Abstract
The inplane optical anisotropy (IPOA) in InAs/GaSb superlattices has been studied by reflectance difference spectroscopy (RDS) at different temperatures ranging from 80 to 300 K. We introduce alternate GaAs and InSblike interfaces (IFs), which cause the symmetry reduced from D_{2d} to C_{2v}. IPOA has been observed in the (001) plane along [110] and [1
0] axes. RDS measurement results show strong anisotropy resonance near critical point (CP) energies of InAs and GaSb. The energy positions show red shift and RDS intensity decreases with the increasing temperature. For the superlattice sample with the thicker InSblike IFs, energy positions show red shift, and the spectra exhibit stronger IPOA. The excitonic effect is clearly observed by RDS at low temperatures. It demonstrates that biaxial strain results in the shift of the CP energies and IPOA is enhanced by the further localization of the carriers in InSblike IFs.Background
InAs/GaSb typeII superlattices (SLs) are a considerable interest in the application of middle and far infrared photodetection. These structures have brokengap band alignment, which allows tuning optical and electronic properties by varying layer thickness [1,2]. As the InAs and GaSb share no common atoms (NCA) across the interface (IF), these IFs have to be controlled by both InAslike, both GaSblike or alternating InAs and GaSblike. Figure 1 illustrates a simplified ballandstick model of InAs/GaSb SL with lower GaAslike and upper InSblike IFs. This kind of CA/C’A’ zinc blende heterostructures lost their ideal T_{d} pointgroup symmetry along the [001] growth direction. C and A represent cation and anion, respectively. If SLs have only one type of IF such as CA’ or C’A, it exists a S_{4} rotationreflection axis, the symmetry is described as D_{2d} pointgroup symmetry. If SLs have both kinds of IFs alternately, the symmetry depends on the number of atomic monolayer (ML) of each components. SLs components with one or both odd numbers of atomic ML belong to the D_{2d} pointgroup symmetry, with both even numbers of atomic ML are corresponding to C_{2v} pointgroup symmetry. If the structure shares a common atom (CA) (A=A’ or C=C’), the IFs have a S_{4} rotationreflection axis corresponding to the D_{2d} pointgroup symmetry. It is supposed that CA bonds lie in the (110) plane and AC’ bonds are in the (10) plane. When a beam of linear polarized light propagates along the [001] direction with its polarized direction parallel to the [110] or [10] direction, it feels different chemical bonds. This kind of anisotropicchemicalbond arrangement leads to inplane optical anisotropy (IPOA) at the IFs, i.e., optical property of [110] and [10] plane is different in the (001) plane. Exactly speaking, the IPOA of upper and lower IFs will cancel each other for the SLs with D_{2d} symmetry. Although, it is hard to realize such perfect IFs by the growth process that has many uncontrollable factors, the weak IPOA is still well observed by reflectance difference spectroscopy (RDS) [3,4]. For the NCA SLs, it has been observed that the IPOA is very strong [58].
Figure 1. Simple stickandball model of InAs/GaSb SL with alternate GaAs and InSb IFs. The purple, blue, green, and brown balls denote In, As, Ga, and Sb atoms, respectively.
RDS is a very sensitive nondestructive optical detection technique for IPOA, which was invented by D.E Aspens [9]. This powerful tool is used to detect IPOA induced by strain, electric field, and atom segregation for bulk, surface, and IF. In this letter, we have measured the IPOA of (001) plane of InAs/GaSb SLs by RDS at different temperatures ranging from 80 to 300 K. In this experiment, two SL examples have different thickness of InSblike IF. The spectra are ranging from 1.5 to 5.0 eV. In the spectra, the energies of main features are assigned to Γ (E_{0}, E_{0}+Δ_{0}), Λ (E_{1}, E_{1}+Δ_{1}), and other critical point (CP) interband transitions of InAs, GaSb, and the coupling of the components whereas the L, X, and Σ CP energies are complex and difficult to analyze. Table 1 shows a list of the CP energies of bulk InAs, GaSb, GaAs, and InSb [10]. Additional CP energies may be related to the IFs. The Λ CP energies are very sensitive to strain. The CP energies show red shift with the increasing temperature, which attributes to the enhancement of electronphonon interaction and thermal expansion. The transitions show a clear exciton characteristic at low temperatures. Compared with sample A, the measured energies of Λ CPs show red shift for sample B and exhibit stronger IPOA. The red shift attributes to the increasing of average lattice constant. IPOA is enhanced by the further localization of carriers in InSblike IFs.
