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Optical study of GaAs1−xSbx layers grown on GaAs substrates by gas-source molecular beam epitaxy
Materials Chemistry and Physics 124 (2010) 558–562
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Optical study of GaAs1−x Sbx layers grown on GaAs substrates by gas-source molecular beam epitaxy H.P. Hsu a,∗ , J.K. Huang a , Y.S. Huang b , Y.T. Lin c , H.H. Lin c , K.K. Tiong d a
Department of Electronic Engineering, Ming Chi University of Technology, 84 Gungjuan RD, Taishan, Taipei 243, Taiwan Department of Electronic Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan Department of Electrical Engineering, National Taiwan University, Taipei 106, Taiwan d Department of Electrical Engineering, National Taiwan Ocean University, Keelung 202, Taiwan b c
a r t i c l e
i n f o
Article history: Received 10 November 2009 Received in revised form 2 March 2010 Accepted 8 July 2010 PACS: 78.55.Cr 78.20.−e 78.66.−w 78.66.Fd
a b s t r a c t The optical properties of GaAs1−x Sbx (5.9% ≤ x ≤ 9.7%) layers grown on GaAs substrates by gas-source molecular beam epitaxy were characterized by photoreflectance (PR) and piezoreflectance (PzR). Identification of conduction to heavy-hole (HH) band and conduction to light-hole (LH) band transitions originated from the strained induced valence band splitting have been achieved by comparing the relative intensities of PR and PzR spectra. The results indicate increases of the valence band splitting with increasing of Sb content. The temperature dependences of near band edge transition energies were analyzed using Varshni and Bose–Einstein expressions in the temperature range from 15 to 300 K. The parameters that describe the temperature variations of the near band edge transition energies and broadening function were evaluated and discussed. © 2010 Elsevier B.V. All rights reserved.
Keywords: Semiconductors Optical properties Molecular beam epitaxy (MBE) Photoreflectance Piezoreflectance
1. Introduction Material systems based on arsenide–antimonide compounds have attracted much attention as candidates for optical device [1–5]. The Sb material systems can cover a wavelength range in fiber communications windows with a type-II [6–8] band gap lineup. Due to the large refractive index difference of GaSb and AlSb, the realization of monolithic vertical-cavity surface-emitting lasers (VCSELs) with fewer distributed-Bragg-reflector (DBR) periods than those of the InGaAsP/InP system in the 1.3 m wavelength range is made possible [9]. Edge-emitting lasers and VCSELs with GaAs1−x Sbx quantum wells (QWs) grown on GaAs substrate have been achieved [10]. The optical studies of GaAsSb/GaAs QWs were also reported by several research groups [11–13]. However, in spite of their potential applications, very little work has been done on the optical properties related to bulk layer materials. For example, the optical transition features originating from the valence band splitting and their temperature dependent near band edge interband
∗ Corresponding author. Tel.: +886 2 29089899x4864; fax: +886 2 29085247. E-mail address: [email protected] (H.P. Hsu). 0254-0584/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2010.07.011
transitions properties is only little known. Hence, further study on the basic optical properties of GaAsSb alloy is not only interesting but also necessary and important for the device design consideration. In this work, we have presented the temperature dependent photoreflectance (PR) and piezoreflectance (PzR) study of the strained GaAs1−x Sbx (x = 5.9–9.7%) layers grown on GaAs substrates by gas-source molecular beam epitaxy (MBE). The identification of conduction to heavy-hole (HH) band and conduction to light-hole (LH) band transitions originated from strain induced valence band splitting has been achieved by comparing the relative intensities of PR and PzR spectra. The temperature dependence behaviors of the transition energies in the range from 15 to 300 K were also studied. The parameters that describe the temperature variations of the near band edge transition energies and broadening function were evaluated and discussed. 2. Experimental The GaAs1−x Sbx layers were grown on (1 0 0) semi-insulating GaAs substrates by a VG-V80 gas-source MBE system. An EPI Sb cracking cell was used to provide the mixed dimmer and monomer Sb beam. The As2 beam source was from a gas cell with a cracking temperature of 1000 ◦ C using AsH3 as the precursor. Gallium flux, calibrated using an ion gauge to keep the growth rate at 1 m h−1 , was provided
H.P. Hsu et al. / Materials Chemistry and Physics 124 (2010) 558–562
559
Table 1 Values of strain related constants for GaAs1−x Sbx materials and the modulation coefficients from theoretical and experimental deduction. Theory
Samples
a (eV)
b (eV)
S11 (10−12 dyn cm−2 )
S12 (10−12 dyn cm−2 )
KPzR
KExpt
GaAs0.941 Sb0.059 GaAs0.916 Sb0.084 GaAs0.903 Sb0.097
−9.6 −9.5 −9.4
−2.0 −2.0 −2.0
1.18 1.19 1.20
−0.37 −0.38 −0.38
0.933 0.932 0.931
2.20 2.22 2.23
2.01 2.14 2.31
by an EPI uni-bulb RF plasma K-cell operating at a radio frequency of 13.56 MHz. A shutter was placed in front of the K-cell to reduce the ionized species. The thickness of the samples in this study was 1 m with a growth temperature of 490 ◦ C. The composition of the GaAs1−x Sbx was quantified by an electron probe X-ray microanalyzer (EPMA) with GaAs, and GaSb as standards for ZAF (atomic number Z, absorption A, and fluorescence F) correction. The Sb contents of the three samples were determined to be 5.9, 8.4, and 9.7%, respectively. For PR measurement, the modulation of the built-in electric field is caused by the photoexcited electron–hole pairs created by a mechanically chopped 670 nm line (∼3 mW) of a laser diode with a modulating frequency at 200 Hz. Piezoreflectance measurements were achieved by sticking the sample with glue on a 0.15 cm thick lead–zirconate–titanate (PZT) piezoelectric transducer driven by a 200 Vrms sinusoidal wave at 200 Hz. The alternating expansion and contraction of the transducer subjects the sample to an alternating strain with a typical rms l/l value of ∼10−5 . The radiation from a 150 W tungsten–halogen lamp filtered by a 0.25 m monochromator provided the monochromatic light. The reflected light was detected by a Si photodetector. The dc output of the photodetector was maintained constant by a servo mechanism of a variable neutral density filter. A dual-phase lock-in amplifier was used to measure the detected signals. Multiple scans over a given photon energy range was programmed until a desired signal-to-noise level has been attained with computer controlled data acquisition procedure. Detailed PR and PzR configuration has been described elsewhere [14,15]. For temperature dependent measurements, a closed-cycle cryogenic refrigerator equipped with a digital thermometer controller with temperature stability better than 0.5 K was used.
