Solutions for HW1
Divija Gogineni
(2.2)
(a)
Mobility of electrons in Si = 1350
cm2
/
V∗s
Mobility of holes in Si =480
cm2
/
V∗s
Velocity of electrons=
µnE=1350 cm2
V∗s0.1V
µm = 1.35 ∗104m/s
Velocity of holes =
µpE=480 cm2
V?s0.1V
µm = 4.8∗103m/s
(b)
Given:
E= 0.1V/µm,
hole concentration is negligible
µn
=1350
cm2/V ∗S
µp= 480cm2/V ∗S
Jtot
=
1mA/µm2=q[µnnE +µppE]≈qµnnE
Therefore,
n=Jtot
qµnE =1mA/µm2
(1.6∗10−19)(1350cm2/V ∗s)(0.1V /µm)= 4.6∗1017cm−3
(2.5)
Since there is no electric eld, the current is due entirely to diusion. If we dene the current as
positive when owing in the positive x direction, we can write:
Itot=Idif f =AJdiff =Aq hDndn
dx −Dpdp
dx i
A= 1µm ∗1µm =10−8cm2
Dn= 34cm2/s
Dp= 12cm2/s
dn
dx =−5∗1016cm−3
2∗10−4cm =−2.5∗1020cm−4
dp
dx =2∗1016cm−3
2∗10−4cm = 1020cm−4
Itot =10−8cm21.602 ∗10−19C34cm2/s−2.5∗1020cm−4−12cm2/s 1020 cm−4
=−15.54µA
(2.6)
Given Area=a, nd total electrons stored
n(x) = −N
Lx+N
Therefore, total electrons stored
=´a∗n(x)dx=´L
0a(−N
Lx+N)dx
=aN −x2
2L+x
|
L
0
=
aNL
2
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