Download Physics of Semiconductor Devices Impurity scattering

Physics of Semiconductor Devices
Impurity scattering
Problem
When a semiconductor is doped, the mobility decreases due to impurity scattering. Undoped GaAs
2
cm2
has an electron mobility of 8500 cm
V s at 300K . After doping, the electron mobility reduces to 7100 V s .
What is the scattering time associated with impurity scattering?
Hint: the total scattering time will be shorter than the scattering time associated with impurity
scattering since there will also be scattering from phonons. The eective mass of electrons in GaAs is
0.067me .
Attention: The parameters are changing everytime. These results are calculated with the above
mentioned values.
Useful physical constants:
Electron mass:
Elementary charge:
me = 9.11 ∗ 10−31 kg
e = 1.602 ∗ 10−19 As
Useful formulas:
Note:
m∗ ...eective mass
τsc ...total scattering time
τsc,lattice ...scattering time caused by phonons (temperature dependent)
τsc,impurity ...scattering time caused by impurity (mostly temperature independent)
Mobility:
µ=
|e| ∗ τsc
m∗
(1)
Matthiessen's rule (The rule to nd the total scattering time):
1
1
1
=
+
τsc
τsc,lattice
τsc,impurity
1
(2)
Solution:
Scattering time of undoped GaAs:
2
τsc,lattice =
0.067 ∗ 9.11 ∗ 10−31 kg ∗ 8500 ∗ 10−4 m
m∗ ∗ µundop
Vs
= 3.24 ∗ 10−13 s
=
e
1.602 ∗ 10−19
(3)
Total scattering time:
2
τsc
0.067 ∗ 9.11 ∗ 10−31 kg ∗ 7100 ∗ 10−4 m
m∗ ∗ µdop
Vs
= 2.705 ∗ 10−13 s
=
=
e
1.602 ∗ 10−19
(4)
Scattering time caused by impurity:
1
1
1
=
+
=⇒ τsc,impurity =
τsc
τsc,lattice
τsc,impurity
2
1
1
τsc
−
1
τsc,lattice
= 1.638 ∗ 10−12 s
(5)