different mole fractions x do not comply with linearity below ~ 3000 cm 1. This aspect requires further investigation. ii) Data from some researchers [9,15–17] indicate that a nonlinear interpolation between the refractive indices of the binary end-materials may be more appropriate to obtain the refractive index of the ternary. iii) The refractive index of a semiconducting material is related to the band gap of the material through the mole fraction x. The current proposed analytical expressions do not take into account the
Acknowledgments The authors wish to thank M. van Greunen for technical assistance. Financial assistance of the National Research Foundation (NRF), South Africa, is gratefully acknowledged. Any opinion, findings and conclu sions or recommendations expressed in this article are those of the au thors, and therefore the NRF does not accept liability in regards thereto. References [1] H.Q. Le, G.W. Turner, S.J. Eglash, H.K. Choi, D.A. Coppeta, Appl. Phys. Lett. 62 (1984) 152. [2] S.R. Kurtz, R.M. Biefield, A.A. Allerman, A.J. Howard, M.H. Crawford, M. W. Pelczynski, Appl. Phys. Lett. 68 (1996) 1332. [3] W. Dobbelaere, J. Deboeck, C. Bruynserede, R. Mertens, G. Borghs, Electron. Lett. 29 (1993) 890. [4] P. Tang, M.J. Pullin, S.J. Chung, C.C. Phillips, R.A. Stradling, A.G. Norman, Y.B. Li, L. Hart, Semicond. Sci. Technol. 10 (1995) 1177. [5] H.H. Wieder, A.R. Clawson, Thin Solid Films 15 (1973) 217. [6] R. Hasegawa, A. Yoshikawa, T. Morishita, Y. Moriyasu, K. Nagase, N. Kuze, J. Cryst. Growth 464 (2017) 211. [7] N.V. Pavlov, G.G. Zegrya, J. Phys. Conf. Ser. 661 (2015), 012052. [8] P.P. Paskov, Solid State Commun. 82 (1992) 739. [9] P.P. Paskov, J. Appl. Phys. 81 (1997) 1890. [10] G. Dhaharaj, K. Byrappa, V. Prasad, M. Dudley (Eds.), Springer Handbook of Crystal Growth, Springer-Verlag, Berlin, 2010, p. 352. [11] R.B. Sanderson, J. Phys. Chem. Solids 26 (1965) 803. [12] O.G. Lorimor, W.G. Spitzer, J. Appl. Phys. 36 (1965) 1841. [13] B.O. Seraphin, H.E. Bennett, Semiconductors and semimetals, in: R.K. Willardson, A.C. Beer (Eds.), Optical Properties of III-V Compounds, vol. 3, Academic Press, NY, 1967, p. 499. [14] D.E. Aspnes, A.A. Studna, Phys. Rev. B 27 (1983) 985. [15] S. Adachi, J. Appl. Phys. 66 (1989) 6030. [16] R.T. Holm, in: E.D. Palik (Ed.), Handbook of Optical Constants of Solids, Academic Press, NY, 1977, p. 491. [17] E.D. Palik, R.T. Holm, in: E.D. Palik (Ed.), Handbook of Optical Constants of Solids, Academic Press, NY, 1977, p. 479.
Fig. 8. Cross-sectional TEM micrograph of InSb0.09As0.91. 4
J.A.A. Engelbrecht et al.
Physica B: Physics of Condensed Matter xxx (xxxx) xxx
[18] S. Adachi, The Handbook on Optical Constants of Semiconductors, World Scientific Publishing Co Pty. Ltd. Singapore, 2012, p. 181, 186. [19] Y. Qian, Y. Liang, X. Luo, K. He, W. Sun, H.-H. Lin, D.N. Talwar, T.-S. Chan, I. Fergason, L. Wan, Q. Yang, Z.C. Feng, Hindawi Adv. Mater. Sci. Eng. 2018 (2018). Article ID 5016435.
[20] J.A.A. Engelbrecht, B. Sephton, E.G. Minnaar, M.C. Wagener, Physica B 480 (2016) 181. [21] S.P. Svensson, W.L. Sarney, H. Hier, Y. Lin, D. Wang, D. Donetsky, L. Shterengas, G. Kipshidze, G. Belenky, Phys. Rev. B 86 (2012) 245205. [22] R.S. Indolia, Int. J. Pure Appl. Phys. 13 (2017) 185. [23] F. Reizman, J. Appl. Phys. 36 (1965) 3804.
5