Electronic and optical properties of modulation doped semiconductor quantum wells

Electronic and optical properties of modulation doped semiconductor quantum wells

Superlattices and Microstructures, 147 Vol. 1, No. 2, 1985 ELECTRONIC AND OPTICAL PROPERTIES OF MODULATION DOPED SEMICONDUCTOR QUANTUM WELLS* G. ...

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Superlattices

and Microstructures,

147

Vol. 1, No. 2, 1985

ELECTRONIC AND OPTICAL PROPERTIES OF MODULATION DOPED SEMICONDUCTOR QUANTUM WELLS*

G. D. Sanders and Y. C. Chang Department of Physics and Materials Research Laboratory University of Illinois at Urbana-Champaign Urbana, Illinois 61801

(Received 13 August 1984 by J. D. Dow)

Optical absorption in modulation doped GaAs-A9.GaAs semiconductor quantum wells is studied with the use of a multiband effective mass theory in which coupling of the heavy and light hole valence bands is taken into The kinetic e?e$gy of the spin 3/Z account. hole is described by a k*p matrix and the well potential is treated by a finite square well plus an additional electrostatic potential. The hole band structure is found to be a complicated function of well width due to mixng of light and heavy hole states. In particular, the hole effective masses for the subbands can be positive or negative. The first hole subband has a positive effective mass of approximately 0.2 m, which is insensitive to the variation of well width whereas the effective masses of the excited hole subbands show considerable variation in their effective masses. Here positive effective mass means that the valence subband energy decreases with increasing wavevector near the zone center. The hole wavefunctions are found to come in doubly degenerate pairs having both even (t3/2,Tl/Z) and odd parity (f1/2,T3/2) spin components at points away from the zone center in the two dimensional Brillouin zone. Our theory thus predicts violation of the An=0 selection rule for inter-band transitions. Interband optical absorption is obtained using Fermi's golden rule in the envelope function approximation explicitly taking into account the vafiation of the optical matrix elements with k. Two dimensional excitonic effects are also included in a model similar to $hat of Shinada and Suganol but including the k-dependence of the optical matrix elements. Lorentzian line broadening with half width I is assumed for band-to-band and excitonic transitions. For the excitonic transitions we take T = nenh meV where ne and nh are principle quantum numbers for conduction and valence band states. These choices of half widths allow us to re reduce published photoluminescence data. B For the interband transitions we assume a half width of 0.5 meV. The actual half width should depend on the experimental situation. *Supported by the Office of Naval Research (ONR) under contract N00014-81-K- 0430.

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We consider modulation doped quantum wells in which the A.&GaAs barriers are doped with The acceptors are ionized with the acceptors. The resulting holes residing in the GaAs wells. electrostatic potential in the GaAs well is taken to be parabolic with height V, corresponding to a uniform hole distribution in the well. In Fig. l(a) and (b) we have generated artificial absorption spectra in which the photons are incident normal to the well for a 1OOA GaAs-A9.D 4GaQ.6As quantum well in the absence of doping and for the case where the first valence band is partly filled by holes and the remaining valence bands are unfilled. For the doping case, we chose V, = 15 meV corresponding to an ave age hole concentration in the well of 8.18 x 101' cmW3 and a Fermi energy EF lying 6.23 meV below the first valence band edge. The sharp peaks labelled by X correspond to the excitonic transitions from heavy-hole (HH) and light-hole (LH) bands to conduction bands (CB). The peaks labelled by B correspond to band-to-band transitions involving subbands with a negative effective mass at the zone center. Modulation doping affects the absorption spectra in two ways. First, exciton and interband transitions involving the first valence band are blocked out to the Fermi wavevector. Secondly, the electrostatic hole potential causes a general shift to higher energies of the absorption features. The partial filling of the HHl band results in a sharp cutoff in the HHl-CBl band-to-band transition below 1650 mev. The B(LHl-CBl) transition due to the negative LHl effective mass is seen to be more pronounced in the doped quantum well case but could easily be masked by the strong X(CHl-CBl) transition or by the excited exciton states which are not included in this calculation.

1. 2.

M. Shinada and S. Sugano, J. Phys. Sot. Jpn 2, 1936 (1966). A. C. Gossard in Treatise on Material Science and Technology Vol. 24, edited by muyand R. RosenbLrg (Academic, New York, 1982) p. 13-16.

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