05 alloy hetero

Semiconductor alloys and heterostructures

Fabrizio Bonani

Dipartimento di ElettronicaPolitecnico di Torino

High speed electron devices Semiconductor alloys and heterostructures

Contents

1 Heterostructure definition

2 Semiconductor alloysThe substrate issue

3 Heterostructures

4 Free charge spatial confinement

5 Conductive channels and modulation doping


Epitaxial growth of different crystals

The epitaxial growth of crystalline materials with differentlattice constant leads to

� interface defects (misfit dislocations)� presence of traps for electrons and holes

If the mismatch between the lattice constants is small/nullan (almost) ideal crystal based on two different materials isobtained⇒ heterostructure� since the properties of the two materials are in general

different, it is also called heterojunctionThe different electrical and optical properties of the layershave important consequences� band discontinuities (potential wells, one or many): spatial

confinement of free carriers� refractive index discontinuities: spatial confinement of

electromagnetic field (photons)


Strained heterostructures

In presence of a small difference in lattice constants, theheterostructure is called strained, or pseudomorphic

a > aL S

a < aL S

Substrate

Epitaxial layerNonepitaxial

growth Pseudomorphic

layer

Substrate

Epitaxial layerPseudomorphic

layer Nonepitaxial

growth

compressive strain

tensile strain


Contents



3 Heterostructures




Semiconductor alloys

Heterostructures are often based on semiconductor alloys,in order to create materials whose properties areintermediate with respect to the “natural” semiconductorcomponents

� for most applications, the main features are lattice constantand energy bandgap

Alloys are often mixtures of compound semiconductorssuch as GaAs, InP, InAs etc.� ternary alloys: realized by two components and three

elements (e.g. AlGaAs, alloy between GaAs and AlAs)� quaternary alloys: realized by four components and

elements (e.g. InGaAsP, alloy among InAs, InP, GaAs andGaP)

In many cases, the alloy characteristics are wellapproximated by a linear combination (or bilinear, forquaternary alloys) of the initial components values


Alloys: composition rules

Compound semiconductors are made of a metal M and anonmetal NTernary alloys are made of two compound semiconductorssharing a metal or a nonmetal(M(1)N

)x

(M(2)N

)1−x

= M(1)x M(2)

1−xN e.g.: AlxGa1−xAs(MN(1)

)y

(MN(2)

)1−y

= MN(1)y N(2)

1−y e.g.: GaAsyP1−y

Quaternary alloys are made of four compoundsemiconductors sharing two metal and two nonmetalcomponents(

M(1)N(1))α

(M(1)N(2)

)β

(M(2)N(1)

)γ

(M(2)N(2)

)1−α−β−γ

= M(1)α+βM(2)

1−α−βN(1)α+γN(2)

1−α−γ

= M(1)× M(2)

1−xN(1)y N(2)

1−y e.g.: InxGa1−xAsyP1−y


Alloys: Vegard law

In many cases (not always!) an alloy property P is thelinear combination (Vegard law) of the components’ sameproperty:

P = xP(1) + (1− x)P(2) (ternary alloy)

P = xP(1) + (1− x)P(2) + yP(3) + (1− y)P(4) (quaternary alloy)

Main exceptions are:

� in some cases, a quadratic correction to the simple linearinterpolation is required (Abeles law)

� for some parameters, a global (i.e., valid for all compositionvalues) interpolation formula is not available because ofstructural discontinuities

I e.g.: an alloy may pass from direct to indirect bandgap as afunction of composition


Matched, pseudomorphic and metamorphic layers

Any layer/epitaxial structure must be grown on a crystallinesubstrate� with the same (lattice matched layer) or with a slightly

different lattice constant (pseudomorphic layer)� with a different lattice constant. To avoid dislocations, a

buffer layer with graded composition (graded layer) isplaced between the substrate and the top layer(metamorphic approach)

For non-matched layers, a critical thickness of the epitaxiallayer exists beyond which structural stability is lost� the critical thickness is a decreasing function of the lattice

constant mismatch


Substrate examples

Substrate examples (in cost increasing order) are:� Si: good for SiGe heterostructures and for GaN growth� GaAs: good for high frequency electronic applications� InP: good for high frequency and large power density

electronic applications, and for large wavelengthoptoelectronic applications

� SiC: good for very large power applications and for GaNgrowth

Alloys are often represented on bandgap - lattice constantgraphs� ternary alloys are repreesented by curves (one degree of

freedom: composition x)� quaternary alloys are represented by surfaces (two degrees

of freedom: compositions x and y )


Eg−composition diagram: SiGe and III-V compounds

Bandgap, eV

GaSb

Ge

Si

InSb

CdTe

HgTe

5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6

Lattice constant, Å

AlAs

Al In As0.48 0.52

GaP

GaAsInP

InAsDirect bandgapIndirect bandgap

2.8

2.4

2.0

1.6

1.2

0.8

0.4

0.0

Wave

length

, mm

0.5

0.6

0.7

0.80.91.0

1.2

1.5

2.0

3.05.010.

