Hetero Structures

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Physics and Electrical Characteristics of

Semiconductor Heterostructures - A Report

Adersh Miglani

EEL732, Semester-I 2013-14, IIT Delhi

Abstract—The Physics of semiconductor heterostructures isdescribed before the introduction of different classes of het-erostructure such as double heterostructures, superlattices, quan-tum wells, quantum wires and quantum dots. Research inheterostructures broadly covers photonic devices and solid statedevices as well. Heterostructures are compound semiconductormaterials. The elements from group II to VI should complycertain criteria, for example matching of lattice constant, to forma heterostructure material with desired optical and electricalcharacteristics. Physical phenomenon in heterostructures such asone way injection, superinjection, electron confinement, opticalconfinement and diagonal tunneling are discussed, which are

generally not seen in homogeneous semiconductors. We discussdevices which primarily exploit physics and electrical propertiesof heterostructures such as highly efficient light emitting diodes,laser devices, solar cells and heterojunction bipolar transistorwith wide-gap emitter.

I. INTRODUCTION

Two third of all the research activities in semiconductor

devices are focusing on heterostructures [1]. Initially, the

research in semiconductor devices concentrated on controlling

the conductivity of a semiconductor devices by doping and

studying non-equilibrium carrier concentration [1]. The combi-

nation of heterostructures in this context provides a generalized

method to control charge carrier flow.

Though complexities are incurred in the composition andtechnology for heterostructures, their compelling advantages

forced communities to use them in most of the devices

currently used in our daily life. This report is limited only

to the introduction of physics and electrical characteristics of

heterostructures. The advanced stuff on this subject shall come

in the next version of this report.

The physics and materials are discussed in section II.

The different kinds of heterostructures and their combinations

along with physical phenomenon are discussed in section III.

The widely used devices such as LED, laser and solar cell are

covered in section IV.

I I . PHYSICS AND M ATERIAL C OMPOSITION A. At Microscopic Level

A perfect crystal has translational invariance property of

a unit cell which has a set of lattice vectors. Translational

invariance means that the lattices vectors for two points in a

crystal differ by three dimensional translation. In an non-ideal

case, a heterojunction has no definite plane which separates the

two different semiconductor materials. Thus, heterojunctions

have abrupt interface. The physics and electrical properties

depend on the crystal structure.

The lattice constants of two semiconductor materials, form-

ing the heterostructure, should match closely. A large number

of crystalline defects (traps) on the epitaxial layer is one of

the side effects of lattice mismatch. This affects the density of

electronic charge which is a periodic function on the crystal

lattice. For example, the lifetime of light emitting devices with

this defect is shortened and its performance also degrades.

Nevertheless, devices with heterojunctions are useful in the

sense that the carrier transport phenomenon due to variations

of bandgap across the interface are exploited in photonic

devices.The materials with matching lattice constants, for example

GaAs and AlAs, are mostly used in photonic devices. Recent

advancements showed that materials with different lattice

constants could also be used to form high-quality devices

(T. P. Pearsall, editor, Strained-Layer Superlattices: Materials

Science and Technology). The key point is that one of the

semiconductor material should have thin layer such that the

deformation should exactly accommodate the strained-layer.

The Si-GexSi1−x is one of the example of such case. The

strains in the material affect electrical properties.

The elements from the same column of periodic table are

called chemically similar. The junction formed by chemically

dissimilar materials may have high density of localized traps.The electrical properties at the junctions are affected and

undesired behavior crop up after adding the dopant atoms. The

research in this area is in progress (A. G. Milnes and D. L.

Feucht, Heterojunctions and Metal-Semiconductor Junctions).

Fig. 1. Example of Dislocation

Apart from lattice mismatch and presence of strains, dis-

locations are also a concern in the materials used to form

heterostructures as shown in Fig. 1. If strain-energy is larger,

strain turns into dislocations. Such dislocations and high

strained regions are, generally, present between active region

and substrate. We generally use graded composition layer in

compound semiconductor materials, for example by control-



ling mole fraction x in AlxGa1−xAs, in between active region

and substrate.

Common Anion Rule: The compound semiconductor materi-

als are used to form heterojunctions. The pair of semiconduc-

tors generally shares a common anion element. For example,

in AlxGa1−xAs-GaAs heterojunction, As is common anion

element. It is a fact that conduction band and valence band

wave functions are derived from atomic wave functions of

cations and anions (Harrison 1980).

