electronic devices - scalak · 2014. 3. 21. · 8 ke g kt e n i t at 2e 2 3 n 300 k 3 1.5 1010cm i...

2014-03-21

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ELECTRONIC DEVICES

Piotr Dziurdzia, Ph.D. C-3, room 413; tel. 617-27-02, [email protected]

AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY IM. STANISŁAWA STASZICA W KRAKOWIE

Faculty of Computer Science, Elelctronics and Telecommunications

DEPARTMENT OF ELECTRONICS

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EiT PD Electronic devices - physics of semiconductors 2

PHYSICS OF

SEMICONDUCTORS

…….. a journey in searching „carriers-conductors” of electrical current ……

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AFTER THIS CHAPTER WE SHOULD EASIER UNDERSTAND WHY:

- in field effect semiconductor devices, the current-voltage characteristics are expressed by square relations ?

- in the junction semiconductor devices, the current-voltage characteristics are expressed by exponential relations ?

- in semiconductors, almost everything depends on

temperature T, which sometimes is called as super parameter ?

R=f(U, I, T)

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WHAT ARE WE GOING TO TALK ABOUT ?

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SEMICONDUCTOR MATERIALS

THE CLASSIFICATION OF MATERIALS IN TERMS OF ELECTRICAL CONDUCTIVITY

S

l S

l

S

lR

1

conductivity

resistivity

m

1

m

INSULATORS

SEMICONDUCTORS

METALS

10E+6(Ωm)E-1 10E-6(Ωm)E-1

12 orders of magnitude!

(in room temperature)

ρ ~ T ρ ~ exp(-T)

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Semiconductors - their important feature is that the conductivity may vary over a wide range due to changes in temperature, light or introduced dopants

IV

C Si Ge Sn

V

P As Sb

III

B Al Ga In

III-V

AlP AlAs GaP

GaAs GaSb

Elementary semiconductors

Complex semiconductors

SEMICONDUCTOR MATERIALS

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SILICON ATOM

+4

According to Niels Bohr’s theory of an isolated atom, the electrons can have strictly defined energy levels expressed in a quantum way:

2

0

22

4

8 hn

mZeE e

atomic number of the element (ZSi=14)

elementary charge of the electron (1.6E-19C)

mass of the electron (1.78E-31kg)

the number of electron shell Planck constant

(6.625E-34Js)

permittivity of the vacuum (8.854E-12F/m)

E

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+4 +4 +4 Sicm31 atoms2310

eV1 eV2310

If the band gap

is: the distance between

energy levels

x

E

+4

SILICON ATOMS

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EV

EC


+4

+4

+4

+4 +4

+4

+4

+4

+4

+4

+4

+4

+4 +4 +4

+4 +4 +4

+4 +4 +4

+4

+4

+4

Two-dimensional model of a semiconductor from IV group

in temperature T=0K

Energy band model

e- e- e- e- e-

valence band

conduction band

np. for Si Eg=1.1eV for Ge Eg=0.67eV

eVEEE gVC energy gap

SEMICONDUCTOR MODELS INTRINSIC SEMICONDUCTORS

e- e-

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in temperature T>0K

e-

e-

e- e- e-

e-

e- EV

EC

generation recombination

+4 +4 +4

+4 +4 +4

+4 +4 +4

+4

+4

+4

Generation of electron-hole pairs can occur, for example under the influence of heat, light, radiation, ionization collision

SEMICONDUCTOR MODELS INTRINSIC SEMICONDUCTORS

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BAND MODEL OF ELECTRIC CONDUCTION

INSULATORS

METALS

e-

e-

e- e-

Eg3eV e- e-

e- e-

SEMIONDUCTORS

10E+6(Ωm)E-1 10E-6(Ωm)E-1

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STATISTICS IN SEMICONDUCTORS

What is the probability that an electron takes any energy state (level) E in

absolute temperature T ?

kT

EE F

e

Ef

1

1

Fermie-Dirac’s function

k=8.62E-5eV/K=1.38E+23J/K - Boltzmann’s constant

What is EF ? 21

1

1

kT

EEF FF

e

Ef

Energy state located at the Fermie’s level can be taken by an electron with the probability of 0.5

E

f(E)

EF

0.5

T=0K

T1

T2

T1>T2

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How can we determine the concentrations of electrons and holes in a semiconductor unit volume?

electrons holes

kT

EEn F

e

Ef

1

1

kTEE

n

F

eEf

dla |E-EF|>3kT

kT

EEp F

e

Ef

1

1

kTEE

p

F

eEf

dla |EF-E|>3kT

The energy density of available energy states for electrons in the conduction band:

Ce

C EEh

mEN

3

2

3*24

The energy density of available energy states for electrons in the valence band:

EEh

mEN V

hV 3

2

3*24

*em effective mass of the electron *

hm effective mass of the hole

C

FC

E

kT

EE

CnC eNdEEfENn

V VF

E

kT

EE

VpV eNdEEfENp

2

3

2

*22

h

kTmN eC

effective density of energy states in the conduction band

2

3

2

*22

h

kTmN hV

effective density of energy states in the valence band


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In intrinsic semiconductor:

inpn

kTE

kT

EE

VCi

gVC

eATeNNnpTn 223

2

43

**

2

4hemm

hA

The law of mass:

npni 2


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kTE

i

g

eATTn 223

310105.1300 cmKni31mmso, in we can find

15 millions of free electrons !!!

and the same number of holes ;))

Sicm31In there is

atoms2310


CURIOSITY I

If the average thermal energy Et

= kT of an electron at room

temperature T = 300K, is

Et = 0.025 eV, then how they can

overcome the energy gap?

Sufficient energy to overcome the energy gap in

silicon at room temperature has one electron to

1.5x10E+13 atoms!!!

In silicon the energy

gap is: Eg=1.1eV

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we should calculate:


CURIOSITY II

What is the sensitivity of free electrons and holes

concentration changes in the intrinsic silicon at

the ambient temperature T = 300K?

222

3

kT

E

Tn

dT

dn

g

i

i

i

W. Janke, „Zjawiska termiczne w elemntach i układach półprzewodnikowych”, WNT1992

after substituting the data

we obtain : %3.8300 Ki

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DOPED SEMICONDUCTORS

At room temperature, electrons pass from the donor band to the conduction band. After losing an electron, dopant atoms will be positive ions.

+4 +4 +4

+4 +4 +5

+4 +4 +4

+4

+4

+4

+5 Donor dopant, for example: P, As, Sb

e-

e-

e- e- e-

e-

e- EV

EC ED

e-

e-

e-

e- e- e- e- e- e- e-

0.05eV

e-

n (number of electrons) ≈ N (the number of dopant atoms) In doped n-type semiconductor, electrons are the majority

carriers and holes the minority ones!

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+4 +4 +4

+4 +4 +3

+4 +4 +4

+4

+4

+4

+3 Acceptor dopant, for example: B, Al, Ga, In

At room temperature the electrons from the valence band pass on the orbits of the dopant atoms. Upon receipt the electrons, the dopant atoms become negative ions.

p (number of holes) ≈ NA (the number of dopant atoms) In doped p-type semiconductor, holes are majority carriers

and electrons the minority ones!

e- EV

EC

EA

e-

0.05eV


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Condition of electrical neutrality: the introduction of dopants into the semiconductor can not change the total charge load, which is in

equilibrium and must be equal to zero.

0 AD NpnN

Dn Nn

Ap Np

D

in

N

np

2

A

ip

N

nn

2

From the law of mass we can determine the concentration of free carriers for a known concentration of dopants:

for donor semiconductors:

for acceptor semiconductors:


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The introduction of dopants causes changes in the position of the Fermi level

The position of the Fermi level is also a function of temperature

NA ND

EF

0 NA=0 ND=0

Ei

EC

EV


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Temperature dependence of carrier concentration in the donor semiconductor

Ge Si

T[K] 100 200 300 400 500

ND

Nu

mb

er

of

fre

e e

lect

ron

s

Doping causes a stabilization of a number of carriers at a relatively high temperature range!

spontaneous generation


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Sicm31In there is

atoms2310


CURIOSIY III

What will be the effect of doping: 1 arsenic atom (As +5)

to 1 million silicon atoms (Si +4) ???

After doping we obtain

17

6

23

1010

10 arsenic atoms

and the same number of free electrons

in room temperature!

mSi 3102

mAsSi

3102

6

3

3

10102

102

AsSi

Si

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ELECTRICAL CONDUCTIVITY IN SEMICONDUCTORS

In the absence of an electric field the electrons follow a chaotic motion. At room temperature, the average thermal velocity is

about ….

?

s

m5102

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Upon application of an external electric field, there appears a uniform movement of electrons – drifting the free carriers in an electric field. At room temperature the velocity of transport is about … ?

s

m34 1010

e- e-

e-

e-

e- e- e- e- e- e- e-

E

contact


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I E

S

Drift current density – 1-D considerations

SdtvepSdtvendQ pn

electric charge flowing through a surface S during time dt:

pn vepvenJ dt

dQ

SJ

1

current density:

EJ

according to Ohm’s Law:

pn pne so, the conductivity:

Ev nn

Ev pp

mobility of electrons

for silicon µn≈3µp

mobility of holes


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Diffusion of electric carriers e-

e-

e- e-

e-

e-

e- e-

e- e-

e-

x

n(x)

0

dx

xdn

Diffusion currents occur in the states of imbalance in a semiconductor material where the carrier concentration becomes heterogeneous. The electric carriers move from an area of high concentration to the area of low concentration, until the distribution of free carriers is homogenous.

dx

xdnqDJ

diffusion coefficient


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KTmVUe

kTDDT

p

p

n

n 30026

dx

xdnDeEenJ nnn

drift

dx

xdpDeEepJ ppp

diffusion


electronic devices - scalak · 2014. 3. 21. · 8 ke g kt e n i t at 2e 2 3 n 300 k 3 1.5 1010cm i...

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