p42_043.pdf

43. (a) The probability that a state with energy E is occupied is given by

P ( E )=

e ( E − E F ) /kT +1

where E F is the Fermi energy, T is the temperature on the Kelvin scale, and k is the Boltz-

mann constant. If energies are measured from the top of the valence band, then the energy

associated with a state at the bottom of the conduction band is E =1 . 11eV. Furthermore,

kT =(8 . 62

10 − 5 eV / K)(300K) = 0 . 02586eV. Forpuresilicon, E F =0 . 555eVand( E

−

E F ) /kT =

(0 . 555eV) / (0 . 02586eV) = 21 . 46. Thus,

P ( E )=

e 21 . 46 +1 =4 . 79

10 − 10 .

For the doped semiconductor, ( E

−

E F ) /kT =(0 . 11eV) / (0 . 02586eV) = 4 . 254 and

P ( E )=

e 4 . 254 +1 =1 . 40

10 − 2 .

(b) The energy of the donor state, relative to the top of the valence band, is 1 . 11eV

−

0 . 15eV =

0 . 96eV. The Fermi energy is 1 . 11eV

−

0 . 11eV = 1 . 00eV. Hence, ( E

−

E F ) /kT =(0 . 96eV

−

1 . 00eV) / (0 . 02586eV) =

−

1 . 547 and

P ( E )=

e − 1 . 547 +1 =0 . 824 .