chap 3. p-n junctionweng/courses/ic_2007... · 2020. 4. 23. · uso for p+/n diode, ufor n+/p...

MOS Device Physics and Designs Chap. 3

Instructor: Pei-Wen LiDept. of E. E. NCU

1

Chap 3. P-N junction

u P-N junction Formationu Step PN Junctionu Fermi Level Alignmentu Built-in E-field (cut-in voltage)u Linearly Graded PN Junctionu I-V Characteristicsu Breakdown



2

Basic Symbol and Structure of the pn Junction Diode



3

Charge Distribution across PN junction



4

Step Junction

ND - NA

Actual Linearly Graded Profile

x

ND

-NA

Ideal step junction

CathodeAnode

Metal contactp-type Si, NA n-type Si, ND

⊕–⊕–⊕–⊕–⊕–

⊕–⊕–⊕–⊕–⊕–

⊕–⊕–⊕–⊕–⊕–

⊕–⊕–⊕–⊕–⊕–



5

Step P-N junction—Band Diagram

EC

EV

EFEFi

EC

EV

EF

EFi

P-Semiconductor N-Semiconductor

EC

EV

EF

EFi

EFi

EC

EV

EF

Band Diagram

Fermi-level alignmentEC

EV

EFEFi

EC

EV

EF

EFi



6

Step Junction

u Recall Poisson’s Equation:

u For 1-D, E = Ex

dE/dx = ρ/ksεo

where ρ = q (p – n + ND – NA)

u For a pn junction, electrons and holes will diffuse through the junction, which would result in net ρ in the space charge region.

oSk

Eε

ρ=•∇

constant dielectric :

density charge :

Skρ



7

P-N Junction

CathodeAnode

Metal contactp-type Si, NA

n-type Si, ND

⊕–⊕–⊕–⊕–⊕–

⊕–⊕–⊕–⊕–⊕–

⊕–⊕–⊕–⊕–⊕–

⊕–⊕–⊕–⊕–⊕–

+

–

⊕⊕⊕⊕⊕

⊕–⊕–⊕–⊕–⊕–

⊕–⊕–⊕–⊕–⊕–

⊕–⊕–⊕–⊕–⊕–

Depletionregion Ionized dopants



8

Charge Distribution in PN Junction

u Net ρ results in the depletion region (or space charge region)

u ρ = -qNA -xp ≤ x ≤ 0qND 0 ≤ x ≤ xp

xn

ρ

x+

–

-xp

{oSoS k

qkdx

dEεε

ρ==Q

nD

pA

xxNxxN

≤≤

≤≤−−

0

0

( ) ( ) ( ) ( )

( ) ( )

( ) ( ) ( ) ( ) nDpApnnDoS

DoS

nDoS

AoS

nn

x

xoS

xNxNxExExxNk

qxNk

qxE

xxNk

qxNk

qxE

dxdVxExEx

kxE

n

=⇒==⇒>−=

<−−=⇒

==+=⇒ ∫

0,00 if

0 if

0,0 ,1

εε

εε

ρε

Q

Charge neutrality



9

Open-Circuit Condition of a pn Junction Diode

Potentialhill

0 Barriervoltage

p-type Si n-type Si

Depletionregion

CathodeAnode

Metal contact

Charge distribution of barrier voltage

across a pn Junction.

( )22

2 nDpAoS

bi xNxNk

qV +−

=ε



10

Width of Space Charge Region

u Recall xnND = xpNA,

u W is dependent on the built-in voltage Vbi.

( )

( )

( )

2/1

2/1

2/1

2

2

2

+

=+=⇒

+

=

+

=⇒

biDA

DAospn

biDAD

Dosp

biDAD

Aosn

VNN

NNq

kxxW

VNNN

Nq

kx

VNNN

Nq

kx

ε

ε

ε



11

Reverse-Biased PN Junction Diode

p n

3 V Lamp

Open-circuit condition(high resistance)

Vbi → Vbi + VA

W ↑ ↑



12

Forward-Biased PN Junction Diode

p n

3 V

Hole flow Electron flow

Lamp

Vbi → Vbi - VA

W ↓ ↓



13

Bias Effect on the PN Junction



14

Bias Effect on the PN Junction Band Diagrams

u Fig. 5.12



15

Linearly Graded PN Junction

u Assume the linearly graded profile is ND – NA = ax, a: grading const.