3. Results and discussion Fig. 1(a), (b) and (c) illustrates the PR and PzR spectra of the three GaAs1−x Sbx samples at 300 K. The experimental spectra reveal doublets near the band edge of GaAs1−x Sbx layers. The experimental data for PR and PzR are shown as dotted curves and the full curves are the least-squares fits to the first-derivative Lorentzian lineshape (FDLL) function of the form [16,17],
R −n Aj ei˚j (E − Ej + ij ) = Re R
(1)
j=1
where Aj and ˚j are the amplitude and phase of the line shape, Ej and j are the energy and broadening parameter of the transitions, and the value of n depends on the origin of the transitions. For the derivative functional form, n = 2 is appropriate for the bound states such as excitons. As shown in Fig. 1, the lineshape fits for both PR and PzR spectra clearly show two features (indicate with arrows) near the band edge of GaAs1−x Sbx . In order to identify the physical origin of the doublets, we make a spectral comparison of the PR and PzR measurements. For the PzR measurement under [0 0 1]-symmetry coplanar stress, the intensity ratio between the conduction to light-hole band transitions (LH) and conduction to heavy-hole band (HH) under the coplanar piezomodulation has been shown to follow the relation [18]. Theory
KPzR
≡
a(2 − ) + b(1 + ) (dELH /dS) = (dEHH /dS) a(2 − ) − b(1 + )
(2)
the variable S refers to the modulating stress applied to the sample. The parameters a and b represent the hydrostatic and the shear deformation potentials, respectively and = −2S12 /(S11 + S12 ), where Sij with i,j = 1 or 2, is the elastic compliance constant. For GaAs1−x Sbx , the numerical values of a, b, S11 , and S12 listed in Table 1 were obtained by linear interpolation of values of the endTheory for point semiconductors GaAs and GaSb [19]. The ratio of KPzR GaAs1−x Sbx is then evaluated to be about 2.20, 2.22, and 2.23 for x = 5.9, 8.4, and 9.7%, respectively (see Table 1). This shows that ELH
Fig. 1. PR and PzR spectra for GaAs1−x Sbx samples with (a) Sb = 5.9%, (b) Sb = 8.4%, and (c) Sb = 9.7% at room temperature. The obtained values of the transition energies are indicated by arrows.
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Fig. 2. PR spectra (dotted curves) of GaAs1−x Sbx samples for (a) Sb = 5.9%, (b) Sb = 8.4% and (c) Sb = 9.7% at 15, 77, 150, and 300 K. The full lines are least-squares fits to FDLL. The obtained values of the transition energies are indicated by the arrows.
Fig. 3. Temperature variations of the experimental PR values for HH and LH transition with representative error bars for GaAs1−x Sbx with (a) Sb = 5.9%, (b) Sb = 8.4%, and (c) Sb = 9.7% as open-circles and open-diamonds, respectively. The full curves are least-squares fits to Eq. (3) and the dotted lines are least-squares fits to Eq. (4).
transition is more sensitive than EHH when under the piezomodulation. To further confirm this calculation, the PR spectrum of the same sample, in which the relative intensity of the spectrum is insensitive to strain, has been made to act as a reference spectrum and allows us to compare its intensity with the PzR spectrum. The ratio of modulation coefficient of the amplitude is relative to [ILH /IHH ]PzR in the PzR spectrum and [ILH /IHH ]PR in the PR spectrum, where ILH and IHH are the amplitudes of ELH and EHH , respectively. In the PR spectrum, the modulation coefficient is the same for all transitions, so that the ratio KExpt ≡ [ILH /IHH ]PzR /[ILH /IHH ]PR directly gives the ratio of the piezomodulation coefficients for the ELH and EHH transitions. Experimentally, if we compare the intensities of the PzR and PR features in Fig. 1, we obtain the experimental values of the modulation coefficient KExpt to be 2.01, 2.14, and 2.31 for the samples with Sb = 5.9, 8.4, and 9.7%, respectively and are listed in
Table 1. These numbers are in reasonable agreement with the theoretical values. The combined analysis of the PzR and PR allows us to identify the features associated with the HH and LH transitions explicitly. The identified transition features are denoted as HH and LH indicated by vertical arrows in Fig. 1. As the Sb content increases, two effects can be noticed: a red-shift of the transitions and the enlarged separation of HH and LH transitions. The separations between HH and LH transitions are 9 ± 2, 12 ± 2, and 13 ± 2 meV for samples with Sb = 5.9, 8.4, and 9.7%, respectively. The results show an increase of the compressive strain when more Sb were incorporated into the GaAs1−x Sbx alloys. Fig. 2(a), (b) and (c) shows experimental PR spectra at several temperatures between 15 and 300 K of samples with Sb = 5.9, 8.4, and 9.7%, respectively. The dotted lines are the experimental curves
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561
Table 2 Values of the Varshni–and Bose–Einstein-type fitting parameters, which describe the temperature dependence of near band edge transition energies for GaAs1−x Sbx in this study. The parameters of GaAs1−x Sbx grown on GaAs or InP substrate and GaAs/GaSb bulk material are also included for comparison. Samples
Feature
Ei (0) (eV) (±0.005 eV)
˛i (meV K−1 ) (±0.05 meV K−1 )
ˇi (K) (±30 K)
aiB (meV) (±10 meV)
iB (K) (± 30 K)
dEi /dT (meV K−1 )
GaAs0.941 Sb0.059 /GaAsa
HH LH HH LH HH LH
1.394 1.399 1.352 1.359 1.335 1.343 Ei (0) (eV)
0.44 0.43 0.47 0.45 0.47 0.45 ˛i (meV K−1 )
165 165 175 175 185 185 ˇi (K)
45 41 47 45 49 47 aiB (meV)
210 210 220 225 230 230 iB (K)
−0.37 −0.36 −0.39 −0.37 −0.39 −0.38 dEi /dT (meV K−1 )
0.806 1.522 0.809
0.42 0.40 0.58 0.53
189 143 300 234
GaAs0.916 Sb0.084 /GaAsa GaAs0.903 Sb0.097 /GaAsa
GaAs1−x Sbx /GaAsb (x = 0.19–0.67) GaAs0.496 Sb0.504 /InPc GaAsd GaSbe a b c d e
Eg Eg Eg Eg
−0.33 −0.34 −0.50 −0.40
This work (photoreflectance). Reference [21] (absorption). Reference [22] (photoreflectance). Reference [23] (absorption). Reference [24] (photoreflectance).
