Chapter 10. Junctions

Junctions

• Surface ~ simplest one; junction between vacuum/surface• Metal/Metal

• Metal/Semiconductor Blocking contact ~ Schottky barrier Ohmic contact ~ low resistance

• Semiconductor/Semiconductora. Homojunction ~ both side of junctions are sameb. Heterojunction ~ each side is differentc. Iso-type ~ types are same to both sides < n types or p types >d. Anisotype < p + n >

• M/I/M, MIS, SIS, MOS

1 2M M potential is set upq q

Surfaces

• As more O2- are formed, the energy bands bend at the surface

of the semiconductor because of the local field that is built up.

Ec

EF

Ev

Surface state

O2-

chemisorption

Chemisorption of oxygen on n-type Semiconductor surface

separation of charge

bending of band gives Ɛ

negatively charged surface state

positively charged depletion region

d-

+ +

-

Termination of the periodic potential → localized states at the surface

Metal/Metal

• Transfer of electron until EF are same for both of metals• A potential difference known as the contact potential is set up between

two metals.•• EF has to be same in thermal equilibrium for whole system

Although an internal field exists, no potential can be measured in an external circuit connecting the two metals together.

Local electric field is measured by the Kelvin Probe method – vibrating method

BqAq

BA

Bq

B A

ƐAq

cpq

contact potential

A B cp A BIf , q q q q q

cp

Metal/Semiconductor – Schottky Barrier

• Blocking contact if for n-type and for p-type• A flow of electrons from the semiconductor to the metal in order to

equalize the Fermi energies in the two materials.• An internal field is developed in the semiconductor.• : diffusion potential, built-in potential• : Energy barrier

Mq Sq S ≡ electronaffinity

( )S S c Fq E E

Mq--

S Sq++

Wd

𝑞Φ 𝑞Φ

𝑞Φ

𝑞Φ 𝑞 Φ Φ

𝐸 𝑞Φ 𝜒

Blocking contact

𝑞Φ 𝑞Φ

Dq

Eb


• The width of the depletion region Ionized donor density = ND

+

0

0

2

20

22

0

: Poisson's equation

2

r

D

r

D

r

DD D

r

E

N qdEdx

dEdx

N qddx

N qq W

Boundary conditions

𝐸𝜕𝜙

𝜕𝑥 0 at 𝑥 𝑊𝜙 𝜙 at 𝑥 𝑊𝜙 0 at 𝑥 0


• In the depletion region Wd, potential change Φ

• If we include the effects of an applied voltage Φapp ,

𝑥 𝑊 , Φ Φ

𝑊2𝜀 𝜀 𝑞Φ 𝑞Φ

𝑞 𝑁

/

𝑊2𝜀 𝜀 𝑞Φ 𝑞Φ 𝑞Φ

𝑞 𝑁

/

→ The more donors, the smaller 𝑊 .

→ The larger applied voltage, the smaller 𝑊 .

The more donors or the larger applied voltage can recued the contact resistance.


𝐶𝜀 𝜀 𝐴

𝑑1

𝐶/𝐴2 𝑞Φ 𝑞Φapp

𝜀 𝜀 𝑞 𝑁

1𝐶/𝐴

app

S DM slope ∝1

𝑁

Method to measure 𝑁 and Φ

𝑊2𝜀 𝜀 𝑞Φ 𝑞Φ

𝑞 𝑁

/

metal semiconductor

depletion region

conductor dielectric nearly conductor

Wd

Metal/Semiconductor – Schottky Barrier• JV characteristics of Schottky barrier (n-type semiconductor)

• Thermionic emission

Metal +Metal -

J

V

M Sq ++

D M S( )q q

S Sc FE E q

𝐽 → 𝐴𝑇 𝑒𝑥𝑝 𝑞Φ 𝜒 /𝑘𝑇𝐽 → 𝐴𝑇 𝑒𝑥𝑝 𝑞Φ 𝜒 𝑞Φapp /𝑘𝑇 (only change by 𝑞Φapp)

Metal/Semiconductor – Schottky Barrier•

• Basic equation for current in a M/S junction

𝐽net 𝐽 → 𝐽 →𝐴𝑇 𝑒𝑥𝑝 𝑞Φ 𝜒 /𝑘𝑇 𝑒𝑥𝑝 𝑞Φapp/𝑘𝑇 1

Metal +forward

Metal –reverse

J

Φapp

J0

𝐽net 𝐽 𝑒𝑥𝑝 𝑞Φapp/𝑘𝑇 1

≡ J0 , not depend on the Φapp

For forward bias with positive 𝑞Φapp

For reverse bias with negative 𝑞Φapp

𝐽forward 𝐽 𝑒𝑥𝑝 𝑞Φapp/𝑘𝑇

𝐽reverse 𝐽


forwardreverse

J

Φapp

J0

• In a forward bias, contact potential is reduced from 𝑞Φ to 𝑞 Φ Φ )→ forward current (metal to semiconductor)