Ga In As0.47 0.53


Eg−composition diagram: GaN

4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6 6.20

1

2

3

4

5

6

7

0.2

0.3

0.4

0.5

1.0

2.0

5.0

AlN

GaN

InN

AlP

GaP

AlAs

GaAs

InP

InAs

UV

IR

Visible

Direct bandgapIndirect bandgap

AlGaN

InGaN

Lattice constant, Å

Bandgap, eV

Wave

length

, mm


Contents



3 Heterostructures




Affinity rule


The behaviour of aheterostructure dependson the band structuredifference between thematerialsWe define

� the affinity difference∆χ = χB − χA

� the bandgap difference∆Eg = EgB − EgA

EgA EgB

qcA

|DE |c

|DE |v

Ec

Ev

U0

qcB

Material A Material B

In the ideal structure, we can evaluate the conduction andvalence band discontinuities according to the affinity rule∆Ec = EcB − EcA = (EcB − U0)− (EcA − U0)

= −qχB + qχA = −q∆χ

∆Ev = EvB − EvA = (EcB − EgB)− (EcA − EgA) = −q∆χ−∆Eg

Heterostructure types

EgA EgB

DE >0c

Ec

Ev

DE <0v

EgA

EgB

Ec

Ev

EgA EgB

DE =0c

Ec

Ev

EgA

EgB

Ec

Ev

Type I Type II

Type IIa Type III

DE <0v

DE <0c

DE <0v

DE <0v

DE <0c


Heterojunction band diagram

Reaching thermal equilibrium in a heterojunction implies anet electron movement for the material with larger (whenisolated) Fermi energy towards the material with lower(when isolated) Fermi level� the same phenomenon can be interpreted in terms of a net

flux of holes moving in the opposite direction� such a movement doesn’t take place if the two materials

have the same workfunctionMobile charge transfer creates not neutral regions, andtherefore a not flat band diagram� if majority carriers are moved, the not neutral region has

dimension of the order of the Debye length� if minority carriers are moved, normally depleted regions

are formed� the built-in potential qVbi = qΦSB − qΦSA drops on the not

neutral region (Vbi is normally given in absolute value)


Heterojunction between intrinsic materials

U0

EFBEFA

el

EvB

EcB

EvA

EcA

U0

EF

Ev

Ec

Type I

U0

EFB

EFA

EvB

EcB

EvA

EcA

U0

EF

Ev

Ec

Type II

lac D= qDc + g

2

EqVbi

el

lac


nn heterojunction

U0

EF

Ev

Ec

Type I

U0

EF

Ev

Ec

Type II

U0

EFB

EFA

EvB

EcB

EvA

EcA

U0

EvB

EcB

EFBEFA

EvA

EcA

= qDc +qVbi logN NcB DAk TB

æçè

ö÷øN NcA DB


pp heterojunction

Type I Type II

U0

Ev

Ec

U0

EvB

EcB

U0

Ev

Ec

U0

EvB

EcB

EvA

EcA EvA

EcA

EFB

EFA EFB

EFA

D= qDc +gEqVbi

logN NvB AAk TB

æçè

ö÷øN NvA AB

+

EF

EF


Type I pn heterojunction

Type I Type In p p n

U0

EvB

EcB

EvA

EcA

EFB

EFA

U0

EvB

EcB

EvA

EcA

EFB

EFA

U0

Ev

Ec U0

Ev

EcEF EF

= qDc -gAEqVbi

logN NcB vAk TB

æçè

ö÷øN NAA DB

+


Contents



3 Heterostructures




Potential energy wells

Heterojunctions among materials with different bandgapallow to realize potential energy wells in the conductionand/or valence bands� if the potential well is narrow enough, quantized energy

levels may take place� within the effective mass approximation, such quantum

structures can be studied using point mass quantummechanics

I the lattice effect is included in the effective mass


Quantum structures

in 3D space, several degrees on confinement are possibleto limit the free carrier motion in a potential well:� 1D confinement (quantum well): if the well takes place in

one spatial direction only. Carriers may move in the twoother directions (two-dimensional gas)

� 2D confinement (quantum wire): if the well takes place intwo spatial directions. Carriers may move in the thirddirection

� 3D confinement (quantum dot): if the well takes place inthree spatial directions. Carriers cannot move


Quantum well and quantum wire

U ( x , y )

x

y

v y , v z

U ( x , y )

x

y

v z

Q u a n t u m w e l l Q u a n t u m w i r e


Density of states in a quantum well

In a confined structure, the density of available states isdifferent than in free spaceFor a quantum well whose allowed energy states are Elone finds

g2D(E) =∑

l

4πm∗

h2 u(E−El) per unit area and unit energy

where u(α) is the step function (0 if α < 0, 1 if α > 0)For electrons in thermal equilibrium, the electron densityper unit area occupying the various levels is

ns =

∫ +∞

Ec

g2D(E)f (E) dE

=4πm∗kBT

h2

∑l

log[1 + exp

(EF − El

kBT

)]


Comparison with the 3D density of states

E-Ec E1 E2 E3 E4

g2D dg3D

d: well thickness


Superlattice

The presence of several coupled quantum wells resultsinto an increased number of allowed energy statesAn infinite (periodic) number of coupled quantum wellsintroduces into the conduction and valence bands asubband structureSuch an artificial structure is called superlattice


Superlattice: band structure

a

A

E g 1 E g 2

E c

E v


Contents



3 Heterostructures




MOdulation doping heterostructure

Carriers spatial confinement properties in the directionorthogonal to the growth axis allow to exploit atwo-dimensional carrier gas as an FET conductive channelTo improve free carrier mobility, modulation doping is used� only the large bandgap layer(s) is(are) doped� the channel takes place in the low bandgap material, which

is intrinsic thus with less scattering events for free carriers(larger mobility)

� at thermal equilibrium, free charges (electrons) provided bydopants populate the potential well at lower energy,creating a spatially confined two-dimensional gas

Actually, the real advantage is not strictly related to themobility improvement (important at low temperature only).Rather, free carriers are much better confined into thechannel


Single and double heterostructure channels

U0

EF

Ev

EcED E1

qcDEc

E0

qND

x

+

-

donor fixed charge

2D electron gas

qND

x

donor fixed charge

2D electron gas

+

U0

EF

Ev

EcEDE1

E0

Single heterostructure Double heterostructure


05 alloy hetero

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