Methods
The InAs/GaSb SLs were grown on GaSb buffer layer, which is deposited on nonintentional doping GaSb (001) substrates by molecular beam epitaxy (MBE). The GaAslike IFs were generated by employing As soaking after GaSb is deposited. The InSblike IFs were formed by InSb deposition. Two samples have the same structure as 100 periods InAs (10 ML)/GaSb (8 ML) without capping layer. The difference of the two examples is only the thickness of InSb layer, 0.43 ML (sample A) and 1.29 ML (sample B), respectively. We used a Bede D1 highresolution Xray diffractometer to characterize structural quality of the samples. The lattice mismatch and oneperiod thickness can be predicted.
We measured the relative reflectance difference between [110] and [10] in (001) plane, obtaining
ranging from 80 to 300 K in a cryogenic Dewar bottle. In the RDS measurement, nearnormal incidence reflectivity of two perpendicular directions was obtained in order to remove the influence of errors induced by optical components, averaging two spectra sample azimuth by 90°. The difference of dielectric functions () has a relation with Δr/r:
Here, α and β are complicated functions of four refractive indices and the wavelength of light. Both the real and imaginary part of Δr/r are linear combinations of real and imaginary part of Δε[11]. The degree of polarization (DOP) is defined as (M_{110} is the transition probability when light is polarized along [110] direction). Im(Δε) is proportional to ΔM, and Im(ε) is proportional to M. It can be deduced from the imaginary part of Δε and the imaginary part of ε: [12].
Results and discussion
Lattice constants of GaAs, InAs, GaSb, and InSb are 5.2430, 6.0173, 6.0959, and 6.8970 Å, respectively [13]. The lattice mismatch between InAs and GaSb is only 0.6%; however, that of GaAs/GaSb and InSb/GaSb are 8% and 6%, respectively. Inserting GaAslike IFs equals to introduce compress strain for the SLs, while InSblike IFs will result in tensile strain. Alternating GaAs or InSblike IF layers can compensate the lattice mismatch between InAs and GaSb by controlling the appropriate thickness of GaAs and InSb layers. If SLs are pseudomorphicgrown on GaSb substrate, the strains of GaAs, InAs, and InSb are determined by the substrate, which can be calculated by:
, , and are the strains of GaAs, InAs, and GaSb for directions parallel and perpendicular to the growth direction, respectively. a_{sub}, a_{i}, and represent crystal constants of GaSb substrate, for each layer, and the layers of SLs after growth, respectively. v_{i} is the Possion ratio. The band gap and energies of CPs will show blue or red shift for compress or tensile biaxial strain, respectively. The two SL samples have the same thickness of GaAslike IFs and different thickness of InSblike IFs. The average lattice constant of superlattice is increased as a result of red shift energies of the CPs.
Xray diffraction (XRD) results indicate that the range of 0th peak of sample A and the substrate is 0.367° and 0.151° for sample B. The full width at half maximum (FWHM) of the first satellite peak is 34 arcsec for sample A and 43 aresec for sample B. Both of the samples show compression strain. The calculated strain is 0.0054 for sample A and 0.0023 for sample B. Increasing the thickness of InSblike IF layers can reduce the average compression strain. We predicted oneperiod thickness from the spacing between the satellites. Each period thickness of sample A is 55.9 Å and 56.8 Å for sample B.
