Inter-band magneto-absorption in a Ga0.47In0.53As-Al0.48In0.52As quantum well

Solid State Communications, Printed in Great Britain.

INTER-BAND

Vo1.60,No.Z,

MAGNETO-ABSORPTION

D.C. Rogers:

R.J. Nicholas:

pp.83-86,

1986.

IN A GaO 471no 53As-Al0 . . S. Ben Amor:

0038-1098/86 $3.00 + .OO Pergamon Journals Ltd.

. 481n0 . 52As QUANTUM WELL

J.C. Portal:*

A.Y. ChoX and D. Sivcox

+ Clarendon Laboratory, Parks Road, Oxford OX1 3PlJ * INSA, Laboratoire de Physique des Solides, Avenue de Rangueil,

31077 Toulouse,

France

0

SNCI-CNRS, BP166, 38042 Grenoble, France x AT & T Bell Laboratories, ID-373, Murray Hill, NJ 07974, U.S.A. (Received

11th June

1986 by C.W. McCombie)

Transitions between the Landau levels of the N = I electron and heavy hole sub-bands have been observed in the inter-band optical absorption of a modulation doped Gao.47In0.53As-Al0.48Ino.52As multi-quantum well in magnetic fields up to 16T. Results are compared with the results of conduction band cyclotron resonance on the same sample to obtain measurements of both the electron and the heavy hole effective mass, It is and the results are compared with known values for bulk GaInAs. shown that the electron states at high energies are in good agreement with the predictions of three-band k.p theory. This is in contrast to the cyclotron resonance results,--for which a substantial polaron correction is required.

0517

The Gao:47Ino.53As-Alo.48Ino.52As quantum well system *s of great practical importance for the fabrication of 1.3pm and 1.55pm semiconductor lasers for use in fibre optical systems. uality quantum wells with widths as small High as 15it can be grown1*2*9 in this system using molecular beam epitaxy (MBE), and band gap enhancements of over 450 meV have been reported More recently, strong in these wells', excitonic structure has been observed in the room temperature optical absorption of GaInAs-AlInAs wells', and in the low temperature photoluminescence of very narrow wells3, associated with both heavy and light hole sub-bands. The electron effective mass in GaInAs-AlInAs quantum wells has been studied at low energies using cyclotron resonance (CR) measurements", but at present neither the high energy behaviour nor the hole effective masses for motion in the plane of the layers are known. We have therefore studied the inter-band magneto-optical absorption of a lightly modulation doped n-type multi-quantum well sample in order to study both the electron and the heavy It is also possible with hole effective mass. this technique to study electron states at energies much greater than the LO-phonon energy, and comparison with CR results on the same sample at energies comparable with hwLG can yield information on polaron effects in these structures. The sample studied was grown by MBE at AT & T Bell Laboratories, with the layer sequence shown in fig. 1. The electron concentration at 4.2K, deduced from Shubnikov-de Haas oscillations, was l.6x10'1cm-2 per well, and comparison with the sheet carrier concentration deduced from the Hall effect indicated that all of the quantum wells were populated. For inter-band absorption measurements the sample was mounted in the bore of a

GaInAs

n,lO1* 150A undoped MA ne3x1017

SOA

undoped SOA undoped IS@ AlInAs

undoped 500&%

1nP:Fe substrate Fig.

I

Growth sequence for the sample studied, giving nominal layer thicknesses and doping levels.

16T superconducting magnet directly above a carbon bolometer, the whole system being immersed in a bath of liquid helium at 2K. Chopped light from a tungsten filament quartz halogen lamp was passed through a Czerny-Turner monochromator and transmitted to the sample by a fibre optical cable, and the detector signal was synchronously detected and recorded Typical spectra, normalised with digitally. respect to background intensity, are shown in fig. 2. At zero applied magnetic field, transmission minima are seen corresponding to AN = 0 transitions between heavy hole and electron sub-bands of the quantum wells. Since the quantum wells are doped n-type, with a Fermi energy of 8 meV, the lowest transition corresponds to free electron excitation and is Moss-Burstein shifted up in energy from the subband edge. It is not clear whether the higher 83

84

A GaO~471nO_53Ae.-A10~481nO_52As

QUANTUM

WELL

Vol. 60, No. 2

.

