A step pn junction diode is made in silicon with the n side having N'D = 2x10^16 cm^-3 and the p side having a net doping of N'A = 5x10^15 cm^-3.
1). Draw to scale the energy band diagram of the junction at equilibrium.
2). Find the built-in voltage, and compare with the value measured off...
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I decided to pick K=0 for the minima of the conduction band and the maxima of the valence band (does this sound right?)
solving for the 2nd derivative:
E(K)c = Ec + 5ev * sin (K*a)^2
E(K)c" = -10*sin(Ka)^2 + 10*cos(Ka)^2
Evaluate m* = hbar^2 / E(K)c" = 1.11x10^-69 (units?)
E(K)v = Ev...
Solving for the 2nd derivative at the maxima/minima, I get 0. :confused: if you plot out the graphs, the maxima/minima are at the same K values for both curves?
I graphed them on the calculator and using Ec and Ev as variables (but assume they are zero with the calculator), the graphs are symmetrical about the x-axis (y=0). Does that make any sense?
For the effective mass, how do you use the 2nd derivative? Isn't it just the slope?
if so, how does...
So I just treat Ec and Ev as variables and mark them arbitrarily on the y-axis for each of the curves?
I graphed them on my calc and they appear to be just almost symmetrical of one another.
So do I have to solve for a numerical value of the effective mass?
Is there a difference between...
I'm having difficulty figuring out how to work this problem:
Assume a material has a given E-K diagram:
E(K)conduction = Ec + E1 * sin^2 (Ka)
E(K)valence = Ev - E2 * sin^2 (Ka)
a=0.5nm
E1 = 5eV
E2 = 4eV
I have to:
* sketch the E-K diagram for the first brillouin zone (-pi/a < k <...