and the solid lines are the fitted spectral data to Eq. (1) with n = 2, which yield transition energies for HH and LH are indicated by arrows. As the general property of most semiconductors, when the measuring temperature is increased, the HH and LH transitions in the PR spectra exhibit an energy red-shift characteristic. The temperature variations of the experimental PR values for HH and LH transitions with representative error bars for samples with Sb content = 5.9, 8.4, and 9.7% are depicted in Fig. 3(a), (b) and (c) as open-circle and open-diamond, respectively. The full curves are the temperature dependence of the HH and LH near band edge transition energies fitted by the Varshni semi-empirical relationship [20] Ei (T ) = Ei (0) −
˛i T 2 ˇi + T
(3)
where Ei (0) is the conduction to heavy-hole or light-hole band transition energies at 0 K. The constants ˛i is related to the electron (exciton)–average phonon interaction strength and ˇi is closely related to the Debye temperature. The values obtained are listed in Table 1. For comparison, the parameters for band gap energies of GaAs1−x Sbx grown on GaAs [21] or InP [22] substrate and GaAs [23]/GaSb [24] bulk material are also listed in Table 2. The temperature dependence of near band edge transition energies can also be described by a Bose–Einstein-type expression [25,26] Ei (T ) = Ei (0) −
2aiB [exp(iB /T ) − 1]
(4)
where Ei (0) is the transition energies for the conduction to heavyhole or conduction to light-hole band transition energies at 0 K, aiB represents the strength of the electron (exciton)–average phonon interaction, and iB corresponds to the average phonon temperature. Shown by the dotted lines are the least-squares fit to Eq. (4).
The values obtained for the various parameters are also presented in Table 2, together with that of the parameters for band gap energies of GaAs1−x Sbx grown on GaAs [21] or InP [22] substrate and GaAs [23]/GaSb [24] bulk material for comparison. The parameter ˛i of Eq. (3) can be related to aiB and iB in Eq. (4) by taking the high temperature limit of both expressions. This yields ˛ = 2aiB /iB . Comparison of the numbers presented in Table 1 show that this relation is satisfied approximately. From Eq. (4), it is straightforward to show that high temperature limit of the slope of E(T) vs. T curve approaches a value of −2aiB /iB . The calculated value of −2aiB /iB for conduction to heavy-hole (light-hole) near band edge transition energies equals to −0.42 (−0.39), −0.42 (−0.40), and −0.43 (−0.41) meV K−1 for Sb = 5.9, 8.4, and 9.7%, respectively, which agrees well with the value of [dEHH(LH) /dT] = −0.37 (−0.36), −0.39 (−0.37), and −0.39 (−0.38) meV K−1 as obtained from the linear extrapolation of the high temperature (150–300 K) PR experimental data. As shown in Table 1, the parameters that describe the temperature variations of near band edge transition energies of GaAs1−x Sbx in this study are comparable to that reported by literatures [21–24]. The values of ˛ and dEi /dT for GaAs1−x Sbx in this study are slightly smaller than that of GaAs [23] bulk material due mainly to the relatively small amount of antimony present in the studied samples. In Fig. 4, we display the temperature dependence of the broadening parameter for the HH transition determined from the theoretical fit of the PR spectra for three GaAs1−x Sbx samples. The solid line in Fig. 4 is the least-squares fit to the phonon-coupling model given by [27].
(T ) = (0) −
LO [exp(LO /T ) − 1]
(5)
Table 3 Values of the parameters that describe the temperature dependence of the broadening function (T) for conduction to heavy-hole band transition of GaAs1−x Sbx samples. Samples
Feature
(0) (meV) (±0.2 meV)
LO (meV) (±1 meV)
LO (K) (±10 K)
GaAs0.941 Sb0.059 /GaAsa GaAs0.916 Sb0.084 /GaAsa GaAs0.903 Sb0.097 /GaAsa
HH HH HH
5.4 5.6 5.9 (0) (meV)
10 10 10 LO (meV)
390 380 380 LO (K)
GaAsb GaSbc
Eg Eg
2.2 10.4
23 7
417 335
a b c
This work (photoreflectance). Reference [27] (photoreflectance). Reference [24] (photoreflectance).
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an expression containing the Bose–Einstein occupation factor for phonons. The parameters that describe the temperature dependence of GaAs1−x Sbx in this study are similar to that reported by literatures for GaAs. This has been attributed to the relatively small quantity of antimony incorporated into the GaAs1−x Sbx layers. The broadening parameters for the Sb-containing samples are larger than those of GaAs, due mainly to the poorer crystalline quality of the Sb-incorporated samples. Acknowledgments The authors acknowledge financial support from Ming Chi University of Technology and the support of National Science Council of Taiwan under Project No. NSC99-2628-E-131-008 and NSC982221-E-011-015-MY2.
