hetrojunction

8/9/2019 HetroJunction

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SEMICONDUCTOR HETEROJUNCTIONS

Nezih Pala [email protected] EEE 6397

Semiconductor Device Theor19

Ap-n junctionis formed when a p-type doped portion of the semiconductor is

d with an n-type doped portion. As a fundamental component for functionssuch as rectification, the p-n junction forms the basic unit of a bipolar transistor.

If both the p-type and the n-type regions are of the same semiconductor

material, the junction is called a homojunction.If the junction layers are made of

different semiconductor materials, it is a heterojunction.

As a matter of convention, if the n-type doped semiconductor material has

larger energy gap than the p-type doped material, it is denoted a p-N

heterojunction.

The use of capital and lowercase Ietters connotes the relative size

the energy gap. Conversely, if the p-type doped material has a larger energygap than the n-type material, the junction is referred to as a P-n heterojunction.


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Heterojunctions -2

20

When semiconductors of different band gaps, work

functions, and electron affinities are brought

together to form a junction, we expectdiscontinuities in the energy bands as the Fermi

levels line up at equilibrium . The discontinuities in

the conduction band ECand the valence band EV

accommodate the difference in band gap between

the two semiconductors Eg.

In an ideal case, ECwould be the difference in

electron affinities q(2- 1), and Evwould be found

from Eg- ECThis is known as theAnderson

affinity rule.

In practice, the band discontinuities are found experimentally for particular semiconductor

pairs.

VC

ggg

EE

EEE

21


Semiconductor Device Theor


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Heterojunctions -4

21

To draw the band diagram, we need:

and

The electron affinity and work functionare

referenced to the vacuum level. The electron affinity

and work function are referenced to the vacuum

level.

dopingNOTmaterial,torsemiconducondepend

)(affinityelectron)(Egapband g

dopingANDmaterial

torsemiconducondepends

functionWork

The true vacuum level(or global vacuum level), Evac, is the potential energy reference when

an electron is taken out of the semiconductor to infinity, where it sees no forces. Hence, the

true vacuum level is a constant




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Heterojunctions -5

22

However, since the electron affinity is a

material parameter and therefore constant

we need to introduce the new concept ofthe local vacuum level, Evac(loc), which

varies along with and parallel to the

conduction band edge, thereby keeping the

electron affinity constant. The local vacuum

level tracks the potential energy of an

electron if it is moved just outside of the

semiconductor, but not far away.

The difference between the local and global vacuum levels is due to the electrical work doneagainst the fringing electric fields of the depletion region, and is equal to the potential energy

qV0due to the built-in contact potential V0in equilibrium. This potential energy can, of

course, be modified by an applied bias.

P-side n-side




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Heterojunctions -6

23

To draw the band diagram for a heterojunction accurately, we must not only use the proper

values for the band discontinuities but also account for the band bending in the junction.

To do this, we must solve Poisson's equation across the heterojunction, taking into account

the details of doping and space charge, which generally requires a computer solution. We

can, however, sketch an approximate diagram without a detailed calculation. Given the

experimental band offsets EVand EC, we can proceed as follows:

1.Align the Fermi level with the two

semiconductor bands separated.

Leave space for the transition region.




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Heterojunctions -7

24

2.The metallurgical junction (x = 0) is located

near the more heavily

doped side. At x = 0 put EVand EC, separated

by the appropriate

band gaps.

3. Connect the conduction band and valence

band regions, keeping t he

band gap constant in each material.

Steps 2 and 3 of this procedure are where the exact band bending is important and must be

obtained by solving Poisson's equation. In step 2 we must use the band offset values EVand

ECfor the specific pair of semiconductors in the heterojunction.




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Heterojunctions -8

25

As a result, electrons collect on the GaAs side of the heterojunction and move the Fermi

level above the conduction band in the GaAs near the interface. These electrons are

confined in a narrow potential well in the- GaAs conduction band. If we construct a device

in which conduction occurs parallel to the interface, the electrons in such a potential well

form a two-dimensional electron gas with very negligible impurity scattering in the GaAs

well, and very high mobility controlled almost entirely by lattice scattering (phonons).

Consider heavily n-type AlGaAs is grown

on lightly doped GaAs where the

discontinuity in the conduction bandallows electrons to spill over from the N+-

AlGaAs into the GaAs, where they become

trapped in the potential well.




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p+-N Heterojunction under equilibrium -1

Nezih Pala [email protected] EEE 6397Semiconductor Device Theory 26

Consider, for example, a p-N heterojunction formed with a p-type GaAs layer doped at

3x1019

cm-3

and an N-type AIGaAs layer doped at 1x1016

cm-3

The band diagrams of individual layers are shown in the figure side by side with their

vacuum levels aligned to illustrate the difference in the Fermi levels in the charge-

neutral condition .


