Homework 2a: Due Tuesday.

preface: For the problem we worked on in class, we characterized our model (which represented a "homogeneous" semiconductor) by an energy gap (1 eV) and by an intrinsic carrier density (at room T) of 10^10 cm-3. An alternative approach to modeling (which is not really much different) is to specify Eg, Nc and Nv, where Nc and Nv are related to the state density at the edge of the CB and VB, respectively (as defined in our discussions in class).

rationale/due date: I got to thinking that if there was no HW due until next Thursday, some people might not work on these things until possibly next Wednesday. I believe, however, that it may be valuable for students to work problems frequently, so that these concepts (like the relationship between mu and carrier concentration) sink in and become "second nature". So with that in mind I decided to creat this short assignment due next Tuesday.

Homework 2a (due Tuesday, April 13):

1. Suppose our semiconductor "model A" has:
an energy gap of 1.0 eV
Nc=5.0 x 10^18 cm-3
Nv=Nc

a) Calculate mu for a doping level of 10^16 donors/cm^3 (e.g., phosphorous atoms).
b) Calculate mu for a doping level of 10^17 donors/cm^3 (e.g., phosphorous atoms).
c) Calculate mu for a doping level of 10^16 acceptors/cm^3 (e.g., boron atoms).
d) Calculate mu for a doping level of 10^17 acceptors/cm^3 (e.g., boron atoms).

2. What doping level would correspond to mu=0.7 eV for this model?

3. What is n_i for the above model?

4. For a model, with Eg=1 eV, but with Nc=5.0 x 10^18 cm-3 and
Nv=2Nc:
a) Calculate mu for a doping level of 10^17 donors/cm^3 (e.g., phosphorous atoms).
b) Calculate mu for a doping level of 10^17 acceptors/cm^3 (e.g., boron atoms).
c) Calculate n_i.

5. Discuss the differences between the 2 models.

6. (Extra credit/optional) Consider a semiconductor (model A) in which the left half (x<0)>0) is doped with 10^17 cm-3 donors. What is it like?