Lecture 4:

Junctions

October 2018

Lecture Outline

1. Drawing energy band diagrams for junctions

2. Different types of junction:

a) Metal-Semiconductor

b) pn-homojunction

c) pn-heterojunction

3. Deriving important junction parameters (Vbi, W)

4. Deriving the Diode equation

L4

Metal-SemiconductorL4

metal SC (n-type)

qφm

qφn

qχ

EG

EV

EC

EF

Schottky Junction

Metal-SemiconductorL4

metal SC (n-type)

qφm

qφn

qχ

EC

EF E

F

EG

EV

Important Rule● Fermi level must be in equilibrium

Metal-SemiconductorL4

metal SC (n-type)

qφm

qφn

qχ

EV

EC

EF E

F

qφm

qφn

qχ

EC

EV

metal SC (n-type)

EG E

G

“Contact”

Metal-Semiconductor

metal SC (n-type)

qφm

qφn

qχ

EC

EV

EF

metal SC (n-type)

EG

qφn

qχ

EC

EV

EF

EG

qφm

qVoqφ

B

Vo = φm

-φn

φB= φ

m - χ

Barrier Height

Band Bending

L4

Metal-SemiconductorL4

metal SC (p-type)

qφm

qφp

qχ

EG

EC

EV

EF

Metal-Semiconductor

metal SC (p-type)

qφm

qφp

qχ

EG

EC

EV

EF

qφp

qχ

EC

V

EF

EG

qφm

bi

qφB E

qV

metal SC (p-type)

Vbi = φm

- φp

φB= EG/q - (φ

m - χ)

L4

Metal-Semiconductor

Semiconductor-Semiconductor

qφp

qχp

EG

EF

p n

qφn

qχn

EV

EG

p-n homojunction

EC

EF

L4

Semiconductor-Semiconductor

qφp

qχp

EG

EF

p n

qφn

qχn

EV

EG

p-n homojunction

EF

EF

EC

EF

L4

Semiconductor-Semiconductor

qφp

qχp

EG

EF

p n

qφn

qχn

EV

EF

EG

p-n homojunction

qφp

qχp

qφn

qχn

EG

p n

EG

EV

EC

EC

EC

EF

EF

EV

L4

Semiconductor-Semiconductor

qφp

qχp

EG

EF

p n

qφn

qχn

EV

EF

EG

p-n homojunction

EF

EF

p n

qVbi

L4

Semiconductor-Semiconductor

qφp

qχp

EG

EF

p n

qφn

qχn

EV

EF

EG

p-n homojunction

EF

EF

p n

qVbi

Ei

Ei

Defining Electrostatic potential, Ψ, for a SC●

iDifference between E and E

f

qΨn

qΨp

Vbi

= Ψn - Ψ

p

Ele

ctr

osta

tic P

ote

ntial,Ψ

Ele

ctr

on e

nerg

y,E

Coming back here shortly to get a more physical picture

L4

Semiconductor-Semiconductor

Everybody's favourite homojunction - Silicon

p-type n-type

http://electronics.howstuffworks.com/diode1.htm

Extrinsically doped

Every bit of electronics you own is jam packed with silicon homojunctions

iPhone 5:1 billion transistors!~ 45 nm wide

Mono-C solar cells~750 μm thick cell size = 1 cm2

L4

Semiconductor-Semiconductor

qφp

qχp

EFp

p n

qφn

qχn

EFn

p-n heterojunction: Different band gaps

ΔEV

ΔEC

wide gap narrow gap

EF

1. Align the Fermi level. Leave some space for transition region.

L4

Semiconductor-Semiconductor

qφp

qχp

EFp

p n

qφn

qχn

EFn

p-n heterojunction: Different band gaps

ΔEV

ΔEC

wide gap narrow gap

EF

2. Mark out ΔEC

and ΔEC

at mid-way

points

ΔEC

ΔEC

L4

Semiconductor-Semiconductor

qφp

qχp

EFp

p n

qφn

qχn

EFn

p-n heterojunction: Different band gaps

ΔEV

ΔEC

wide gap narrow gap

EF

Barrier to hole transport

3. Connect the C.B. and V.B. keeping the band gap constant in each material

Difference in band gaps give rise to discontinuities in band diagrams. This limits the carrier transport by introducing potential barriers at the junction