B. Band Diagram

The first step in modeling a semiconductor device is to

draw the band diagram. The energy band diagram is used

to compute the electrostatic potential, electric field in the

junction and charge densities at various sites of the device. The

energy levels in the band diagram are measured with respect

to the reference vacuum level (E 0). Electron affinity (χs) is

the energy required to raise an electron from conduction band

to the vacuum level. So, the conduction band edge is given by

Fig. 2. Energy Band Diagram of Uniform Semiconductor Junction

E C =

E 0 − χs

(1)

The work function (Φs) of a semiconductor is the difference

between vacuum level and Fermi level (E f ). The difference

between the conduction band minimum edge and valence

band maximum edge is termed as energy band gap ( E g). The

valence band edge can be expressed as follows

E V = E C − E g = E 0 − χs −E g (2)

A homojunction has zero conduction and zero valence

band offset. Therefore, understanding the band diagram of a

homojunction is prerequisite for that of heterostructure which

has non-zero band offset.

1) Homojunction: For a uniform semiconductor junction,the three electrical quantities - electrostatic potential, electric

field and charge density - are computed using the following

techniques,

1) The gradient in the conduction band, valence band or

intrinsic Fermi level is used to compute the electrostatic

potential.

2) Slope of conduction band, valence band or Fermi level

is proportional to the electric field. The constant of

proportionality is 1

q .

Fig. 3. Energy Band Diagram of Uniform Semiconductor Homojunction

3) The second derivative of E C , E V or E i is proportional

the charge density. The constant of proportionality is

q

s .These three techniques, as is, do not work for a heterojunc-

tion. Once, the understanding of the band diagram for uniform

semiconductor junction is clear, same is easily modified for

the heterojunctions. In the presence of electrostatic potential,

V (x), the energy of charge particle changes, say, by amount

E ,

E = −qV (x) (3)

Conduction band edge is a function of x

E C (x) = E 0 − χs − qV (x) (4)

Similarly, valence band would also be a function of x in the

junction

E V (x) = E 0 − χs − E g − qV (x) (5)

Let us consider a PN-junction with uniform semiconductor

as shown in the Fig. 3. The difference between Fermi level,

E FP , and valence band of a p-type semiconductor is δ P =E FP −E V . Similarly, for n-type semiconductor, δ N = E C −

E FN . The difference between Fermi levels is given by

E FN −E FP = E g − δ N − δ P (6)

After contact, the electron would transfer from Fermi level

to lower Fermi level until a build-in potential (V bi) is estab-

lished. The build in potential is give by the difference between

the Fermi energy levels of p-type and n-type semiconductors.

qV bi = E FN − E FP = kT logN AN D

n2

i

(7)

where N D and N A are donor and acceptor impurity concen-

tration and ni is intrinsic carrier concentration.



2) Heterojunction: For uniform semiconductor structure,

the band slope under an electric field is same for conduction

and valence bands. Therefore, electrons and holes possess

equal but opposite force and move across the metallurgical

junction as shown in Fig. 4(a). For non-uniform semiconductor

structures, there can be different possibilities of changes in the

conduction and valence band edges at the junction. Two of

such cases are given in Fig. 4(b) and Fig. 4(c). Electric force

in the last two cases is called quasi-electric field.

Fig. 4. (a) Same slope in conduction and valence bands of a homogeneoussemiconductor. (b) Zero slope in conduction band and non-zero slop in valenceband. (c) Non-zero and different slope in conduction and valence bands.

When a heterojunction is formed between n-type and p-typesemiconductors, above equation would not be valid. First, let

us consider the high level steps to draw the band diagram of

a heterojunction (Fig. 7).

1) The Fermi levels must coincide on both sides of semi-

conductor and common Fermi level should be horizontal.

2) The vacuum level is parallel to the band edges and is

continuous every where.

3) The discontinuities are present at conduction and valence

band edge at the junction. The discontinuities in conduc-

tion band edge (E C ) and valence band edge (E V )

are not function of doping in case of non-degenerate

semiconductor.4) To draw the band diagram, the signed conduction band-

offset (±E C ) and signed valence band-offset (±E V )

are added at the metallurgical junction point.