Fig, 2

Typical spectra at different magnetic fields, with observed transitions indicated, The lowest transition at 6T is the n = 0 Landau level transition, which disappears below 5T due to filling of the electron level,

transitions will be excitonic or free-carrier in character, however the fact that their intensity is very similar to that of the N = 1 transition suggests that they are also free carrier transiIn practice the distinction will make tions, little difference to the transition energies, since the 2-D exciton binding energy for a GaInAs quantum well of order 200 2 will be of No light hole transitions could order 5 meV, be identified in any of the spectra, When a magnetic field is applied perpendicular to the layers, additional minima evolve which we interpret as An = 0 transitions between the Landau levels of the N = 1 heavy hole and electron sub-bands (where N denotes the quantum well sub-band quantum number and n the Landau level quantum number). The positions of the observed transmission minima are plotted against magnetic field in fig. 3. It can be seen that the n = 0 Landau level transition is not observed at fields below 5T. This is because

this level is completely filled below 3.2 T, because of the doping, and the transition can only be seen once there is a significant number of available final states for the transition from the n = 0 heavy hole level. Extrapolation of the n = 0 transition to zero field gives an intercept approximately 8 meV below the onset of the zero field absorption, in agreement with the known Fermi energy, The observed zero field transition energies have been modelled using a simple envelope function calculation5 for the electron levels Thfs with a band offset assumed to be 0.6AEg3" allows us to dedHce a value of the quantum well thickness of 190A. It is not possible to make

I

I

1

I

I

I

I

2

4

6

8

IO

12

14

Magnetic Fig. 3

field

I 16

(T )

Transition energies plotted against magnetic field. Solid lines show the best theoretical fit to the results, with m*, = .0405 m. and m*hh = - 0.75 a$-,.

very accurate conclusions on the magnitude of AEc, due to the absence of any structure due to light holes, or of AN f 0 transitions, which allow a much more accurate measurement of the separate electron and hole energy levels5. However the fact that five strong electron transitions are seen allows us to put a lower bound upon the conduction band offset, since the fact that they all have a comparable oscillator strength suggests that they are all bound within the well. This gives the not unexpected result that AE, >, 0.4AEg. To model the field dependence of the Landau levels we assume the conduction band to be well described by the expression derived by Bowers and Yafet6, in the limit E, << Eg + 2A/3,

where,

(2)

and the heavy hole band is modelled by a simple parabolic expression with a constant heavy hole mass Ch. heB Ehh (n,B,N) = Eg + + E(N), %h

(3)

The sub-band energies E(N), are deduced from the combination of the zero field transition energies

Vol. 60, No. 2

A Gag 471no 53A~-A10

85

4BIno 52A~ QUANTUM WELL

.

In contrast to and the envelope function fits. a previous work on semi-insulating GaAs-GaAlAs quantum wells7, we have neglected all Coulomb binding effects, since the doping of the sample appears to result in most transitions becoming An free carrier like, as discussed above, attempt to model the results including excitonic shifts results in a substantial under estimate of the transition energies close to the band The observed transition energies are edge. therefore assumed to be simply ET

(n,B) = E,

(n,B,B) + Ehh

(n,B,N)

(4)