Fig. 4. Temperature variations of the broadening parameter of HH transition for GaAs1−x Sbx samples. Representative error bars are shown. The solid curves are leastsquares fits to Eq. (5).
In Eq. (5), (0) represents the broadening invoked from temperature-independent mechanisms, such as electron–electron interaction, impurity, dislocation, and alloy scattering. The second term is caused by the exciton–LO phonon (Fröhlich) interaction. The quantity LO represents the strength of the exciton–LO phononcoupling while LO is the LO phonon temperature. The obtained values of (0), LO , and LO are listed in Table 3 together with the numbers for GaAs and GaSb. The values of (0) for the Sbcontaining samples are larger than those of the GaAs, due mainly to the poorer crystalline quality of the Sb-incorporated samples. The obtained values of LO and LO is reasonably located between the values of GaAs and GaSb reported by literatures [24,27]. In view of the small concentration of antimony in the GaAsSb samples, the values of LO are closer to that of GaAs and showed a slight shift to that of GaSb with an increase of Sb content. The smaller value of LO is presumably related to the lower effective longitudinal optical phonon energy of the Sb-containing samples. 4. Conclusion We have studied the optical properties of GaAs1−x Sbx grown on GaAs substrate with Sb = 5.9, 8.4, and 9.7% by PR and PzR techniques. A comparison of the PR and PzR spectra has led to the identification of HH and LH transitions originated from the valence band splitting of the samples. As the Sb content increases, both the PR and PzR spectra show red-shifts of the band edge transition features and enlarged separation of the HH and LH transitions. The increase of the valence band splitting indicates an increase of the compressive strain when more Sb is incorporated into the GaAs1−x Sbx layers. The temperature dependences of these near band edge transition energies were analyzed using the Varshni expression and
References [1] H.K. Choi, J. Eglash, Appl. Phys. Lett. 61 (1992) 1154. [2] H. Lee, P.K. York, J. Menna, R. Martinelli, D.Z. Garbuzov, S.Y. Narayan, J.C. Connolly, Appl. Phys. Lett. 66 (1995) 1942. [3] M. Peter, R. Kiefer, F. Fuchs, N. Herres, K. Winkler, K.H. Bachem, J. Wangner, Appl. Phys. Lett. 74 (1999) 1951. [4] P.W. Liu, M.H. Lee, H.H. Lin, J.R. Chen, Electron. Lett. 38 (2002) 1354. [5] P.W. Liu, G.H. Liao, H.H. Lin, Electron. Lett. 40 (2004) 177. [6] J.R. Meyer, C.A. Hoffman, F.J. Bartoli, L.R. Ram-Mohan, Appl. Phys. Lett. 67 (1995) 757. [7] D.L. Smith, C. Mailhiot, J. Appl. Phys. 62 (1987) 2545. [8] R.H. Miles, D.H. Chow, Y.H. Zhang, P.D. Brewer, R.G. Wilson, Appl. Phys. Lett. 66 (1994) 1921. [9] M. Yamada, T. Anan, K. Tokutome, K. Nishi, A. Gomyo, S. Sugou, Conf. Proc. LEOS, Orlando, 1998, p. 149. [10] T. Anan, M. Yamada, K. Tokutome, S. Sugou, L. Nishi, A. Kamei, Electron. Lett. 34 (1999) 903. [11] X.D. Luo, C.Y. Hu, Z.Y. Xu, H.L. Luo, Y.Q. Wang, J.N. Wang, W.K. Ge, Appl. Phys. Lett. 81 (2002) 3795. [12] M. Dinu, J.E. Cunningham, F. Quochi, J. Shah, J. Appl. Physiol. 94 (2003) 1506. [13] Y.S. Chiu, M.H. Ya, W.S. Su, Y.F. Chen, J. Appl. Physiol. 92 (2002) 5810. [14] Y.S. Huang, F.H. Pollak, Phys. Stat. Sol. A 202 (2005) 1193. [15] F.H. Pollak, H. Shen, Mater. Sci. Eng. R 10 (1993) 275. [16] D.E. Aspnes, in: T.S. Moss (Ed.), Handbook on Semiconductor, vol. 2, NorthHolland, New York, 1996, p. 109. [17] D.E. Aspnes, A.A. Studna, Phys. Rev. B 7 (1973) 4605. [18] H. Mathieu, J. Allègre, B. Gil, Phys. Rev. B 43 (1991) 2218. [19] I. Vurgaftman, J.R. Meyer, L.R. Ram-Mohan, J. Appl. Phys. 89 (2001) 5815. [20] Y.P. Varshni, Physica 34 (1967) 149. [21] R. Lukic-Zrnic, B.P. Gorman, R.J. Cottier, T.D. Golding, C.L. Littler, A.G. Norman, J. Appl. Phys. 92 (2002) 6939. [22] H. Chouaib, C. Bru-Chevallier, G. Guillot, H. Lahreche, P. Bove, J. Appl. Phys. 98 (2005) 123524. [23] M.B. Panish, H.C. Casey Jr., J. Appl. Phys. 40 (1969) 163. ˜ [24] M. Munoz, F.H. Pollak, M.B. Zakia, N.B. Patel, J.L. Herrera-Pérez, Phys. Rev. B 62 (2000) 16600. ˜ [25] L. Vina, S. Logothetidis, M. Cardona, Phys. Rev. B 30 (1984) 1979. [26] P. Lautenschlager, M. Garriga, S. Logothetidis, M. Cardona, Phys. Rev. B 35 (1987) 9174. [27] H. Qiang, F.H. Pollak, C.M. Sotomayor Torres, W. Leitch, A.H. Kean, M.A. Stroscio, G.J. Lafrate, K.W. Kim, Appl. Phys. Lett. 61 (1992) 1411.
