New efficient approach to calculations of exciton resonance position and width for quantum-confined Stark effect in shallow quantum wells

We develop a new computationally efficient approach to the quantum-confined Stark effect in shallow quantum wells that provides a deeper physical insight, significantly reduces required computational resources, and yields some analytical results for the case of shallow quantum wells. The approach is based on a combination of the self-consistent field approach and the complex-coordinate exterior-scaling procedure that allows one to find the resonance position and the broadening for the exciton electro-absorption spectra in quantum wells. In this approach, the exciton envelop function is presented as a product of three functions. The first two describe effective one-dimensional motion of an electron and a hole in the film growth-direction, and the last one is related to a lateral motion in the plane of a quantum well. Each of these wave functions is determined by self-consistent coupled equations with effective potentials. For a shallow quantum well we derive a simple analytical formula for the exciton's resonance position and broadening.