Semiconductor Devices 4thamano/H30/G30/4th.pdf · -2.00-1.00 0.0 1.00 2.00 3.00 4.00 5.00 TIME -1.000 v(IVm1) -1.000 v(IVm2) -1.000 D(TIME) -1.000 D(v(IVm2)) -1.002 Q ： Draw waveform

November 5, 2018 14:45～16:15 IB012

Semiconductor Devices 4th

Chap.3 p-n Junction

Automotive Engineering Graduate Program

Today’s target* To understand band lineup of pn-junction diode* To understand the I-V characteristic of pn-junction diode

1/60

http://www.semicon.toshiba.co.jp/contact/faq/product/diode/answer08.html

Difference of I-V charasteristics of pn diode and Schottky barrier diode

Si pn junction diode Si Schcottky barrier diode

2/60

http://lazyecology.web.fc2.com/reverb/special/choi_lab/1_diode.html

Si pn junction diode Si Schcottky barrier diode

Minority carrierstorage effect

Difference of I-V charasteristics of pn diode and Schottky barrier diode

3/60

Phot diode is also pn junction diode

pn

pin

APD

4/60

SiC SBD

http://www.semicon.toshiba.co.jp/product/diode/sic/index.html

5/60

Zener diode and Avalanche diode

Avalanche breakdown

Zener breakdowntunneling

https://wikihost.uib.no/ift/index.php/PET_Projecthttp://www.intechopen.com/books/photodiodes-from-

fundamentals-to-applications/physical-design-fundamentals-of-high-performance-avalanche-heterophotodiodes-with-separate-

absorptio

Vz:1.8-100V VB:17-＞40,000V

6/60

https://wikihost.uib.no/ift/index.php/File:MAPD_geigermode.jpg

https://wikihost.uib.no/ift/index.php/PET_Project

http://pdf1.alldatasheet.com/datasheet-pdf/view/151048/EIC/R2KY.html

Temp. higher

+25℃⇒＋125℃Vz decreases.

Motorola 1N2804 Zener diode

Tunnel current

Avalanche diode

ΔVz

Vz

Zener diode and Avalanche diode

7/60

Esaki diode

http://www.shmj.or.jp/museum2010/exhibi302.htm 8/60

I-V characteristic of pn diod

p n Forward current

Reverse current

Reverse voltage

Forward voltage

Zener diode

9/60

Voltage [V]

Current [A]

0.7V

20mA10mA

0V

I-V characteristic of pn diod

10/60

0V1

1K

R1

D1

8.20nIVm1

Amplitude ：5VSi pn diode

オシロスコープ

Circuit1-Transient-6-Graph Time (s)

0.0 200.00u 400.00u 600.00u 800.00u 1.00m 1.20m 1.40m 1.60m 1.80m

-5.00

-4.00

-3.00

-2.00

-1.00

0.0

1.00

2.00

3.00

4.00

5.00

TIME -1.000 v(IVm1) -1.000 v(IVm2) -1.000 D(TIME) -1.000 D(v(IVm2)) -1.002

Q：Draw waveform of voltage between pn diode shown in the oscilloscope screen.

Circuit1-Transient-4-Graph Time (s)

0.0 200.00u 400.00u 600.00u 800.00u 1.00m 1.20m 1.40m 1.60m 1.80m

(V)

-5.00

-4.00

-3.00

-2.00

-1.00

0.0

1.00

2.00

3.00

4.00

5.00

TIME -1.000 v(IVm1) -1.000 D(TIME) -1.000 D(v(IVm1)) -1.000

time

+5V

-5V

時間

Oscilloscope

11/60

I-V characteristic of red LED

2.0V

λpeak=630 nm

12/60

2.5V

λpeak=520 nm

I-V characteristic of green LED

13/60

2.8V

I-V characteristic of blue LED

λpeak=450 nm

14/60

Q：Explain the relationship between operating voltage and color of LEDs.

Operating voltage [V]

Photon energy [eV]

Red LED 2.0 1.97Green LED 2.5 2.39Blue LED 2.8 2.76

]eV[.