• In a reverse bias, contact barrier increases to 𝑞 Φ Φ )→ negligible electron flow from semiconductor

to metal• In both cases, metal-to-semiconductor electron

flow is determined by 𝑞 Φ 𝜒• Diode equation: 𝐼 𝐼 𝑒𝑥𝑝 𝑞Φapp/𝑘𝑇 1

• Electrons flow without any barrier contact does not make any change in J.

Mq Sq S

e-

n-semiconductormetal

D S M( )q q

S Mq

Accumulation region(reservoir of e-)

n-type:

p-type:

(opposite of Schottky barrier)

𝑞Φ 𝑞Φ

𝑞Φ 𝑞Φ

Ohmic contact

Ohmic contact• The accumulation layer in the semiconductor serves as a ready

reservoir of electrons for conduction in the material available at the contact, and thus application of an electric field measures only the conductivity (R) of the semiconductor.

J

V

R

p-n junction - homojunctions

nq n

pq

𝜒

p-type n-typeh+

e-

Wp Wn

Depeletion regionW = Wp+ Wn

Similar to two Schottky barriers

𝑞Φ 𝑞Φ 𝑞Φ𝜒 𝐸 𝐸 𝐸 p

𝜒 𝐸 𝐸 p

p-type n-type

Majority carrier

Majoritycarrier

Minoritycarrier

Minoritycarrier

x

pn

np

When no electric field is applied (Φapp = 0)

app /q kTnp e

app /q kTpn e

appq

D appq q

Majority carriers ~ e- in n-type, h+ in p-typeMinority carriers ~ h+ in n-type, e- in p-type

x

y y


When an electric field (Φapp) is applied


•

• The p-n junction shows the similar form with a Schottky barrier (Φapp dependence of J )

𝐽 𝐽 𝐽

𝐽 𝐽 𝑒 app/ 1

𝐽𝑞𝐷 𝑛

𝐿𝑞𝐷 𝑝

𝐿 p +p -

J

Φapp

J0

Note: The pre-exponential reverse saturation current (J0) has a different definition with Schottky barrier.

Applications of p-n junctions

• Rectifier• Amplifier• p-n-p type transistor• Field-effect transistor• Photodetector• Phototransistor• Solar cell• Light emitting diode• Tunnel diode

Photodetector: operating under a reverse bias

• Increase of current by light irradiation

J

ΦappΔI

- +

-

+

light

e-h pair

Photoconductivity gain ≡number of collected electronsnumber of absorbed photons

1


Solar cell: no applied bias

OShort circuit current

Open circuit voltage

- +

The band gap of about 1.4 eV proves to be optimal for solar energy conversion application.


-

+

light

e-h pair

Light emitter: Forward biased p-n junction

+ -

LED, Laser


-

+

e-h pair

-

+

• Direct band gap materials are favored for light emitting application.• GaAsP (R), InGaN (B), GaN (B)• By coating a blue LED with phosphor materials, a portion of the blue

light can be converted to red and green (or yellow) lights for white light.

Semiconductor-semiconductor junctions: Heterojunctions

1 2

2 1 2 1

c

v G G

EE E E

1 1 1 2 2 2

2 1 1 1 2 2

( ) ( )/ /

D c F c F

D D D D

q E E E EN N

An isotope heterojunction between two n-type materials with the same electron density, but showing a discontinuity at the interface because of a difference in electron affinities.

A positive value of Δ𝐸 or a negative value of Δ𝐸 implies a spike impeding the transport of electrons or holes, respectively.

Semiconductor-semiconductor junctions: Heterojunctions

Energy band diagrams for p-n heterojunctions. The materials in (a) and (b) have the same band gaps, but in (a) the p-type material has a smaller electron affinity than the n-type material, whereas in (b) the situation is reversed.

Appl. Phys. Lett. 102, 012111 (2013)

van der Waals Heterojunctions

EF

MoS2

MoS2WSe2

WSe2WSe2 MoS2

Multiple quantum well (MQW)laser

Epitaxially grown MQW Lattice mismatch

2D semiconductors van der Waals heterostructure

• Stacking of 2D semiconductors for heterostructure• Less interaction between layers (almost flat band)• No issue of lattice mismatch

Chapter 10. Junctions - Seoul National...

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