GaAs strained quantum wells from magneto-absorption measurements

Solid State Communications,Vol. 70, No. 11, pp. 997-1000, 1989. Printed in Great Britain.

THE DETERMINATION

OF EXCITON BINDING ENERGY IN InGaAs/GaAs STRAINED FROM MAGNETO-ABSORPTION MEASUREMENTS H. Q. Hou*,

Y. Segawa,

Y. Aoyagi

and

0038-1098/89$3.00+.00 Pergamon Press plc

QUANTUM WELLS

S. Namba

Institute of Physical & Chemical Research, Wako-shi, Saitama, 351-01, Japan and J. M. Zhou Institute of Physics, Chinese Academy of Sciences, P. 0. Box 603, Beijing, P. R.China (Received on 28 February, 1989 by H. Kamimura)

Magneteoptical absorption spectra were measured in InGaAs strained multi-quantum wells confined within GaAs layers under a steady magnetic field of up to 6 Tesla. The Landaulevel related transitions have been identified with Landau indices up to n=4. By extrapolating the photon energies of the absorption peaks to zero magnetic field, the binding energy of the heavy hole exciton was obtained for the first time.

1.8meV, at 1.8K. Optical absorption measurements were carried out at 1OK under a magnetic field of up to 6 Tesla, which was provided by a superconducting solenoid immersed in liquid helium. A 50W broadband tungsten lamp was used as the light source. The transmitted light from the sample was focused onto the entrance slit of a 5Ocm focal length monochromator, and detected by a GaAs photomultiplier. The signal was measured by a lock-in amplifier, and recorded by a computer.The spectral resolution of this system was 3A. Figure 1 shows the typical magneto-absorption spectra obtained at different values of magnetic field applied parallel to the growth axis. Several transitions can be well resolved. The structures labeled by letters A, C, D are due to the bound state transitions of the excitons between the first electron (le), and first heavy hole (lHH), light hole (1LH) subbands, as well as the parity-forbidden transition between le and the second heavy hole (2HH) subbands in the quantum wells respectively. They were assigned according to calculations based on the enveloue function model and the recently proposed value for the bidoffset, AE&).68AEs, by our hydrostatic pressure experiments. 1141When a field is applied, a series of Landau-level related transitions evolve from the le-1HH exciton transition, labeled by index numbers in Fig. 1, and move to the high energy side-rapidly. These structures can be observed at fields as low as IT. The n=O interband transition can not co-exist with the 1s exciton since unbound electron-hole pairs are not optically active in finite fields. 1151 As is well known. the electrons and holes are confined as two-dimensional p&ticles in quantum wells. Under high magnetic fields, the motion within the well plane is also resticted in the different Landau cyclotron orbits. In this case, the excitons become dimensionless, and the density-of-state is enhanced to a series of delta functions. The increase of the absorption intensity with the magnetic field is attributed to the gradual change in the dimensionality. In order to determine the transition energies accurately, the magneto-absorption spectra were subtracted from the absorption spectra obtdned for the same kind of GaAs thin film material. The insert in Fie. 1 shows the result obtained at 3.OT by this method.

In recent years considerable effort has been focused on two-dimensional systems. The fact that the well thickness can be of the same order of the exciton Bohr radius allows the experimental study of excitonic states, which behave like a quasi-two-dimensional hydrogen atom. One of the most important questions regarding the effect of spatial confinement on excitons in auantum wells concerns the freeexciton bindingenergy(Eaj. Many authors have presented determinations of Ea for excitons confined in GaAs/GaAlAs auantum wells exDerimentallv and theoreticallv. 11-71 The iotential interest ii strained simiconductor heterbstructures has been demonstrated. [s.91The possibility of getting rather large lattice mismatches has provided new prospects for modern material science. The electronic structure of InxGa,xAs/GaAs strained multi-quantum wells (SMQW’s), which is modulated both by the strain and the periodic potential along the growth direction, has been frequently studied. [s-111However, to our knowledge, no determination of the exciton binding energy for this material system has been presented so far. Many people simply used values analogous to the GaAs/GaAlAs ones. (91Magneto-optics measurement has proved to be a valuable tool in building up an understanding of the electronic properties of quantum wells and superlattices. [*21In this paper, we report the magneto-absorption determination of the exciton-binding energy in In,Gal.yAs/GaAs for the first time. ?he In~G&:~As/GaAs SMQW sample was grown on a Cr-doped GaAs substrate with a (100) surface using a Chinese molecular beam epitaxy machine.Using optimum growth conditions, [I31the sample was not intentionally doped. After depositing a lpm GaAs buffer layer at a substrate temperature of 6OOoC, a 15period InO,,Gao.gAs (80A)/GaAs(l50& SMQW structure was grown at 52oOC. The indium composition was determined from the different growth rates of GaAs and InGaAs using the intensity oscillation of the reflection high energy electron diffraction and double crystal X-ray diffraction. The photoluminescence measurements show a very sharp exciton line, of width *On leave from the Institute of Physics, Chinese Academy of Sciences, Beijing, China. 997