For a heterostruture, small and capital letters are used

for materials with smaller bandgap and wider bandgap. The

detailed band diagrams of a nP-heterojunction before contact is

shown in figure 5(a) [2]. After contact, the band diagram under

thermal equilibrium is shown in figure 5(b). The total build-in

potential at equilibrium is sum of electrostatic potentials of

Fig. 5. Energy Band Diagram of Type-I Semiconductor (a) Before and (b)After. (From [2])

the two semiconductors.

V bi = V b1 + V b2 (8)

The expression for depletion widths on two sides and capaci-

tance are obtained as follows [2]:

x1 =

2N A2 ε1ε2(V bi − V )

q N D1(ε1N D1 + ε2N A2)

1/2(9)

x2 =

2N D1 ε1ε2(V bi − V )

q N A2(ε1N D1 + ε2N A2)

1/2(10)

C =

qN D1N A2ε1ε2

2(ε1N D1 + ε2N A2)(V bi − V )

(11)

In each of the semiconductors, the relative voltages V 1 and V 2in terms of doping concentrations are given by the following

expression [2],

V b1 − V

V b2 − V =

N A2ε2

N D1ε1

(12)

where V = V 1 + V 2.

The sketch of space charge density, electric field and elec-

trostatic potential with respect to position are shown in figure

(6).



Fig. 6. Example quantitative sketch of electrostatics for a p-n heterostructure(a) space charge density (b) electric field (c) electrostatic potential (From [2])

C. Energy Band Alignments

For heterojunction, merely the knowledge of differences

between energy levels is not enough. It is important how

energy bands are lined up at the junction. The device designer

use band discontinuities at the junction to alter the motion and

confinement of charge carriers. Therefore, heterojunctions are

classified into three basic categories, type-I, type-II and type-

III.

Fig. 7. Type-I (From [2])

1) Type-I: The band gap of one semiconductor straddle the

band gap of second semiconductor. It means that conduction

band of first semiconductor is above the conduction band of

second semiconductor and valence band of first semiconductor

is below the valence band of second semiconductor. This type

of configuration is called straddling heterojunction as shown

in figure (7). For this kind of heterojunctions

E C = χ2 − χ1 (13)

This is called electron affinity rule. The difference between

energy band gap is equal to the sun of the difference be-

tween conduction band and difference between valence band

(E G = E C + E V ). The AlAs-GaAs, GaP-GaAs and

AlxGa1−xAs-GaAs are examples of type-I heterojunction.

2) Type-II: Both the conduction band and valence band

of first semiconductor are above or below the conduction

band of second semiconductor with some overlap in the

bandgap. This type of configuration is also called staggered

heterojunction. The examples of type-II heterojunction are

InxGa1−xAs-GaxSb1−xAs and AlxIn1−xAs-InP.

3) Type-III: Both the conduction band and valence band of first semiconductor are above or below the conduction band

of second semiconductor with no overlap in their bandgaps

as shown in Fig. 8. The example of type-III heterojunction is

GaSb-InAs.

Fig. 8. Ga-Sb : InAs/P-n Type-3 (From [2])

D. Flow of Charge Carriers

When two semiconductors form a heterojunction, the flow

of charge carriers at the junction is slightly different from

that of uniform semiconductor junction. The figure 9 shows

an example of N-p junction. Before contact the Fermi level

of N-type semiconctor is above the Fermi level of p-type

semiconductor. After contact, the electrons from N-side would



Fig. 9. Flow of Charge Carrier in a Hetero N-p junction (From [2])

flow from higher Fermi level to lower Fermi level (N-to-p) and

accumulation region is formed. Also, the electron from lower

Fermi level to higher Fermi level would see a potential barrier

and depletion region is formed. Conversely, holes would flow

from lower Fermi level to higher Fermi level (p-to-N). There is

potential barrier due to difference between the valence bands

of N-type and p-type semiconductors.

Under equilibrium, the net potential barrier is created due

to electric field in the depletion region at the junction. The net

potential barrier is the sum of potential barriers due to slope

in conduction and valence bands. Another example to depict

this case is also shown in Fig. 5.