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Optical study of GaAs1−x Sbx layers grown on GaAs substrates by gas-source molecular beam epitaxy H.P. Hsu a,∗ , J.K. Huang a , Y.S. Huang b , Y.T. Lin c , H.H. Lin c , K.K. Tiong d a
Department of Electronic Engineering, Ming Chi University of Technology, 84 Gungjuan RD, Taishan, Taipei 243, Taiwan Department of Electronic Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan Department of Electrical Engineering, National Taiwan University, Taipei 106, Taiwan d Department of Electrical Engineering, National Taiwan Ocean University, Keelung 202, Taiwan b c
a r t i c l e
i n f o
Article history: Received 10 November 2009 Received in revised form 2 March 2010 Accepted 8 July 2010 PACS: 78.55.Cr 78.20.−e 78.66.−w 78.66.Fd
a b s t r a c t The optical properties of GaAs1−x Sbx (5.9% ≤ x ≤ 9.7%) layers grown on GaAs substrates by gas-source molecular beam epitaxy were characterized by photoreflectance (PR) and piezoreflectance (PzR). Identification of conduction to heavy-hole (HH) band and conduction to light-hole (LH) band transitions originated from the strained induced valence band splitting have been achieved by comparing the relative intensities of PR and PzR spectra. The results indicate increases of the valence band splitting with increasing of Sb content. The temperature dependences of near band edge transition energies were analyzed using Varshni and Bose–Einstein expressions in the temperature range from 15 to 300 K. The parameters that describe the temperature variations of the near band edge transition energies and broadening function were evaluated and discussed. © 2010 Elsevier B.V. All rights reserved.
Keywords: Semiconductors Optical properties Molecular beam epitaxy (MBE) Photoreflectance Piezoreflectance
1. Introduction Material systems based on arsenide–antimonide compounds have attracted much attention as candidates for optical device [1–5]. The Sb material systems can cover a wavelength range in fiber communications windows with a type-II [6–8] band gap lineup. Due to the large refractive index difference of GaSb and AlSb, the realization of monolithic vertical-cavity surface-emitting lasers (VCSELs) with fewer distributed-Bragg-reflector (DBR) periods than those of the InGaAsP/InP system in the 1.3 m wavelength range is made possible [9]. Edge-emitting lasers and VCSELs with GaAs1−x Sbx quantum wells (QWs) grown on GaAs substrate have been achieved [10]. The optical studies of GaAsSb/GaAs QWs were also reported by several research groups [11–13]. However, in spite of their potential applications, very little work has been done on the optical properties related to bulk layer materials. For example, the optical transition features originating from the valence band splitting and their temperature dependent near band edge interband
∗ Corresponding author. Tel.: +886 2 29089899x4864; fax: +886 2 29085247. E-mail address: [email protected] (H.P. Hsu). 0254-0584/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2010.07.011
transitions properties is only little known. Hence, further study on the basic optical properties of GaAsSb alloy is not only interesting but also necessary and important for the device design consideration. In this work, we have presented the temperature dependent photoreflectance (PR) and piezoreflectance (PzR) study of the strained GaAs1−x Sbx (x = 5.9–9.7%) layers grown on GaAs substrates by gas-source molecular beam epitaxy (MBE). The identification of conduction to heavy-hole (HH) band and conduction to light-hole (LH) band transitions originated from strain induced valence band splitting has been achieved by comparing the relative intensities of PR and PzR spectra. The temperature dependence behaviors of the transition energies in the range from 15 to 300 K were also studied. The parameters that describe the temperature variations of the near band edge transition energies and broadening function were evaluated and discussed. 2. Experimental The GaAs1−x Sbx layers were grown on (1 0 0) semi-insulating GaAs substrates by a VG-V80 gas-source MBE system. An EPI Sb cracking cell was used to provide the mixed dimmer and monomer Sb beam. The As2 beam source was from a gas cell with a cracking temperature of 1000 ◦ C using AsH3 as the precursor. Gallium flux, calibrated using an ion gauge to keep the growth rate at 1 m h−1 , was provided
H.P. Hsu et al. / Materials Chemistry and Physics 124 (2010) 558–562
559
Table 1 Values of strain related constants for GaAs1−x Sbx materials and the modulation coefficients from theoretical and experimental deduction. Theory
Samples
a (eV)
b (eV)
S11 (10−12 dyn cm−2 )
S12 (10−12 dyn cm−2 )
KPzR
KExpt
GaAs0.941 Sb0.059 GaAs0.916 Sb0.084 GaAs0.903 Sb0.097
−9.6 −9.5 −9.4
−2.0 −2.0 −2.0
1.18 1.19 1.20
−0.37 −0.38 −0.38
0.933 0.932 0.931
2.20 2.22 2.23
2.01 2.14 2.31
by an EPI uni-bulb RF plasma K-cell operating at a radio frequency of 13.56 MHz. A shutter was placed in front of the K-cell to reduce the ionized species. The thickness of the samples in this study was 1 m with a growth temperature of 490 ◦ C. The composition of the GaAs1−x Sbx was quantified by an electron probe X-ray microanalyzer (EPMA) with GaAs, and GaSb as standards for ZAF (atomic number Z, absorption A, and fluorescence F) correction. The Sb contents of the three samples were determined to be 5.9, 8.4, and 9.7%, respectively. For PR measurement, the modulation of the built-in electric field is caused by the photoexcited electron–hole pairs created by a mechanically chopped 670 nm line (∼3 mW) of a laser diode with a modulating frequency at 200 Hz. Piezoreflectance measurements were achieved by sticking the sample with glue on a 0.15 cm thick lead–zirconate–titanate (PZT) piezoelectric transducer driven by a 200 Vrms sinusoidal wave at 200 Hz. The alternating expansion and contraction of the transducer subjects the sample to an alternating strain with a typical rms l/l value of ∼10−5 . The radiation from a 150 W tungsten–halogen lamp filtered by a 0.25 m monochromator provided the monochromatic light. The reflected light was detected by a Si photodetector. The dc output of the photodetector was maintained constant by a servo mechanism of a variable neutral density filter. A dual-phase lock-in amplifier was used to measure the detected signals. Multiple scans over a given photon energy range was programmed until a desired signal-to-noise level has been attained with computer controlled data acquisition procedure. Detailed PR and PzR configuration has been described elsewhere [14,15]. For temperature dependent measurements, a closed-cycle cryogenic refrigerator equipped with a digital thermometer controller with temperature stability better than 0.5 K was used.
