Semiconductor Device Physics

Lecture 8PN Junction Diodes: I-V Characteristics

Dr. Gaurav Trivedi,EEE Department,

IIT Guwahati

Empirical Observations of VBR

Dominant breakdown mechanism is tunneling

BR 0.75B

1 V

N

• VBR : breakdown voltage

VBR decreases with increasing N,

VBR decreases with decreasing EG.

Breakdown Voltage, VBR

Breakdown Mechanism: Avalanching

Breakdown Mechanism: Zener Process

Effect of R–G in Depletion Region

Effect of R–G in Depletion Region

Effect of R–G in Depletion Region

Effect of R–G in Depletion Region

Effect of Series Resistance

Effect of High-Level Injection

High-Level Injection Effect

Summary

Minority-Carrier Charge Storage

Charge Control Approach

Charge Control Approach

P

n p n n

( )

n P np( )

1J

x J x x

dqA p dx A d qA p dx

dt

J

P

P n

( )

P P P n

( )

( ) ( )J

J x

A d A A x

J J J

P PP n

p

( )dQ Q

A xdt

J 0 In steady state

QP QP

Integrating over the n quasineutral region (after all terms multiplied by Adx),

Furthermore, in a p+n junction,

So:

P n( )A x J0

Charge Control Approach

NN p

n

( )Q

I x

P PP n

p

( ) 0dQ Q

A xdt

J

In steady state, we can calculate pn junction current in two ways: From slopes of Δnp(–xp) and Δpn(xn) From steady-state charges QN and QP stored in each “excess minority charge

distribution”

Therefore,

Similarly,

PP n P n

p

( ) ( )Q

A x I x

J

Charge Control Approach

N p( ) 0x J

P PDIFF

p

dQ Qi

dt

DIFF P n( )xJ J

0 In steady state

Moreover, in a p+n junction:

Narrow-Base Diode

0x 0 x

cxnx

n-side contact

cx

Narrow-base diode: a diode where the width of the quasineutral region on the lightly doped side of the junction is on the order of or less than one diffusion length.

px

Narrow-Base Diode I–V

An n0( 0) ( 1)qV kTp x p e

P Pn 1 2( ) x L x Lp x Ae A e

A

c P c P

n0 1 2

1 2

( 1)

0

qV kT

x L x L

p e A A

Ae A e

We have the following boundary conditions:

n c( ) 0p x x

Then, the solution is of the form:

Applying the boundary conditions, we have:

Narrow-Base Diode I–V

cc P cc P

A

cc P cc P

( ) ( )/

n n0 c( ) ( 1) , 0x x L x x L

qV kTx L x L

e ep x p e x x

e e

A c Pn n0 c

c P

sinh ( )( ) ( 1) , 0

sinhqV kT x x L

p x p e x xx L

Solving for A1 and A2, and substituting back:

Note that sinh( ) , cosh( )2 2

e e e e

The solution can be written more compactly as

Narrow-Base Diode I–V

A c Pn n0

c P

( )( ) ( 1)qV kT x x L

p x p ex L

An n0

c

( ) ( 1) 1qV kT xp x p e

x

With decrease base width, xc’0:

02

0

limsinh( )

lim cosh( ) 12

• Δpn is a linear function of x due to negligible thermal R–G in region much shorter than one diffusion length• JP is constant

• This approximation can be derived using Taylor series approximation

Narrow-Base Diode I–V

Because , then

A P c PP P n0

c P

1 cosh ( ) ( 1)

sinhqV kT L x x L

qD p ex L

J

nP P

( )p xqD

x

J

A

2c PP i

DIFF PP D c P

cosh( )( 0) ( 1)

sinh( )qV kT x LD n

I A x qA eL N x L

J

2c PP i

0P D c P

cosh( )

sinh( )

x LD nI qA

L N x L

ADIFF 0 ( 1)qV kTI I e

Then, for a p+n junction:

Narrow-Base Diode I–V

2 2P i P P i

0P D c c D

D n L D nI qA qA

L N x x N

2c P

c P

( )1

2( )

x L

x L

If xc’ << LP,

02

0

limsinh( )

lim cosh( ) 12

c PP

c

( )

2

x LL

x

P

c

L

x

c P

c P

cosh( )

sinh( )

x L

x L

Resulting

Increase of reverse bias means• Increase of reverse current• Increase of depletion width• Decrease of quasineutral region xc’=xc–xn

Wide-Base Diode

A c Pn n0

c P

sinh ( ) /( ) ( 1)

sinh /qV kT x x L

p x p ex L

c P c P

A

c P c P

( ) ( )

n n0( ) ( 1)x x L x x L

qV kTx L x L

e ep x p e

e e

A Pn n0( ) ( 1)qV kT x Lp x p e e Back to ideal

diode solution

Rewriting the general solution for carrier excess,

For the case of wide-base diode (xc’>> LP),

pc P c PP

A

c P c P

// //

n0 ( 1)x Lx L x Lx L

qV kTx L x L

e e e ep e

e e

Wide-Base Diode

A

2c PP i

DIFFP D c P

cosh( )( 1)

sinh( )qV kT x LD n

I qA eL N x L

A

2P i

DIFFP D

( 1)qV kTD nI qA e

L N Back to ideal

diode solution

Rewriting the general solution for diffusion current,

For the case of wide-base diode (xc’>> LP),

lim sinh( )2

lim cosh( )2

e

e

Small-Signal Diode Biasing

V0 << VA

RS : serial resistance

C : capacitanceG :

conductanceY : admittance

When reversed-biased, a pn junction diode becomes functionally equivalent to a capacitor, whose capacitance decreases as the reverse bias increases.

Biasing additional a.c. signal va can be viewed as a small oscillation of the depletion width about the steady state value.

Y G j C

Total pn Junction Capacitance

DCD

IC

kT q

sJC A

W

Junction / depletion capacitance,

due to variation of depletion charges

i

J DC C C av

1R G

Diffusion capacitance,due to variation of stored minority charges in the quasineutral regions

Minority carrier

lifetime

• CJ dominates at low forward biases, reverse biases.• CD dominates at moderate to high forward biases.

Relation Between CJ and VA

2

bi A2 2 2 2J s B S

1 2( )

WV V

C A qN A

sbi A

B

2W V V

qN

NB : bulk semiconductor doping, NA or

ND as appropriate.

For asymmetrical step junction,

Therefore,