Observation of strong anisotropic forbidden transitions in (001) InGaAs/GaAs single-quantum well by reflectance-difference spectroscopy and its behavior under uniaxial strain
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The strong anisotropic forbidden transition has been observed in a series of InGaAs/GaAs single-quantum well with well width ranging between 3 nm and 7 nm at 80 K. Numerical calculations within the envelope function framework have been performed to analyze the origin of the optical anisotropic forbidden transition. It is found that the optical anisotropy of this transition can be mainly attributed to indium segregation effect. The effect of uniaxial strain on in-plane optical anisotropy (IPOA) is also investigated. The IPOA of the forbidden transition changes little with strain, while that of the allowed transition shows a linear dependence on strain.
PACS 78.66.Fd, 78.20.Bh, 78.20.Fm
KeywordsQuantum Well Optical Anisotropy Uniaxial Strain Segregation Effect Anisotropic Strain
averaged hybrid energy
in-plane optical anisotropy
symmetry reduction effect
It is well known that in-plane optical anisotropy (IPOA) can be introduced in a (001)-grown zinc-blende quantum well (QW) when the symmetry is reduced from D2dto C2υ[1, 2, 3, 4, 5, 6]. There are two kinds of symmetry reduction effect (SRE), one is bulk SRE, and the other is interface SRE [2, 4]. The bulk SRE can be introduced by electric field, compositional variation across the QW and uniaxial strain [7, 8, 9, 10]. The IPOA induced by uniaxial strain in GaAs/Al x Ga1-xAs QWs has been reported by Shen , Rau  and Tang . However, as far as we know, this effect in In x Ga1-xAs/GaAs QW has never been reported.
The interface SRE, which origins from C2υsymmetry of a (001) zinc-blende interface, can be introduced by special interface chemical bonds, segregation effect and the anisotropic interface structures [2, 3, 6]. It was found that the interface-induced IPOA was very strong in the QWs sharing no-common-atom, while the IPOA in QWs sharing common atoms such as GaAs/AlGaAs was too weak to be observed by conventional polarized spectroscopy [2, 4, 10]. Fortunately, the weak IPOA in the AlGaAs/GaAs and InGaAs/GaAs QWs can be well observed by the reflectance-difference spectroscopy (RDS) [2, 4, 6]. Wang et al. has studied forbidden transitions in In x Ga1-xAs/GaAs by photoreflectance (PR) and attributed the forbidden transition to the built-in electric field . Chen et al.  and Ye et al.  observed anisotropic forbidden transition in In x Ga1-xAs/GaAs by RDS. Chen ascribed the anisotropic forbidden transition to the interplay of interface C2νsymmetry and built-in electric field, while Ye attributed it to both the built-in electric field and segregation effect. In this study, we observed strong anisotropic forbidden transitions in a series of In x Ga1-xAs/GaAs single-quantum well (SQW) with well width ranging between 3 nm and 7 nm at 80 K. Numerical calculation within the envelope function framework have been performed to analyze the origin of the optical anisotropic forbidden transition. Detailed theory-experiment comparisons show that the anisotropic forbidden transition can be mainly attributed to indium (In) segregation effect. Besides, the effect of uniaxial strain on in-plane optical anisotropy (IPOA) is also investigated. It is found that, the IPOA of the forbidden transition nearly does not change with strain, while that of the allowed transition shows a linear dependence on strain. Finally, an interpretation of the IPOA by perturbation theory is given out.
Samples and experiments
A series of In0.2Ga0.8As/GaAs SQW with different well widths were grown on (001) semi-insulating GaAs by molecular beam epitaxy. The SQW was sandwiched between two thick GaAs layers. The nominal well widths of the three samples were 3, 5, and 7 nm, respectively. All epilayers were intentionally undoped. The setup of our RDS, described in Ref. , is almost the same as Aspnes et al. , except the position of the monochromator. The relative reflectance difference between  and [11 0] directions, defined by Δr/r = 2(r110 - r11 0)/(r + r[11 0]), was measured by RDS at 80 K. Here r (r[11 0]) is the reflective index in the  ([11 0]) direction. We also did the reflectance measurements, and thus obtained the ΔR/R spectra. Here R is the reflectivity of the sample and ΔR is the reflectivity difference between samples with and without QW layer.
Here J0 is the deformation at the strip center, h is the thickness and 2a is the length of the strip. The relative reflectance difference between the  and [11 0] directions at the center of the strip (3 × 4 mm2) is measured by RDS at room temperature.
Results and discussion
Models and calculation results
for the basis |3/2, 3/ 2 > , |3/ 2, 1/2 > , |3/2, -1/2 > , |3/ 2, -3/2 > , |1/2, 1/2 > , and |1/ 2, -1/2 >. Here b and D are the Bir-Pikus deformation potentials, F is the electric field along the z direction, d14 is the piezoelectric constant, ϵ ij denotes the symmetric strain tensor, P1 (P2) is the lower (upper) interface potential parameter describing the effect of C2ν interface symmetry , l1 (l2) is the In segregation length in the lower (upper) interface, and z = ±w/2 is the location of the interfaces of QW. The interface potential parameter P1 and P2 are equal for a symmetric QW, and anisotropic interface roughness will make them unequal . According to the model suggested in Ref. , we assume that the segregation lengths on the two interfaces are equal, i.e., l1 = l2.
