Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal...

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Semiconductor/ Semiconductor p-n junctions Dr. Katarzyna Skorupska

Transcript of Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal...

Page 1: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Semiconductor/ Semiconductor

p-n junctions

Dr. Katarzyna Skorupska

Page 2: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Space charge regions in semiconductors

flatband Depletion Inversion Accumulation

Page 3: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

1. semiconductor – metal

Schottky contact

2. semiconductor – semiconductor

p-n junction

homojunction (p-Si : n-Si) , heterojunction

3. semiconductor - electrolyte

Schottky like contact

Page 4: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Space charge layer

Leads to spatial separation of charges minority carriers are driven to the surface by

electric field

Field acceleration impacts excess energy to both carriers

Page 5: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

semiconductor – semiconductor

p-n junction

homojunction (p-Si : n-Si) , heterojunction

Page 6: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Contact potentials and space charge layers

With the Ansatz that the charge is distributed evenly with x (homogenous doping) one considers the relation of :

charge,

electric field,

electrostatic potential

and energy:

Poisson´s equation connects charge and potential:

0

Here, since d 0, which holds for homojunctions, we have set Y and continue to use the latter from now on.

+ + + + + +

-

-

-

-

-

x

donors

acceptors

neutral neutral -Wp

Wn

p-type n-type

– Galvani potential

y– Volta potential (electrostatic)

d – surface dipole changes

– charge density

Δ – LaPlace operator

dy

Page 7: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

+ + + + + +

-

-

-

-

-

x

donors

acceptors

neutral neutral -Wp

Wn

p-type

pAqN 0 xWp

0 pWx

nDqN nWx 0

0 xWn

n-type

Wn,p - spatial limit of charged areas

Page 8: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

First integration of φ with respect to x

d2j

dx2= -

rnene0

= -qND

ene0

, r = -qNDd2j

dx2= -

rp

epe0

= -(-qNA )

epe0

, rp = qNA

with E’ as electric field:

dx

dE

dx

d

dx

d

dx

d

dx

d

dx

dx

gradE

'

)('

'

2

2

2

2

The first integral yields the electric field since E’= -grad φ

Page 9: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

p-type n-type

-dE '

dx=qNA

e pe0

dE '

dx= -qNA

e pe0

E '(x) = -qNA

e pe0

ò dx

E '(x) = -qNA

e pe0

x +C '

for -Wp £ x £ 0

-dE '

dx= -qND

ene0

dE '

dx=qND

ene0

E '(x) =qND

ene0

ò dx

E '(x) =qND

ene0

x +C

for 0 £ x £Wn

-Wp Wn

Page 10: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

for x = 0

E '(x) = -qNA

epe0

x +C '

E '(x) =C '

forx = 0

E '(x) =qND

ene0

x +C

E '(x) =C

-Wp Wn

p-type n-type

For x=0 the electric field attains its maximum value.

Page 11: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

p-type n-type

p

p

A

p

p

A

p

A

p

WqN

C

CWqN

CxqN

xE

xEWxfor

0

0

0

'

'0

')('

0)('

n

n

D

n

n

D

n

D

n

WqN

C

CWqN

CxqN

xE

xEWxfor

0

0

0

0

)('

0)('

-Wp Wn

The integration constant is determined by the boundary condition that E’(x) vanishes outside the charged region

Page 12: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

p-type n-type

p

p

A

p

p

A

p

A

p

p

A

p

A

p

p

A

p

A

p

WxqN

xE

WqN

xqN

xE

WqN

xqN

xE

WqN

C

CxqN

xE

xWfor

0

00

00

0

0

)('

)('

)('

'

')('

0

n

n

D

n

n

D

n

D

n

n

D

n

D

n

n

D

n

D

n

WxqN

xE

WqN

xqN

xE

WqN

xqN

xE

WqN

C

CxqN

xE

Wxfor

0

00

00

0

0

)('

)('

)('

)('

0

-Wp Wn

Electric field is given by

Page 13: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Graphic integration for semiconductor pair

DqN

E '(x) =qND

ene0

x -Wn( )E '(x) = -qNA

epe0

x+Wp( )

AqN

p-type n-type

Page 14: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

p-type n-type

0

0

)0('

0)0('

0

p

pA

p

p

A

WqNE

WqN

E

xfor

0

0

)0('

0)0('

0

n

nD

n

n

A

WqNE

WqN

E

xfor

For x=0 the electric field attains its maximum value.

