How Does an Electric Field Affect Energy Levels in a Quantum Well?

[Cerkit]

Hi. Does anyone know how to perform perturbation theory for a finite well under the influence of an electric field?
If not or also what other method is there to calculate the shift in subband energies under the influence of an E field in a quantum well?

Thanks

 

[Cthugha]

The very first treatments of the QCSE were performed with variational methods, see for example:

"Band-Edge Electroabsorption in Quantum Well Structures: The Quantum-Confined Stark Effect" by Miller et al. (Phys. Rev. Lett. 53, 2173–2176 (1984)) or the more detailed follow-up paper "Electric field dependence of optical absorption near the band gap of quantum-well structures" also by Miller et al. (Phys. Rev. B 32, 1043–1060 (1985)).

A perturbation approach is given in "A Semi-Empirical Model for Electroabsorption in
GaAsIAlGaAs Multiple Quantum Well Modulator Structures" by Lengyel et al. (IEEE J. Quantum Electron. 26 (1990), p. 296.).

 

[Cerkit]

Ok. Well as of now I have read through the variational method. I have also found a variational method for a triangle potential well but that is for an infinite well. The only explicit variational method I have found for a finite well is G.Bastard, E.E. Mendez ,Variational calculations on a quantum well in an electric field but the problem with that is that it only gives the calculations for weak fields and says that the expectation values of the hamiltonian for strong fields is not shown because it is too complicated. I am trying to find a fairly simple method which can account for both weak and strong fields. In general I just need an approximation to the perturbation/difference in the energy levels.

 

[Cerkit]

Also does anyone have any idea what kind of accuracy can be obtained through using infinite well approximation rather than the finite one?

 

[jrosen13]

Just do the math, its not that bad. You find the unperturbed wavefunction and calculate first order shift in energy as usual.

 

[Cerkit]

Which method do you advise me to use as a first timer. Perturbation theory apparently doesn't account for strong fields...?