where N0 is the normalization coefficient, and

Next, the effect of an electric field on the subband energies is calculated by using the Hamiltonian

where ^ = |e|E. E is the electric field strength applied in the x, y plane and 6 is the angle between the electric field and the x axis. The trial function in this case is modified to be fi1 (x, y) = N1fi0(x, y) exp[-¡3(x cos 6 + y sin 6)/L]

where N1 is the normalization coefficient and ¡ is the vari-ational parameter.

With an impurity at (xt, y, 0) the Hamiltonian becomes

2m* dz2

The trial function for this problem is taken to be fi2(x,y,z)=N2fi1(x,y)

where N2 is the normalization constant and A is a variational parameter. The binding energy of the electron is written with respect to the subband energy calculated in the presence of an applied electric field. Numerical results are found for the GaAs/Ga1-xAlxAs system where, within the finite barrier model that has been taken, it has been considered that the finite barrier potential and dielectric constant depend on the x concentration of Al as follows:

For cylindrical quantum well wires, the Hamiltonian for the relative motion is given by

H =- — (— + 1 — + -—) + y(r ç) 2m* \ dr2 r dr r2 dç2 /


The wavefunction for the ground state becomes k = J2m*eo/h2 k2 = ^2m*(Vo - eo)/h2 (167) fio(r, ç) = No

For the infinite potential barrier model K0 is taken to be infinite and the wavefunction outside the barrier is taken to be zero. Matching the wavefunction and its derivative at the boundaries yields


2m h2

With an applied electric field in the x, y plane, the Hamil-tonian becomes where the cross-section has been taken to be a square with sides Lx = Ly = L.

0 0

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