cse 477. vlsi systems design - guc · dr. hassan mostafa ىفطصم نسح .د...

ELCT 503: Semiconductors German University in Cairo (GUC)

ELCT503

Semiconductors Fall 2014

Lecture 02: Intrinsic Semiconductors (Cont.)

Dr. Hassan Mostafa

حسن مصطفى. د

hmostafa@aucegypt.edu

Contents

Semiconductors

Crystal structure

Band diagram

Intrinsic carrier concentration

Influence of temperature

Electrons and holes in si

Eg = 1.12 eV

Conduction band

Valence band

electron

Prohibited band

INTRINSIC CARRIER CONCENTRATION

Intrinsic = no impurities (Pure Silicon)

Fermi distribution function F(E):

The probability that an electron occupies an electronic state with energy E

Probability that a hole occupies an electronic state with energy E = 1-f(E)

kTEE F

EF Fermi level

k Boltzmann’s constant

T temperature in kelvins

INTRINSIC CARRIER CONCENTRATION

Electron density n : the number of electrons per unit volume (Units: cm-3)

n(E) = the electron density at energy level E

N(E) = density of states = number of allowed energy states per energy

range per unit volume

Number of electrons in the conduction band:

This looks like you sum the product of each energy level by the

probability of finding electrons in that energy level

f(E)N(E)dEn

Density of energy states

e )E(E)m(h

πN(E)

h E)(E)m(h

πN(E)

in the conduction band:

in the valence band:

where: h – Planc’s constant, [h] = J·s=kg ·m2 · s-1

me – effective mass of electron

mh – effective mass of hole

Density of energy states

There are a large number of allowed states in the conduction band. However, for an intrinsic semiconductor, the probability of an electron occupying one of these states is small. Thus, there will not be many electrons in the conduction band.

There also are a large number of allowed states in the valence band. the probability of an electron occupying one of these states in the valence band is nearly unity. Thus, most of these energy states are occupied by electrons.

Note that there will be only a few unoccupied electron states in the valence band, that is, holes, in the valence band.

Carrier concentration

i f(E)N(E)dEnpn

n(E),p(E)

density of states carrier

concentration

0 1 0.5

Fermi distribution

function

Electrons in conduction band

Total number of electrons in the conduction band:

)/kTE(E

CeNf(E)N(E)dEn

Nc – Effective density of states in the conduction band

kTmπN

For silicon: For gallium arsenide:

k – Boltzman’s constant, [k] = J· K-1

Holes in valence band

Total number of holes in the valence band:

)/kTE(E

V eNN(E)dEf(E)p 1

NV – Effective density of states in the valence band

kTmπN

Fermi level in intrinsic semiconductor

VVCiFi

NkTEEEE ln

)/kTE(E

VVFeNp

)/kTE(E

CFCeNn

inpn Hence:

For an intrinsic semiconductor (thermal equilibrium), the number of

electrons per unit volume in the conduction band is equal to the

number of holes per unit volume in the valence band, that is, n = p =

ni, where ni is the intrinsic carrier density.

Fermi level in intrinsic semiconductor

VVCiFi

NkTEEEE ln

At room temperature, the second term is much smaller than the

bandgap. Hence, the intrinsic Fermi level E, of an intrinsic

semiconductor generally lies very close to the middle of the bandgap.

Intrinsic carrier density

VCgeNNpn

kT/ENNn gVCi 2exp

Influence of temperature on band gap

K636KeV1073.4eV170.1

K204KeV10405.5eV519.1

Influence of temperature on ni

1000K 250K

Summary

VCgeNNpn

)/kTE(E

V eNN(E)dEf(E)p 1

)/kTE(E

CeNf(E)N(E)dEn

Short Break

ELCT503

Semiconductors Fall 2014

Lecture 03: Extrinsic Semiconductors

Dr. Hassan Mostafa

حسن مصطفى. د

hmostafa@aucegypt.edu

content

n-type semiconductors

p-type semiconductors

Mass action law & Charge neutrality

Majority and minority carriers

Influence of temperature on carrier concentration

+5 - -

- - +4

+4 - -

ED donor energy level

Small binding energy to donor atom

EC – ED = Ionization energy

Silicon and other semiconductors

Period II III IV V VI

2 B C N O

3 Mg Al Si P S

4 Zn Ga Ge As Se

5 Cd In Sn Sb Te

6 Hg Pb Bi

donors: pentavalent elements from group V (P,As,Sb,Bi)

→ release of electrons → n-type semiconductor

The most famous are P (Phosphorus) and As (Arsenic)

ionization of donors

complete ionization

of donors:

ionization energy of impurities

S.M.Sze

Again: Intrinsic carrier concentrations

F(E) 0 0.5 1

n(E), p(E)

Fermi distribution

function density of states carrier

concentration

Extrinsic carrier concentrations (n-type)

F(E) 0 0.5 1

n(E), p(E)

Fermi distribution

concentration

f(E)N(E)dEn

Ascending fermi level

DCFC NNkTEE ln

)/kTE(E

CFCeNn

Valence band

Conduction band

Efi = Ei

Electron concentration in doped semiconductor

)/kTE(ENn FCC exp

)/kTE(Enn iFi exp

)/kTE(E)/kTE(EN FiiCC expexp

)/kTEEE(EN FiiCC exp

Valence band

Conduction band

Efi = Ei

DCFC NNkTEE ln

Short Break

- - +4

+4 - -

EA acceptor energy level

EA – EV = Ionization energy

Silicon and other semiconductors

Period II III IV V VI

2 B C N O

3 Mg Al Si P S

4 Zn Ga Ge As Se

5 Cd In Sn Sb Te

6 Hg Pb Bi

acceptors: trivalent elements from group III (B, Al, Ga, In)

→capture of electron→hole remains → p-type semiconductor

The most famous is B (Boron)

ionization of impurities

ionization energy of impurities

complete ionization

of acceptors:

S.M.Sze

Intrinsic carrier concentrations

Fermi distribution

concentration

N(E) 0.5

n(E), p(E) F(E)

Extrinsic carrier concentrations (p-type)

Fermi distribution

concentration

N(E) 0.5

n(E), p(E) F(E)

N(E)dEf(E)p0

Descending fermi level

AVVF NNkTEE ln

)/kTE(E

VVFeNp

Valence band

Conduction band

Efi = Ei

Hole concentration in doped semiconductor

)/kTE(ENp VFV exp

)/kTE(Enp Fii exp

)/kTEEE(EN ViiFV exp

)/kTE(E)/kTE(EN iFViV expexp

Valence band

Conduction band

Efi = Ei

AVVF NNkTEE ln

Mass action law

)/kTE(En)/kTE(Enpn iFiFii expexp

This equation holds for both intrinsic and extrinsic semiconductors

charge neutrality

DA NpNn

In general both acceptors and donors can be present

positive ions negative ions

charge neutrality = zero net charge density

majority and minority carriers

electrons holes

n-doped

(ND > NA)

MAJORITY

carrier

MINORITY

carrier

p-doped

(ND < NA)

MINORITY

carrier

MAJORITY

carrier

Majority and minority carrier (n-type)

majority electrons:

nin nnp /2

1iADADn nNNNNn

DADnAD NNNnNN

minority holes:

inn nnp DnAn NpNn from: and

Majority and minority carrier (p-type)

majority holes:

pip pnn /2

1iDADAp nNNNNp

ADApDA NNNpNN

minority electrons:

ipp nnp DpAp NpNn from: and

Non-degenerate semiconductor

CFCD EENNn

VFVA EENNp

DCFC NNkTEE ln

AVVF NNkTEE ln

The approximations used for f(E) can not be used for degenerate semiconductors

(such as heavily doped semiconductors for which NC < n or NV < p and

Fermi levels lie in the conduction band (n-type) and in the valence band (p-type)),

All the above formulas does not work and the integral should be done numerically

Influence of temperature on carrier concentration

electron temperature vs. temperature

S.M.Sze

cse 477. vlsi systems design - guc · dr. hassan mostafa ىفطصم نسح .د...

Documents

elct 501: digital system design - guc

guc products

advertisement for bids - guc

comm 602 digital signal processing - guc

elct 201: digital logic design - guc

ىفطصم يرهزأ د راثلآا ملع يف...

advertisement for bids - guc brackets... · c4821-a or...

list of eligible guc recipients -...

guc tutorial package (9.0)

popular annual financial report - guc

ةيمرب سيردا نسح فرشأ.د دعاسم...

tour organizing application - guc

anthony robbins sinirsiz guc

sameera baig jessica caron hatice guc nadia islam

ation post system/ / mops.twse.com.tw / guc … ·...

moodle student orientation - guc eguru

worldgn guc bulutlari - solar panel yatirimcisi olun

general study regulations for guc

problem set 5 solution - guc

table of content - guc-asic.com · center ai training chip...