HW #3 (along with HW #2b) contains a lot of what we understand about p-n junction equilibrium. This includes the depletion ansatz, the charge density, electric field and electric potential near the junction, how the depletion width is established through its relationship to the potential step need to allow mu to remain constant.
In actually doing these problems i realized the importance of starting on the left, x<-x_0, and systematically integrating to get phi(x) in all regions. Because of the way integrals are defined and used, that seemed the best way. (Setting phi(x) =0 for x less than -x_0 got things started. then one can integrate from -x_0 to zero and then use the value of phi(x) at zero to set the integration constant for the 0 to +x_0 integration.
In problem 1, you can see where i initially forgot the 11.8 (epsilon) and then added that in. What do you think of the values of 76 nm (1), and 145 nm and 3 nm (problem 2). Do those seem correct?
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