Electric field effect on the diffusion modified AlGaAs/GaAs single quantum well

Abstract

The electron subband energies and wave functions in an interdiffusion-induced Al x Ga 1Ϫx As/ GaAs/Al x Ga 1Ϫx As single quantum well are calculated in the presence of the dc electric field using the finite difference method. The mean lifetimes are obtained from the time-dependent probability of tunneling of the wave packet out of the well by the applied electric field. The effect of the applied electric field on the subband energies in the well is the same as in the as-grown square quantum well when the interdiffusion length is below 20 Å. In the well with higher diffusion length the barrier height reduces so that the wave function tunnels out of the well. The linear and nonlinear intersubband absorption coefficients and the change in the real part of the index of refraction are calculated with the applied electric field at 100 kV/cm and without the field in both the as-grown square well and the diffusion modified well with the interdiffusion length at 20 Å.

Stark effect in diffused quantum wells

“…The finite differences method was applied in [19] to calculate the electron subband energies and wavefunctions in interdiffused AlGaAs/GaAs quantum wells in the presence of a longitudinal electric field. Both studies [18,19] use the effective-mass approximation in one-dimensional models.…”

“…Because of this, the real interfaces of the semiconductor quantum well structures are not abrupt but have widths at least of the order of two lattice parameters [20,21]. This changes their electric field characteristics, especially for relatively thin wells and barriers [17][18][19][20][21]. In [21], the influence of nonabrupt interfaces in the high electric field resonances of single AlGaAs/GaAs barriers in GaAs was studied theoretically within the effective-mass model.…”

“…In [18], the quantum confined Stark effect in arbitrarily shaped single quantum wells was studied by means of the Fourier series method. The finite differences method was applied in [19] to calculate the electron subband energies and wavefunctions in interdiffused AlGaAs/GaAs quantum wells in the presence of a longitudinal electric field.…”

“…The quantum confined Stark effect [1][2][3] occurs then in these quantum well structures and gives rise to some of the practical applications of the devices. The experimental and theoretical investigations of the Stark effect mainly concern rectangular quantum wells [1][2][3][4][5][6][7][8][9][10][11] but there are also some studies for graded composition quantum wells [12][13][14][15][16] and diffused quantum wells [17][18][19].…”

Numerical spurious solutions in the effective mass approximation

“…28 There exist several proposals to solve the k"p spurious solution problem ranging from methods to eliminate them 29,30 to pointing out the necessity of keeping them for a complete description. 31 The finite difference method ͑FDM͒ has been used extensively to solve the EMA equations [32][33][34][35][36] because external fields can be included straightforwardly in this formalism. In this article a class of spurious solutions ͑SSs͒ particular to the FDM is studied.…”