gt sdp lecture 7

8/11/2019 Gt Sdp Lecture 7

1/17

Semiconductor Device Physics

Lecture 7

PN Junction Diodes: I-V Characteristics

Dr. Gaurav Trivedi,

EEE Department,

IIT Guwahati


2/17

Qualitative Derivation

Majority

carriers

Majority

carriers


3/17


4/17

Ideal Diode: Assumptions

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 RG take place inside the diode.


5/17

Current Flow in a pnJunction Diode

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 density J= JN(x) + JP(x)

JN(x) and JP(x) may vary with position, but Jis constant throughout the diode.

Yet an additional assumption is now made, that thermal recombination-generation isnegligible throughout the depletion regionJNand JPare therefore determined to beconstants independent of position inside the depletion region.


6/17

Carrier Concentrations atxp, +xn

n-sidep-side

p0 p A

2

ip0 p

A

( )

( )

p x N

nn x

N

n0 n D

2

in0 n

D

( )

( )

n x N

np x

N

p p A( )p x N n n D( )n x N

Consider the equilibriumcarrier concentrations at VA= 0:

If low-level injection conditions prevail in the quasi-neutral regions when VA 0, then:


7/17


8/17

Excess Carrier Concentrations atxp, xn

p p A( )p x N

n-sidep-side

n n D( )n x N

A

2i

p p

A

( ) ( 1)qV kT n

n x eN

A2i

n n

D

( ) ( 1)qV kT n

p x eN

A

A

2

i

p p

A

p0

( )

qV kT

qV kT

n e

n x N

n e

A

A

2

i

n nD

n0

( )

qV kT

qV kT

n ep x

N

p e


9/17

Excess Carrier Distribution

A

n n n0( ) ( 1)qV kT p x p e

2

n nP 2

p

0 , 0d p p

D xdx

P P

n 1 2( ) x L x L

p x A e A e

0x 0 x

P P pL D

for 0x

From the minority carrierdiffusionequation,

We have the following boundary

conditions:

n( ) 0p

For simplicity, we develop a newcoordinate system:

Then, the solution is given by:

LP: hole minority carrierdiffusion length


10/17

Excess Carrier Distribution

A

n n0( 0) ( 1)qV kT

p x p e

A P

n n0( ) ( 1) , 0qV kT x L

p x p e e x

P P'/ '/

n 1 2( ) x L x L

p x A e A e

NA

p p0( ) ( 1) , 0x LqV kT n x n e e x

A /

1 n0 ( 1)qV kT

A p e 2 0A

New boundary conditions

n ( ) 0p x

From the x ,

From the x 0,

Therefore

Similarly,


11/17

pnDiode IVCharacteristic

A Pn PP P n0

P

( )( ) ( 1)qV kT x Ld p x Dx qD q p e edx L

J

NAp N

N N p0

N

( )( ) ( 1)

x LqV kT d n x D

x 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 kT D D

qn eL N L N

J


12/17

pnDiode IVCharacteristic

A0

2 N P0 i

N A P D

( 1)qV kT

I I eD D

I AqnL N L N

I A J A2 N PiN A P D

( 1)qV kT D D

Aqn eL N L N

Shockley Equation,

for ideal diode I0can be viewed as the drift

current due to minority carriersgenerated within the diffusionlengths of the depletion region


13/17

Diode Saturation Current I0

I0can vary by orders of magnitude, depending on the semiconductor material, due to ni2

factor.

In an asymmetrically doped pnjunction, the term associated with the more heavily dopedside is negligible.

If the pside is much more heavily doped,

If the nside is much more heavily doped,

2 NP

0 iP 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


14/17

Diode Carrier Currents

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

Total current density isconstant inside the diode

Negligible thermal R-G throughoutdepletion region

dJN/dx= dJP/dx= 0


15/17

Carrier Concentration: Forward Bias

n0p

p0p

p0

n

n0n

A2

i

qV kT

np n e

p A

n D

p N

n N

Excess minoritycarriers

Excess minoritycarriers

A P

n n0( ) ( 1)qV kT x L

p x p e e NA

p p0( ) ( 1) x LqV kT n x n e e

Law of the Junction

Low level injection conditions


16/17

Carrier Concentration: Reverse Bias

Deficit of minority carriers near the depletion region.

Depletion region acts like a sink, draining carriers from the adjacent quasineutral regions


17/17

Deviations from the Ideal I-VBehavior

gt sdp lecture 7

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