Thermionic Emmision in Abrupt Junction Diffusion … 5: I-V of Heterojunction diodes 2011-01-19...

Lecture 5: I-V of Heterojunction diodes

2011-01-19 1Lecture 5, High Speed Devices 2011

•Thermionic Emmision in Abrupt Junction•Diffusion current in graded Junctions•Generation Currents•Iso-type Junctions

Thermionic Emission, Metal-semiconductor junction


Ef

φs

φb Va

φs

φb Assumption: Carriers with an energy over s are able to pass over the barrier.

22

0

*

3

2**

2*

/1204

1expexp

KcmAm

m

h

kmA

kT

qV

kT

qTAJ

ee

bth

A* is Richardson’s constant

Forward Bias

Reverse Bias

Thermionic Emission, Metal-semiconductor junction


Ef

φsΦb’

VaN

φs

1expexp

'2*

kT

qV

kT

qTAJ anb

th

Identify Φb’ and VaN for p+N junction

Forward Bias

Reverse Bias

Φb’

1)1

exp()/exp(

1

1

'2*

1

1

'

K

V

kT

qkTqTAAI

N

NK

VN

N

N

NV

N

N

qN

N

q

EE

q

aBDd

ap

dN

a

ap

dN

ap

dNan

ap

dNN

ap

dNpcgpNNOB

Graded junctions I: Quasi Fermi Levels


ia

i

fpv

v

cfn

c

nkT

qVnnp

kT

EENp

kT

EENn

)exp(

)exp(

)exp(

Fermi levels are only defined under equilibrium conditions

For device under external bias, we define quasi-fermi-levels:

Efn

Efp

XN-Xp

Va

XN, Xp: depletion width edge

Efn: Fermi-level for electronsEfp: Fermi-level for holes

2 minute exercise: Quasi Fermi level


-Xp

Xn

EfnEfp

-Xp

Xn

-Xp Xn

log

(n,p

)

HolesElectrons

Equilibriumconcentrations

Add out of equilibriumn,p concentrations!

Graded junctions II: Carrier Concentration


Assume no recombination and small currents: the quasi fermi levels are constant in the depleted region

Efn

Efp

XN

-Xp

Va

-Xp

XN

Efn

Ef

Efp

d

WG

iN

aNN

a

NG

ip

app

N

nXp

kT

qVXpXp

N

nXn

kT

qVXnXn

2

00

2

00

)(exp)()(

)(exp)()(

Positive Va: Increase in minority carrier concentration at edges of depleted region

Negative Va: Decrease in minority carrierconcentration

kT

EENn

cfn

c exp

Graded junctions III: Carrier Concentration


Injected carriers will diffuse and recombine with majority carriers

Efn

Efp

XN

-Xp

Va

0

0

22

2

0

2

20

n

nnn

n

n

L

n

x

xn

DLnnn

nn

x

xnD

n = excess electron concentrationLn = minority electron diffusion length

0

22

2

pL

p

x

xp Same for holes on N-side..

x

n, p

n(0)

p(0)

Recombination

Recombination

Graded junctions IV: Carrier Concentration (Long diode)


Boundary value problem, 2nd order:

Efn

Efp

XN

-Xp

Va

x

n, p

n(0)

p(0)

1exp

0

0kT

qVpXp

p

aN

n

na

a

NG

i

p

Na

d

WG

i

L

XX

kT

qV

N

nxn

L

XX

kT

qV

N

nxp

exp1exp

exp1exp

2

2

NXx

pXx

p(0)

n(0)

For GaAs:~1nsDn~25 cm2/sDp~1 cm2/sLn=1.6 mmLp=0.3 mm

Graded junctions: Evaluation of current (Long diode)


Efn

Efp

XN

-Xp

Va

x

n, p

n(0)

p(0)

1exp

22

kT

qV

N

n

L

D

N

n

L

DqAI a

a

NG

i

n

n

d

WG

i

p

p

dD

x

XpqDpq

x

pqDJ N

pXxpppN

m

0minority

x

XnqDnq

x

nqDJ

p

nXxnnnp

m

Hole current Electron current

?

NXxnnn nqx

nqDJ m

Majority n>>0

0

We not not evaulate the electron current on the N-side, since:

Dn>Dp, niWG>>ni

NG

2 minute exercise: el/hole currents


-Xp

Xn

EfNEfp

x

XpqDJ N

pp

x

XnqDJ

p

nn

Assume that the diode has Dn=Dp and Ln=Lp

Which one is correct:

A Jp = Jn

B Jp >> Jn

C Jn >> Jp

Graded junctions: Short diode


n, p

n(0) p(0)

If XB-Xp is much shorter than Ln, the diffusion lenghth is replaced by the junction thickness. E.g. Base of an HBT!

-Xp XN

XE-XB

0)()( EB XpXn

In a short diode the excess electron/hole concentrations are forced to zero due to epitaxial thicknesses

1exp

22

kT

qV

N

n

XX

D

N

n

XX

DqAI a

a

NG

i

PB

n

d

WG

i

NE

p

dD

Recombination in forward bias


p+ region: p >> n

)2( i

i

npn

nnpU

Recombination rate, SRH

N

p

X

WG

X

NG

rec xdxUqxdxUqJ0

0

)()(

kT

qVJ

kT

xEE

kT

qVn

nU a

rec

ifaNG

i

NG exp

expexp

N region: n=p gives Umax

kT

qVJ

kT

qVn

U arec

aWG

iWG

2exp

2

2exp

max

h=1

h=2

Depending on which term is dominating, 1<h<2, usually h~2For a p+N junction, the hole current is usually dominated by recombination

Generation in reverse bias


ii

i

npnn

npn

nnpU i

,

2)2(

2

Generation Rate, SRH

N

p

X

X

gen xdxUqJ )(

abipN

igen VXX

qnJ

2

V

I

kT

qVI a

Dh

exp

Summary for p+N diode


In a p+N junction, the current is essentially set by the electrons!Reverse current increases due to generation

1exp0

kT

qVII a

Dh

ap

dN

N

N

h 1

1 Graded Junction

Abrupt Junction

V

I

kT

qVI a

Dh

exp

agenD VIII 0

If recombination is important: 1<h<2

Isotype heterojunction


•nN heterojunction•Fabrication of ohmic contacts are much easier on small bandgap material

InPInGaAs

Ef

•Mostle tend to to be n++N++ junctions, which makes analytic modelling difficult•Can be graded to minimize effect of potential spike

N InPp++ In0.53Ga0.47As

n In0.53Ga0.47As

N++ InPn++ In0.53Ga0.47As

Ohmic metal

Thermionic Emmision in Abrupt Junction Diffusion … 5: I-V of Heterojunction diodes 2011-01-19...

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