ideal diode equation - nanohubidealdiodeequationi_s16.pdf“ideal diode equation” “shockley...
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Lundstrom ECE 305 S16
ECE-606: Fall 2016
Ideal Diode Equation
Professor Mark Lundstrom Electrical and Computer Engineering
Purdue University, West Lafayette, IN USA [email protected]
2/25/15
Pierret, Semiconductor Device Fundamentals (SDF) pp. 235-259
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equilibrium e-band diagram
2
EFEF
EC
EV
x
W
E
qVbi
I = 0
VA = 0
−xn xp
Lundstrom ECE 305 S16
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e-band diagram under bias
3
EC
EV
x
W
E
−xn xp
V = 0
VA > 0
qVAFn
Fp
q Vbi −VA( )
Lundstrom ECE 305 S16
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electrostatics under bias
4
W = 2KSε0q
NA + ND
NDNA
⎛⎝⎜
⎞⎠⎟Vbi −VA( )⎡
⎣⎢
⎤
⎦⎥
1/2
E 0( ) = 2 Vbi −VA( )
W
xn =NA
NA + ND
W
xp =ND
NA + ND
W
N P
ND = 1016
depletion region xp−xn 0
E 0( )
Vbi =kBTqln NDNA
ni2
⎛⎝⎜
⎞⎠⎟
WNA = 1016
Lundstrom ECE 305 S16
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outline
5
1) Ideal diode equation (qualitative)
2) Law of the Junction
3) Ideal diode equation (long base)
4) Ideal diode equation (short base)
Lundstrom ECE 305 S16
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ECE 255
6
VA
− VA +
I mA( )
0.6 − 0.7 V
I = I0 eqVA kBT −1( )
“ideal diode equation” “Shockley diode equation”
I = I0 eqVA kBT −1( )
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questions
7
“ideal diode equation” “Shockley diode equation”
I = I0 eqVA kBT −1( )
1) Why does the current increase exponentially with the applied forward bias?
2) Why is the reverse bias current independent of the reverse bias voltage?
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e-band diagram under bias
8
EC
EV
x
E
−xn xp
qVAFn
Fp
q Vbi −VA( )
Lundstrom ECE 305 S16
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e-band diagram under bias
9
EC
EV
x
E
−xn xp
qVAFn
Fp
q Vbi −VA( )
Lundstrom ECE 305 S16
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P0 = e−ΔE kBT = e−qVbi kBT
NP junction in equilibrium
10
ΔE = qVbiEF
P0
P0 = ?
Lundstrom ECE 305 S16
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P0 = e−ΔE kBT = e−qVbi kBT
NP junction in equilibrium
11
ΔE = qVbiEF
P0
P0 =
n0Pn0N
=ni2 NA( )ND
= ni2
NAND
qVbi = kBT lnNDNA
ni2
⎛⎝⎜
⎞⎠⎟
FN→P0
FP→N0
n0P =ni2
NA
Lundstrom ECE 305 S16
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NP junction under bias
12
Fn
q Vbi −VA( )
Fp
P
P = e−ΔE kBT = e−q Vbi−VA( ) kBT =P0eqVA kBT
Lundstrom ECE 305 S16
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NP junction under bias
13
Fn
q Vbi −VA( )Fp
P
P =P0eqVA kBT
I = qA FN→P − FP→N( )
FN→P = FN→P0 eqVA kBT
FP→N = FP→N0
FN→P
FP→N
Lundstrom ECE 305 S16
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questions
14
“ideal diode equation” “Shockley diode equation”
I = I0 eqVA kBT −1( )
1) Why does the current increase exponentially with the applied forward bias?
2) Why is the reverse bias current independent of the reverse bias voltage?
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Excess carriers under forward bias
q Vbi −VA( )
p0P ≈ NA
Fp
nP >> n0Pn0P =
ni2
NA
Lundstrom ECE 305 S16 15
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recombination and current
16
minority carriers injected across junction
Fn FPqVA
−VA +ID
Every time a minority electron recombines on the p-side, one electron flows in the external current.
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excess electrons on the p-side of junction
17
Fn
q Vbi −VA( )
p0P ≈ NA
nP >> n0Pn0N ≈ ND
Fp
0x
What is Δn(x) on the p-side? Ans. Solve the MCDE.
WP
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boundary conditions for the MCDE
18
Fn
q Vbi −VA( )
p0P ≈ NA
Δn WP( ) = 0
Fp
0x
WP
Δn 0( ) = ?
Lundstrom ECE 305 S16
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outline
19
1) Ideal diode equation (qualitative)
2) Law of the Junction
3) Ideal diode equation (long base)
4) Ideal diode equation (short base)
Lundstrom ECE 305 S16
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NP junction in equilibrium
20
ΔE = qVbi
EF
n0P =ni2
NA
p0P = NA
0x
WP
Lundstrom ECE 305 S16
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NP junction under forward bias
21
Fn
q Vbi −VA( )
pP ≈ NA
Fp
0x
WP
np =ni2
NA
eqVA kBT
np 0( ) pp 0( ) = ni2eqVA kBT
“Law of the Junction”
Lundstrom ECE 305 S16
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excess carriers
22
Fn
q Vbi −VA( )
pP ≈ NA
Fp
0x
WN
np =ni2
NA
eqVA kBT Δnp 0( ) = ni2
NA
eqVA kBT − np0
“Law of the Junction”
Δnp 0( ) = ni2
NA
eqVA kBT −1( )
Lundstrom ECE 305 S16
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Law of the Junction another way
23
Fn
q Vbi −VA( )
pP ≈ NA
Fp
0x
WN
np 0( ) = nie Fn−Ei( ) kBTAssume QFLs are constant across the transition region
pp 0( ) = nie Ei−Fp( ) kBT
np 0( ) pp 0( ) = ni2e Fn−Fp( ) kBT
np 0( ) pp 0( ) = ni2eqVA kBT
Lundstrom ECE 305 S16
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outline
24
1) Ideal diode equation (qualitative)
2) Law of the Junction
3) Ideal diode equation (long base)
4) Ideal diode equation (short base)
Lundstrom ECE 305 S16