Figure 2a,b shows the real parts of the relative reflectance difference measured at 300 and 80 K, respectively. The resonances of two samples have the same lineshape. In the spectra, the sharp peak near 2.05 eV(CP1), which is related to E_{1}energy of GaSb. The lineshape of real part is almost the derivative of the imaginary part. A small feature is observed at this region, which is coincidence that the InAs E_{1} and GaSb E_{1}+Δ_{1}energies are both near 2.50 eV(CP2). The InAs E_{1}energy is a little larger than GaSb E_{1}+Δ_{1} energy. Another feature is observed near 2.78 eV(CP3) corresponding to the critical point energy of InAs E_{1}+Δ_{1}. Two shoulderlike features were marked in Figure 2b on both sides of the sharp peak near 2.05 eV, which may be attributed to InSblike IFs. The energy positions are near the E_{1} and E_{1}+Δ_{1}energies of bulk InSb, and it is more clearly shown in the 80K measurement. However, the IPOA structures about GaAs are not observed. In comparison with sample A, it is observed that GaSb E_{1} and InAs E_{1}+Δ_{1}features show red shift for sample B, which attributes to the compensation of stress by increasing the thickness of InSblike IF layer. It is anomalous that a blue shift peak is corresponding to InAs E_{1} and GaSb E_{1}+Δ_{1}. D. Behr et al. reported that it is complicated by inhomogeneity for E_{1} and transition of InAs and E_{1}+Δ_{1} of GaSb [14].
Figure 2. Real part of RD spectra of samples A and B measured at 300 and 80 K. (a) At 300 K. (b) At 80 K. The arrows indicate the CP energies.
For SL sample, reflectivity can be described by a threephase model:
with
where the indices i and j take the value 1, 2, and 3 for the substrate, SL layer, and air, respectively. is complex refractive index of the ith layer, d_{2}is the thickness of the SL layer, Λ is the wavelength of light in vacuum [15]. SL layer are treated as uniaxial medium, is the weighted average refractive index of 100 periods of InAs (10 ML)/GaSb (8 ML) SL layer. We chose a simple threephase model, with no capping layer:
ε_{s} is the dielectric function of GaSb substrate, d is the thickness of the superlattice, and Λ is the wavelength of light [16]. The ε_{s}data of GaSb substrate is taken from Aspnes’ measurement [17]. Figure 3a,b shows the real and imaginary parts of anisotropy dielectric function Δε by Equation 5, respectively. The peaks and valleys in the imaginary anisotropic dielectric function spectra are corresponding to the CP energies. The imaginary part of ε is related to absorption, and the real part corresponds to transmittance properties.
Figure 3. Calculated imaginary (a) and real (b) parts of Δ ε of samples A and B. The arrows indicate the CP energies.
Figure 4a,b shows the measured IPOA of samples at different temperatures ranging from 80 to 300K. Figure 5a shows the temperature dependence of measured CP energy positions. Figure 5b shows the reflectance difference intensity of CP1 as a function of temperature. The energies of CPs show blue shift, and the amplitudes increase with the decreasing of measured temperature. There are no additional peaks observed. All the observed features are corresponding to CP energies. This kind of IPOA is stable and not caused by defects accumulated on the IF. The shoulderlike CP energy features about InSb clearly show character at low temperatures. Compared with sample A, all the spectra measured at different temperatures indicate that the CP energy are positioned on the red shift with a stronger RD intensity for sample B. J.S. Hang has reported that the GaSb critical point energies shift with temperature, as described by the Varshni expression [18], while J. Kim described the InAs CP energies and temperature dependence as BoseEinstein statics [19]. We use the Varshni empirical formula to fit the temperature dependence:
Figure 4. Real part ofΔ r/r of samples A and B measured ranging from 80 to 300 K.
Figure 5. Measured CP energies of samples A and B as function of temperature and RD instensity of CP1. (a) Measured CP energies of samples A (squares) and B (circles) as a function of temperature. The lines are the Varshni empirical formula fitting. (b) Temperaturedependent RD intensity of CP1.
where β is a constant (K), E_{o}is the width of semiconductor band gap, α is a fitting parameter (eVK^{−1}), and T is the temperature. Table 2 lists the Varshni coefficients of samples A and B. It is found that excitonic transitions have important contributions to E_{1} and E_{1}+Δ_{1} transitions. For this kind of transitions along eight equivalent Λ axes 〈111〉 direction of the Brillouin zone, the FWHM of the spectra decreases with the temperature decreasing. Since the spin orbit interaction in the valence band is large, the E_{1} transition split into E_{1}and E_{1}+Δ_{1} transitions. Δ_{1} is approximately 2/3 of Δ _{0} at the Brillouin zone center [20]. The symmetry reduction remove the degeneracy of the four equivalent bands of two sets. As mentioned above, Δr/r is related to Δε; therefore, the line shape also depends on the symmetry of CP [21]. One electron approximation cannot explain the lifetime broadening; thus, it is suggested that Coulomb interaction should be taken into consideration [22]. The sharpening of spectra with reduction temperature indicates that excitons associate with the E_{1} transition [23].
