I have a Si p-i-n diode structure with semiconducting iron disilicide quantum wells inside the i-Si layer. The width of the QWs is about 25 nm. Under reverse bias (at the avalanche mode), clear and significant red shift of the photoresponse edge is observed. I suppose that it results from quantum cinfined Stark effect. Next, I want to calculate energy shift of the ground state and compare it with experimental results. One can easily solve it for the case of the infinite quantum wells and weak field regime. In my case, the quantum well is finite and high field is applied.
Could anyone please help me with this situation?
As a starting point I have chosen Article (see attachement).
Applied Field range: 0,2-2,4 MV/m.
m*=0.83 m0(electrones) and 0.21 m0 for holes.
Barriers height is about 0.2 eV
Quantum well width is 25 nm
The above article can be really helpful.
There are also two ways of analytic calculation.
(1) If the field is not very strong, so that potential drop across the well is smaller than energy separation between the ground state and the first excited level then it is possible to make use of perturbation theory. In symmetric well the electric field mixes the ground state with only odd excited levels (1st, 3rd and so on). The admixture of continuum states has to be neglected because it contributes rather to the width of the level than to its shift.
(2) If the field is so strong that the admixture of the first excited level cannot be considered as a perturbation then it is necessary to solve exactly the Schrodinger equation inside and outside of the well and match the solutions at the boundaries. Both solutions are expressed in Airy functions and the boundary conditions give an equation for the energy. The energy is going to be complex where the imaginary part is related to the life time of the particle in the well with respect to tunneling across the barrier. There is a good chance, by the way, that somebody have already done the procedure in eighties or even earlier. Related to this tunneling across triangular barrier was studied back in thirties (Fowler‐Nordheim field emission) and probably can be found in books.
You know the potential profile of the QW. Then why not solving the envelope function equation for this potential profile. You will need a numerical procedure for finding the eigenstates of a matrix. Maybe nextnano3 can help for this.
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