1 deviations from simple theory and metal-semiconductor junctions 5.6 deviation from the simple...

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1 Deviations from simple theory and metal- semiconductor junctions 5.6 Deviation from the simple theory 5.6.1 Effects of contact potential on carrier injection 5.6.2 Recombination and generation in the transition region 5.6.3 Ohmic losses 5.6.4 Graded junctions 5.7 Metal-semiconductor junctions 5.7.1 Schottky barriers 5.7.2 Rectifying contacts 5.7.3 Ohmic contacts 5.7.4 Typical Schottky barriers

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Page 1: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

1

Deviations from simple theory and metal-semiconductor junctions

• 5.6 Deviation from the simple theory– 5.6.1 Effects of contact potential on carrier injection– 5.6.2 Recombination and generation in the transition region– 5.6.3 Ohmic losses– 5.6.4 Graded junctions

• 5.7 Metal-semiconductor junctions– 5.7.1 Schottky barriers– 5.7.2 Rectifying contacts– 5.7.3 Ohmic contacts– 5.7.4 Typical Schottky barriers

Page 2: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

2

Effects of contact potential on carrier injection

• The contact potential limits the ultimate voltage that will appear across the junction.– Assumed high level injection (take into

account changes majority carrier concentration)

kTVVq oe /)(

pp

nn

nn

pp

Δnn

Δnn

Δpp

Δpp

• Simple theory will not predict this (eqV/kT) – Assumed low level injection (neglect changes

majority carrier concentration)

Page 3: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

3

Effects of contact potential on carrier injection

1/

kTqV

pn

nn

p

p enL

Dp

L

DqAI

kTqV

n

i

n

pnkTqV

p

i

p

np

kTVVq

kTqV

en

n

L

nDe

p

n

L

pD

e

eqAI

o

/2

2/

2

2

/2

/

111

1

region)-nin (h/400

region)-pin (e /300

101

101

104

2

-2

6

316

318

sVcm

sVcm

s

cmN

cmN

p

n

np

d

a

300K)(At

cm101.5n into up rolled are

m and , m ,E

:diode Si/n p aFor

310i

*h

*eg

Page 4: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

4

Effects of contact potential on carrier injection

Diode IV

0

1

2

3

4

5

6

0.5 0.6 0.7 0.8 0.9 1

Voltage (V)

Cur

rent

(A)

I Simple Theory

I (eq. 5-70)

Diode IV

0

1

2

3

4

5

6

-3 -2 -1 0 1

Voltage (V)

Cur

rent

(A)

I Simple Theory

I (eq. 5-70)

Page 5: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

5

Recombination and generation in the transition region

• Significant recombination and thermal generation of EHPs can occur if the depletion width is similar in length to Ln and Lp.– Forward bias: Recombination within W can lower

current and is proportional to ni and forward bias (e qV/2kT). Recombination within the neutral regions is proportional to ni

2/N(d or a) and forward bias (e qV/1kT).

– This gives rise to the ideality factor, n.

1enL

Dp

L

DqAI qV/nkT

pn

nn

p

p

Page 6: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

6

Recombination and generation in the transition region

• Significant recombination and thermal generation of EHPs can occur if the depletion width is similar in length to Ln and Lp.– Reverse bias: Carrier generation can increase reverse

saturation current, and even become voltage dependant with a trap near mid-gap.

(a)(b)

I

V

Rn G n

G p Rp

Ec

E r

Ev

Page 7: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

7

Ideality Factor

Page 8: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

8

Ohmic losses• Ohmic losses will become significant when:

– One of the neutral is very lightly doped– The area is close to the length of the neutral regions.– Operating at very high currents

• Ohmic losses will reduce current because less voltage is falling across the junction

• The resistance is dependant on the current, thus we can not add a simple series resistance.

Ohmic effects

Page 9: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

9

Graded junctions• Not all junctions are abrupt

– Drive-in diffusions are linearly graded around the junction. (Pre-dep diffusions are considered abrupt.)

GxNNnpq

dx

dE

GxNN

ad

ad

Im

pu

rity

Co

nce

ntr

atio

n

D is tance from the surface

N d

N a

Linear A pproxim ation

Page 10: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

10

Graded junctions• Not all junctions are abrupt

– Drive-in diffusions are linearly graded around the junction. (Pre-dep diffusions are considered abrupt.)

x x

N d-N a S pace charge

W /2

W /2

|Q|=qAGW 2/8

+

-x x

E V

E o

V o

• Boundaries between space charge and neutral regions are blurred. No analytic solutions available.

Page 11: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

11

Schottky barriers

• Diode like behavior can be mimicked by applying clean metal to a clean semiconductor.– Easy to do and faster switching times can be realized.

• n-type– Semiconductor bands bend up causing a more positive

region near the interface, which attracts electrons from the metal to the interface interface.

• p-type– Semiconductor bands bend down causing a more

negative region near the interface, which attracts holes from the metal to the interface.

Page 12: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

12

Schottky barriersn-type

E cE Fs

qm qsq

M etal

Semiconductor

E FM

E v

m > s

M etal

E cE FM

E v

qbqm

E Fs

q(m sqV o

W

p-type

E c

E Fs

qm qsq

M etal

Semiconductor

E FM

E v

m < s

M etal

E c

E FM

E v

E Fs

q(s mqV o

W

Page 13: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

13

Rectifying contacts

• Apply a forward bias to the Metal of the M/S(n) diode and the contact potential is reduced by Vo-V

– Allows electrons to diffuse into metal.• Apply a forward bias to the Semiconductor of the

M/S(p) diode and the contact potential is reduced by Vo-V

– Allows holes to diffuse into metal.

Page 14: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

14

Rectifying contacts

• Apply a reverse bias to the Metal of the M/S(n) diode and the contact potential is increased by Vo+Vr.

– Electrons have to overcome a voltage independent barrier to diffuse into metal.

• Apply a reverse bias to the Semiconductor of the M/S(p) diode and the contact potential is reduced by Vo+Vr.

– Holes have to overcome a voltage independent barrier to diffuse into metal.

Page 15: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

15

Rectifying contacts

• Current flows primarily by majority carriers is both cases.

• Very little charge storage occurs, which leads to fast switching speeds.

Page 16: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

16

Ohmic contacts

• Metal/semiconductor ohmic contacts– linear near the origin, non-rectifying

• Two methods of fabrication– Choose a metal with a workfunction that aligns the

fermi levels with majority carriers. (Al for p-type Si, Au for n-type Si

– Dope the semiconductor heavily so that W is very thin so that tunneling occurs (Al on p+ or n+ Si)

– Heavy doping all ways improves ohmic behavior.

Page 17: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

17

Ohmic contactsp-type

E c

E Fs

qm qsq

M etal

SemiconductorE FM

E v

m > s

M etal

E c

E FM

E v

E Fs

q(m sqV o

W

Page 18: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

18

Ohmic contactsn-type

E cE Fs

qm qsq

M etal

Semiconductor

E FM

E v

m < s

M etal

E cE FM

E v

qbqm

E Fsq(s mqV o

W

Page 19: 1 Deviations from simple theory and metal-semiconductor junctions 5.6 Deviation from the simple theory –5.6.1 Effects of contact potential on carrier injection

19

Real Schottky barriers

• In Si, there is a thin oxide in between the metal and semiconductor.

• Surface states arise from the crystal ending– This can pin the fermi level to midgap in GaAs

• If a metal semiconductor junction is alloyed the interface is blurred between metal/metal-semiconductor/semiconductor.

• Contact design is very dependant on your process.