Page 15: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

nDpA

nDpA

np

nDn

pA

p

nDnn

pA

pp

nnnppp

WNWN

WqNWqN

DD

WqND

WqND

WqNE

WqNE

EDED

xsufracetheatntdisplacemedielectricD

00

00

00

)0()0(

)0()0(

)0(')0('

)0(')0()0(')0(

0

Extension of space charge layer is inversely proportional to the respective doping layer.

higher relative doping –smaller the space charge layer

Page 16: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

p-type n-type

second derivative to know φ (electrostatic potential)

'2

1)(

)(

)()(

)()(

)()('

)(')(

)('

)(

)('

0

2

0

00

0

0

0

DxWqN

xqN

x

WqN

xqN

x

dxWxqN

x

dxWxqN

x

WxqN

xE

dxxEx

dxxE

ddxxE

dx

dxE

p

p

A

p

A

p

p

A

p

A

p

p

A

p

p

A

p

p

A

DxWqN

xqN

x

WqN

xqN

x

dxWxqN

x

WxqN

xE

dxxEx

dxxE

ddxxE

dx

dxE

n

n

D

n

D

n

n

D

n

D

n

n

D

n

n

D

0

2

0

00

0

0

2

1)(

)(

)()(

)()('

)(')(

)('

)(

)('

Page 17: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

p-type n-type

at the surface (x=0) Galvani potential is equal zero (φ=0)

0'

'000

00

D

D

xfor

0

000

00

D

D

xfor

0' DD

xWx

qNx p

p

An

2

0 2

1)(

xWx

qNx n

n

Dn

2

0 2

1)(

The energetic position of the band edges at the surface of each material remains unaltered.

Page 18: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Graphic integration for semiconductor pair

DqN

n

n

D WxqN

x 0

)(

p

p

A WxqN

x 0

)(

AqN

p-type n-type

)2

1()( 2

0

xWxqN

x p

p

A

)

2

1()( 2

0

xWxqN

x n

n

D

E = ej = -qj

electric field

galvani potential

energy

Page 19: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Graphic integration for semiconductor pn junctions

Junction geometry and charge distribution (which material has a higher doping concentration?)

The charge profile

The electrical field across the contact (E = - d/dx)

Second integration: Galvani or electrostatic

potential

Energy E = e = -q sign change

Page 20: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

p-type n-type

diffusion potential defined by the electric potential difference

Vp = f(0)-f(-Wp )

fp(x) =qNA

e pe0

1

2x2 +Wpx

æ

èç

ö

ø÷

Vp =qNA

e pe0

(0 + 0)-qNA

e pe0

1

2Wp

2 + (Wp × (-Wp )æ

èç

ö

ø÷

Vp = -qNA

e pe0

1

2Wp

2 -Wp

èç

ö

ø÷

Vp = -Wp

2 qNA

epe0

1

2-1

æ

èç

ö

ø÷

Vp = - -1

2

æ

èç

ö

ø÷Wp

2 qNA

e pe0

Vp =qNAWp

2

2epe0

Vn = f(Wn )-f(0)

fn (x) = -qND

ene0

1

2x2 -Wnx

æ

èç

ö

ø÷

Vn = -qND

ene0

1

2Wn

2 - (Wn ×Wn )æ

èç

ö

ø÷- -

qNA

epe0

(0 + 0)æ

èçç

ö

ø÷÷

Vn = -qND

ene0

1

2Wn

2 -Wn

èç

ö

ø÷

Vn = -Wn

2 qND

ene0

1

2-1

æ

èç

ö

ø÷

Vn = - -1

2

æ

èç

ö

ø÷Wn

2 qND

ene0

Vn =qNDWn

2

2ene0

Page 21: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

nD

pA

DnA

ApD

p

n

pn

np

pnn

npp

p

n

p

n

D

A

pnA

npD

pA

p

n

nD

p

n

N

N

NN

NN

V

V

W

W

WW

WW

V

V

W

W

N

Nbecause

WN

WN

WqN

WqN

V

V

2

2

2

2

2

2

2

0

0

2 2

2

Page 22: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

p-type n-type

D

nnn

DnDnn

n

n

nDn

qN

VW

qNWqNV

WqNV

0

2

0

0

0

2

2

\2

2\2

A

pp

n

ApApp

p

p

pA

p

qN

VW

qNWqNV

WqNV

0

2

0

0

0

2

2

\2

2\2

Page 23: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Graphic integration for semiconductor pn junctions

