Institute of Solid State Physics Technische Universität Graz

Extrinsic semiconductors

The introduction of impurity atoms that can add 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. Institute of Solid State Physics Technische Universität Graz n and p

The electron density and hole density are: EE EEFc vF nN exp pN v exp c  kT kTB B

The law of mass action:

2 Eg np nivc N N exp  kTB Ionization of dopants

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

me4 En  222 8 0 hn

2 m*  Ionization energy is smaller by a factor: 0 m  r 0

Ionization energy ~ 25 meV acceptors in Si donors in Si Crystal growth

Czochralski Process

add dopants to the melt

images from wikipedia Crystal growth

Float zone Process

Neutron transmutation

30Si + n  31Si +  31Si  31P + 

image from wikipedia Gas phase diffusion

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

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

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

image from wikipedia Ion implantation

Implant at 7º to avoid channeling http://www.synopsys.com Donors

Five valence electrons: P, As States are added in the band gap just below the conduction band

E c EF(T=0) ED

Eg

Ev

D(E)

n-type: n ~ ND Many more electrons in the conduction band than holes in the valence band. majority carriers: electrons; minority carriers: holes Acceptors

Three valence electrons: B, Al, Ga States are added in the band gap just above the valence band

Ec

Eg E A E (T=0) Ev F

D(E)

p-type: p ~ NA Many more holes in the valence band than electrons in the conduction band. majority carriers: holes; minority carriers: electrons Donor and Acceptor Energies

Energy below the conduction band Energy above the valence band

Temperature dependence

Intrinsic

Extrinsic p  NA

kTBD E

Freeze-out 200 K 1000 K Eg nNNivcexp kTB n-type

n-type ND > NA, p ~ 0

EEF  c nNDc Nexp kTB

Nc EEkTFcB ln  ND

For n-type, n ~ density of donors, 2 p = ni /n p-type

p-type NA > ND, n ~ 0

EEvF pNAv Nexp kTB

Nv EEkTFvB ln  N A

For p-type, p ~ density of acceptors, 2 n = ni /p Intrinsic / Extrinsic

Intrinsic: n = p Conductivity strongly temperature dependent near room temperature

Extrinsic: n ≠ p Conductivity almost temperature independent at room temperature Intrinsic semiconductors Extrinsic semiconductors

intrinsic extrinsic

-3 Ge ) cm ) i n ( Si freeze-out 10

log GaAs

At high temperatures, extrinsic 1/T semiconductors have the same 300 K temperature dependence as intrinsic semiconductors. Eg nNNivcexp 2kTB Why dope with donors AND acceptors?

Bipolar transistor

collector base emitter

n+ p n

lightly doped p substrate MOSFET

Bipolar Junction Transistor Ionized donors and acceptors

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

 N D  N ND  A EE N A  FD EE 12exp  14exp AF kTB  kTB 4 for materials with light holes and heavy holes (Si) 2 otherwise

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

+ - Mostly, ND = ND and NA = NA Charge neutrality

Carrier concentration vs. Fermi energy

- + n + NA = p + ND Calculating EF(T) numerically http://lamp.tu-graz.ac.at/~hadley/psd/L4/eftplot.html degenerately doped semiconductor Degenerate semiconductor

Heavily doped semiconductors are called degenerately doped

ND > 0.1 Nc -> EF in the conduction band

NA > 0.1 Nv -> EF in the valence band

Heavy doping narrows the band gap

The Boltzmann approximation is not valid

Degenerate semiconductors = metal

Institute of Solid State Physics Technische Universität Graz Carrier Transport

Ballistic transport Drift Diffusion Generation and recombination The continuity equation High field effects Ballistic transport

    dv FmaeEm dt   eEt  vv  m 0   eEt 2  xvtx  2m 00

Electrons moving in an electric field follow parabolic trajectories like a ball in a gravitational field.