We calculate the effects of the Hartree and the exchange-correlation potential on the subband levels of a doped GaAs/AlxGa1−xAs quantum well within the local density approximation. The intersubband transition energy appropriate to infrared detectors is calculated including both exciton and depolarization shifts. These effects are all known to be very important in the Si inversion layer and are shown here to be significant for the intersubband transitions in doped quantum wells. The effects of an applied electric field on these energy levels is explicitly included in the calculation. The Hartree potential is shown to effectively screen the electric field significantly reducing the Stark effect.

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Two very accurate methods are developed, one based on the shooting method and the other on the relaxation method, for calculating the eigenenergies and eigenfunctions of states in a quantum well with an applied electric field. These methods, which give accuracies greater than 0.001 meV, are well controlled, give the quantum-well eigenfunctions, and are easily applied to situations of varying potential and effective mass. Comparisons with the variational approach of Bastard and others are made. These techniques allow one to follow the development of the quantum-well eigenstate outside the well and to determine the validity of the quasi-bound state approximation. Recent results in the literature showing that the ground-state hole eigenfunction becomes unbound at moderate electric fields are shown to be erroneous. Detailed calculations are presented for the electron (ground and first excited) and hole (ground) eigenstates of a quantum well with width 85 Å, and barrier heights of 240 (conduction band) and 160 meV (valence band) for applied electric fields varying from 0 to 150 kV/cm. Also, we have calculated the overlap integrals and the dipole matrix elements appropriate to quantum confined Stark effect modulators and infrared quantum-well detectors, respectively.

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GaAs quantum well infrared detectors with peak responsivity at 8.2 μm and significant response beyond 10 μm have been demonstrated with detectivities of 4×1011 cm (Hz)1/2 /W at 6 K; this detectivity is the highest reported for a quantum well detector. The detectors comprised 50 GaAs quantum wells of width 40 Å with an average Si doping density of 1×1018 cm−3 separated by 280-Å barriers of Al0.28Ga0.72As. In this design, the state to which electrons are excited by infrared absorption and from which they are subsequently collected lies in the continuum above the energy of the Al0.28Ga0.72As conduction-band minimum. The maximum detector responsivity was mesured to be 0.34 A/W. The device dark current density is 5.5×10−6 A/cm2 with the detector biased for maximum detectivity (3.5 V), and the dark current remains constant with increasing temperature up to 50 K. The detector noise current was observed to be a constant fraction (70%) of the shot noise down to noise currents of 10−14 A/(Hz)1/2. A theoretical model for the dark conduction process in a quantum well detector has been developed which successfully predicts the observed dark current noise.

The surface states of a semi-infinite superlattice with a step discontinuity in the potential at the interface has been calculated within the framework of the Kronig-Penney model. An explicit solution is obtained for the eigenenergy of the surface state. Surface states are shown to exist only for certain values of the barrier widths and/or heights of the semi-infinite superlattice and of the potential step discontinuity at the interface. Approximate, but very accurate, formulas are derived for the surface-state energy and its respective characteristic decay length, allowing one to readily determine the conditions for the existence of surface states.

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