We use a sructure consisting of two 10nm wide Al(0.1) Ga(0.9) As barriers that a
ID: 1915469 • Letter: W
Question
We use a sructure consisting of two 10nm wide Al(0.1) Ga(0.9) As barriers that are separated by a 10nm GaAs layer. Assume electros with unity aplitude are incident fro the left on a double barrier similar to the picture (taking the left barrier edge at x=0 and assigning variables bw and bs to the barrier width and barrier separation, respectively). Solve for the transmission coefficient as a function of energy, T(E). (psi amplitude constant squared for Region 5). For certain energies, this coefficient is unity, meaning the barrier is completely transparent. Reproduce the T(E) vs. E<.1 eV and find the two resonant energies to 4 decimal places. Also include graphs of |psi|^2 for the complete wave function in all 5 regions (i.e. graph of the piecewise wavefunction) for E equal to the first resonance energy and for E between the two resonant energies, E=.06 eV.
Explanation / Answer
The solutions Schrodinger's equation for rectangular barrier potentials are given in this page. You have to find out the constants by giving the appropriate boundary conditions in each region( continuity of psi and continuity of derivative of psi). http://en.wikipedia.org/wiki/Rectangular_potential_barrier