ECE 663

Ideal Diode I-V characteristic

ECE 663

Real Diode I-V characteristic

ECE 663

Real Diode – Forward Bias (semi-log scale)

ECE 663

Real Diode – Reverse Bias

ECE 663

What’s wrong with this picture?

• Forward Bias– For V < 0.35 volts slope is kT/2q– For 0.35V < V < 0.7volts, slope is kT/q

– For V > 0.7 volts, slope less than kT/q (V~Vbi)

– I0 ~10-14A from intercept of semi-log plot in FB

ECE 663

What’s wrong with this picture?

• Reverse Bias– Current ~103 times larger than FB I0– Reverse current doesn’t saturate

– Breakdown – large current above Vbd

• Avalanche breakdown• Zener (tunneling) process

ECE 663

Reverse Bias Avalanche Breakdown

Depletion width larger than mean free path lots of collisions

ECE 663

Avalanching

• Minority carriers accelerated by electric field in depletion region

• The average energy lost per collision goes up as E field (voltage) goes up (v = E )

• At some critical field (Ec), the average energy lost per collision will be enough to “ionize” lattice atoms – knock out more carriers

• Those carriers will also be accelerated by E>Ec and make more carriers when they collide, etc…….

• Many collisions=huge multiplication in number of carriers= avalanche breakdown

ECE 663

Max. FieldDoping

ChargeDensity

Electric Field

ElectrostaticPotential

NAxp = NDxn

= WD/(NA-1 + ND

-1)

Ks0Em = -qNAxp = -qNDxn

= -qWD/(NA-1 + ND

-1)

Vbi = ½|Em|WD

ECE 663

Maximum Field

Em = 2qVbi/ks0(NA-1+ND

-

1)

ECE 663

Avalanching

BBR

DA

DABR

BRDA

DA

Sc

BRBRbiAbi

NV

NNNN

V

VNN

NNK

qE

VVVVV

1

2

0

2

One-sided junctions

ECE 663

Experimental Data on VBR

75.0

1

B

BRN

V

ECE 663

Zener Breakdown - Tunneling

Barrier must be thin: depletion is narrow doping on both sides must be large

Must have empty states to tunnel into Vbi + VBR > EG/q

2

1

02

applbi

AD

DAS VVNNNN

qK

W

ECE 663

Zener diode I-V characteristic

ECE 663

Reverse bias R-G in the depletion region

n

p

x

xGR

thermalGR dx

tn

qAI

ECE 663

R-G Current

• In depletion region we don’t have low level injection because number of carriers is small and injected carriers is large

n

p

x

x pp

iGR

pp

i

GRthermal

dxppnn

nnpqAI

ppnnnnp

tn

)()(

)()(

11

2

11

2

But, in depletion n,p 0

ECE 663

npi

ni

p

x

x

i

in

ip

inp

iGR

np

nn

WqAn

np

nn

qAWndxpn

nqAI

n

p

21

21

21

110

01111

2

2

1

02

applbi

AD

DAS VVNNNN

qK

WBut

0

2/1_

biasreverseGR

VI

Reverse bias current=lifetime measurement

ECE 663

Forward Bias R-G

ECE 663

Forward Bias R-G current

n and p cannot be neglected in the depletion region in FB so the integral is not so easy as in RB.

n

p

x

x pp

iGR dx

ppnnnnp

qAI)()( 11

2

0

11

/2/00

pn

i

kTqVi

kTqVnnnn

npn

enenpnp

n

p

x

x inn

kTqVi

GR dxnpn

enqAI

)2(1

0

/2

Estimate value of integral using maximum value of integrand = constant

ECE 663

Forward Bias R-G current

n

p

x

x inn

kTqVi

GR dxnpn

enqAI

)2(1

0

/2

Integrand maximum when n + p is minimum or n = p

kTqVinnnn

kTqVinn

enpnpn

enpn2/

/2

kTqViGR

kTqV

kTqVi

GR

x

xikTqV

ikTqV

i

kTqVi

GR

eWqAn

I

een

qAI

dxnenen

enqAI

n

p

2/

0

2/0

/

2/2/0

/2

2

)1(21

)2(1

W

ECE 663

Ideality factor

kTqVeII /0

Forward Bias with High Currents: High Level injection

np = ni2eqV/kT

n ~ p ≈ nieqV/2kT

Use in boundary condition

ECE 663

Forward Bias with High Currents: Series Resistance

I = I0[eqV/kT-1]

I = I0[eq(V-IRs)/kT-1]

ECE 663

Real Diode I-V curve summary

A. Breakdown (VB~1/NB)B. R-G RB (I~V)C. R-G FB (slope~q/2kT)D. High Level Inj.(slope ~ q/2kT)E. Series Resistance – slope over

ECE 663

Narrow Base P-N junction Diode

P-side N-side

np pn

LpLn

xnxp

What happens if the diode is smaller than the minority carrier diffusionlength(s)?

Diffusion lengths can be 20-30 microns

ECE 663

1/0 kTqV

n

npnpp e

W

pqD

dxpd

qDJ

Similarly for Jn

1/0 kTqV

p

pnn e

W

nqDJ

ECE 663

Total diode current

1/00

kTqV

n

np

p

pnpntotal e

W

pqD

W

nqDJJJ

Compare to result from wide base ideal diode:

1/00

kTqV

p

np

n

pn eL

pqD

L

nqDJ

Replace minority carrier diffusion length with diode width

pn WL np WL

ECE 663

Charge control methodology

x -xp

np

• Analyze by examining injected minority carrier charge:• e.g. electrons injected into p side of FB diode

• Total negative charge on p-side:

nnn

LxxkTqVpppp

DL

eennnn np

//00 1

px

pnegativetotal AqdxxnQ )(

ECE 663

Charge control method

• Approximate total charge by diffusion length times charge at boundary of QN-depletion regions:

• Non-equilibrium injected electrons with average lifetime of n

• Recombination Rate=charge/time=current

AqenLQ kTqVpnnegativetotal 1/

0

1

1/

/0

/0

kTqV

n

pnn

nkTqV

n

pnnn

enL

qJ

AJenL

qAQI

ECE 663

Charge control

n

n

nn

n

n

n

n

nn

n

n

LD

DDDDL

1/0

kTqV

n

pnn e

L

nDqJ

but

Similarly for holes on the n-side:

1/0

kTqV

p

npp e

L

pDqJ

ECE 663

Total current:

• Same result as before but we didn’t have to solve the minority carrier diffusion equations

• Stored charge and recombination = current needed to resupply

1/00

kTqV

p

np

n

pnpn e

L

pD

L

nDqJJJ