President University Erwin Sitompul SDP 6/1
Dr.-Ing. Erwin SitompulPresident University
Lecture 6
Semiconductor Device Physics
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Majoritycarriers
Majoritycarriers
Qualitative DerivationChapter 6 pn Junction Diodes: I-V Characteristics
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Current Flow in a pn Junction DiodeChapter 6 pn Junction Diodes: I-V Characteristics
When a forward bias (VA > 0) is applied, the potential barrier to diffusion across the junction is reduced.
Minority carriers are “injected” into the quasi-neutral regions Δnp > 0, Δpn > 0.
Minority carriers diffuse in the quasi-neutral regions, recombining with majority carriers.
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Ideal Diode: AssumptionsChapter 6 pn Junction Diodes: I-V Characteristics
Steady-state conditions.Non-degenerately doped step junction.One-dimensional diode.Low-level injection conditions prevail in the quasi-neutral
regions.No processes other than drift, diffusion, and thermal R–G take
place inside the diode.
President University Erwin Sitompul SDP 6/5
N n N n N
( )( )
dn d nx q n qD q n qD
dx dx
J E E
P p P p P
( )( )
dp d px q p qD q p qD
dx dx
J E E
Current Flow in a pn Junction DiodeChapter 6 pn Junction Diodes: I-V Characteristics
Current density J = JN(x) + JP(x)
JN(x) and JP(x) may vary with position, but J is constant throughout the diode.
Yet an additional assumption is now made, that thermal recombination-generation is negligible throughout the depletion region JN and JP are therefore determined to be constants independent of position inside the depletion region.
President University Erwin Sitompul SDP 6/6
n-sidep-side
p0 p A
2i
p0 pA
( )
( )
p x N
nn x
N
n0 n D
2i
n0 nD
( )
( )
n x N
np x
N
p p A( )p x N n n D( )n x N
Carrier Concentrations at –xp, +xn
Chapter 6 pn Junction Diodes: I-V Characteristics
Consider the equilibrium carrier concentrations at VA = 0:
If low-level injection conditions prevail in the quasi-neutral regions when VA 0, then:
President University Erwin Sitompul SDP 6/7
i P
N i
( )i
( )i
E F kT
F E kT
p n en n e
A2i qV kTnp n e
N ii P
N P
( )( )2i
( )2i
F E kTE F kT
F F kT
np n e e
n e
p nfor x x x
“Law of the Junction”Chapter 6 pn Junction Diodes: I-V Characteristics
The voltage VA applied to a pn junction falls mostly across the depletion region (assuming that low-level injection conditions prevail in the quasi-neutral regions).
Two quasi-Fermi levels is drawn in the depletion region:
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p p A( )p x N
n-sidep-side
n n D( )n x N
A
2i
p pA
( ) ( 1)qV kTnn x e
N A
2i
n nD
( ) ( 1)qV kTnp x e
N
Excess Carrier Concentrations at –xp, xn
Chapter 6 pn Junction Diodes: I-V Characteristics
A
A
2i
p pA
p0
( )
qV kT
qV kT
n en x
N
n e
A
A
2i
n nD
n0
( )
qV kT
qV kT
n ep x
N
p e
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A 0.6 0.02586 12 3p p p0( ) 100 1.192 10 cmqV kTn x n e e
12 12 3p p p p p0( ) ( ) 1.192 10 100 1.192 10 cmn x n x n
Example: Carrier InjectionChapter 6 pn Junction Diodes: I-V Characteristics
A pn junction has NA=1018 cm–3 and ND=1016 cm–3. The applied voltage is 0.6 V.
a) What are the minority carrier concentrations at the depletion-region edges?
b) What are the excess minority carrier concentrations?