D

nn

nqN

VW 02

D

nn

nqN

VW 02

Important relations for pn junctions

(to memorize)

nDpA WNWN

Electroneutrality condition

D

A

p

n

N

N

W

W

Diffusion voltage relations

Dn

Ap

p

n

N

N

V

V

pn

np

p

n

W

W

V

V

Page 24: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

The width of the space charge layer depends on:

• doping level

• voltage drop

Page 25: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Eg=1.12 eV

NCB=3.2 1019 cm-3

ND=1017 cm-3

Eg=1.12 eV

NVB=1.8 1019 cm-3

NA=1015 cm-3

p-type n-type

kT=26 meV

Page 26: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

n-type p-type

Position of nEF before contact Position of pEF before contact

EF = EVB - kT lnNVB

NAEF = ECB - kT ln

NCB

ND

EF -EVB = kT lnNVB

NAECB -EF = kT lnNCB

ND

ECB -EF = 26 ln3.2 ×1019

1017meV

cm-3

cm-3

é

ëê

ù

ûú

ECB -EF = 26 ln3.2 ×102

ECB -EF = 26 ×5.7

ECB -EF =150meV

ECB -EF = 0.15meV

EF -EVB = 26 ln1.8 ×1019

1015meV

cm-3

cm-3

é

ëê

ù

ûú

EF -EVB = 26 ln1.8 ×104

EF -EVB = 26 ×9.8

EF -EVB = 254.8meV

EF -EVB = 0.25meV

Page 27: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

ECB ECB

EVB EVB

EF

E

F 0.25 eV

0.15 eV

Page 28: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Contact potential difference

ECB ECB

EVB EVB

EF

E

F 0.25 eV

0.15 eV

eVC

eVC = nEF - pEF = eVn -eVp = e(Vn -Vp ) =

= Eg - (nEF + pEF ) =1.12 - (0.15+ 0.26) = 0.71eV

Page 29: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Changes of position of nEF and pEF after contact formation

pEF® eVpnEF® eVn eVc = nEF - pEF = eVn + eVp

Vn

Vp=NA

ND

a =NA

ND=

1015

1017=10-2 = 0.01

Vn =NA

NDVp

Vn = aVp

VC =Vn +Vp

VC = aVp +Vp =Vp(a +1)

Vp =VC

(a +1)

Page 30: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Vn =VC -Vp

Vn = 0.71- 0.703 = 0.007

Vp =VC

(a +1)

Vp =0.71

0.01+1= 0.703

Page 31: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Wn =2e0enVnqND

en =11.7

ND =1017cm-3

Vn = 0.007eV

Wp =2e0e pVp

qNA

e p =11.7

NA =1015cm-3

Vp = 0.703eV

Wn =2 ×8.85 ×10-14 ×11.7 ×0.007

1.6 ×10-19 ×1017

Wn =1.45 ×10-14

1.6 ×10-2

Wn = 0.9 ×10-12

Wn = 9.5 ×10-7

Wp =2 ×8.85 ×10-14 ×11.7 ×0.703

1.6 ×10-19 ×1015

Wp =145 ×10-14

1.6 ×10-4

Wp = 90.6 ×10-10

Wp = 9.5 ×10-5

e0 = 8.85 ×10-14[Fcm

]

q =1.6 ×10-19[C]

Page 32: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

e0

F

cm=A × s

V ×cm

é

ëê

ù

ûú

ND[cm-3]

q[C = A × s]

W =

A × s

V ×cmV

A × s ×cm-3=A × s

cmA × s ×cm-3 = cm

Page 33: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Current voltage characteristic at p-n junction

Page 34: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

For simplicity we consider:

- homojunction

- electron current

- voltage dependence of n-type side of the junctions

Absence of generation and recombination of carriers within the space charge layer

Page 35: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Electron current (from n-type to p-type) jnr

– number of e- on the n-type side that can thermally overcome the barrier given by

energetic distance between ECBn and ECB

p

Majority carriers (e-) on the n-type side become minority carriers on the p-type side

where they recombine.