( )3

1

12

−=⇒ Abi

oS VVqakW ε



16

Continuity Equations

u There will be a change in carrier concentrations within a given small regions of the semiconductor if an imbalance exists between the total currents into and out of the region.

u Minority Carrier Diffusion Equation

P

N

Jtpq

Jtnq

•−∇=∂∂

•∇=∂∂

( )

( )

( )2

2

2

2

2

2

2

2

2

2

2

2

xpqD

xpqD

tpq

xnqD

xnqD

tnq

xnqD

xnqD

xnqDJ

NP

NP

N

PN

PN

P

NNNN

∂∆∂

=∂

∂=

∂∂

∂∆∂

=∂

∂=

∂∂

⇒

∂∆∂

=∂∂

=

∂∂

•∇=•∇



17

Continuity Equations

u If thermal R-G is considered, continuity equations would be modified

u ⇒Minority carrier Diffusion equations become

const. time: , 1

1

G-Rthermal

G-Rthermal

G-Rthermal

nn

P

N

ntn

tpJ

qtp

tnJ

qtn

ττ∆

−=∂∂

∂∂

+•∇−

=∂∂

∂∂

+•∇=∂∂

( )

( )p

nNP

N

n

PPN

P

pxpD

tp

nx

nDt

n

τ

τ

∆−

∂∆∂

=∂

∂

∆−

∂∆∂

=∂

∂

2

2

2

2



18

Diffusion Length

uThe average distance minority carriers can diffuse into a sea of majority carriers before being annihilated.

material type-p ain electronscarrier minority

material type-nan in holescarrier minority

---

---

nNN

pPP

DL

DL

τ

τ

≡

≡



19

Quasi-Fermi levels

uAre energy levels used to specify the carrier concentrations inside a semiconductor under nonequilibrium conditions.

( )

( )cases riumnonequilibunder holesfor level fermi-quasi

cases riumnonequilibunder electronsfor level fermi-quasi

: lnor

: lnor

−≡≡

+≡≡

−

−

iiPi

iiNi

npkTEFenp

nnkTEFenn

kTPFEiE

kTiENFE

Under equilibrium

ECEFEi

EV

ECFNEi

EV

FP

Under non-equilibrium



20

PN Diodes: I-V Characteristics



21

Forward and Reverse Electrical Characteristics of a Silicon Diode

120 100 80 60 40 20

.4 .8 1.2 1.6

+ I

- V + V

- I

Breakdownvoltage

Leakagecurrent

Reverse bias curve

Forward bias curve

Junction voltage

( )

torssemiconduc on the depending

magnitude of ordersmany by can vary which

current, saturation: ,1

oo IeII refVAV −

=



22

Composite energy-band/circuit diagram of a reverse-biased pn diode



23

I-V Characteristics

u From deviation:

u So for p+/n diode,

u For n+/p diode,

u As a general rule, this suggests that the heavily doped side of an asymmetrical junction can be ignored in determining the electrical characteristics of the junction.

+=

D

i

P

P

A

i

N

No N

nLD

Nn

LDqAI

22

D

i

P

PoDA N

nLDqAINN

2

≅⇒>>

A

i

N

NoAD N

nLDqAINN

2

≅⇒>>



24

Derivation of I-V Characteristics

( ) ( )

dxdpqDpEqJ

dxdnqDnEqJ

xJxJJ

PpP

NnN

PN

−=

+=

+=

µ

µ

p-type Si n-type Si

Depletionregion

Quasi-neutral p region

E ~ 0

Quasi-neutral n region

E ~ 0

E≠0



25

Derivation of I-V Characteristics

u In quasi-neutral regions, E = 0, so consider diffusion and thermal R-G currents only.

u In Depletion Region:

