Semiconductor Devices › materials › Semiconductor_ch1.pdf · Department of Semiconductor and...

IFE T&CS

Semiconductor Devices

lectures 30 hours

lab. exercises 30 hours

Prof. Zbigniew Lisik

room: 116

e-mail: [email protected]

Department of Semiconductor and

Optoelectronics Devices

[email protected]

Fundamentals of Semiconductor Physics

Chapter 1

T

T

T

Metal Semiconductor Isolator

very low medium very large


Chapter 1

What are semiconductors ?

1. They are crystals

2. They can be:

● atom crystals like: Si, Ge, C-diamond

● compound crystals like: GaAs, InSb, SiC, GaN

3. When they are pure, their resistivity is in

a middle range


Chapter 1

Basic semiconductors:

Si - silicon

Ge - germanium

GaAs - gallium arsenide

SiC - silicon carbide

GaN - gallium nitride


Chapter 1

Structure of crystal – energy band model

● - electron

●●

+

W W3

W2

W1●

●

●●

+

●●

+

R

W W3

W2

W1●●

●●

single atom

atoms in

crystal

Pauli restriction – elektrons must be recognisable

R


Chapter 1

Structure of silicon crystal – so called

diamond structure

Crystal bond between 2 atoms

The bond arises when 2 atoms are so

close that two of their valance

electrons become common, which

results in quantum nature attraction

atom A atom B

electrons


Chapter 1


diamond structure

Crystal bond between 2 atoms

The bond arises when 2 atoms are so

close that two of their valance

electrons become common, which

results in quantum nature attraction

two atoms molecula

two electron bond


Chapter 1


diamond structure

Si

3D 2D

Si Si


Chapter 1

Structure of silicon crystal –

2D representation

SiSiSiSi

SiSiSiSi

SiSiSiSi

SiSiSiSi


Chapter 1

2D Structure of silicon crystal

SiSiSiSi

SiSiSiSi

SiSiSiSi

SiSiSiSi

T = 0 K If the temperature of crystal T = 0K

all the valance electrons take part

in the atom bonds

W2

W1

W3

●●

●●

Conduction Band

Valence Band


Chapter 1


SiSiSiSi

SiSiSiSi

SiSiSiSi

SiSiSiSi

The crystal temperature can,

however, increase and then T> 0K.

If the sufficient energy is delivered

to the valance electron, it can leave

its position in the interatom bond

and can become a free electron.

T = 0 K If the crystal temperature T = 0K

all the valance electrons take

part in the atom bonds


Chapter 1


SiSiSiSi

SiSiSiSi

SiSiSiSi

SiSiSiSi

The valance electron taking

sufficient energy leaves its

position in the bond and

becomes free electron.

T > 0 K

Such a free electron can move in

the crystal without any restriction

and is called conduct electron in

contrast to the electrons in bonds

called valance electrons


Chapter 1


SiSiSiSi

SiSiSiSi

SiSiSiSi

SiSiSiSi

T > 0 K The valance electron taking

sufficient energy leaves its

position in the bond and

becomes free electron.

The empty place in the bond

structure is called hole and can

also move through the crystal as

the result of valance electrons

hopping from one bond to another.


Chapter 1


SiSiSiSi

SiSiSiSi

SiSiSiSi

SiSiSiSi

T > 0 K Conduct electrons are not connected

with any bonds and can freely move

inside the crystal. Since they are

negative charge –q their movement can

create an electric current

Holes are not connected with any

particular bond and can freely move

inside the crystal. Since the hole

means the lack of an electron, it is

connected with the local excess of

positive charge +q. This charge moves

together with the hole creating an

electric current.


Chapter 1


The presented process is called

electron-hole pair generation

and has its energy band model:

Wg = Wc - Wv

T > 0 K

SiSiSiSi

SiSiSiSi

SiSiSiSi

SiSiSiSiWC

WV

Conduction Band

Valence Band


Chapter 1


The presented process is called

electron-hole pair generation

and has its energy band model:

WC

WV

Wg = Wc - WvValance band

Conduction band

Band gap

WC

WV

Electrons – fermions

fulfilling the Pauli restriction


Chapter 1

Dopands in Silicon T = 0K

SiSiSiSi

SiSiGaSi

SiAsSiSi

SiSiSiSi acceptors

As donors

GaIII Mendeleiew group

Ga, B, Al

V Mendeleiew group

As, Sb, P


Chapter 1

SiSiSiSi

SiSiGa-Si

SiAs+SiSi

SiSiSiSi

Dopands in Silicon T > 0K

Ga

As

acceptor

donor

Ionization energy of

dopands is very low

Wi << Wg


Chapter 1

SiSiSiSi

SiSiGa-Si

SiAs+SiSi

SiSiSiSi

Dopands in Silicon T > 0K

WC

WV

WA

WD

Ionization energy of

dopands is very low

Wi << Wg

Energy band model:


Chapter 1

Carrier concentration in doped semiconductor

Types of semiconductors

Na > Nd pp0 > np0 p-type

Na < Nd pn0 < nn0 n-type

Na = Nd p0 = n0 = ni i-type

Charge balance:nd + Na + nT = pT + Nd + pa

n0 + Na = p0 + Nd


Chapter 1

Equilibrium carrier concentration

Thermodynamic equilibrium state

n0 , p0

The state of the system being in constant temperature

without any energy exchange with surroundings - so

called adiabatic conditions.

The equilibrium densities

of electrons and holes, n0

and p0, result from the

balance of generation and

annihilation processes:

gdT=rdT and gT=rT

WC

WV

WA

WD

rTgT

gdT rdT

Type n


Chapter 1

Statistical physics

● It is used to describe physical phenomena that are created

by huge number of elements – e.g. properties of gases that

can be considered as the set of molecules.

● The phenomenon is described by the parameters that

represent the behaviour of the set of elements being

related to the average value of particular element feature

Temperature – average kinetic energy of molecules

Pressure – average momentum of molecules


Chapter 1

Statistical physics

● The set of elements is characterised by the probability

function that determines the probability that the

considered parametr of an element has particular

magnitude.

● In the classical approach,

the probability function has

a bell-like shape with the maximum

value corresponded to the average

value of parameter (energy in

the figure) .

f(W)

Wav W

Boltzman distribution


Chapter 1

Statistical physics

● If we want to know how many particles (e.g. electrons)

have their energy in the range <W1,W2>, it is enough to

calculate the integral:

dW f(W) N(W) n 2

1

W

W

where:

N(W) – state density function (in classical approach,

total number of particles N(W) = N)

f(W) – probability that the state of energy W is

occupied


Chapter 1

Statistical physics

Classical approach – Bolzmann distribution

kT

W exp f(W)

Quantum approach – Fermi-Dirac distribution

1 kT

W-Wexp

1 f(W)

F

WF – Fermi energy (Fermi lavel)

f(W)

Wśr W

f(W)

WF W

0.5

1


Chapter 1

Statistical physics

Classical approximation – (W – WF) > 2kT

Quantum approach – Fermi-Dirac distribution

1 kT

W-Wexp

1 f(W)

F

WF – Fermi energy (Fermi lavel)

kT

W-Wexp f(W) F


Chapter 1

Statistical physics

Classical approximation – (W – WF) > 2kT

If this approach can be used to estimate the electron and

hole density in semiconductor, such a semiconductor is

called non-degenerated

kT

W-Wexp f(W) F

Only such semiconductors will be considered in our lectures


Chapter 1


Classical aproximation for electrons

Conduction

band

Wc

Wc1

states occupied by

electrons

dW f(W) N(W) n C1

C

W

W

0

Concentration of electrons in

conduction band:

Under the assumption: WC1

kT

W-Wexp N n FC

C0

2/3

2

efeC

h

kTm2 N

NC – effective density of states

in the conduction band


Chapter 1


Classical aproximation for holes

Concentration of holes in

valance band:

dWf(W) - 1N(W) p V

V1

W

W

0

kT

W-Wexp N p VF

V0

states occupied by holes

Valance

band

Wv1

Wv

Under the assumption: WV1 -

NV – effective density of states

in the valance band

2/3

2

efhV

h

kTm2 N


Chapter 1

Equilibrium in intrinsic semiconductor n0 = p0

kT

W-Wexp N

kT

W-Wexp N VFi

VFiC

C

efe

efhVC

C

VVC Fi

m

mln kT

4

3 WW

2

1

N

Nln kT

2

1 WW

2

1 W

From the equilibrium condition:

one can calculate WFi, the

Fermi energy for intrinsic

semiconductor :

WC

0.5 (WC – WV)

WFi

WV


Chapter 1

Equilibrium in doped semiconductor

Transformation of electron equation:

n0 ≠ p0

kT

W-Wexp n

kT

W-Wexp

kT

W-Wexp N

kT

W-WW-Wexp N

kT

W-Wexp N n

FFii

FFiFiCC

FFiFiCC

FCC0


Chapter 1


Transformation of hole equation:

n0 ≠ p0

kT

W-Wexp n

kT

W-WW-Wexp N

kT

W-Wexp N p

FFii

VFiFiFV

VFV0


Chapter 1


Product of hole and electron

concentration:

n0 ≠ p0

kT

W-Wexp n

kT

W-Wexp n pn FFi

iFFi

i00

n pn 2

i00

At constant temperature n0p0 is constant

independently on the dopand concentration


Chapter 1


Transformation of hole and electron

product:

n0 ≠ p0

pn n 00

2

i

kT

W-Wexp N

kT

W-Wexp N pn VF

VFC

C00

kT

Wexp

300

T B

kT

Wexp NN

kT

W-Wexp NN

kT

W-Wexp N

kT

W-Wexp N n

g

3

2

g

VCVC

VC

VFV

FCC

2

i

ni = f(T)