InGaAs/GaAs STRAINED QUANTUM WELLS

998

860

640

Vol. 70, No. 11

820 F J 6 k 5

1.480

1.470

1.460

1.450 0.0

1.0

2.0

3.0

4.0

5.0

6.0

Magnetic Field (T) Fig. 2. Transition energies as a function of magtic field. The straight line drawn through the data are the results from the least-squares fit.

860

840 850 Wavelength

830 (nm)

820

Fig. 1. Typical magneto-absorption spectra at 4,2K with magnetic field at (a). OT, (b). lST, (c). 3.OT, (d). 6.OT. The transitions are identified by letters and numbers (see text). The insert is the spectrum obtained from (c) by subtracting from the absorption of GaAs. In Fig. 2 the transition energies are shown plotted against magnetic field. All the transitions observed at zero field are shifted up in proportion to the square of the magnetic field. For the le-1HH exciton, the diamagnetic shift (1.9meV at 6.OT) is much smaller than that of bulk GaAs material. This fact suggests that the transition is due to two-dimensional excitons which experience higher Coulomb binding energy than three-dimensional ones. 15.61On the other hand, the absorption peaks associated with interLandau level transitions show an energy shift almost in proportion to the magnetic field. The least-squares method was used to fit the data of each level to a straight line. An effect of the Coulomb interaction is seen on the energy shift at the peak with n=l, which shows small bending in the low magnetic field region. The origin of shoulder B, near the le1HH transition, is not understood. The energy difference of transitions labeled by A and B (4.4meV) is much larger than that caused by one monolayer fluctuation of the wellwidth. It is also unreasonable for an assignment of the 2s state of the le-1HH exciton from its energy dependence on the magnetic fields (diamagnetic shift). (151Additional evidence in support of this assertion is provided by the temperature dependance of peak B. Its absorption at 77K is still very clearly resolved, at this temperature the 2s exciton state is completely thermally ionized. Recently Rogers et al. 171analyzed the magneto-optical data of GaAs/GaAlAs quantum wells, applying the semiempirical theory to the high magnetic field and careful linear

extrapolation to the low field limit respectively. They obtained consistent values of Es by these two methods, and also the intercept of the extrapolating lines for low-field data has the same value as the observed onset of the continuum of the exciton. This means that it is feasible to ascertain the subband gap between electron level and heavy hole level by extrapolation of the low field data to zero magnetic field. In this case the magneto-induced states splitting from the exciton degenerate states are weakly bound to the Landau levels, therefore they can be approximately described as the transitions of free electron and hole states. For InGaAs/GaAs strained quantum wells, large lattice mismatch leads to the generation of biaxial compressive strains in the InGaAs well layer. The effect on the band structure equals that caused by hydrostatic pressure and uniaxial tensile strain along the growth direction. As is well known, the former only enlarges the bandgap; while the latter lifts the degeneracy of J=3/2 valence band states into heavy and light hole bands, shown in Fig. 3. For the sample used in this experiment, the layer strain of InGaAs is 0.7% and the splitting caused by the strain is about 45 meV. In this case, the light hole is even confined to the GaAs layer, 191 hence the valence band mixing of HH and LH is much smaller than that of the GaAs/GaAlAs system within a 6T field, and is negligible. The magneto-photoluminescence experiments for modulation doped InGaAs/GaAs QW’s were carried out recently. tlo.lll The transition energies are quite linearly dependent on the magnetic fields. Hence, the nonparabolicity effect is also neglected in our consideration. As seen in Fig. 2 the least-squares method gives a good matching of the data to straight lines for the levels with n>2. By extrapolating the lines from high energy magnetic fields to zero Tesla for these levels, it is found that the lines converge at one point with an energy error rfr0.2meV. As previously reported, I71we can interpret that the energy of the convergent point gives the effective bandgap between the le and 1HH levels at the low field limit. Therefore the energy difference between the convergent point and the zero field value of the exciton transition is the binding energy of the free exciton le-1HH; Ea=6.3meV.