E. Role of Band Offset

The optical and electrical properties of a heterojunction

depend on how the bands of two dissimilar semiconductors

are lined up. The quantum mechanical barrier for electron

propagation is determined by these band offsets. There are

multiple techniques to compute the band offsets. As per

the Anderson’s rule for the bands’ alignment, the difference

between the two band gaps E 2g − E 1g is E c + E v, where

E c and E v are conduction and valence band offsets [3].

This is also known as electron-affinity rule. The electron

affinity rule is not proven to be reliable to compute the band

offset. The electron affinity depends on the surface changes

and dipoles. But, we know that band offset should not depend

on the surface properties. Later, electron affinity rule was

overridden by the common anion rule. Other theories are also

came up including Tersoff’s Quantum Dipole Theory, band

offset from Schottky barrier heights [3].

F. Materials for Heterostructures

AlAs and GaAs have very similar lattice constants. As a re-

sult, structure with these materials are extensively used in pho-

tonic devices. There are examples of ternary and quaternary

alloys to create lattice-matched systems. The heterostructure

with ternary alloy is InxGa1−xAs-InP. For achieving better

control over the bandgap energy, quaternary alloys are used

such as GaxIn1−xAsyP1−y and In1−x−yAlxGayAs. Though

lattice matching is important for heterojunction but very thin

layers are useful for making high performance lasers even

when there is substantial mismatch in lattice constants.

For photonic devices, the recombination process is impor-

tant. The type of semiconductor material - direct bandgap

and indirect bandgap - is important for absorption and emis-

sion of photons. In direct bandgap material the electrons in

minimum conduction band have same momentum as electron

in maximum valence band. This is not the case for indirect

bandgap materials as shown in the E-k digram in figure

(10). For indirect bandgap material, one or more phonons

are required to conserve the momentum. The interaction of

electron, hole, photon and phonon particles is required. The

involvement of multiple particles lessens the recombination

efficiency. Therefore, direct bandgap materials are appropriate

for efficient radiative recombination which is required for LED

and laser diodes.

Fig. 10. E-k diagram (a) direct bandgap material (b) indirect bandgap material

For radiative recombination, composition of materials is

important. Most of the III-V compounds radiate in the infrared.

The direct band semiconductor span larger range of wave-

length as compared to indirect band semiconductor. The II-VI

compounds are all direct semiconductor. The most common

elements used to form compound semiconductors are shown

in table I.

TABLE ISHORT P ERIODIC TABLE

II III IV V VI

N

Al Si P S

Zn Ga Ge As Se

Cd In Sb Te

Hg

Wavelength of light emitted from a heterostructure depends

on the bandgap energy and type of bandgap − direct or indirect



bandgap. The wavelength (λ) and bandgap (E g) are related as

follows,

E g = hν = h c

λ ⇒ λ =

h c

E g=

1.24

E g(14)

where E g is bandgap energy in eV.

In case of compound semiconductor the type of bandgap

and properties of resultant materials are controlled by the

composition of elements. For example specific properties of AlxGa1−xAs depend on mole fraction x. This is shown

in figure 11. If 0 < x < 0.45, the resultant material is

direct bandgap otherwise it has indirect bandgap which is not

suitable for photonic devices. By changing the bandgap, the

wavelength of photon in case of radiative emission is altered.

Fig. 11. Bandgap energy of AlxGa1−xAs as a function of mole fraction x

[2]

Another compound semiconductor, whose bandgap can

be controlled by mole fraction of constituent elements, is

GaAs1−xPx. For 0 < x < 0.45, alloy is direct bandgap and

becomes indirect bandgap for x > 0.45. It means that GaP is

indirect bandgap with x = 1 and GaAs with x = 0 is direct

bandgap.

III. CLASSIFICATION OF H ETEROSTRUCTURES

The first patent filed by W. Shockley in 1951 has description

of p − n junction transistor with wide-gap emitter to have

one-way injection. Heterojunctions possess extremely highinjection efficiencies which is certainly not likely in homo-

junctions. This phenomenon is the basis for photonic devices.

The density of injected carriers can be increased by using

double heterostructures so that more carriers would confine in

the active region. This is the most desired change for laser

devices [1].

1) Initially, heterojunctions were popular due to super

injection of carriers, optical confinement and electron

confinement.

2) Stimulated emission for optical devices is achieved by

double injection in double heterostructures with having

highly doped or degenerate middle layer. This leads to

the high concentration of light in the middle layer though

there are optical losses in outer emitter layers.