Electron current (from p-type to n-type) jng

- thermal generation of e- in the neutral region of the p-type junction

- Drift to the n-type side

- Minority carriers (e-) on the p-type side become majority carriers on the n-type

side

r – recombination

g - generation

Page 36: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

The recombination current jnr from n-type to p-type at the equilibrium:

-by contact potential difference Vd

jnr (Va = 0) = jnr (Vd ) = en thn(Vd ) = en thn0eeVd

kT

Va – applied potential

Vd – potential difference

vth - thermal velocity

n(Vd)- carrier concentration

n0 – concentration of e- at the bottom of conduction band (given by doping level)

Thermal excitation of e- at the p-type side

in the EVB across the Eg

jng = qn thNVBeEg

kT = qn thnp

np – e- concentration in the neutral region of ECB of p-type sc

Page 37: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

eVd +ECB -EFC << Eg

jnr ¹ jng

Page 38: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Applying negative voltage (forward) to the n-type side:

- decrease of band bending

- jnr increase

- jng is not influenced

jnr (Va ) = en thn0e

e Vd-Va( )kT = jnr (0)e

eVa

kT

Va – applied potential

Vd – potential difference

vth - thermal velocity

n(Vd)- carrier concentration

n0 – concentration of e- at the bottom of conduction band (given by doping level)

jnr (0) = en thn0eeVd

kT

Page 39: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Applying positive voltage (reverse) to the n-type side:

- increase of band bending

- Jnr decrease exponentially with the increase barrier height

- jng is not influenced

jnr (Va ) = en thn0e-e Vd+Va( )kT = jnr (0)e

-eVa

kT jnr (0) = en thn0eeVd

kT

Page 40: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

jng(Va ) = jnr (0) = j0eeVd

kT

jn(Va ) = j0eeVd

kT eeVa

kT -1æ

èç

ö

ø÷ = jng e

eVa

kT -1æ

èç

ö

ø÷

jD(Va ) = jn(Va )+ jp(Va )Total current:

Total e- dark current: sum of generation and recombination currents (opposite sign)

jn(Va ) = jnr (Va )- jng(Va )

jnr (Va ) = en thn0e-e Vd+Va( )kT = jnr (0)e

-eVa

kT

using:

jng(Va ) = jng(0) = - jnr (0)

Page 41: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

jD = jng + jpg( ) eeV

kT -1æ

èç

ö

ø÷

Diode relationship by Shockley

jD = js eeV

kT -1æ

èç

ö

ø÷

js – reverse saturation current described by

metal glow emission properties jng+ jpg – diffusion constants and minority

carrier diffusion lengths

js = jng + jpg =eDpp0

Lp+eDnn0

Ln

Page 42: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,
Page 43: Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal Schottky contact 2. semiconductor – semiconductor p-n junction homojunction (p-Si : n-Si) ,

Constant illumination- number of absorbed photons per second and cm2 mulitiled by

elementary charge

Light induced photocurrent: jL = enph(Eg )(1-R)

- p-type – photoactive part

- positive dark current under forward bias

from p-type absorber to n-type emitter

- photocurrent is opposite sign

- photocurrent does not exhibit voltage

dependent (simple approach)

Where:

jPh- photocurrent

jD- dark current

Js- dark saturation current

jL- light-induced current

nPh- number of absorbed photons per second and

cm2

R- sample reflectivity

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Photocurrent – dark- and light induced current (having opposite sign)

jph = jD - jL = js eeV

kT -1æ

èç

ö

ø÷- jL

- p-type – photoactive part

- positive dark current under forward bias

from p-type absorber to n-type emitter

- photocurrent is opposite sign

- photocurrent does not exhibit voltage

dependent (simple approach)

