13.9)
E = 5.6 eV
Ef = 5.48 eV
1
f(E) =
𝑒 +(𝐸−𝐸𝑓)/𝑘𝑇 +1
(𝐸 − 𝐸𝑓) = 0.12 eV
f(E) = 0.25 from 25% filled
k = 86.2*10^-6 eVK^-1
T = 1267 K
13.12)
For silicon:
Eg = 1.107 eV
(𝐸 − 𝐸𝑓) = Eg/2 = 0.5535 eV
k = 86.2*10^-6 eVK^-1
T = 298 K
1
f(E) =
𝑒 +(𝐸−𝐸𝑓)/𝑘𝑇 +1
f(E) = 4.39*10^-10
For diamond:
Eg = 5.5 eV
(𝐸 − 𝐸𝑓) = Eg/2 = 2.75 eV
Same process as 13.9
T = 1480 K
13.24)
R = pl/A
l = 10mm
p = resistivity of tungsten at 1000 C = 24.93 μΩ·cm
A = (πd^2)/4
d = 100 um
A = 7.854*10^-9
R = 31.74
V = IR, I = V/R
I = 3.466 A
13.32)
D= ε0*k*E
ε0 = permittivity of a vacuum = 8.854*10^-12 C/V*m
k = dielectric constant = 4.5
E = electric field strength = 3 kV/mm
D = 1.33*10^-4 C/m^2
13.36)
o = conductivity = nq(ue + uh)
n = conduction electron density = 14*10^15
q = electron charge = 1.6*10^-19 coulombs
ue = conduction electron mobility = 0.14
uh = mobility of electron hole = 0.038
o = (2.24*10^-3)(0.14 + 0.038) = 3.987*10^-4
a) Electrons:
Fraction = (2.24*10^-3)(0.14)/( 3.987*10^-4) = 0.7866
b) Electron holes
Fraction = (2.24*10^-3)(0.0.38)/( 3.987*10^-4) = 0.2135
13.48)
Volume of silicon for 100g = 100/(2.33*100^3) = 4.292*10^-5 m^3
For 100g silicon there will be 10^-6 g boron
(6.023*10^23)(10^-6)/10.81) = 0.557*10^17 atoms of boron for 100g silicon.
n = (0.557*10^17)/( 4.292*10^-5 m^3) = 1.298*10^21 = carrier density
o = conductivity = nq(ue + uh)
ue = conduction electron mobility = 0.14
uh = mobility of electron hole = 0.038
q = electron charge = 1.6*10^-19 coulombs
o = 36.97