.,]m[]s/m[.

]eV/J[.]sJ[.

]m[]s/m[.]sJ[.

chh

971630

8239110630

1003106021

10626610630

1003106266

9

8

19

34

9

834

=

=

××

×⋅×

=

××

⋅×=

=

−−

−

−−

λνRed LED

][10602.1-]/[10998.2][10626.6

19

8

34

CqsmcsJh

−

−

×=

×=

⋅×=

15/60

Junction of n-type and p-type semiconductors

p-type

－－－－－

－－

－

－

－

－

－

－

－－

n-type

＋

＋

＋＋

＋＋

＋

＋＋＋

＋

＋＋

＋

＋Electron

Hole

16/60

－－－－－

－－

－

－

－

－

－

－

－－

＋

＋

＋＋

＋＋

＋

＋＋＋

＋

＋＋

＋

＋

Depletion region

p-type n-type

17/60

Q：Calculate Fermi energy Ef of Si doped with Al of 1015,1016,1017,1018[cm-3] and P of 1015,1016,1017,1018[cm-3].

Effective density of states in conduction band NC[cm-3]

2.86×1019

Effective density of states in valence band NV[cm-3]

2.66×1019

Bandgap energy Eg[eV] 1.12

Intrinsic carrier concentration ni[cm-3]

9.65×109

kB=1.38×10-23[J/K]q=-1.602×10-19[C]

@300K

18/60

−−⋅=

TkEE

NnB

fCC

nexp

−−⋅=

TkEE

NpB

VfV

pexp

In case of Si at 300K, n-type：n=NDp-type：p=NA

n:Free electron conc. p:Free hole conc.

Statistics

19/60

Ans.

Al(p-Si) P(n-Si)1015[cm-3] EV+0.263 EC-0.2651016[cm-3] EV+0.204 EC-0.2061017[cm-3] EV+0.144 EC-0.1461018[cm-3] EV+0.085 EC-0.087

Unit ： eV

20/60

Alドープの場合 p-Si

Efp

EC

EV

0.263eV1015[cm-3]

1018[cm-3]0.085eV

Pドープの場合 p-Si

Efn

EC

EV

0.265eV1015[cm-3]

1018[cm-3]0.087eV

Eg=1.12[eV]

Ans.

21/60

n-Si

Efn

p-Si

Efp

Junction

Fermi energy Efn and Efp becomes the same level

22/60

Band lineup

FermienergyEf

Donor level ED

n-type p-type

Vacuum level

Depletion region

Built in voltage qVD(diffusion voltage VD)

ECp

EVp

Acceptor levelEA

Negative ion

Electron affinity χ

－－－－－－

＋＋＋＋＋＋

－

Positive ion

ーー

＋＋

EVn

ECn

23/60

Reverse bias

Depletion region expands.

pt-ypen ー＋

－－－－－

－－

－

－

－

－

－

－

－－

＋

＋

＋＋

＋＋

＋

＋＋＋

＋

＋＋

＋

＋

ー＋

24/60

Before reverse bias is applied.

n-type p-type

EC

EV

－－－

－－－－

－

＋＋＋＋＋＋

－－－

Many carriers → Low resistivity

Many carriers → Low resistivity

Depletion region : Nocarrier ⇒high resistivity

25/60

Majority of the bias isapplied to the depletionregion.

Reverse bias is applied.

p-type

n-type

26/60

Forward bias

EC

EV

－－－

－－－－

－

＋＋＋＋＋＋

－－－

－－－－－－－－－－

＋＋＋＋＋＋＋＋＋＋＋＋

p-typen-type

ー＋

Hole：p⇒nElectron：n⇒p

27/60

EC

EV

EF

0=⋅∇

=⋅∇∂∂

−=×∇

∂∂

+=×∇

B

DtBE

tDJH

ρ

Ener

gy

ρ=⋅∇ D

ϕ

ε

−∇=

=

E

ED

Analysis of pn junction

(ρ : electric charge density)

n-type

p-type

ερϕ −=∇2

Poisson eq.

Maxwell eq.