Where:

jPh- photocurrent

jD- dark current

Js- dark saturation current

jL- light-induced current

nPh- number of absorbed photons per second and

cm2

R- sample reflectivity

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45

Photocurrent

The approximation for the light induced current (jL)

jph = jD - jL = js eeV

kT -1æ

èç

ö

ø÷- jL

Photocurrent dependence follows dark-current-voltage behavior

)1()( REhenj gPhL

Where:

jPh- photocurrent

jD- dark current

Js- dark saturation current

jL- light-induced current

nPh- number of absorbed photons per second and

cm2

R- sample reflectivity

Short circuit current jL (Rext ~ 0)

Open circuit voltage VOC (R ∞)

Maximum power point MPP (largest area under jPh curve)

Current and voltage at Maximum power point jMP , VMP

Output power Pout = jMP x VMP

Solar Cell efficiency h = Pout / Pin , Pin : light intensity

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Semiconductor/Metal Schottky type junctions

Dr. Katarzyna Skorupska

1

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4.05 eV

Evac

Ev

Ec

EF

Wor

k fu

nctio

n

Elec

tron

affin

ity

0.2-0.3 eV

1.12 eVEg

ECB-energy of conduction band lowest unoccupied level EVB- energy of valence band highest occupied level Eg- band gap energy distance between EVB and ECB EF- Fermi level

2

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Work function -is the minimum energy (usually measured in electronvolts) needed to remove an electron from a solid to a point immediately outside the solid surface (or energy needed to move an electron from the Fermi level into vacuum). Electron affinity - is the energy difference between the vacuum energy and the conduction band minimum

semiconductor – metal Schottky contact

Thermionic interaction - Contact formation based on energetic considerations - Interfacial effects neglected

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4

semiconductor metal

EFsc

EFm

mobile nature of charges

under contact formation development of electrical field Potential drop across interface

EFsc EF

m

redistribution of charges on the metal side

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Metal - semiconductor Schottky contact (rectifying semiconductor-metal junction)

Definition: contact potential difference

∆Εc = EFSC – EF

M = ΦM - ΦSC

The junction is characterized by • the semiconductor and metal

work function (ΦSC- given by doping) • the semiconductor electron

affinity and its energy gap.

Contact formation (ideal case: absence of surface states) Consider a neutral but doped (n-type) semiconductor and a metal with higher work function before contact:

5

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Schottky junction formation

Consider a n-type semiconductor-metal contact where the work function of the metal is higher: a macroscopic gap between the phases decreases successively until contact;

connected by a conductive wire : equilibrium formation

Metal (high e- concentration -> electrostatic field at top most layer (0.1Å) - the potential drop can be neglected

Electrostatic effects are restricted to the SC side

contact energy difference eVc drops exclusively across the interlayer gap d (the vacuum level course)

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Schottky junction formation cont´d Definitions: barrier height and band bending; relation between them:

Barrier height defines in Schottky (photo)diodes the reverse saturation current as will be shown below.

Lowered distance d - lowered energetic drop across the interlayer eVc

(1) - Partial contact energy difference in the SC eVc

(2)

Distance d=0 - difference in EF

M and EFSC drops completely in the SC space

charge region

Barrier height – energetic barrier e- have to overcome to enter the other phase. ΦBh- energetic distance between EF

M (after contact formation EF

M=EFSC) and the band edge ECB

ΦBh = eVbb + ECB - EF

n

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Short circuiting semiconductor and metal and decreasing their distance: • electrons flow from the semiconductor to the metal the metal becomes negatively charged,

the semiconductor positively

• at small, finite distance, the contact potential VC drops across the air gap and the

semiconductor surface region

• the relative distribution of VC follows where CM and CSC denote metal and semiconductor capacitance, respectively

Schottky Junctions

The electron depletion of the semiconductor during contact formation leads to a charged region near the surface;

8

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Schottky barrier: Decreasing the gap to zero:

Origin of the spatial dependence of the energy bands and the vacuum level: Poisson´s equ. in 1dimension

• the contact potential drops almost exclusively across the semiconductor near surface region

(depending on doping and contact potential difference, i.e. extension of the charged region). • BARRIER HEIGHT (Φbh): energetic

barrier which metal electrons have to overcome (thermally) to reach the semiconductor.