3. Results and discussion Fig. 1(a), (b) and (c) illustrates the PR and PzR spectra of the three GaAs1−x Sbx samples at 300 K. The experimental spectra reveal doublets near the band edge of GaAs1−x Sbx layers. The experimental data for PR and PzR are shown as dotted curves and the full curves are the least-squares fits to the first-derivative Lorentzian lineshape (FDLL) function of the form [16,17],
R −n Aj ei˚j (E − Ej + ij ) = Re R
(1)
j=1
where Aj and ˚j are the amplitude and phase of the line shape, Ej and j are the energy and broadening parameter of the transitions, and the value of n depends on the origin of the transitions. For the derivative functional form, n = 2 is appropriate for the bound states such as excitons. As shown in Fig. 1, the lineshape fits for both PR and PzR spectra clearly show two features (indicate with arrows) near the band edge of GaAs1−x Sbx . In order to identify the physical origin of the doublets, we make a spectral comparison of the PR and PzR measurements. For the PzR measurement under [0 0 1]-symmetry coplanar stress, the intensity ratio between the conduction to light-hole band transitions (LH) and conduction to heavy-hole band (HH) under the coplanar piezomodulation has been shown to follow the relation [18]. Theory
KPzR
≡
a(2 − ) + b(1 + ) (dELH /dS) = (dEHH /dS) a(2 − ) − b(1 + )
(2)
the variable S refers to the modulating stress applied to the sample. The parameters a and b represent the hydrostatic and the shear deformation potentials, respectively and = −2S12 /(S11 + S12 ), where Sij with i,j = 1 or 2, is the elastic compliance constant. For GaAs1−x Sbx , the numerical values of a, b, S11 , and S12 listed in Table 1 were obtained by linear interpolation of values of the endTheory for point semiconductors GaAs and GaSb [19]. The ratio of KPzR GaAs1−x Sbx is then evaluated to be about 2.20, 2.22, and 2.23 for x = 5.9, 8.4, and 9.7%, respectively (see Table 1). This shows that ELH
Fig. 1. PR and PzR spectra for GaAs1−x Sbx samples with (a) Sb = 5.9%, (b) Sb = 8.4%, and (c) Sb = 9.7% at room temperature. The obtained values of the transition energies are indicated by arrows.
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Fig. 2. PR spectra (dotted curves) of GaAs1−x Sbx samples for (a) Sb = 5.9%, (b) Sb = 8.4% and (c) Sb = 9.7% at 15, 77, 150, and 300 K. The full lines are least-squares fits to FDLL. The obtained values of the transition energies are indicated by the arrows.
Fig. 3. Temperature variations of the experimental PR values for HH and LH transition with representative error bars for GaAs1−x Sbx with (a) Sb = 5.9%, (b) Sb = 8.4%, and (c) Sb = 9.7% as open-circles and open-diamonds, respectively. The full curves are least-squares fits to Eq. (3) and the dotted lines are least-squares fits to Eq. (4).
transition is more sensitive than EHH when under the piezomodulation. To further confirm this calculation, the PR spectrum of the same sample, in which the relative intensity of the spectrum is insensitive to strain, has been made to act as a reference spectrum and allows us to compare its intensity with the PzR spectrum. The ratio of modulation coefficient of the amplitude is relative to [ILH /IHH ]PzR in the PzR spectrum and [ILH /IHH ]PR in the PR spectrum, where ILH and IHH are the amplitudes of ELH and EHH , respectively. In the PR spectrum, the modulation coefficient is the same for all transitions, so that the ratio KExpt ≡ [ILH /IHH ]PzR /[ILH /IHH ]PR directly gives the ratio of the piezomodulation coefficients for the ELH and EHH transitions. Experimentally, if we compare the intensities of the PzR and PR features in Fig. 1, we obtain the experimental values of the modulation coefficient KExpt to be 2.01, 2.14, and 2.31 for the samples with Sb = 5.9, 8.4, and 9.7%, respectively and are listed in
Table 1. These numbers are in reasonable agreement with the theoretical values. The combined analysis of the PzR and PR allows us to identify the features associated with the HH and LH transitions explicitly. The identified transition features are denoted as HH and LH indicated by vertical arrows in Fig. 1. As the Sb content increases, two effects can be noticed: a red-shift of the transitions and the enlarged separation of HH and LH transitions. The separations between HH and LH transitions are 9 ± 2, 12 ± 2, and 13 ± 2 meV for samples with Sb = 5.9, 8.4, and 9.7%, respectively. The results show an increase of the compressive strain when more Sb were incorporated into the GaAs1−x Sbx alloys. Fig. 2(a), (b) and (c) shows experimental PR spectra at several temperatures between 15 and 300 K of samples with Sb = 5.9, 8.4, and 9.7%, respectively. The dotted lines are the experimental curves
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561
Table 2 Values of the Varshni–and Bose–Einstein-type fitting parameters, which describe the temperature dependence of near band edge transition energies for GaAs1−x Sbx in this study. The parameters of GaAs1−x Sbx grown on GaAs or InP substrate and GaAs/GaSb bulk material are also included for comparison. Samples
Feature
Ei (0) (eV) (±0.005 eV)
˛i (meV K−1 ) (±0.05 meV K−1 )
ˇi (K) (±30 K)
aiB (meV) (±10 meV)
iB (K) (± 30 K)
dEi /dT (meV K−1 )
GaAs0.941 Sb0.059 /GaAsa
HH LH HH LH HH LH
1.394 1.399 1.352 1.359 1.335 1.343 Ei (0) (eV)
0.44 0.43 0.47 0.45 0.47 0.45 ˛i (meV K−1 )
165 165 175 175 185 185 ˇi (K)
45 41 47 45 49 47 aiB (meV)
210 210 220 225 230 230 iB (K)
−0.37 −0.36 −0.39 −0.37 −0.39 −0.38 dEi /dT (meV K−1 )
0.806 1.522 0.809
0.42 0.40 0.58 0.53
189 143 300 234
GaAs0.916 Sb0.084 /GaAsa GaAs0.903 Sb0.097 /GaAsa
GaAs1−x Sbx /GaAsb (x = 0.19–0.67) GaAs0.496 Sb0.504 /InPc GaAsd GaSbe a b c d e
Eg Eg Eg Eg
−0.33 −0.34 −0.50 −0.40
This work (photoreflectance). Reference [21] (absorption). Reference [22] (photoreflectance). Reference [23] (absorption). Reference [24] (photoreflectance).
