EE105 Fall 2011Lecture 3, Slide 1Prof. Salahuddin, UC Berkeley Lecture 3 OUTLINE Semiconductor...
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Transcript of EE105 Fall 2011Lecture 3, Slide 1Prof. Salahuddin, UC Berkeley Lecture 3 OUTLINE Semiconductor...
EE105 Fall 2011 Lecture 3, Slide 1 Prof. Salahuddin, UC Berkeley
Lecture 3
OUTLINE• Semiconductor Basics (cont’d)
– Carrier drift and diffusion
• PN Junction Diodes– Electrostatics– Capacitance
Reading: Chapter 2.1-2.2
EE105 Fall 2011 Lecture 3, Slide 2 Prof. Salahuddin, UC Berkeley
Recap: Drift Current• Drift current is proportional to the carrier velocity
and carrier concentration:
Hole current per unit area (i.e. current density) Jp,drift = q p vh
Total current Jp,drift= Q/t
Q= total charge contained in the volume shown to the rightt= time taken by Q to cross the volume
Q=qp(in cm3)X Volume=qpAL=qpAvht
EE105 Fall 2011 Lecture 3, Slide 3 Prof. Salahuddin, UC Berkeley
Recap: Conductivity and Resistivity• In a semiconductor, both electrons and holes
conduct current:
• The conductivity of a semiconductor is– Unit: mho/cm
• The resistivity of a semiconductor is– Unit: ohm-cm
EEnpqJ
EqnEqpJJJ
EqnJEqpJ
npdrifttot
npdriftndriftpdrifttot
ndriftnpdriftp
)(
)(
,
,,,
,,
np qnqp
1
EE105 Fall 2011 Lecture 3, Slide 4 Prof. Salahuddin, UC Berkeley
Electrical Resistance
where is the resistivity
Resistance Wt
L
I
VR (Unit: ohms)
V
+_
L
tW
I
homogeneously doped sample
EE105 Fall 2011 Lecture 3, Slide 6 Prof. Salahuddin, UC Berkeley
A Second Mechanism of Current Flow is Diffusion
EE105 Fall 2011 Lecture 3, Slide 7 Prof. Salahuddin, UC Berkeley
Carrier Diffusion• Due to thermally induced random motion, mobile
particles tend to move from a region of high concentration to a region of low concentration. – Analogy: ink droplet in water
EE105 Fall 2011 Lecture 3, Slide 8 Prof. Salahuddin, UC Berkeley
Carrier Diffusion• Current flow due to mobile charge diffusion is
proportional to the carrier concentration gradient.– The proportionality constant is the diffusion constant.
dx
dpqDJ pp
Notation:Dp hole diffusion constant (cm2/s)Dn electron diffusion constant (cm2/s)
EE105 Fall 2011 Lecture 3, Slide 9 Prof. Salahuddin, UC Berkeley
Diffusion Examples• Non-linear concentration profile varying diffusion current
L
NqD
dx
dpqDJ
p
pdiffp
,
dd
p
pdiffp
L
x
L
NqDdx
dpqDJ
exp
,
• Linear concentration profile constant diffusion current
dL
xNp
exp
L
xNp 1
EE105 Fall 2011 Lecture 3, Slide 10 Prof. Salahuddin, UC Berkeley
Diffusion Current• Diffusion current within a semiconductor consists of
hole and electron components:
• The total current flowing in a semiconductor is the sum of drift current and diffusion current:
)(
,
,,
dx
dpD
dx
dnDqJ
dx
dnqDJ
dx
dpqDJ
pndifftot
ndiffnpdiffp
diffndiffpdriftndriftptot JJJJJ ,,,,
EE105 Fall 2011 Lecture 3, Slide 11 Prof. Salahuddin, UC Berkeley
The Einstein Relation• The characteristic constants for drift and diffusion are
related:
• Note that at room temperature (300K)
– This is often referred to as the “thermal voltage”.
q
kTD
mV26q
kT
EE105 Fall 2011 Lecture 3, Slide 12 Prof. Salahuddin, UC Berkeley
The PN Junction Diode• When a P-type semiconductor region and an N-type
semiconductor region are in contact, a PN junction diode is formed. VD
ID
+–
EE105 Fall 2011 Lecture 3, Slide 13 Prof. Salahuddin, UC Berkeley
Diode Operating Regions • In order to understand the operation of a diode, it is
necessary to study its behavior in three operation regions: equilibrium, reverse bias, and forward bias.
VD = 0 VD > 0VD < 0
EE105 Fall 2011 Lecture 3, Slide 14 Prof. Salahuddin, UC Berkeley
Carrier Diffusion across the Junction• Because of the differences in hole and electron concentrations on
each side of the junction, carriers diffuse across the junction:
Notation:nn electron concentration on N-type side (cm-3)pn hole concentration on N-type side (cm-3)pp hole concentration on P-type side (cm-3)np electron concentration on P-type side (cm-3)
EE105 Fall 2011 Lecture 3, Slide 15 Prof. Salahuddin, UC Berkeley
Depletion Region• As conduction electrons and holes diffuse across the
junction, they leave behind ionized dopants. Thus, a region that is depleted of mobile carriers is formed.– The charge density in the depletion region is not zero.– The carriers which diffuse across the junction recombine
with majority carriers, i.e. they are annihilated.
width=Wdep
quasi-neutral region
quasi-neutral region
EE105 Fall 2011 Lecture 3, Slide 16 Prof. Salahuddin, UC Berkeley
Some Important Relations
dE
dx
E dV
dx
Energy=-qV
EE105 Fall 2011 Lecture 3, Slide 17 Prof. Salahuddin, UC Berkeley
The Depletion Approximation
In the depletion region on the N side:
bxqN
E
qN
dx
dE
si
D
si
D
si
(x)
x-qNA
qND
In the depletion region on the P side:
xaqN
E
qN
dx
dE
si
A
si
A
si
DA bNaN
a
-b
Because charge density ≠ 0 in the depletion region, a large E-field exists in this region:
EE105 Fall 2011 Lecture 3, Slide 19 Prof. Salahuddin, UC Berkeley
PN Junction in Equilibrium• In equilibrium, the drift and diffusion components of
current are balanced; therefore the net current flowing across the junction is zero.
diffndriftn
diffpdriftp
JJ
JJ
,,
,,
0,,,, diffndiffpdriftndriftptot JJJJJ
EE105 Fall 2011 Lecture 3, Slide 20 Prof. Salahuddin, UC Berkeley
Built-in Potential, V0
• Because there is a large electric field in the depletion region, there is a significant potential drop across this region:
qppE qDpdp
dx pp
dV
dx
Dp
dp
dx
p dV x1
x2
Dpdp
ppn
p p
V (x2) V (x1) Dpp
lnpppn
kT
qln
NAni
2 /ND
ln 20
i
DA
n
NN
q
kTV (Unit: Volts)
EE105 Fall 2011 Lecture 3, Slide 21 Prof. Salahuddin, UC Berkeley
Built-In Potential Example• Estimate the built-in potential for PN junction below.
– Note that
N P
ND = 1018 cm-3 NA = 1015 cm-3
mV603.2mV26)10ln( q
kT
EE105 Fall 2011 Lecture 3, Slide 22 Prof. Salahuddin, UC Berkeley
• A forward bias decreases the potential drop across the junction. As a result, the magnitude of the electric field decreases and the width of the depletion region narrows.
PN Junction under Forward Bias
(x)
x-qNA
qND
a
-b
V(x)
xa-b
V0
ID
0