0,

0 ,

2

2

2

2

for

for

=∆

−∆

=∂∂

≥∆

−=

=∆

−∆

=∂∂

−≤∆

=

n

nnPn

nPP

n

ppNp

pNN

pdx

pdDtpxx

dxpdqDJ

ndx

ndD

tnxx

dxnd

qDJ

τ

τ

( )

( )PN

nPP

pNNN

n

pN

JJJxJJ

xJJdx

dJnJ

qtn

+===

−==⇒=⇒∆

+•∇=∂∂

=

const. ,similarily

const.010thermal

τ



26

Boundary conditions and quasi fermi level inside a forward-biased diode



27

Carrier Concentration inside a pn diode under forward and reverse biasing.



28

Experimental I-V Characteristics



29

Reverse-Bias Breakdown

u Large reverse current flows when the reverse voltage exceeds a certain value, VBR. The current must be limited to avoid excessive “heating”.

u Practical VBR measurements typically quote the voltage where the reverse current exceeds 1 µA.

u Factors to affect VBR:– 1. Bandgap of the

semiconductor.– 2. doping on the lightly doped

side of the pn junction, NB.

u Breakdown Mechanism:– Avalanche process– Zener process

75.0

1

BBR N

V ∝



30

Avalanching

•As VA << VBR, the reverse current is due to minority carriers randomly entering the depletion region and being accelerated by the E-field.

•The acceleration is not continuous but is interrupted by energy-losing collisions with the semiconductor lattice.

•Since the mean free path between the collisions is ~10-6 cm, and a median depletion width is ~10-4 cm, a carrier can undergo 10-1000 collisions in crossing the depletion region.

•The energy lost by the carrier per collision is small.

•The energy transferred to the lattice simply causes lattice vibration --- local heating.



31

Avalanching

u As VA → VBR, the amount of energy transfer to the lattice per collision increases dramatically, and becomes sufficient to ionize a semiconductor atom. That is to causes an electron from the valence band to jump to conduction band. ⇒“impact ionization”

u The electrons created by impact ioization are immediately accelerated by the large E-field in the depletion region, and consequently, they make additional collisions and create even more energetic electrons. ⇒“Avalanching”

Impact ionization



32

Zener Process

u The occurrence of “tunneling” in a reverse-biased diode.

u Two major requirements for tunneling to occur and be significant:

– There must be filled states on one side of the barrier and empty states on the other side of the barrier at the same energy.

– The width of the potential energy barrier must be very thin (< 10 nm).

– That is the doping on the “lightly”doped Si is in excess of 1017 cm-3.

– Zener process is only important in diodes that are heavily doped on both sides.



33

R-G Current

u When diode is reverse biased, the carrier concentrations in the depletion region are reduced below their equilibrium values, leading to the thermal generation of electrons and holes throughout the region.

u The large E-field in the depletion region rapidly sweeps the generated carriers onto the quasi-neutral regions, thereby adding to the reverse current.

Reverse-biased generation

Forward-biased recombination



34

Hetero-Junction

EC

EV

EF

EFi

Semiconductor AEC

EV

EFEFi

Semiconductor B

EV

EC∆EC < 20 meV

bulk Si

Eg = 1.17 eV

Strained Si0.8Ge0.2

Eg ~ 1.0 eV

∆EV ~ 0.15 eV

∆EC ~0.15 eV

∆EV ~ 0.05 eV

Relaxed Si0.7Ge0.3

Eg ~ 1.08 eVStrained Si

Eg ~ 0.88 eV

Type I Alignment Type II Alignment



35

Quantum Well

Hole Confinement

∆EC ~ 0.02 eV

relaxed Si0.7Ge0.3

Eg = 1.08 eV

Strained Si0.3Ge0.7

Eg ~ 0.72 eV

∆EV ~ 0.48 eV

Strained Si

Eg = 0.88 eV

∆EC ~0.18 eV

∆EV ~0.34 eV

Electron Confinement

chap 3. p-n junctionweng/courses/ic_2007... · 2020. 4. 23. · uso for p+/n diode, ufor n+/p...

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