500c(m^(2))/(V)-s , and its saturation velocity is 10^(6)c(m)/(s) for fields above 100k(V)/(c)m
calculate the hole drift current. What are the electron and hole diffusion cur-
rents in the middle of the bar?
3.22 Use Eq. (3-45) to calculate and plot the mobility vs. temperature mu (T) from
10K to 500K for Si doped with N_(d)=10^(14),10^(16), and 10^(18) donors cm^(-3). Consider
the mobility to be determined by impurity and phonon (lattice) scattering.
Impurity scattering limited mobility can be described by
mu _(I)=3.29 imes 10^(15)(epsi lon_(r)^(z)T^((3)/(2)))/(N_(d)^(+)((m_(n)^(**))/(m_(0)))^((1)/(2))[ln(1+z)-(z)/(1+z)])
where
z=1.3 imes 10^(13)epsi lon_(r)T^(2)((m_(n)^(**))/(m_(0)))(N_(d)^(+))^(-1)
Assume that the ionized impurity concentration N_(d)^(+)is equal to N_(d) at all tem-
peratures. The conductivity effective mass m_(n)^(**) for Si is 0.26m_(0). Acoustic phonon
(lattice) scattering limited mobility can be described by
mu _(AC)=1.18 imes 10^(-5)c_(1)((m_(n)^(**))/(m_(0)))^(-(5)/(2))T^(-(3)/(2))(E_(AC))^(-2)
where the stiffness (c_(1)) is given by
c_(1)=1.9 imes 10^(12) dyne cm^(-2) for Si
and the conduction band acoustic deformation potential (E_(AC)) is
E_(AC)=9.5eV for Si
3.23 Rework Prob. 3.22 considering carrier freeze-out onto donors at low T. That is,
consider
N_(d)^(+)=(N_(d))/(1+exp((E_(d))/(k)T))
as the ionized impurity concentration. Consider the donor ionization energy
(E_(d)) to be 45meV for Si.
500 cm/V-s,and its saturation velocity is 10cm/s for fields above 100 kV/cm
calculate the hole drift current. What are the electron and hole diffusion cur rents in the middle of the bar?
3.22 Use Eq. (3-45) to calculate and plot the mobility vs. temperature (T) from 10 K to 500 K for Si doped with Na = 1014, 1016, and 1018 donors cm-3.Consider the mobility to be determined by impurity and phonon (lattice) scattering Impurity scattering limited mobility can be described by
e?T3/2
= 3.29 X 1015 N1(m/mo)1/21n(1 + z)
7
1+
where
z = 1.3 X 1013e,T2(mn/mo)(N)-1
Assume that the ionized impurity concentration Ni is equal to Na at all tem peratures. The conductivity effective mass m, for Si is 0.26 mo. Acoustic phonon (lattice) scattering limited mobility can be described by
Ac = 1.18 X 10-5 c1(m/mo)-5/2T-3/2(EAc)-2 where the stiffness (c) is given by ci = 1.9 X 1012 dyne cm-2 for Si
and the conduction band acoustic deformation potential (EAc) is
Eac = 9.5 eV for Si
3.23 Rework Prob. 3.22 considering carrier freeze-out onto donors at low T. That is. consider
Na
as the ionized impurity concentration. Consider the donor ionization energy (Ea) to be 45 meV for Si.