28/60

EC

EV

Distribution of electric charge

EF

Ener

gy

x=0x=-xn x=xp x

ND＋

xNA

-

n-type

p-type

Positive charge

Negative charge

29/60

EC

EV

EF

Ener

gy

x=0

x=-xn x=xpx

ND＋

xNA

-

ερϕ −=∇2

Cx +−=∇ερϕ

x<0，F=0 at x=-xn

DD

nD

xqNC

CxqNF

ε

εϕ

−=

=−−=−∇=

1

1 0)(

ｘ>0，F=0 at x=xp

pA

pA

xqNC

CxqNF

ε

εϕ

−=

=−−

=−∇=

2

2 0

Low resistive

Low resistive


30/60

x<0

nDD xqNxqNxF

εε−−=− )(

ｘ>0

pAA xqNxqNxF

εε−=− )(

EC

EV

EF

Ener

gy

x=0

x=-xn x=xpx

xElectric field F

NDxn=NAxp

Charge neutrality


Continuous at x=0

31/60

Voltage distribution

EC

EV

EF

Ener

gy

x=0

x=-xn x=xp

x

x

32

21 CxxqNxqN

nDD +⋅−−=

εεϕ

Let ϕ=0 at x=-xn

23 2 n

D xqNCε

−=n-type

p-type

42

2CxxqNxqN

pAA +−=

εεϕ

ϕ is continuous atx=0 C4=C3

X<0

22

21

21

nD

nDD xqNxxqNxqN

εεεϕ −⋅−−=

X>0

Diffusion voltageVD 22

22 nD

pAA xqNxxqNxqN

εεεϕ −⋅−=

32/60

Diffusion voltage VD

22

22 nD

nDD xqNxxqNxqN

εεεϕ −⋅−−=

22

22 nD

pAA xqNxxqNxqN

εεεϕ −⋅−=

x<0 (n-type)

x>0 (p-type)

VD

VD=0-ϕ(xp)=

)(2

22nDpA xNxNq

⋅+⋅ε

EC

EV

EF

Ener

gy

x=0

x=-xn x=xp

n-type

p-type

Diffusion voltageVD

Voltage ϕ

33/60

Depletion layer width at bias V

xD=｜xn｜＋|xp｜

continuous at x=0 → NA・xp=ND・xnϕ(x=-xn)-ϕ(x=xｐ）＝VD-V

Then,

)(2 VVNN

NqN

x DAD

A

Dn −

+=

ε )(2 VVNN

NqN

x DDA

D

Ap −

+=

ε

( )VVNNq

x DDA

D −

+=

112ε

34/60

Junction capacitance C

Dpn xxxS

dSC εεε =

+=

==)1(

VVNNNNqC

DDA

DA

−+=

12ε

( )VVNNq

x DDA

D −

+=

112ε

35/60

Built in potential at zero bias

)exp(

)exp(

TkEE

Np

TkEE

Nn

B

fppVV

B

fnnCC

−⋅=

−−⋅=

p typen typeECp

EVn

EfpEfn

qVD

Confirm the following equation.Eg=EC-EV=qVD+(ECn-Efn)+(Efp –EVp)

⋅−=

⋅+=

VBpVfp

CBnCfn

NpTkEE

NnTkEE

ln

ln

EgECn

EVp

n-Si p-SiElectron

conc.ND

Holeconc.

NA

D

i

Nn 2

A

i

Nn 2

36/30

Built in potential at zero bias

)ln( 2i

ADBD n

NNqTkV ⋅

⋅=

Eg=EC-EV=qVD+(ECn-Efn)+(Efp –EVp)

)exp(

)exp(

TkEE

Np

TkEE

Nn

B

fppVV

B

fnnCC

−⋅=

−−⋅=

TkE

VCiB

g

eNNn−

⋅⋅=2

Q: Derive the following eq.