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When the two regions are brought into contact, the Fermi level on the N side is

initially higher than that on the p-side. Therefore, the electrons in a p-N junction lend toflow from regions of higher Fermi level (N regions) to regions or lower Fermi levels (p

regions).

On the other hand, the holes flow from the region with a lower Fermi level toward the

region with a higher Fermi level. Therefore, the holes flow from the p- type layer toward

the N-type layerconsistent with the fact that there are more holes in the p-typeregion and they tend to diffuse to the region with less holes.

As these mobile carriers move toward the other sides, they leave behind the

uncompensated dopant atoms near the junction. In the p-type region, the

uncompensated acceptors are negative ions.In the N-type region, the uncompensated

donors are positive ions.Therefore, the carrier diffusion results in a electric field pointingfrom the N-type region to the p-type region. This electric field retards further electron

diffusion from the N-type toward the p-type as well as hole diffusion in the opposite

direction. Hence, there is a natural negative feedback mechanism such that the more

carrier movement takes place, the larger the electric field becomes and the tendency of

the carrier movement is reduced.


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Eventually, an equilibrium condition sets in and the tendency of the carrier diffusion isexactly counterbalanced by the electric field that impedes the carrier movement.

At this precise movement, the Fermi levelsat the two regions are aligned.The above

exchange of carriers occurs on a very short time scale. So the whole process can be

thought of as instantaneous.

The two side immediately adjacent to the junction where the dopants become

uncompensated are called the depletion region, meaning that they are depleted of

mobile carriers. (Another name for the depletion region is the space-charge region).

At the two extreme ends away from the actual junction, carrier movement has never

occurred. Their dopant atoms are still compensated by their respective electronsor holes. These are called the neutral regions because the net charge concentrations

there are zero.


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Fermi level during thermal

equilibrium lines up throughout

the entire semiconductor.

At regions far away from the

junction where the semiconductor

remains neutral, the relative

positions of Efwith respect to

Ec and to Ev are unmodified fromthose prior to the joining of the

two sides.

The conduction and valence band

edges at the sides are not at the

same level, since it is the Fermilevel that must be aligned.

The conduction and valence band edges across

the depletion region must be connected

somehow to form continuous curves.


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The Poisson equation must be solved to ascertain the manner in which the conduction and

valence band edges are connected across the depletion region:

)( adS

NNnpq

dx

d

Considering that, in the p-side depletion region, the net charge concentration is the negative

acceptor density and in the N-side depletion region the net charge concentration

is the donor density (depletion approximation). Therefore, the last equation simplifies to

Let us define that x = 0 correspond to the junction boundary, with the p side in the

-x direction and the N side in the + x direction. Moreover, x = - Xpo is the boundary separating

the neutral and the depletion regions on the p side, and XN0the boundary on the N side. The

subscript 0 emphasizes that we are considering the thermal equilibriumcondition.

0

0

0for

0for

Nd

N

pa

p

XxNq

dx

d

x-XNq

dx

d


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After integrating and applying the boundary conditions that the electric fields at Xp0and at

XN0are zero, the electric field within the depletion region can be found as

00

00

0forx)-()(

0for)(x)(

NNd

N

ppa

p

XxXNq

x

x-XXNq

x

In the p-side, thepotential profileis obtained by integrating (x)

0forCx)2

x()()( 00

2

x-XXNq

dxxxV ppap

Since it is the relative value or potentials rather than their absolute values that is of

importance, we arbitrarily define the zero potential at a convenient location, namely,

at x =-Xpo.With the boundary condition that V(- Xpo) = 0, V(x) is written as

0for)2

Xx

2

x()( 0

2

p0

0

2

x-XXNq

xV ppap


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The built-in potential on the p side (p0 ) is the difference in the potentials at x=0 and x=-Xp0. It

is readily verified that

X2

2

p00 a

p

p Nq

where p0is a positive number. The band diagram, being an energy diagram for the

negatively charged electron, shows that the electron energy decreases with the associated

increase in V(x).Similarly the potential profile on the N side can be obtained by integrating the appropriate

electric profile. Taking the boundary condition that V(0) = p0,

0p0

2

0 0for2

x-x)( NNd

N

XxXNq

xV

The built-in potential on the N side ( N0 ) is the difference in the potentials at

x = 0 and x = XN0. V(XN0) - V(0) is then equal to

X2

2

N00 d

N

N Nq


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The overall built-in junction potential (bi) is the potential difference from the neutral region

on one side the neutral region on the other. It is equal to

X2

X2

2

p0

2

N000 a

p

d

N

pNbi Nq

Nq

Xp0and XN0 can be determined by solving two linearly independent equations relating these

two variables. One of the required equations is obtained by enforcing the continuity of the

electric flux density D =in the absence of an interfacial charge density at the junction:

XX p0N0 ad NN

The equality ensures that charge neutrality exists in the overall p-N junction. The second

equation relating Xp0and XN0is found by taking the ratio of the built in potentials on the N

side to those on the p side:

2

p0

2

N0

0

0

X

X

aN

dp

p

N

N

N


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Substituting the charge conservation relationship into the above equation, we rewrite the

ratio as

dN

ap

p

N

NN

0

0

From this equation, the built-in potential of the junction is

000

0

11 pdN

ap

pp

N

bi N

N

Alternatively, from an examination

of the band diagram biis equal to

q

EE Npcgpbi

where Egpis the energy gap of the p-side

material


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p and Nrepresent the differences of the Fermi levels with respect to the valence band edge

and the conduction band edge, respectively, in the neutral regions. That is,

xfcN

xvfp

EE

EE

|

|

Both p and Nare calculated from the equilibrium statistics equations given in

Once the doping levels are specified,

bifor the heterojunction is readily

calculated.

Other quantities such as N0and

V(x) are then obtained from the

Equations derived above.

kTEE

c

cf

eNn

kTEE

v

fv

eNp


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EXAMPLE

Let us draw a band diagram for a (p) GaAs/(N) AI0.35Ga0.65As. As heterojunction at thermal

equilibrium. The doping level and relevant material parameters are

Egap(GaAs) =1.42 eV Egap(AlAs) =2.16 eV

Nd=1x1016cm-3 Na=3x10

19cm-3

eV

N

pA

N

pA

N

pA

N

pA

N

p

kT

EE

VVVVV

fv

p 103.0ln

4

4

3

3

2

21

eVN

nkTEEeNn

d

cfn

kT

EE

C

cf

093.0101

1072.3ln0259.0ln

16

17

With A1=3.53x10-1, A2=-4.95x10

-3, A3=1.48x10-4, A4=-4.42x10

-6 Nv=4.7x1018cm-3


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eVxx

xxAsGaAlE xxg 86.1

0.45for x143.0125.090.1

45.00for247.1424.1)(

21

Energy gap of the AlxGa1-xAs material is determined by the valley at x0.45. The energy gap (in eV) is given as:

The energy gap difference (Eg) in an AlxGa1-xAs/GaAs heterojunction is shared between the

conduction band and the valence band. That is Eg= Ec+ Evwhere Ec is the conductionband discontinuity and Evis the valence band discontinuity. The amount of Evis linearly

dependent on the aluminum mole fraction (x) for all values of x. Evand Ec in an AlxGa1-

xAs/GaAs heterojunction are therefore given by

xxEv 55.0)(

0.45 x143.0)55.0125.0(476.0

0.45x055.0247.1

)( 2xx

x

xEc

E0. is 0.244 eV. Egp the energy gap of the narrower gap material (GaAs), is 1.424 eV.

Therefore, the built-in voltage is found

eVbi 678.1093.0)103.0(244.0424.1


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The relative dielectric constants are 13.18 for GaAs and 12.09 for Al0.35Ga0.65As. p0can be

found as

V

N

N

N

N

dN

ap

bipp

dN

ap

bi

4

16

19

00

1013.5)101(09.12

)103(18.131/678.1

1/1

N0which is equal to bi- p0 is 1.678 - 5. 13 x 10-41.6775 V. It is clear from this calculation

that if one side is significantly more heavily doped than the other practically all of the built -

in potential drops across the depletion region of the lightly doped side. Once N0and p0 are

determined, XN0 and Xp0are calculated from

cm104.74677.1)101)(106.1(

)1085.8)(09.12(22XX2

5-

1619

14

0N0

2

N00

N

d

Nd

N

NqN

Nq

cm101.581013.5)103)(106.1(

)1085.8)(18.13(2

2XX

2

8-4

1919

14

0p0

2

p00

p

a

p

a

p

pqN

Nq


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The depiction thickness of the heavily

doped side is merely 1.58 which is

practically zero. With the calculatedparameters, the band diagram is drawn as

shown in the figure.