Chapter 1


T

ni

p0

n0

TiTs

ln n0

ln p0

Typ n

WC

WV

WD

n0 = nd + nT

p0 = pT

Ts – saturation temperature

Ti – intrinsic temperature


Chapter 1


T

ni

p0

n0

TiTs

ln n0

ln p0

Type n

Ts – saturation temperature

Ti – intrinsic temperature

T

TiTs

ρ


Chapter 1

Thermal limitation for semiconductor devices

T

ni

p0

n0

TiTs

ln n0

ln p0

Recommended area

If semiconductor devices are to keep their data sheet ratings,

the concentration of majority carriers cannot change

considerably. Condition 1: It is true when Tmin not lower than Ts.

For Si Tmin ≈ -50 °C

Ts[C]


Chapter 1


T

ni

p0

n0

TiTs

ln n0

ln p0

Recommended area



considerably. Condition 2: It is true when Tmax lower than Ti.

For Si Tmax < 400 °C


Chapter 1


T

ni

p0

n0

TiTs

ln n0

ln p0

Recommended area



considerably. Condition 2: It is true when Tmax lower than Ti.

Typical ranges defined for

silicon devices in catalogues:

Range [C]

Commercial 0 – 70

Industrial -25 – 85

Extended industrial -40 – 125

Military -55 – 125


Chapter 1

Current filamentation – hot spot

T

TiTs

ρ

Safe area

If T inside <Ts,Ti>, the negative thermal feedback

occurs:

Current is pushed out from warmer

area and heat dissipation decreases

Silicon chip

Q

T

J

Ti


Chapter 1


T

TiTs

ρ

Safe area

If T inside <Ts,Ti>, the negative thermal feedback

occurs:

Current is pushed out from warmer

area and heat dissipation decreases

Silicon chip

Q

T

J


Chapter 1


T

TiTs

ρ

Safe area

If T outside <Ts,Ti>, the positive thermal feedback

occurs:

Current is squeezed in warmer area

and heat dissipation increases

Silicon chip

Q

T

J

Ti


Chapter 1


T

TiTs

ρ

Safe area

If T outside <Ts,Ti>, the positive thermal feedback

occurs:

Current is squeezed into small area

and hot spot is generated

Silicon chip

Q

T

J


Chapter 1

Nonequilibrium carrier concentration

Equilibrium concentrations

n0 , p0

n = n0 + Dn

p = p0 + Dp

Nonequillibrum concentrations

WC

WV

h

Dn

Dp

Δn, Δp – excess concentrationsDn = Dp

usually:


Chapter 1


Quasi-Fermi level

n = n0 + Dn

p = p0 + Dp

kT

WWexpN p

kT

WWexpN p

kT

WWexpN n

kT

WWexpN n

vFhv

vFv

Fecc

Fcc

D

D

kT

W-Wexp N n FC

C0

kT

W-Wexp N p VF

V0


Chapter 1


Quasi-Fermi level

kT

WWexpN p p p

kT

WWexpN n n n

vFhv0

Fecc0

D

D

WFe – quasi-Fermi level for electrons

WFh – quasi-Fermi level for holes

Wc

Wv

WF

WFe

WFh

n-type

Wc

Wv

WF

WFe

WFh

p-type

Phenomena in Semiconductors

Chapter 2

Recombination processes

WC

WV

gT rT

n0

p0

Equillibrum state:

gT – rate of electron-hole pairs

thermal generation

rT – rate of electron-hole pairs

thermal anihilation

gT = rT

Steady state

constant carrier concentrations

Phenomena in Semiconductors

Chapter 2

Recombination processes

WC

WV

h gT r

n0 + Δn

p0 + Δn

Non-equillibrum state:

gT – rate of electron-hole pairs

thermal generation

r – rate of electron-hole pairs

anihilation

gr + gT = r

gr

gr – rate of electron-hole pairs

radiative generation

Steady state

constant carrier concentrations

Semiconductor Devices › materials › Semiconductor_ch1.pdf · Department of Semiconductor and...

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Transcript of Semiconductor Devices › materials › Semiconductor_ch1.pdf · Department of Semiconductor and...