⋅⋅

−=

−

−=

VC

ADBD

V

AB

C

DBD

NNNNTkqV

NNTk

NNTkqVEg

ln

lnln

TkE

NNnB

gVCi −⋅= ]ln[]ln[2 ]ln[2]ln[ iBVCBg nTkNNTkE −⋅⋅=

]ln[]ln[]ln[2]ln[ VCBADBDiBVCB NNTkNNTkqVnTkNNTk ⋅⋅+⋅−=−⋅⋅

]ln[ 2i

ADBD n

NNqTkV ⋅

=∴

37/60

38/60

pn junction current

Forward bias V

Frow

ard

curre

ntR

ever

secu

rren

t

Reverse bias

VR>>VF

VF

VR

Anode Cathode

＋ー

Forward bias

39/60

pn junction current

n型

－－－－－－－

－－－－

－－－

－－

＋＋＋＋＋＋＋＋＋＋＋＋p型

Depletionregion

EC

EV

qVD

EF

Energy

VD: Diffusion voltage orBuilt in potential

Voltage or potential

nn0

n for electron p for hole

layer0 means concentration at zero bias

Notation

40/60

pn junction current Diffusion current

ECp

)exp(0 TkEE

NnB

nfCnCn

−−⋅=

n type

p type

Depletionlayer

EV

Efp

ECnEfn At zero bias Efn=Efp=Ef

)exp(0 Tk

EENn

B

pfCpCp

−−⋅=

Ener

gy＝

qVD

ECn-ECp=－q・VD

At zero bias


⋅−⋅=

−⋅

−−⋅=

−−⋅=

TkVqn

TkEE

TkEE

NTk

EENn

B

Dn

B

CpCn

B

fCnC

B

fCpCp

exp

expexp)exp(

0

0

q×(-VD)

)exp(0 TkEE

NnB

nfCnCn

−−⋅=

Electron conc. In n layer)exp(0 Tk

EENn

B

pfCpCp

−−⋅=

Electron conc. In p layer

Electron conc. In n layer Built inpotential

⋅−⋅=

TkVqnn

B

Dnp exp00

41/60

42/60


n type

ECp

EV

q・VD

Efn

ECn

Efp

Energy＝

x

q･V(x)

V(x): potential at xV(xn)=-VD

AssumingV(x)=0

( ))exp()( 0 TkxVqnxn

Bn ⋅

⋅⋅=

p type

43/60


Diffusion current density isxnqDj e ∂

∂=

Diffusion constant D

ECp

EVp

q・VD

Efn

ECn

Efp

Energy＝

x

q･V(x)

EVn

44/60


n型

ECp

EVp

q・VD

Efn

ECn

Efp

Energy

＝

x

q･V(x)

High conc. Low conc.

Electron diffusionCurrent

EVn

45/60


－－－－－

－－

－

－

－

－

－

－

－－

＋

＋

＋＋

＋＋

＋

＋＋＋

＋

＋＋

＋

＋n layer p layer

Built in electricfield

Fixed negativelycharged layer

Fixed positivelycharged layer

46/60

pn junction current Drift current

p layer

n layer

ECp

EV

q・VD

Efn

ECn

Efp

Energy

＝

q･V(x)

Electric field E

ｊ=qnµeE µe: electron mobility [m2/V・s]

vF=µE ：drift velocity current density j=charge × conc. × velocityElectron

47/60

pn junction current Diffusion current and drift current

p layer

n layer

ECp

EV

q・VD

Efn

ECn

Efp

Energy＝

x

q･V(x)

E

High conc. Low conc.

Diffusion currentDrift current

EqnxnqDj eee µ+

∂∂

=

48/60

pn junction current Diffusion current and drift current

At zero bias, 0)( =+∂∂ Exqn

xnqD ee µ

( ))exp()( 0 TkxVqnxn

Bn ⋅

⋅⋅=

FqnxnqDj eee µ+

∂∂

=

FqpxpqDj hhh µ+

∂∂

−=

Electron current density

Hole current density

49/60

pn junction current When bias is applied,

p layern layer

EC

EV

qVV：Applied bias

External bias is mostly applied to the depletion region.