Vol. 70, No. 11 GaAs

InGaAsfGaAs STRAINED QUANTUM WELLS GaAs

n

GaAe

GaAs

t---i

r1.490

InGaAs

A-EC/ rp

InGaAs

F L

“B

J--K ------LH

(a)

1.460 6 t 15

(b)

1.470

Fig.3. A schematic diagram of the possible band structure of the strained InGaAs/GaAs auantum well. (a). The built-in strain is not so large-that boih the HI-I and LH ate confined in InGaAs layer; (b). The large strain lifts the LH band beyond the GaAs valence bandedge, the LH is confined to GaAs layer.

0.0

3.0

6.0 (n+1/2)B

This result is smaller than the value of binding energy (about 8.lmeV) for GaAs/GaAlAs quantum wells with the same structural parameters deduced theoretically and experimentally. t1-7nt61 This can be attributed mainly to the difference in the valence band structure Roughly sneaking, the Ea of the exciton is proportional to its reduced mask Following the theoretical model given before, t1.21and taking into account the difference between the reduced masses of GaAs wells and InGaAs wells, we may estimate Ea for the le-IHH exciton in this sample as being approximately 7SmeV, which is larger than the value from this experiment. The main reason for this discrepancy is due to the approximation of the free-carrier Landau interband transition. Indeed, all the lines observed in finite fields are bound exciton states. t7~12.151 The extrapolating intercept may be underestimated as the onset of the continuum of the le1HH exciton. Another reason is that for a realistic structure, the nonparabolicity should be taken into account. Recent theoretical calculations [*5.17lhavere-interpreted the previous experimental data obtained by Mann et al.t41, and Ossau et al.[sl at high magnetic fields in terms of the magneto-exciton states, rather than Landau interband transitions of free carriers. According to their theories, the mixing of the valence band and the magneto-excitonic nature induce a nonlinear dependence of the transition energy on the magnetic field and anticrossing of excitonic transitions, also some extra transitions appear in the magneto-optical spectra. As a result, the experiments neglecting the above band effects overestimated the binding energy of the exciton compared with calculations Ii,*.161and those deduced by other methods. ~1 In our experiment, no additional transitions attributable to magneto-excitons appeared due to the special valence band structure of the InGaAs quantum well, so Landau interband transitions were employed as the explanation in this paper. In Fig. 4 the recombination energies are plotted as the function of normalized magnetic field (n+1/2)B. The slopes of the lines equal the values of eh/(2np), where u is the

9.0

12.0

15.0

(T)

Fig. 4. The dependence of transition energy on the normalized field (n+1/2)B for the different Landau levels.

reduced mass of the exciton. In this manner, the reduced masses for the fiit, second, and third Landau interbands are 0.064mo, 0.058mo,0.055mo respectively, where m. is the mass of the free electron. These values are slightly larger than the results (0.048-0.051mo)obtained by Jones et al. from n-type and p-type doped InGaAs/GaAs structures, tie1 and the interpolated value (0.049mo) for Ino.tGaesAs using the currently quoted effective masses of free electron and heavy hole for GaAs and InAs. A systematic decrease of the reduced mass results from the smaller Coulomb binding for the higher Landau interband transitions, since the slope of the fitted line may be affected by this different binding. For the n22 interband transition, the Coulomb interaction is very small compared with the Ea. As a result, this method should give a good approximation of Ea in this SMQW structure. Detailed research is in progress. In summery, we have determined the binding energy of heavy hole excitons in InGaAsfGaAs SMQW’s for the fit time. It is smaller than that in GaAs/GaAlAs quantum wells. The special strain-induced band structure in InGaAs well shows that it is advisable to estimate the Ea of excitons in terms of Landau interband transitions for low-field data. The difference in the reduced mass for each Landau interband indicates that different Coulomb bindines are experienced, and become progressively smaller for kgher index levels. Acknowledgement---The authors are indebted to Drs. J. Kusano, S. Shimomura, and Y. Iimura for helpful discussions, Mrs. P. O’Keeffe and P. Keating for comments in preparing the manuscript. One of the authors @IOU)is grateful for the encouragement of professor L. Li.

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InGaAs/GaAs STRAINED QUANTUM WELLS

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11. S. K. Lyo, E. D. Jones, and J. F. Klem, Phys. Rev. Left. 61, 2265(1988). 12. For a review, see J. C. Mann, Surf Sci. 196, 518(1988). 13. H. ‘Q. Hou, Y. Huang, and J. M. Zhou, (to be published). 14. H. Q. Hou, L. J. Wang, R. M. Tang, J M. Zhou, (unpublished). 15. S. IR. E. Yang, and L. J. Sham, Phys. Rev. Left., 58, 2598(19871. 16. D. M. Whittaker, and R. J. Elliott, Solid State Commun. 68, l(l988). 17. G. E. W. Bauer, and T. Ando, Phys. Rev. B38, 6015(1988); and Phys. Rev. B37, 3130(1988).