Let us consider the case of photon emission to under-

stand the behavior of altering carrier concentrations over

the junctions under thermal equilibrium and non-equilibriumconditions. There are three ways a photon and charge carriers

can interact [4].

Fig. 12. Schematic diagram showing (a) induced absorption (b) spontaneousemission (c) stimulated emission processes [4]

1) Induced absorption: when an electron in valence band

absorbs incident photon and raised to conduction band,

this process is called induced absorption, as shown in

figure 12(a).

2) Spontaneous emission: If an electron spontaneously

makes the transition from conduction band to valence

band, this is called spontaneous emission process as

shown in figure 12(b). This is the basis for light emitting

diode.

3) Stimulated or induced emission: When an incident pho-ton interact with an electron in conduction band and

causes electron transition to the valence band. This

transition from higher energy band to lower energy band

produces a photon. Since, this process was initiated by

the incident photon, this is called stimulated emission.

The result is two coherent photons and optical gain. This

emission is the basis for laser devices.

A. Physical Phenomena in Heterostructures

1) Population Inversion: Under thermal equilibrium the

concentration of electrons in the higher energy states is

inadequate (N 2 < N 1) to produce coherent and incoher-

ent spectral output. For efficient spontaneous and stimulatedemission, the junction should come under non-equilibrium

condition to increase concentration at higher energy levels

(N 2 > N 1). This is called population inversion. The current

required to bring semiconductor structure into this stage is

called threshold current. The population inversion is easily

achieved in degenerate p-type and degenerate n-type junction.

The equilibrium condition is shown in figure 13(a) and non-

equilibrium condition is shown in figure 13(b). Under forward

bias, there is a region in which population inversion occurs.



In p-type region at the junction Fermi level E Fn is below the

conduction band, that region becomes more n-type. Similarly,

there is a region in n-type semiconductor near junction which

becomes more p-type. This population inversion is required

for lasing operation.

Fig. 13. Degenerated doped pn-junction (a) thermal equilibrium (b) forwardbias

The population inversion can be achieved by degenerating

the semiconductor. Also, there are heterojunctions where dou-

ble injection solves the population inversion problem without

using degenerate semiconductors.

2) Re-absorption: The re-absorption is the problem in

homojunction, the direct bandgap materials. The re-absorption

would happen when photon energy hν is greater than thebandgap energy. For such photons, the absorption coefficient is

not zero. This problem is fixed by using double heterojunctions

in which narrow bandgap material is surrounded by wider

bandgap materials as cladding layers. In this case, most of

the photons have energy less than the bandgap of materials

forming cladding layers. Thus, the absorption coefficient is

close to zero.

3) Other Physical Phenomenon: Following are the most

important physical phenomenon in heterostructures as shown

in figure 14 [5].

1) One-sided injection

2) Superinjection

3) Diffusion in build-in electric field

4) Electron and optical confinement

B. Classification

1) Double Heterostructure: The double heterostructure

(DH) has two semiconductor materials forming a sandwich.

One material is used as two outer layers also called cladding

layers and another material is used as inner layer. The material

used for cladding layers has wider bandgap as compared to

that of inner material. The most common example of DH is

Fig. 14. (a) One-sided injection (b) Superinjection (c) Diffusion in build-inquasielectric field (d) electron and optical confinement

p-i-n structure (AlGaAs-GaAs-AlGaAs). Two cladding layers

are doped with acceptor and donor impurity atoms. The inner

layer is formed of intrinsic semiconductor. The energy dis-

continuities at the two junctions facilitate the better control of concentration of charge carriers. Under forward bias condition,

the electrons and holes are confined to the smaller band gap

material. These electrons and holes recombine and leads to the

generation of photons. Thus electron and optical confinement

is one of the property of this example of heterostruture, as

shown in figure 14(d). The wavelength of photons depends

on the material composition of heterostructures. A double

heterostructure is used to create quantum structures like tunnel

barriers and quantum wells.

2) Tunnel Barriers: In a tunnel barrier, bandgap of cladding

layers is narrower than that of inner layer. The tunneling bar-

rier is used to control the flow of hot-electrons in a transistor.

The probability of passing through the barrier depends on thetransmission coefficient of the barrier.

