3
If an electric field
ε
(a vector) is applied, electrons will gain
velocity/accelerate
a
in the direction of the force,
F
n
= –
q
ε
,
on average
as (remember)
where
m
n,cond
is
conductivity effective mass
for electrons
(… which, from “motion” notes,
is for electrons in Si
or
in terms of the “longitudinal”
and “transverse” masses
m
l
and
m
t
respectively.)
(Singh, 5.15,
modified)
m
l
=
0.98
m
e
Δ
-valleys
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
≡
t
l
cond
n
m
m
m
2
1
3
1
1
,
cond
n
cond
n
n
drift
n
m
q
m
t
,
,
,
ε
F
a
v
ε
−
=
=
=
∂
∂
e
cond
n
m
m
26
.
0
,
≅
m
t
=
0.19
m
e
6
scatt
n
drift
n
scattering
drift
n
t
,
,
,
τ
v
v
−
=
∂
∂
However, the
electrons are also
frequently
(!)
―
~ 10
12
to 10
14
times/sec typically
―
subject to
velocity randomizing/reducing
(and energy dissipating)
scattering processes …
… that is, dopants, lattice vibrations or anything else that makes
the crystal potential not perfectly periodic (such that the Bloch
functions
ψ
k
(
r
) with associated expected velocities
v
k
are no
longer true energy eigenstates and, thus, must evolve in
time/scatter).
If
τ
n,scatt
is the
average
time required for an electron to have its
velocity direction randomized by scattering processes, then the
rate of deceleration due to scattering can be written,