and the solid lines are the fitted spectral data to Eq. (1) with n = 2, which yield transition energies for HH and LH are indicated by arrows. As the general property of most semiconductors, when the measuring temperature is increased, the HH and LH transitions in the PR spectra exhibit an energy red-shift characteristic. The temperature variations of the experimental PR values for HH and LH transitions with representative error bars for samples with Sb content = 5.9, 8.4, and 9.7% are depicted in Fig. 3(a), (b) and (c) as open-circle and open-diamond, respectively. The full curves are the temperature dependence of the HH and LH near band edge transition energies fitted by the Varshni semi-empirical relationship [20] Ei (T ) = Ei (0) −
˛i T 2 ˇi + T
(3)
where Ei (0) is the conduction to heavy-hole or light-hole band transition energies at 0 K. The constants ˛i is related to the electron (exciton)–average phonon interaction strength and ˇi is closely related to the Debye temperature. The values obtained are listed in Table 1. For comparison, the parameters for band gap energies of GaAs1−x Sbx grown on GaAs [21] or InP [22] substrate and GaAs [23]/GaSb [24] bulk material are also listed in Table 2. The temperature dependence of near band edge transition energies can also be described by a Bose–Einstein-type expression [25,26] Ei (T ) = Ei (0) −
2aiB [exp(iB /T ) − 1]
(4)
where Ei (0) is the transition energies for the conduction to heavyhole or conduction to light-hole band transition energies at 0 K, aiB represents the strength of the electron (exciton)–average phonon interaction, and iB corresponds to the average phonon temperature. Shown by the dotted lines are the least-squares fit to Eq. (4).
The values obtained for the various parameters are also presented in Table 2, together with that of the parameters for band gap energies of GaAs1−x Sbx grown on GaAs [21] or InP [22] substrate and GaAs [23]/GaSb [24] bulk material for comparison. The parameter ˛i of Eq. (3) can be related to aiB and iB in Eq. (4) by taking the high temperature limit of both expressions. This yields ˛ = 2aiB /iB . Comparison of the numbers presented in Table 1 show that this relation is satisfied approximately. From Eq. (4), it is straightforward to show that high temperature limit of the slope of E(T) vs. T curve approaches a value of −2aiB /iB . The calculated value of −2aiB /iB for conduction to heavy-hole (light-hole) near band edge transition energies equals to −0.42 (−0.39), −0.42 (−0.40), and −0.43 (−0.41) meV K−1 for Sb = 5.9, 8.4, and 9.7%, respectively, which agrees well with the value of [dEHH(LH) /dT] = −0.37 (−0.36), −0.39 (−0.37), and −0.39 (−0.38) meV K−1 as obtained from the linear extrapolation of the high temperature (150–300 K) PR experimental data. As shown in Table 1, the parameters that describe the temperature variations of near band edge transition energies of GaAs1−x Sbx in this study are comparable to that reported by literatures [21–24]. The values of ˛ and dEi /dT for GaAs1−x Sbx in this study are slightly smaller than that of GaAs [23] bulk material due mainly to the relatively small amount of antimony present in the studied samples. In Fig. 4, we display the temperature dependence of the broadening parameter for the HH transition determined from the theoretical fit of the PR spectra for three GaAs1−x Sbx samples. The solid line in Fig. 4 is the least-squares fit to the phonon-coupling model given by [27].
(T ) = (0) −
LO [exp(LO /T ) − 1]
(5)
Table 3 Values of the parameters that describe the temperature dependence of the broadening function (T) for conduction to heavy-hole band transition of GaAs1−x Sbx samples. Samples
Feature
(0) (meV) (±0.2 meV)
LO (meV) (±1 meV)
LO (K) (±10 K)
GaAs0.941 Sb0.059 /GaAsa GaAs0.916 Sb0.084 /GaAsa GaAs0.903 Sb0.097 /GaAsa
HH HH HH
5.4 5.6 5.9 (0) (meV)
10 10 10 LO (meV)
390 380 380 LO (K)
GaAsb GaSbc
Eg Eg
2.2 10.4
23 7
417 335
a b c
This work (photoreflectance). Reference [27] (photoreflectance). Reference [24] (photoreflectance).
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an expression containing the Bose–Einstein occupation factor for phonons. The parameters that describe the temperature dependence of GaAs1−x Sbx in this study are similar to that reported by literatures for GaAs. This has been attributed to the relatively small quantity of antimony incorporated into the GaAs1−x Sbx layers. The broadening parameters for the Sb-containing samples are larger than those of GaAs, due mainly to the poorer crystalline quality of the Sb-incorporated samples. Acknowledgments The authors acknowledge financial support from Ming Chi University of Technology and the support of National Science Council of Taiwan under Project No. NSC99-2628-E-131-008 and NSC982221-E-011-015-MY2.