The band profiles vary parabolically with

position as given by equations:

p0

2

0 2

x-x)(

Nd

N

XNq

xV

)2

Xx2x()(

2

p00

2

pap

XNqxV


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Semiconductor Heterojunctions


To construct a band diagram for an abrupt p-n heterojunction, we proceed in the same

manner as for the p-n homojunction. We begin with two separate materials. Since thematerials have different bandgaps, there must exist a discontinuity in the conduction band

(Ec) and/or the valence band (Ev) at the interface . The difference in the bandgap between

the two materials is equal to the sum of the conduction band and valence band discontinuities

N-type p-type

vcggg EEEEE 21

Abrupt p-n heterojunction


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Graded p-n heterojunction


Although the abrupt p-n heterostructure discussed in the previous section did result in an

increase in the barrier to hole injection, the notch in the conduction band at the interfacealso caused an undesirable increase in the barrier to electron injection. While the net effect

was still an increase in the ratio In/Ip, eliminating this notch further increases In/Ipto a value

Tk

E

LND

LND

I

I

B

g

nap

pdn

hetp

n exp


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Graded p-n heterojunction -2


In order to reduce this notch, the bandgap of the

p material can be graded upwards from thejunction, as shown in the figure. For example, in

an n-AlGaAs/p-GaAs graded heterostructure, the

n material is GaAs at the junction and is graded to

the final AlGaAs composition over a short

distance. The final shape of the notch depends on

the length and profile of the grade; longer gradingtypically gives a smaller notch. However, it is

important that the grade is contained well within

the depletion region. If the grade ends outside the

depletion region, then the barrier seen by holes

decreases, thus reducing the benefits of the

heterojunction. Note that the barrier to holes inboth abrupt and graded heterojunctions is the

same. It is just the barrier for electron flow that is

reduced in the graded structures, allowing for the

increased ratio of In/Ip.


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Example: Designing a p-n heterojunction grade


Consider four different n-p+Al0.3Ga0.7As/GaAs heterojunctions with ND= 1017and

NA= 5 1018. The AlGaAs in these junctions is graded from x = 0 to x = 0.3 over

XGrade= 0(abrupt), XGrade = 100A, XGrade= 300A, and XGrade= 1. Calculate and plot the energyband diagrams for the above four cases.


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Example: Designing a p-n heterojunction grade



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Quasi-electric fields


In a homogeneous semiconductor, the

separation between the conduction and

valence bands is everywhere equal to thesemiconductor bandgap. Any electric field

applied to the material therefore results in an

equal slope in the conduction and valence

bands, as indicated in the figure.

When a hole or electron is placed in this

structure, a force of magnitude eE will act on

the particle.

The magnitude of the force is equal to the

slope of the bands and is the same for both

electrons and holes. However, the direction of

the force is opposite for the two particles.


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Quasi-electric fields -2


An interesting phenomenon arises in

semiconductors with graded bandgaps, such as

the bipolar transistor emitter-base structureshown at the top figure .

In the graded region, the bandgap is not constant,

so the slopes in the conduction and valence bands

are no longer equal. Hence the forces acting on

electrons and holes in this region are no longerequal in magnitude.

It is in general possible for a force to act on only

one type of carrier, as shown in the top figure, or

for forces to act in the same direction for both

electrons and holes, as in the bottom figure. Suchbehavior cannot be achieved by pure electric

fields in homogeneous materials. These fields,

which were first described by Herbert Kroemer in

1957, are therefore referred to as quasi-electric

fields.


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In a given material, the total field acting on a hole or an electron is always the sum of the

applied field and the quasi field, or

The applied field, which results from applying a voltage difference between the ends of the

material, will always be the same for both electrons and holes, but the quasi field could be

different for both. The band profiles in figures in the last slide can therefore be achieved in a

number of different ways. For example, the profile in top figure could be achieved in the

following two ways:

quasieapptote ,, quasihapptoth ,,

1. An undoped (intrinsic) material with a graded composition and zero applied electric field

typically results in the profile in the lower figure. If an electric field app= e,quasiis then

applied to this material, the resulting profile will be the one shown in the upper figure.

2. A uniformly doped n-type material with a graded composition and zero applied electric

field will also result in the profile in the upper figure. In this case, the doping ensures that

the separation between the conduction band and the Fermi level remains approximately

constant. Notice that the resulting quasi-electric field in this structure acts only on minority

carriers.


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Quasi-electric fields provide engineers with additional tools that can beexploited in device design. They have proven to be very useful in decreasing

transit times in devices that rely on minority carrier transport.

For example, in bipolar technology, a highly doped graded base layer is often

used to speed up the transport of minority carriers from the emitter to the

collector. For a base with uniform bandgap, minority carriers injected from the

emitter must diffuse across the base, a process that is generally slow. By using a

highly doped graded base to generate a quasi-electric field, such as was

described in the second example above, minority carriers can be swept across

much more quickly, thus reducing the base transit time and improving the

device RF performance.

hetrojunction

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