Temperature Dependence of Photoresponse in p-Type GaAs/AlGaAs Multiple Quantum Wells: Theory and Experiment
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Mat. Res. Soc. Symp. Proc. Vol. 607 C 2000 Materials Research Society
trends, in particular, for the MWIR QWIP, while the comparison for the LWIR QWIP is less conclusive. THEORY The electronic structure and the BC absorption in p-type GaAs/A1GaAs MQWs was calculated based on an 8x8 EFA formalism, with the continuum states represented as scattering states [2,9]. Oscillator strengths expressions which explicitly account for band mixing and finite height potentials [3,10] were used. The 8x8 model explains the normal incidence absorption as the result of the admixture of s-like conduction band states into the nominally p-like valence bands, in particular the light-hole states [2,9]. For that reason, we have been advocating [2,9,11 13] the placement of the LH2 at the top of the well in order to optimize BC absorption. Since [2, 9] fully explain the calculational formalism used in this paper, only enough detail is provided to explain the role and presence of quasi-bound resonances. In each layer of the quantum well, the envelope wave function for the given subband is a function of parallel momentum in the plane of the well, k11. The envelope function is expressible as the sum of exponentials
i=1
where exponents k, and K -component eigenvectors C(k1 i, kz ) are solutions of the bulk
k * p secular equation [14]
of order K (here, K
=
8). Equation 2 yields 2K solutions for eigenvectors C(k11 , kz ) and
exponents kz (kil, E), which are wave vector- and energy-dependent and, in general, complex [14]. Clearly, real and imaginary kzcorrespond to propagating and evanescent solutions, respectively, while complex solutions correspond to both. While at the center of the Brillouin zone, the energies for the onsets of free HH and LH propagation (i.e., the onsets of continuum conduction in the barrier material) coincide, away from the zone center, these energies are different. For example, Fig. 1 shows the band structure of a 40 A wide GaAs/Al 0215Gao.7 ssAs MQW (designated NRC-I1) and the positions of the HH and LH continua onsets. Only bound bands are possible above the HH continuum, and both HH and LH propagating solutions exist below the onset of the LH continuum. However, between the HH and LH continua onsets, heavy holes can propagate freely whereas light holes can be quasibound.
we construct tecontinuum states as scattering statesfE k,1,.v)whre k) , denote the energy and the in-plane wave vector, and v =HH, LH, or SO label the incident channel of the hole. The hole wave function for the scattering state incident on the well from the side of the left-hand barrier is represented as a K-component vector
188
K
Im(ki) >O
F(k1 ,, z) = C(k,,, k,)exp(ikvz) + XciC(k 11 , -ki)exp(-ikiz),
(3)
i=!1
where the first term denotes the incident state and has a real positive exponent
k, (k11, E) > 0;
the second term gives the backscattered states. Boundary conditions determine the corresponding solution in the well and the transmitted state in the right-hand barrier. Next, the left- and right-hand-incident states are superpose
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