lecture 9 outline pn junction diodes – electrostatics (step junction) reading: pierret 5; hu...
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Lecture 9
OUTLINE• pn Junction Diodes– Electrostatics (step junction)
Reading: Pierret 5; Hu 4.1-4.2
pn Junctions• A pn junction is typically fabricated by implanting or diffusing
donor atoms into a p-type substrate to form an n-type layer:
EE130/230A Fall 2013 Lecture 9, Slide 2
• A pn junction has a rectifying current-vs.-voltage characteristic:
C. C. Hu, Modern Semiconductor Devices for ICs, Figure 4-2
C. C. Hu, Modern Semiconductor Devices for ICs, Figure 4-1
Terminology
Doping Profile:
Lecture 9, Slide 3EE130/230A Fall 2013
Net
R.F. Pierret, Semiconductor Fundamentals, Figure 5.1
Idealized pn Junctions
Lecture 9, Slide 4
• In the analysis going forward, we will consider only the net dopant concentration on each side of the pn junction:
NA net acceptor doping on the p side: (NA-ND)p-side
ND net donor doping on the n side: (ND-NA)n-side
EE130/230A Fall 2013
R.F. Pierret, Semiconductor Fundamentals, Figure 5.2
Electrostatics (Step Junction)
Band diagram:
Electrostatic potential:
Electric field:
Charge density:
Lecture 9, Slide 5EE130/230A Fall 2013R.F. Pierret, Semiconductor Fundamentals, Figure 5.4
“Game Plan” to obtain (x), E(x), V(x)1. Find the built-in potential Vbi
2. Use the depletion approximation (x)(depletion widths xp, xn unknown)
3. Integrate (x) to find E(x)Apply boundary conditions E(-xp)=0, E(xn)=0
4. Integrate E(x) to obtain V(x)Apply boundary conditions V(-xp)=0, V(xn)=Vbi
5. For E(x) to be continuous at x=0, NAxp = NDxn
Solve for xp, xn Lecture 9, Slide 6EE130/230A Fall 2013
Built-In Potential Vbi
i
A
isidepFi
n
NkT
n
pkTEE
ln
ln)(
sideniFsidepFisiden Ssidep Sbi )()( EEEEqV
i
D
isideniF
n
NkT
n
nkTEE
ln
ln)(
For non-degenerately doped material:
Lecture 9, Slide 7EE130/230A Fall 2013
R.F. Pierret, Semiconductor Fundamentals, Figure 5.4a
What if one side is degenerately doped?
sideniFsidepFibi EEEEqV )()(
p+n junction n+p junction
Lecture 9, Slide 8EE130/230A Fall 2013
The Depletion ApproximationIn the depletion region on the p side, = –qNA
Lecture 9, Slide 9
ps
A
s
A xxqN
CxqN
x
1)(
In the depletion region on the n side, = qND
xxqN
CxqN
x ns
A
s
D
1)(
EE130/230A Fall 2013
R.F. Pierret, Semiconductor Fundamentals, Figure 5.6
Electric Field Distribution
The electric field is continuous at x = 0
NAxp = NDxn
Lecture 9, Slide 10
xxn-xp
E(x)
EE130/230A Fall 2013
On the p side:
Choose V(-xp) to be 0
On the n side:
12)(
2)( Dxx
qNxV p
s
A
22
2 )(2
)(2
)( xxqN
VDxxqN
xV ns
Dbin
s
D
Lecture 9, Slide 11
Electrostatic Potential Distribution
V(xn) = Vbi
EE130/230A Fall 2013
• At x = 0, expressions for p side and n side must be equal:
• We also know that NAxp = NDxn
Lecture 9, Slide 12
Derivation of Depletion Width
EE130/230A Fall 2013
Depletion Width• Eliminating xp, we have:
• Eliminating xn, we have:
• Summing, we have:
)(
2
DAD
Abisn NNN
N
q
Vx
)(
2
DAA
Dbisp NNN
N
q
Vx
DA
bispn NNq
VWxx
112
Lecture 9, Slide 13EE130/230A Fall 2013
Depletion Width in a One-Sided Junction
If NA >> ND as in a p+n junction:
What about a n+p junction?
where density dopantlighter NNN AD
1111
nD
bis xqN
VW
2
0 ADnp NNxx
qNVW bis2
Lecture 9, Slide 14EE130/230A Fall 2013
Peak E-Field in a One-Sided Junction
biVWdx )0(2
1
s
bibi qNV
W
V
22
)0(
bis V
qNW
2
Lecture 9, Slide 15EE130/230A Fall 2013
V(x) in a One-Sided Junction
Lecture 9, Slide 16
biDA
D VNN
NV
)0(
p side n side2)(
2)( p
s
A xxqN
xV
2)(2
)( xxqN
VxV ns
Dbi
EE130/230A Fall 2013
Example: One-Sided pn JunctionA p+n junction has NA=1020 cm-3 and ND =1017cm-3. Find (a) Vbi (b) W (c) xn and (d) xp .
i
DGbi n
N
q
kT
q
EV ln
2
D
bis
qN
VW
2
Wxn
ADnp NNxx
Lecture 9, Slide 17EE130/230A Fall 2013
Voltage Drop across a pn Junction
Note that VA should be significantly smaller than Vbi in order for low-level injection conditions to prevail in the quasi-neutral regions.
Lecture 9, Slide 18EE130/230A Fall 2013
R.F. Pierret, Semiconductor Fundamentals, Figure 5.10
Effect of Applied Voltage
Lecture 9, Slide 19
DAAbi
s
NNVV
qW
11)(
2
EE130/230A Fall 2013R.F. Pierret, Semiconductor Fundamentals, Figure 5.11
Summary• For a non-degenerately-doped pn junction:
Built-in potential
Depletion width
• For a one-sided junction:
Built-in potential
Depletion width
2ln
i
ADbi n
NN
q
kTV
DA
Abispn NNq
VVxxW
112
i
Gbi n
N
q
kTEV ln
2
qN
VVW Abis
2
Lecture 9, Slide 20
WNN
Nx
DA
Dp W
NN
Nx
DA
An
EE130/230A Fall 2013
Linearly Graded pn Junction
Lecture 9, Slide 21EE130/230A Fall 2013