Fig. 4. Temperature variations of the broadening parameter of HH transition for GaAs1−x Sbx samples. Representative error bars are shown. The solid curves are leastsquares fits to Eq. (5).
In Eq. (5), (0) represents the broadening invoked from temperature-independent mechanisms, such as electron–electron interaction, impurity, dislocation, and alloy scattering. The second term is caused by the exciton–LO phonon (Fröhlich) interaction. The quantity LO represents the strength of the exciton–LO phononcoupling while LO is the LO phonon temperature. The obtained values of (0), LO , and LO are listed in Table 3 together with the numbers for GaAs and GaSb. The values of (0) for the Sbcontaining samples are larger than those of the GaAs, due mainly to the poorer crystalline quality of the Sb-incorporated samples. The obtained values of LO and LO is reasonably located between the values of GaAs and GaSb reported by literatures [24,27]. In view of the small concentration of antimony in the GaAsSb samples, the values of LO are closer to that of GaAs and showed a slight shift to that of GaSb with an increase of Sb content. The smaller value of LO is presumably related to the lower effective longitudinal optical phonon energy of the Sb-containing samples. 4. Conclusion We have studied the optical properties of GaAs1−x Sbx grown on GaAs substrate with Sb = 5.9, 8.4, and 9.7% by PR and PzR techniques. A comparison of the PR and PzR spectra has led to the identification of HH and LH transitions originated from the valence band splitting of the samples. As the Sb content increases, both the PR and PzR spectra show red-shifts of the band edge transition features and enlarged separation of the HH and LH transitions. The increase of the valence band splitting indicates an increase of the compressive strain when more Sb is incorporated into the GaAs1−x Sbx layers. The temperature dependences of these near band edge transition energies were analyzed using the Varshni expression and
References [1] H.K. Choi, J. Eglash, Appl. Phys. Lett. 61 (1992) 1154. [2] H. Lee, P.K. York, J. Menna, R. Martinelli, D.Z. Garbuzov, S.Y. Narayan, J.C. Connolly, Appl. Phys. Lett. 66 (1995) 1942. [3] M. Peter, R. Kiefer, F. Fuchs, N. Herres, K. Winkler, K.H. Bachem, J. Wangner, Appl. Phys. Lett. 74 (1999) 1951. [4] P.W. Liu, M.H. Lee, H.H. Lin, J.R. Chen, Electron. Lett. 38 (2002) 1354. [5] P.W. Liu, G.H. Liao, H.H. Lin, Electron. Lett. 40 (2004) 177. [6] J.R. Meyer, C.A. Hoffman, F.J. Bartoli, L.R. Ram-Mohan, Appl. Phys. Lett. 67 (1995) 757. [7] D.L. Smith, C. Mailhiot, J. Appl. Phys. 62 (1987) 2545. [8] R.H. Miles, D.H. Chow, Y.H. Zhang, P.D. Brewer, R.G. Wilson, Appl. Phys. Lett. 66 (1994) 1921. [9] M. Yamada, T. Anan, K. Tokutome, K. Nishi, A. Gomyo, S. Sugou, Conf. Proc. LEOS, Orlando, 1998, p. 149. [10] T. Anan, M. Yamada, K. Tokutome, S. Sugou, L. Nishi, A. Kamei, Electron. Lett. 34 (1999) 903. [11] X.D. Luo, C.Y. Hu, Z.Y. Xu, H.L. Luo, Y.Q. Wang, J.N. Wang, W.K. Ge, Appl. Phys. Lett. 81 (2002) 3795. [12] M. Dinu, J.E. Cunningham, F. Quochi, J. Shah, J. Appl. Physiol. 94 (2003) 1506. [13] Y.S. Chiu, M.H. Ya, W.S. Su, Y.F. Chen, J. Appl. Physiol. 92 (2002) 5810. [14] Y.S. Huang, F.H. Pollak, Phys. Stat. Sol. A 202 (2005) 1193. [15] F.H. Pollak, H. Shen, Mater. Sci. Eng. R 10 (1993) 275. [16] D.E. Aspnes, in: T.S. Moss (Ed.), Handbook on Semiconductor, vol. 2, NorthHolland, New York, 1996, p. 109. [17] D.E. Aspnes, A.A. Studna, Phys. Rev. B 7 (1973) 4605. [18] H. Mathieu, J. Allègre, B. Gil, Phys. Rev. B 43 (1991) 2218. [19] I. Vurgaftman, J.R. Meyer, L.R. Ram-Mohan, J. Appl. Phys. 89 (2001) 5815. [20] Y.P. Varshni, Physica 34 (1967) 149. [21] R. Lukic-Zrnic, B.P. Gorman, R.J. Cottier, T.D. Golding, C.L. Littler, A.G. Norman, J. Appl. Phys. 92 (2002) 6939. [22] H. Chouaib, C. Bru-Chevallier, G. Guillot, H. Lahreche, P. Bove, J. Appl. Phys. 98 (2005) 123524. [23] M.B. Panish, H.C. Casey Jr., J. Appl. Phys. 40 (1969) 163. ˜ [24] M. Munoz, F.H. Pollak, M.B. Zakia, N.B. Patel, J.L. Herrera-Pérez, Phys. Rev. B 62 (2000) 16600. ˜ [25] L. Vina, S. Logothetidis, M. Cardona, Phys. Rev. B 30 (1984) 1979. [26] P. Lautenschlager, M. Garriga, S. Logothetidis, M. Cardona, Phys. Rev. B 35 (1987) 9174. [27] H. Qiang, F.H. Pollak, C.M. Sotomayor Torres, W. Leitch, A.H. Kean, M.A. Stroscio, G.J. Lafrate, K.W. Kim, Appl. Phys. Lett. 61 (1992) 1411.