3) Superlattices: A superlattice is a periodic structure con-

sisting of alternate layers of two dissimilar semiconductor

materials. The thickness of each layer is of the order of

nanometer. Therefore, superlattice has multiple and alternate

layers of wells and barriers. They are used to filter the electron

energies and to absorb electron to detect infrared radiation. If

the barriers between wells are thicker, the tunneling between

wells is not very effective and properties of superlattice are

not realized.

4) Quantum Well: Unlike double heterostructures, quantum

wells have discrete energy values. In double heterostrutures, if

the width of inner layer is reduced to the order of de Brogliewavelength, the resulting DH becomes quantum well. This

width is of the order few hundred angstroms. The inner layers

in DH has continuous energy states whereas the quantum well

has discrete energy levels. Therefore, quantum confinement

phenomenon takes place in this region. The energy levels in

the quantum well are called energy subbands. For example,

AlGaAs-GaAs-AlGaAs structure provides well for both con-

duction and valence bands a shown in Fig. 15. The schematic

diagrams for density of states and carrier distributions for



quantum well and bulk materials are shown in figure 16.

Fig. 15. Quantum Well

Fig. 16. Schematic drawing of density of states function for bulk, quantumwell, quantum wire and quantum dot structures (black lines) and occupiedelectron states under excitation (red lines) [from ”Y. Arakawa and H. Sakaki

/ Appl. Phys. Lett. 40(11), 1982”]

5) Quantum Wire: If quantum confinement takes place in a

electrical conducting wire, it becomes a quantum wire. So, fur-

ther lowering the dimensions of quantum well heterostructures

results in quantum wire and quantum dot. In quantum wire,

the electrons move in discrete quantized energy states when

quantum wire is conducting. The conductance of quantum wire

is quantized in multiples of 2e2

h , where h is Planck’s constant

and e is electron charge. The conventional Ohm’s law does

not work.

6) Quantum Dots: The quantum dot is small enough that its

excitons are confined in all the three spatial directions. Theseare nanocrystals. In quantum dots, the size and bandgap are

inversely related. The emission frequencies increases as the

size of quantum dots decreases. Thus by changing the size of

quantum dots the color of emission changes.

Heterostructures are impacted by the reduction in dimen-

sional of semiconductor. The most important property is

density of states, which is shown in figure 17, with respect to

the dimension reduced from single heterostructure to double

heterostructure, quantum wire and finally quantum dots [5].

Fig. 17. Impact of dimension on the density of states

IV. DEVICES WITH H ETEROSTRUCTURE

A. Solar Cells

When light incident upon a semiconductor material, it

comes under non-equilibrium condition. The electrons from

valence band absorb photons and jump into conduction band.

This results in generation of electron-hole pairs. This is called

photovoltaic effect. The semiconductor structure possesses

build-in potential and photo current (I L) flows through it. As

a result, optical energy is converted into electrical energy. So,

the solar cell is a reversed-biased p-n junction with a resistive

load. The voltage drop across the resistive load tries to bring

p-n junction into forward bias with current (I F ) [4]. The net

current flows through in reverse-bias direction is given by the

following expression,

I = I L − I F = I L − I S

exp

eV

kT

− 1

(15)

The conversion efficiency of a solar cell is given by the

following expression

η = P m

P in× 100% =

I mV m

P in× 100% (16)

where P in is incident optical power and P m is maximum

solar power at current I m and voltage V m. The conversion

efficiency depends on the energy bandgap E g and other

non-ideal effects such as series resistance and reflection of

light from semiconductor material. The conversion efficiency

decreases with lattice temperature. The variation of conversion

efficiency with varying energy bandgap and temperature under

fixed recombination current is shown in figure 18.

B. Lasers

Lasers are sources of coherent light generated by recombi-

nation of electrons and holes using stimulated photon emission

process. The wavelength of light depends on the bandgap of

semiconductor material. The region of recombination is called

active region of lasers. This active region should be formed

of direct semiconductors. Other regions, also called cladding

layers, can be formed of indirect semiconductors. If cladding



Fig. 18. Conversion efficienty of solar cell vs. bandgap with varyingtemperature

layers are of different materials, the structure is called double

heterostructures.

When current is below threshold value, the semiconductor

structure produces incoherent light through spontaneous emis-

sion and stimulated emission to produce coherent light starts

after threshold current. The threshold current for transition

from spontaneous to stimulated emission is shown in the figure

19. The electron confinement and optical confinement are the

most desired properties of a laser device and achieved by using

double heterostructure.