• Band banding (eVbb)

9

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C - capacitance; Q - charges on the plates; V - the voltage between the plates; A - area of overlap of the two plates; εr - relative static permittivity (sometimes called the dielectric constant) of the material between the plates (for a vacuum, εr = 1); ε0 - electric constant (ε0 ≈ 8.854×10−12 F m–1); d - separation between the plates.

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Space charge regions in semiconductors

flatband Depletion

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Space charge regions in semiconductors II

Inversion

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Space charge regions in semiconductors III

Inversion Accumulation

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forward current – from n-SC to metal reverse current – from metal to n-SC

Dark current – influence of applied voltage to determine electron currents from: • semiconductor to metal (forward current) • metal to semiconductor (reverse current) to find the expressions for the currents based on the thermionic emission model for an applied voltage (forward and reverse currents)

n-semiconductor

interface barrier

metal

14

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15

The thermionic emission model

(i) the barrier height is much larger than the thermal energy (Φbh >>kT),

(ii) thermal equilibrium exists in the plane of emission (x =0) and (i) non-degenerate semiconductors

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• the band edge positions at the surface (x=0) remain unaltered hence the barrier height does not change

• the (cathodic) voltage reduces the band bending • the Fermi levels on both sides of the junction are different

The dark current from semiconductor is given:

16 νth- thermal velocity

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17

Expression for the forward current (SC to M)

using the Boltzmann exponential term

The voltage dependence of the current density is given by the energetic shift of the Fermi level EF(0) to EF(V) using EF(V) = EF(0) + eVc one obtains for the (increased) carrier concentration at the semiconductor surface:

the forward current is given:

The expression ECB-EF(0) represents the barrier height of the junction (Φbh). The forward dark current density can then be expressed in terms of the barrier height and applied voltage:

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18

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19

The expression of the thermal velocity (vth) and the effective density of states (DOS) at the conduction band edge (ECB) by their dependence on temperature and effective electron mass (m*

e)

thermal velocity effective DOS

using the expression for the effective Richardson constant which describes the glow-emission properties of a material

one obtains the equation for the dark current in forward direction

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20

Current from metal to semiconductor (reverse current)

In the equilibrium situation considered for V=0 The forward current (SCM) must be equal and opposite in sign to the reverse current (MSC) Therefore:

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21

To ta l c u r r e nt

js

The pre-factor called reverse saturation current (js) • contains material properties • temperature • and gives the current at V=0

kTs

bh

eTAjΦ

−= 2*

DIODE CHARACTERISATION

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22

DIODE CHARACTERISATION

question: which sign for voltage and current for an n-type semiconductor-metal junction?

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23

Photocurrent

The approximation for the light induced current (jL)

Photocurrent dependence follows dark-current-voltage behavior

)1()( REhenj gPhL −⋅>= ν

Where: jPh- photocurrent jD- dark current Js- dark saturation current jL- light-induced current nPh- number of absorbed photons per second and cm2 R- sample reflectivity Short circuit current jL (Rext ~ 0)

Open circuit voltage VOC (R ∞)

Maximum power point MPP (largest area under jPh curve)

Current and voltage at Maximum power point jMP , VMP

Output power Pout = jMP x VMP

Solar Cell efficiency η = Pout / Pin , Pin : light intensity

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Illumination of the semiconductor with photons of energy greater than Eg, - accumulates the electrons in semiconductor side and - holes in the metal side of the depletion region. There occurs an electron-hole pair generation. The light splits the Fermi level and creates a photovoltage V, equal to the difference in the Fermi levels of semiconductor and metal far from the junction.

Vph

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At open-circuit voltage (VOC) the photocurrent is equal zero IPh=0

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26

Photovoltage (Vph) is given by jph=0

+== 1ln

s

LOCPh j

jq

kTVV

the photovoltage changes logarithmically with the light intensity

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27

VPh = 0.74V

+== 1ln

s

LOCPh j

jq

kTVV

Example: