Semiconductors

Institute of Solid State PhysicsTechnische Universität Graz

Semiconductors

32

exp300

cc

B

ETn Nk T

32

exp300

vv

B

ETp Nk T

density of electrons in the conduction band

density of holes in the valence band

effective density of states in the conduction band at 300 K

effective density of states in the valence band at 300 K

The electrical contribution to the thermodynamic properties of insulators depend on band edges

http://lamp.tu-graz.ac.at/~hadley/ss1/semiconductors/intrinsic.php

Narrow bandgap semiconductors

Ev Ec

Use the programs for metals for small bandgap semiconductors.

Large gap -> large effective mass

22

2

*

2

1

d E tadk

mt

2 cos( )kE t ka

narrow bands -> large effective mass

2*

2

2

md Edk

Measuring the effective mass

*ceBm

Cyclotron resonance

Resonant absorption occurs when rf waves with the cyclotron resonance frequency are applied. This can be used to experimentally determine the effective mass.

Knowing the effective mass, the scattering time can be calculated from the measured conductivity.

2

*scne

m

direct bandgap:k = 0

photons can be emitted

indirect bandgap:k = 0

phonons are emitted

Direct and indirect band gaps

Momentum must be conserved when photons are absorbed or emitted.

Light emitting diodes

Extrinsic semiconductors

The introduction of impurity atoms that can and electrons or holes is called doping.

n-type : donor atoms contribute electrons to the conduction band. Examples: P, As in Si.

p-type : acceptor atoms contribute holes to the valence band. Examples: B, Ga, Al in Si.

Ionization of dopants

Easier to ionize a P atom in Si than a free P atom

4

2 2 208nmeE

h n

2*0

0r

mm

Ionization energy is smaller by a factor:

Ionization energy ~ 25 meV

images from wikipedia

Czochralski Process

add dopants to the melt

Crystal growth

Neutron transmutation

30Si + n 31Si + 31Si 31P +

image from wikipedia

Float zone Process

Crystal growth

image from wikipedia

Chemical vapor deposition

Epitaxial silicon CVD SiH4 (silane) or SiH2Cl2 (dichlorosilane)PH3 (phosphine) for n-doping or B2H6 (diborane) for p-doping.

http://www.microfab.de/foundry/services/diffusion/index.html

Gas phase diffusion

AsH3 (Arsine) or PH3 (phosphine) for n-doping B2H6 (diborane) for p-doping.

Ion implantation

Implant at 7º to avoid channeling

Donors

Five valence electrons: P, As

States are added in the band gap just below the conduction band

Ec

Eg

Ev

ED

n-type: n ~ ND Many more electrons in the conduction band than holes in the valence band.

majority carriers: electrons; minority carriers: holes

D(E)

(T=0)

Acceptors

Three valence electrons: B, Al, Ga

States are added in the band gap just above the valence band

Ec

Eg

Ev

EA

p-type: p ~ NA Many more holes in the valence band than electrons in the conduction band.

majority carriers: holes; minority carriers: electrons

(T=0)

D(E)

Donor and Acceptor Energies

Energy below the conduction band Energy above the valence band

n-type

For n-type, n ~ density of donors, p = ni

2 /n

n-type ND > NA, p ~ 0

exp cD c

B

En N Nk T

ln cc B

D

NE k TN

p-type

For p-type, p ~ density of acceptors, n = ni

2/p

p-type NA > ND, n ~ 0

exp vA v

B

Ep N Nk T

ln vv B

A

NE k TN

exp2

gi v c

B

En N N

k T

Intrinsic semiconductors

intrinsicextrinsic

freeze-out

1/T

log 1

0(n i

) cm

-3

GaAs

Si

Ge

300 K

Extrinsic semiconductors

At high temperatures, extrinsic semiconductors have the same temperature dependence as intrincic semiconductors.

Energy spectra of donors in silicon

Ionized donors and acceptors

For Ev + 3kBT < < Ec- 3kBT Boltzmann approximation

1 4exp

AA

A

B

NNE

k T

1 2exp

DD

D

B

NNE

k T

4 for materials with light holes and heavy holes (Si)2 otherwise

Mostly, ND+ = ND and NA

- = NA

ND = donor density cm-3 ND+ = ionized donor density cm-3

NA = donor density cm-3 NA- = ionized donor density cm-3

Charge neutrality

n + NA- = p + ND

+

Carrier concentration vs. Fermi energy

Why dope with donors AND acceptors?

collector base emitter

n pn+

lightly doped p substrate

Bipolar transistor

MOSFET

Bipolar Junction Transistor