- #1

jameson2

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## Homework Statement

Given Silicon at T=300K, with a boron concentration of 10^15 cm^-3. Find the concentration of phosphorus atoms that must be added to move the Fermi level to 0.25eV below the conduction band edge. Also find the final electron and hole concentrations.

Have: effective densities of states [tex] N_C=2.9\times 10^{19} cm^{-3} , N_V=1.05\times 10^{19} cm^{-3} [/tex] from previous part of question.

## Homework Equations

[tex] n=N_C e^{-(E_C-E_F)/kT } [/tex]

[tex] p=N_V e^{-(E_F-E_V)/kT } [/tex]

[tex] np=N_VN_C e^{-(E_C-E_V)/kT }=N_VN_C e^{-E_G/kT } [/tex]

[tex] E_F=\frac{1}{2}(E_C + E_V)-\frac{1}{2}kT ln(\frac{p}{n})+\frac{3}{4}kT ln(\frac{m_h}{m_e}) [/tex]

[tex] \frac{m_h}{m_e}=\frac{0.56}{1.1} [/tex]

[tex] E_F=E_C-0.25eV [/tex]

[tex] E_G=1.12eV [/tex]

## The Attempt at a Solution

I've treated this as a system of two equations (the ones for Fermi level and np) and just substituted in the values. I'm just not getting the right answers. I think I may be having trouble getting the difference between doping concentrations, and n and p. The answers given are [tex] [P]=2.91 \times 10^{15} cm^{-3} , n=1.91 \times 10^{15} cm^{-3} , p=7.8 \times 10^{4} cm^{-3} [/tex]

Any tips would be much appreciated.

Thanks.