50/60

pn junction current Diffusion current by the excess carrier

Electrons injected from n layer to p layer

Electrons in p layer

p typen type

EC

EV

qVForward voltage

Electric field in p layer is ignored. → Drift current = 0Only diffusion current should be considered.

xnqDj ee ∂

∂=

Electric field=0

51/60


p layern layer Depletion

EC

EV

qV

x=0

∆np np0

}1){exp()0( 0 −⋅==∆Tk

qVnxnB

pp

52/60


EC

EV

qV

x=0np0

x

2

2

xn

Dx

nD

xn

D pe

x

pe

dxx

pe ∂

∂=

∂

∂−

∂

∂

+

dx Life time of electron in p-layer : τn

n

pppe

nnxn

Dτ

02

2 −=

∂

∂

n

ppe

nxn

Dτ

∆=

∂

∆∂2

2

p layern layer

53/60


)exp()0(

)exp()0(

)exp(}1){exp()( 0

ep

p

Bpp

Lxn

neDxn

neDx

TkqVnxn

−∆=

−∆=

−−⋅=∆

τ

τn

ppe

nxn

Dτ

∆=

∂

∆∂2

2

At x→∞, np=np0

Le: Diffusion length of electrons in p layernee DL τ⋅=

De[m2/s]：Diffusion coefficientτn[s]：Carrier lifetime

54/60


p layern layer

EC

EV

qV

x=0

∆np

np0

Electron current density je by diffusion is

−⋅∆−=

∂

∆∂=

ep

e

epee L

xnL

qDxn

qDj exp)0(

55/60


p layern layer

EC

EV

qV

x=0Recombination

Injected electron recombine with holes in the p layer.→Holes are supplied from the electrode.

+ electrode- electrode

−

⋅−=∆−=+= 1exp)0( 0 Tk

qVnL

qDnL

qDjjjB

pe

ep

e

ehen

56/60


−

⋅−=∆−= 1exp)0( 0 Tk

qVpL

qDpL

qDjB

nh

hn

h

hp

Holes in n layer

Total current density is

−⋅

+

−=+= 1)exp(}{ 00 Tk

qVpL

qDnL

qDjjjB

nh

hp

e

epn

}1){exp(0 −⋅=Tk

qVjjB

Considering the direction ofcurrent,

}{ 000 nh

hp

e

e pL

qDnL

qDj

+

=

j0：Reverse saturation current density


−⋅

+

= 1)exp(}{ 00 Tk

qVpL

qDnL

qDjB

nh

hp

e

e

−⋅

+

= 1)exp(}{

22

TkqV

Nn

LqD

Nn

LqDj

BD

i

h

h

A

i

e

e

}{22

0D

i

h

h

A

i

e

e

Nn

LqD

Nn

LqDj

+

=

]/[5.28]/[06.9

2

2

scmDscmD

e

h

=

=

][4.53][1.30

mLmL

e

h

µµ

==

Q: Determine j0[A/cm2] in the following case.

][1031.9

][1031.9

322

0

332

0

−

−

×==

×==

cmNnn

cmNnp

A

ip

D

in

][A/cm1044.1 211-

22

0

×=

+

=

D

i

h

h

A

i

e

e

Nn

LqD

Nn

LqDj

57/60

58/60http://ecee.colorado.edu/~bart/book/book/chapter4/ch4_4.htm

n=1

n=2

Generation-recombination currents and high-injection levels

59/60

Series resistance

n-Si

p-Si

Cross sectional view of Si pn junction diode

Electrode metal

Electrode metal

Contact resistance

Series resistance

Series resistance

Contact resistance

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.410-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

電流

[A]

電源電圧[V]

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.410-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

電流

[A]　

電源電圧[V]　

Ideal Real

0.0 0.5 1.0 1.5

10-3

10-2

10-1

100

Curr

ent[

A]

Voltage [V]

}1)({0 −=Tk

qVExpIIB

V＝R×I

Series resistance

60/60

Semiconductor Devices 4thamano/H30/G30/4th.pdf · -2.00-1.00 0.0 1.00 2.00 3.00 4.00 5.00 TIME -1.000 v(IVm1) -1.000 v(IVm2) -1.000 D(TIME) -1.000 D(v(IVm2)) -1.002 Q ： Draw waveform

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