The extrapolation of the lowest transition to zero field, together with the envelope function calculations of the energy levels then gives the values for Eg = 0.805 eV, E(e,l) = 16.5 meV, and E (hh,l) = 1.5 meV, where the heavy hole level was deduced using a constant bulk hole mass of 0.465 me*. This value of the energy gap is in good agreement with the known value for bulk GaInAs when lattice matched to InP, and is a good test of the accuracy of the alloy composition. The value of the bulk band edge effective mass in lattice matched GaInAs is known to be 0.0405 + .0005 from frequency dependent cyclotron resonance measurements made below the optic This value of band edge effectphonon energy. ive mass is also known to give a good fit to similar inter-band magneto-optical data on bulk GaInAsg*10 over a considerable range of energies. When this value is inserted into equation (1) the majority of the transition energy has been determined, and the only unknown parameter in the fit is the heavy hole mass, m*hh 1 The heavy holes will only make a relatively small contribution to the total transition energy, so that the measurements will be relatively insensiIt is found to be possible to tive to its value. fit the data shown in fig. 3, using a hole mass +h = (0.75 + O.lO)me, which is substantially larger than for the bulk material. The theoretical calculations are shown as solid lines. The behaviour of hole states in quantum wells has been a subject of co:&l;rable , and a theoretical interest recently ' number of authors have shown that the sub-bands can become highly non-parabolic due to the The effects of heavy and light hole mixing. detailed behaviour of any single level is a highly complex function of the energy, the positions of other levels and its quantum number (in the case of Landau levels), and under a number of circumstances the levels can even reverse their character and become electronIn view of this it is hardly surprising like. that we should find such a large change in the heavy hole mass in the present case. As a further test of the model of the electron levels equation (1) was used to calculate the cyclotron resonance transition energies from BCB

(B) = E, (l,B,l) - Ea (O,B,l)

(5)

in the limit of only the lowest Landau level This was compared with the data being populated. of Brunei et al4 taken on the same sample, and is shown in fig. 4. The transition given by equation (4) should dominate for fields above

0

2

4

6

8

10 12

14 8

Magnetic field(T 1 Fig. 4

Cyclotron resonance energy plotted against magnetic field for the same sample (results from reference 4). The broken line gives the transition energy predicted by equation 4 with m*, = .0405 mo; the solid line is calculated from equation 5 with m*e = .0405 m. and K2 = - 1.4,

3T. It can be seen that in contrast to the inter-band results the calculation does not give a good description of the transition energy, which is substantially overestimated. In order to fit this transition it would be necessary to increase the band edge mass used in equation (I) to approximately 0.0435, which is well above the value found in all measurements on hoth bulk and other GaInAs based 2-D systems '+'I3 ~ The reason for this discrepancy is the influence of polaron dressing of the electron There has been a considerable amount of mass. controversy recently on the magnitude of the polaron effect in both two and three dimensional semiconductors 4$14-25 1 In bulk materials there has been some uncertainty over the magnitudes of both the band and polaron contributions to the effective mass, with recent measurements in both GaAs and GaInAs 13-16 demonstrating that the increase in cyclotron mass, measured below the phonon frequencies, is almost double that predicted by either the Bowers and Yafet model6 or other three band k.p calculations26,27. In contrast interband m
86

A GaO~471nO~53As-A10~4aInO~52As

heavily doped superlattices however-the influence of polaron coupling still seems to be substantia14. In the sample studied in this report, both the electron confinement energy and the cyclotron frequency are separately below the optic phonon frequencies, however above 6T the total energy is above the energies of the GaInAs optic phonons. There does not appear to be any evidence for a discontinuity in the behaviour of the energy levels at this field. It is possible to model the cyclotron energy as a function of field using the relation

ECR (B) =

‘$ ,

-&

=&

[I +z)

(6)

where K2 is a parameter which is equal to - 1.4 as found in measurements on bulk GaInAs, provided that this mass enhancement is also applied to the electron confinement energy. This is also shown

QUANTUM

WELL

Vol. 60, No. 2

in fig, 4 as a solid line, The three band k.p relations of Palik et a126 and Bowers and Yafet6 predict values for K2 of - 0.84 and - 1.0 respectively, The conclusion would thus seem to be that there is still a substantial polaron enhancement of the effective mass due to both the electron confinement and the cyclotron motion whenever either of these parameters remains below the optic phonon energies. In conclusion we have shown that inter-band magneto-optical measurements on GaInAs-AlInAs quantum wells give information on the form of the dispersion relations up to energies of 300 meV above the band edge. These are found to be well described by conventional perturbation formulae, in agreement with results found on bulk materials. In contrast cyclotron resonance results reported earlier4 show that polaron effects should also be taken into account when describing all motion within the quantum wells.

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