In order to estimate the value of built-in electric field, we perform photoreflectance measurements. However, no Franz-Keldysh oscillations presents, which can be attributed to the fact that the layers are all intentionally undoped and the residual doping is very low. Thus, the residual electric field is weak enough to be neglected.
here Γ is the linewidth of the transition, and E nm (P nm ) is the transition energy (probability) between n e and m lh or between n e and m hh. In the calculation, the adopted Luttinger parameters are: γ1 = 6.85, γ2 = 1.9, γ3 = 2.93 for GaAs, and γ1 = 21.0, γ2 = 8.3, γ3 = 9.2 for InAs. The band-offset is taken as Qc = 0.64 , and the strain-free In x Ga1-xAs band gap at 80 and 300 K are taken from Refs.  and , respectively. The other band parameters are got from Ref. . The anisotropic transition probability ΔM is proportional to Δr/r. Therefore, we can compare the theoretical calculated ΔM with experimental data Δr/r, and thus to find out the reason responsible for the observed strong anisotropic forbidden transitions. It is noteworthy that even under zero uniaxial strain, there will still be residual anisotropic strain exists, which may be due to a preferred distribution of In atoms . In the following, we will discuss the interface potential, segregation and anisotropic strain effect separately.
We should first estimate the value of interface potential parameter, denoted as P0. So far, there are four theoretical models estimating the value of P0: boundary conditions (BC) model by Ivchenko , perturbed interface potential model (called "H BF ") by Krebs , averaged hybrid energy (AHE) difference of interfaces model and lattice mismatch model by Chen . Given that BC model is equivalent to H BF model, we need to consider only one of them . Thus using H BF , AHE and lattice mismatch model and then adding them up, we obtain the value of P0 is about 600 meV Å.
If there is only anisotropic strain effect in the QW (i.e., P1 = P2 = P0, l = 0), only one free parameter ϵ xy can be fitted to the experimental data. The fitting result is shown in Figure 5b. The ϵ xy value we adopt is 0.003 × ϵ xx = - 4.24 × 10-5. Again, there is no forbidden transition presents. Therefore, the observed anisotropic forbidden transition cannot be attributed to anisotropic strain effect.
If there is only atomic segregation effect (i.e., P1 = P2 = P0, ϵ xy = 0), one can fit free parameter l to the experimental data. The fitting result is shown in Figure 5c. The fitted segregation length l is 1.8 nm, which is in reasonable agreement with that reported in Ref. . Apparently, the segregation effect will lead to a strong IPOA for the forbidden transition 1e2hh, but do not change its average transition probability, which is still very small. Besides, for the sample with well width 3 nm, a strong IPOA is also present for the transition 1e1lh. Therefore, the observed anisotropic forbidden transition is closely related to In atomic segregation effect.
From Figure 5c, we can see that, if there is only segregation effect, the sign of the transition 1e1hh is negative, which is not consistent with the experiment. Therefore, there must be some other effect existing, such as anisotropic interface structures or anisotropic strain effect. When we take both the anisotropic strain and segregation effect into account, the calculated results are not consistent with the experimental data. However, the results obtained by both the anisotropic interface structure and the segregation effect are in reasonable agreement with the experiment, as shown in Figure 5d. In the calculation, we adopt interface parameter P1 = 595 meV Å, P2 = 775 meV Å, and the segregation length l = 1.8 nm. The obtained interface potential difference ΔP/P0 is about 30%, which is much larger than that obtained in GaAs/Al x Ga1-xAs QW (about 6%) . The reason may be that lattice mismatch will enhance the interface asymmetry of the QWs.
Interpretation of IPOA by perturbation theory
Here 〈1E|nH〉 is the overlap integral between the first electron and the n th heavy-hole states. 〈1H|R(z)|1L〉 is the hole-mixing strength between 1H and 1L. E1L- E nH is the energy separation between 1L and nH. It can bee seen that, ΔM is directly proportional to the coupling strength of holes and inversely proportional to their energy separation. For the three samples, there is little difference in the term R(z). However, E1L- E2Hof the sample with 3 nm well width is smaller than that of the other samples, which results in much stronger IPOA.
in which the first integral is nearly a constant, and 〈1L|2H〉 〈2H|1E〉 is mainly determined by the segregation effect and interface potential. Therefore, for the forbidden transition 1e2hh, the change of IPOA induced by a weak uniaxial strain (in the order of 10-5) will be too weak to be observed in experiment. However, for the allowed transitions, such as 1e1hh, the strain will also couple 1H and 1L, and will remarkably change the IPOA. From Figure 3 we can see that the RD intensity of transition 1e1lh does not show significant change as the strain increases. The reason may be that the light-hole band configuration is weak type I for the current alloy composition , which result in the change of the potential has little influence on its wave function.
We have observed strong anisotropic forbidden transition in a series of In0.2Ga0.8As/GaAs SQW with well width ranging between 3 nm and 7 nm at 80 K. Using a 6 band K · P theory, we have calculated the optical anisotropy induced by interface composition profile due to In segregation, anisotropic interface structures and anisotropic strain. It is found that the observed anisotropic forbidden transition can be mainly attributed to the In segregation effect. Besides, the effect of uniaxial strain on IPOA is also investigated. It is found that the IPOA of the forbidden transition changes little with strain, while that of the allowed transition shows a linear dependence on strain. Finally, an interpretation of IPOA by perturbation theory is also given out.
This study was supported by the 973 program (2006CB604908, 2006CB921607), and the National Natural Science Foundation of China (60625402, 60990313).
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