Fig. 19. Light vs. current relationship

The band diagram, index of refraction and intensity of

light with respect to the distance are shown in figure (20)

for a heterostructure laser. The advantages of using double

heterostructure in laser devices over single heterostructure and

homojunction laser devices are detailed out in figure 21. The

change in the refractive index from p-GaAs to p-AlxGa1−xAs

is 5% while for GaAs PN-homojunction is merely 1%. The

confinement of light is better in double heterostructure as

compared to other device configuration [6].

Fig. 20. Forward biased heterostructure (a) band diagram (b) referectiveindex (c) light intensity with respect to distance

Fig. 21. Comparision of band diagram under forward bias, refractive indexand intensity of light for (a) homojunction (b) single-heterostructure (c)double-heterostructure lasers. [Panish, Hayashi and Sumski, Ref. 48]

1) Buried Heterostructure Lasers: In practical semiconduc-

tor lasers, to achieve excellent carrier and optical confinement

the active region is buried inside a higher bandgap and lower

index material. This is called buried heterostructure (BH) laser

as shown in figure (22) [7]. The configurations in figure 22(b)

and (c) with semi-insulating (SI) regrowth are SI-BH lasers.

Because of low carrier concentrations the SI semiconductor

materials have high resistivity and due to large depletion of

carriers they have small capacitance. It is well known that



devices with small parasitic capacitance are high speed devices

[7].

Fig. 22. Schematic cross sections of heterostructure with buried active layer(a) oxide (b) p-n reversed (c) semi-insulating (SI) stripe structures.

C. Light Emitting Diodes

A forward biased p-n junction produces spectral output due

to recombination of injected charge carriers at the metallur-

gical junction. This effect is called injection electrolumines-

cence. Such devices are Light Emitting Diode (LED). LEDs

with ordinary homojunction suffer from the following common

problems,

1) At the junction, high concentration of electrons and

holes are not achievable due to diffusion in the bulk

regions.

2) The concentration of electrons and holes is controlled

by the potential barriers which is same for both chargecarriers. These barriers are a function of only material

doping.

3) The emitted photons can be reabsorbed. Due to nonzero

absorption coefficient, efficiency of emitted light is re-

duced.

4) The high carrier concentration is achieved by employing

higher doping concentrations. This intern will increase

the probability of absorption.

But, in heterojunctions the potential barriers for electrons and

holes are different at the interface due to doping and difference

in energy bandgap of two different materials. To increase

the electron confinement, LED with double heterostructures

with wide-bandgap cladding layers is the choice. The spectralefficiency of a LED increases due to higher electron confine-

ment and optical confinement [8]. The difference in the carrier

concentrations for homojunction and double heterojunction is

shown in the figure 23. The double heterostructure forms a

quantum well therefore recombination rate is increased.

Under electric field, the charge carriers in quantum well

shift and, thus, emission is impacted with a shift called

”red-shift”. This effect can be reduced by decreasing the

size of quantum well thickness. Since, number of discrete

energy states in quantum well are limited due to quantum

confinement, saturation in the optical power occurs. The easier

solution is to increase the thickness of quantum well, But,

this would raise ”red-shift” effect. The efficient solution to

overcome this problem in a highly efficient LED is to use

multiple quantum wells. Figure 24(a) and 24(b) shows band

diagram of LED with quantum well and multiple quantum

wells. Therefore, a heterostructure LED is brighter than a

homojunction LED.

Fig. 23. Carrier concetrations under forward bias (a) homojunction (b) doubleheterostructure

Fig. 24. Schematic diagram for (a) quantum well LED (b) multiple quantumwell LED

D. Heterojunction Bipolar Transistor

The heterojunction bipolar transistor (HBT) has wide-gap

emitter. This results in higher value of current gain β (= I CI B

) as

compared to bipolar transistor with homojunctions [9]. Figureshows various currents in HBT as described below

1) I n, due to electrons injected from emitter into the base

2) I p, due to holes injected from base into the emitter

3) I s, due to recombination in the forward biased emitter-

base junction

4) I r, due to recombination of electrons part of I nThe net current in the three regions are expressed in terms of

these four current components

I E = I n + I p + I s (17)

Hetero Structures

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