ECE 663

P-N Junctions – Equilibrium

P N

W

Vappl = 0

Vbi = (kT/q)ln(NAND/ni2)

W = 2ks0Vbi(NA+ND)/q(NAND)

Vbi

EF

ECE 663

P-N Junctions – Forward Bias

P N

W

Vappl > 0

Vbi = (kT/q)ln(NAND/ni2)

W = 2ks0(Vbi-Vappl)NA+ND)/q(NAND)

Vbi-Vappl

EFp EFn

-+

EFn - EFp = qVappl in QNR

ECE 663

P-N Junctions – Reverse Bias

P N

W

Vappl < 0

Vbi = (kT/q)ln(NAND/ni2)

W = 2ks0(Vbi+Vappl)NA+ND)/q(NAND)

Vbi+Vappl

EFp

EFn

-+

EFn - EFp = -qVappl in QNR

Voltage variation

x

E

x

V

x

ECE 663

Equilibrium: Forward and Reverse Currents cancel

ECE 663

+ Forward Bias -

Forward Bias: Reverse thermionic flow increases

nie(EFn-Ei)/kT

ECE 663- Reverse Bias +

Reverse Bias: Forward currents win

ECE 663

I-V Curve for Ideal Diode

qkT

V

eII VVA

0

/0 )1( 0

ECE 663

Ideal P-N Junction Diode

Assumptions:

• Steady-State conditions• Non-degenerate doping• One-dimensional• Low Level Injection• Only drift, diffusion,thermal R-G (no photons)

ECE 663

Ideal P-N Junction Diode

DP - = 0∂2pn

∂x2

pn

PDN - = 0∂2np

∂x’2

np

N

xx'

ECE 663

Boundary Conditions

DP - = 0∂2pn

∂x2

pn

P

x

np = ni2(eFn-Fp)

np = ni2eqV/kT in QNR regions

ECE 663

Condition in the Depletion Region

xx'

GRThermal

ppp

p

GRThermal

nnn

n

tp

dx

dJ

qRG

dx

dJ

qtp

tn

dxdJ

qRG

dxdJ

qtn

10)(

1

10)(

1

0dx

dJ

dxdJ pn

ECE 663

Condition in the Depletion Region

xx'

No RG

Jn

JnJp

Jp

≈ -qDP

∂pN

∂x

≈ qDN

∂nP

∂x

≈ -qDN

∂nP

∂x’

ECE 663

Condition in the Depletion Region

xx'

Jn

JnJp

Jp

Jp(xn)

Jn(-xp) = Jn(xn)

J = Jn(-xp) + Jp(xn)

J

ECE 663

Minority Carrier Diffusion Equations – n side QNR

0

0

0

20

2

2

02

2

2

2

p

nnn

ppp

pp

nnn

p

nnp

n

L

pp

dxpd

DL

Dpp

dxpd

pdxpd

Dtp

Boundary Conditions:

)1( /

0

0

kTqV

nnn

nn

epxxp

pxp

ECE 663

Solution

kTxxkTqVnnnn

neepppp //00 )1(

Use continuity equation to find current density at edge of depletion x=xn

1)(

)(

/0

kTqVn

p

pnp

xx

npnp

epL

qDxJ

dxdp

qDxxJn

ECE 663

For the p-side

nnn

LxxkTqVpppp

DL

eennnn np

//00 1

Boundary Conditions:

)1( /

0

0

kTqV

ppp

pp

enxxn

nxn

1)(

)(

/0

kTqVp

n

npn

xx

pppn

enLqD

xJ

dx

dnqDxxJ

p

Current Density from continuity equation

-

ECE 663

Total Diode Current

1

1

1

)()(

/

/

/00

kTqVs

kTqVs

kTqV

n

pn

p

np

nppntotal

eII

or

eJJ

eL

nqD

L

pqDJ

xJxJJ

Ideal diode equation or Shockley Equation

ECE 663

Saturation Current Density

D

i

n

in

n

pn

p

nps

Nn

nn

p

L

nqD

L

pqDJ

2

0

2

0

00

A

i

p

io N

npn

n2

0

2

0

1/22

22

kTqV

An

in

Dp

ip

An

in

Dp

ips

eNLnqD

NL

nqDJ

NLnqD

NL

nqDJ

ECE 663

Larger by eqV/kT

Forward Bias

ECE 663

Smaller by eqV/kT

Reverse Bias

ECE 663

Ideal Diode I-V characteristic

ECE 663

Real Diode I-V characteristic