6. Si is donor-doped with $10^{16} cm^{-3}$ of arsenic (As) atoms. Assuming complete
ionization of As and $n_i = 1.45 \times 10^{10} cm^{-3}$,
(a) find the majority (n) and minority (p) carrier concentrations, and the Fermi level,
$E_F$ and donor ionization energy, $E_D$, (specified in eV from the bottom of the
conduction band) at room temperature (300 K).
(b) What is $E_F$ if specified from $E_i$?
(c) Show calculations and illustrate your results
pictorially by replacing the question marks in the
figure below with numbers (in eV); verify that
their sum is $1/2E_g$.
Given: Boltzmann constant, $k = 8.617 \times 10^{-5} eV. K^{-1}$
Assume effective densities of states:
$N_c = 2.81 \times 10^{19} cm^{-3}$ and $N_v = 1.6 \times 10^{19} cm^{-3}$
(6 points)
(Not to scale)
Vacuum level $E_0$
Electron
$\chi_{Si} =$ affinity
$E_c$
$E_c - E_{d,As} = 0.054 eV$
$E_c - E_f = ?? eV$
$E_d$
$E_F$
$E_f - E_i = ?? eV$
$E_g = 1.1 eV$
$E_i$
$E_v$
