656
F Review of Solid State Concepts
while for electrons in a crystal, we have instead
dI 0
dt
=
1
¯
h 2 e
2 E
1
π
k a
−k a
d 2
dk 2 dk
≡
e 2 E
m e
N eff .
(F.3.19)
We see from this expression that N eff is given by
N eff =
1
π
m e
¯
h 2
d
dk
k=k a
−
d
dk
k=−k a
=
2
π
m e
¯
h 2
d
dk
k=k a
.
(F.3.20)
This is a very important result, as it tells us that the effective number of electrons
capable of contributing to electrical conduction depends upon the slope of the vs.
k curve at the highest occupied energy level. As
d
dk
= 0 at the highest level in the
band, we can conclude that the effective number of electrons for a full band is zero,
and hence for a filled energy band, there is no electrical conduction.
F Review of Solid State Concepts
while for electrons in a crystal, we have instead
dI 0
dt
=
1
¯
h 2 e
2 E
1
π
k a
−k a
d 2
dk 2 dk
≡
e 2 E
m e
N eff .
(F.3.19)
We see from this expression that N eff is given by
N eff =
1
π
m e
¯
h 2
d
dk
k=k a
−
d
dk
k=−k a
=
2
π
m e
¯
h 2
d
dk
k=k a
.
(F.3.20)
This is a very important result, as it tells us that the effective number of electrons
capable of contributing to electrical conduction depends upon the slope of the vs.
k curve at the highest occupied energy level. As
d
dk
= 0 at the highest level in the
band, we can conclude that the effective number of electrons for a full band is zero,
and hence for a filled energy band, there is no electrical conduction.