If two periodic potentials have the following unit cells: V(x) = Voi sin (2- nx 2...

 

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If two periodic potentials have the following unit cells: V(x) = Voi sin (2- nx 2 V2(x) = Voz (+) 1) Derive the necessary equation for the two periodic potentials to have identical dispersion relations Hint: Refer to the delta-barrier approximation. 2) You wish to design the 1st periodic potential so that the width of the 1st allowed energy band is 0.1 eV given that the effective mass is m=0.07* m0 within the structure. Find the values of V01 & L1 that satisfy this condition. Use the values in the equation derived in step #1 to adjust the 2nd periodic potential as well. Hint: Refer to the graphical representation of the condition function in A.J. Levi's Applied Quantum mechanics textbook 3) Using the values found in step #2, Plot the dispersion relation for the energy range from 0 to 5 eV within the first Brillouin zone You can use MATLAB in plotting 4) Indicate on your plot the values of the wavenumber k that would give minimum and maximum group velocity for the electron wave and mention your reasoning behind choosing these values (intuitive, no calculations needed) If two periodic potentials have the following unit cells: V(x) = Voi sin (2- nx 2 V2(x) = Voz (+) 1) Derive the necessary equation for the two periodic potentials to have identical dispersion relations Hint: Refer to the delta-barrier approximation. 2) You wish to design the 1st periodic potential so that the width of the 1st allowed energy band is 0.1 eV given that the effective mass is m=0.07* m0 within the structure. Find the values of V01 & L1 that satisfy this condition. Use the values in the equation derived in step #1 to adjust the 2nd periodic potential as well. Hint: Refer to the graphical representation of the condition function in A.J. Levi's Applied Quantum mechanics textbook 3) Using the values found in step #2, Plot the dispersion relation for the energy range from 0 to 5 eV within the first Brillouin zone You can use MATLAB in plotting 4) Indicate on your plot the values of the wavenumber k that would give minimum and maximum group velocity for the electron wave and mention your reasoning behind choosing these values (intuitive, no calculations needed)