A 4 0.6 0.02586 14 3n n n0( ) 10 1.192 10 cmqV kTp x p e e
14 4 14 3n n n n n0( ) ( ) 1.192 10 10 1.192 10 cmp x p x p
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An n n0( ) ( 1)qV kTp x p e
2n n
P 2p
0 , 0d p p
D xdx
P Pn 1 2( ) x L x Lp x A e A e
0x 0 x
P P pL D for 0x
Excess Carrier DistributionChapter 6 pn Junction Diodes: I-V Characteristics
From the minority carrier diffusion equation,
We have the following boundary conditions:
n ( ) 0p
For simplicity, we develop a new coordinate system:
Then, the solution is given by:
• LP : hole minority carrier diffusion length
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An n0( 0) ( 1)qV kTp x p e
A Pn n0( ) ( 1) , 0qV kT x Lp x p e e x
P P'/ '/n 1 2( ) x L x Lp x A e A e
NAp p0( ) ( 1) , 0x LqV kTn x n e e x
A /1 n0 ( 1)qV kTA p e 2 0A
Excess Carrier DistributionChapter 6 pn Junction Diodes: I-V Characteristics
New boundary conditions
n ( ) 0p x
From the x’ → ∞,
From the x’ → 0,
Therefore
Similarly,
President University Erwin Sitompul SDP 6/12
A Pn PP P n0
P
( )( ) ( 1)qV kT x Ld p x Dx qD q p e e
dx L
J
NAp NN N p0
N
( )( ) ( 1) x LqV kTd n x Dx qD q n e e
dx L
J
n-side
p-side
p nN P N P0 0x x x x x x
J J J J J
A2 N Pi
N A P D
( 1)qV kTD Dqn e
L N L N
J
pn Diode I–V CharacteristicChapter 6 pn Junction Diodes: I-V Characteristics
President University Erwin Sitompul SDP 6/13
A0
2 N P0 i
N A P D
( 1)qV kTI I e
D DI Aqn
L N L N
I A J
pn Diode I–V CharacteristicChapter 6 pn Junction Diodes: I-V Characteristics
A2 N Pi
N A P D
( 1)qV kTD DAqn e
L N L N
• Shockley Equation,for ideal diode
• I0 can be viewed as the drift current due to minority carriers generated within the diffusion lengths of the depletion region
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I0 can vary by orders of magnitude, depending on the semiconductor material, due to ni
2 factor. In an asymmetrically doped pn junction, the term associated
with the more heavily doped side is negligible. If the p side is much more heavily doped,
If the n side is much more heavily doped,
2 NP0 i
P D N A
DDI Aqn
L N L N
2 P0 i
P D
DI Aqn
L N
2 N0 i
N A
DI Aqn
L N
Diode Saturation Current I0
Chapter 6 pn Junction Diodes: I-V Characteristics
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N P J J J
N p n N p
P p n P n
( ) ( )
( ) ( )
x x x x
x x x x
J J
J J
Diode Carrier CurrentsChapter 6 pn Junction Diodes: I-V Characteristics
• Total current density is constant inside the diode
• Negligible thermal R-G throughout depletion region dJN/dx = dJP/dx = 0
President University Erwin Sitompul SDP 6/16
n0p
p0p
p0n
n0n
A2i qV kTnp n e
p A
n D
p Nn N
Excess minoritycarriers
Excess minoritycarriersA P
n n0( ) ( 1)qV kT x Lp x p e e NAp p0( ) ( 1) x LqV kTn x n e e
Carrier Concentration: Forward BiasChapter 6 pn Junction Diodes: I-V Characteristics
Law of the Junction
Low level injection conditions
President University Erwin Sitompul SDP 6/17
Carrier Concentration: Reverse BiasChapter 6 pn Junction Diodes: I-V Characteristics
Deficit of minority carriers near the depletion region.Depletion region acts like a “sink”, draining carriers from the
adjacent quasineutral regions
President University Erwin Sitompul SDP 6/18
Forward-bias current Reverse-bias current
“Breakdown”
“Slope over” No saturation
Smaller slope
Deviations from the Ideal I-V BehaviorChapter 6 pn Junction Diodes: I-V Characteristics
Si pn-junction Diode, 300 K.
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This time no homework.Prepare well for midterm examination.
HomeworkChapter 6 pn Junction Diodes: I-V Characteristics