L4

Semiconductor-Semiconductor

http://pubs.rsc.org/en/content/articlehtml/2013/ee/c3ee41981a#cit111

Examples of p-n heterojections

Most thin-film PV technologies

L4

Semiconductor-Semiconductor

Examples of p-n heterojections

III-V multi-junction devices

Being able to control the band offsets of a material can help eliminate barriers

L4

Physical Picture

Drawing band schematics for junctions all day is fun, but what is actually going on here?

http://www.youtube.com/watch?v=JBtEckh3L9Q

Excellent qualitative description6:27 – Didactic Model of Junction formation

L4

Physical Picture

J = J (drift ) +J (diffusion)= 0

http://en.wikipedia.org/wiki/File:Pn-junction-equilibrium.png

Equilibrium Fermi Levels – Explained – our one rule for drawing band schematics!

In thermal equilibrium, i.e. steady state: not net current flows

L4

Physical Picture

Lets look at hole current:

L4

Physical Picture

Lets look at hole current:

L4

Physical PictureL4

Physical Picture

dEF =0dx

The same is true from consideration of net electron current, Jn

L4

Abrupt JunctionL4

Abrupt JunctionL4

Abrupt JunctionL4

Abrupt JunctionL4

Abrupt JunctionL4

Abrupt JunctionL4

Under Bias

What happens to our ideal p-n junction if we put a forward or reverse bias across it?

L4

Under Bias

p n

0 wn-wp

W

EF

ZERO BIAS

Vbi

L4

Under Bias

p n

0 wn-wp

W

EF

FORWARD BIAS

Vbi - V

EF

+ -

●

●

●

●

●

Electron energy levels in p side lowered relative to those in n side Energy barrier qVbi reduced by V

Flow of electrons from n to p increasesFlow of holes from p to n increasesDepletion width decreases

L4

Under Bias

p n

0 wn-wp

W

EF

REVERSE BIAS

Vbi + V

EF

- +

●

●

●

●

Electron energy levels in p sideraised relative to those in n sideEnergy barrier qVbi increased by V

Flow of electrons from n to p reducedJunction width increases

L4

Ideal Dark JV curveL4

L4

Ideal Dark JV curve

Deriving Shockley Equation

Steady State again (i.e. no bias) Consider electron drift current

– Ieo from p to n

L4

Deriving Shockley Equation

Steady State again (i.e. no bias) Consider electron drift current

– Ieo from p to n

W

Le

L4

Deriving Shockley Equation

Steady State again (i.e. no bias) Consider electron drift current

– Ieo from p to n

W

Le

L4

Deriving Shockley Equation

Steady State again (i.e. no bias) Consider electron drift current

– Ieo from p to n

W

Le

L4

Deriving Shockley Equation

What happens under forward bias?

●

●

Drift (p to n)? - Nothing. No potential barrier in this directionDiffusion (n to p)? - Increases by exponential factor:

If we assume occupation of states in CB is given by Boltzmann distribution

L4

Deriving Shockley Equation

What happens under forward bias?

●

●

Drift (p to n)? - Nothing. No potential barrier in this directionDiffusion (n to p)? - Increases by exponential factor:

If we assume occupation of states in CB is given by Boltzmann distribution

L4

Deriving Shockley EquationL4

Deriving Shockley EquationL4

Deriving Shockley EquationL4

Deriving Shockley EquationL4

Lecture SummaryL4

1. Drawing energy band diagrams for junctions

2. Different types of junction:

a) Metal-Semiconductor

b) pn-homojunction

c) pn-heterojunction

3. Deriving important junction parameters (Vbi, W)

4. Deriving the Diode equation