Table 2. Varshni parameters for temperaturedependence fitting CPs of samples A and B
Samples A and B are both with GaAslike and InSblike alternate IFs and even number of InAs and GaSb MLs. The SLs possess C_{2v}symmetry in the ideal condition. At successive IFs, if InSb bonds lie in the (110) plane, while InAs bonds lie in the (10) plane. Linearly polarized light propagates along the (001) direction. When the polarized direction is parallel to [110] and [10] directions, it feels different chemical bonds at IFs. As a result, the optical properties along the [110] and [10] directions are different. In the RDS spectra, InSb features were not observed clearly in room temperature, since the features of E_{0}, E_{1}, and E_{1}+Δ_{1}CPs are very broadening with few ML [24]. This effect is identified as the spread of carrier wave function of the ultrathin IF to surrounding layers. Figure 6a shows the ΔE_{c}and ΔE_{v} of unstrained GaAs, InAs, InSb, and GaSb system at Γ point [25,26]. E_{1}and E_{1}+Δ_{1}take place along the Λ directions of the Brillouin zone where the valence and conduction bands are nearly parallel. The energy gap of L and Λ are nearly equal. We have inferred the band alignment of L point in Figure 6b. The reflectance peaks of L transitions are not observed, since these transitions are too weak or hidden in the Λ transition structures [22]. In Figure 6b, the Λ _{1}conduction band offset between InAs and GaSb is 0.234 eV, and the Λ _{3}valence band offset is 0.544 eV. The staggered band alignment of bulk materials imply that in every InAs/GaSb SL, there is a InAslike conduction band minimum and GaSblike valence band maximum. The Λ _{3}valence band of InSb is much higher than GaSb, and the Λ _{1}conduction band is much higher than InAs. The Λ _{3}valence band splits into Λ _{(4,5)}and Λ _{6}since the spinorbital interaction. The red lines show the Λ _{6}energy positions. The Λ _{6}band of InSb is higher than Λ _{(4,5)}band of InAs. As the thickness of InSb layers is increasing from 0.43 to 1.29 ML, compared to sample A, the effect of quantum well structures is enhanced. More holes are localized in InSb layers. However, there is no such effect for the GaAs layer. The IPOA intensities of CP1, CP2, and the shoulderlike CP about InSb are increased. While the IPOA intensities of CP3 are decreased and the transition energy position of CP2 are anomalous, blue shift may attribute to the coupling of these states.
Figure 6. Band alignments of InAs, GaAs, GaSb and InSb binary system. (a) At Γ point of Brillouin zone. (b) At L point of Brillouin zone. The red lines are the spinorbital splitting energies at L point.
Conclusions
The IPOA of InAs/GaSb SLs with InAslike and GaSblike alternate IFs were observed by RDS. The main mechanism can attribute to the symmetry reduction to C_{2v}. The increasing of InSb IFs’ thickness release the mismatch between the SL layer and substrate. The red shift of CP energies was observed. Meanwhile, the holes are further localized in the InSb IFs, leading to the intensities of IPOA further increased.
Abbreviations
IPOA: Inplane optical anisotropy; SLs: Superlattices; RDS: Reflectance difference spectroscopy; CP: Critical point; IFs: Interfaces; NCA: No common atom; ML: Monolayer; MBE: Molecular beam epitaxy; DOP: Degree of polarization.
Competing interests
The authors declare that they have no competing interests.
Authors’ contributions
SW carried out the analysis, did the measurements, and drafted the manuscript. YC conceived of the study and participated in its design and coordination. JY and HG participated in the design of the study. JY and CJ participated in the revision of the manuscript and discussed the analysis. JH, YZ, and YW prepared the samples and measured the quality by XRD. WM designed the structure and supervised the preparation of samples. All authors read and approved the final manuscript.
Acknowledgements
This work was supported by the 973 Program (2013CB632805, 2012CB921304 and 2010CB327602) and the National Natural Science Foundation of China (No. 60990313, No. 61176014, and No. 61290303).
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