Physics and Electrical Characteristics ofSemiconductor Heterostructures - A Report

Adersh MiglaniAdersh.Miglani@gmail.com

EEL732, Semester-I 2013-14, IIT Delhi

AbstractThe 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 aregenerally 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 semiconductordevices are focusing on heterostructures [1]. Initially, theresearch in semiconductor devices concentrated on controllingthe conductivity of a semiconductor devices by doping andstudying non-equilibrium carrier concentration [1]. The combi-nation of heterostructures in this context provides a generalizedmethod to control charge carrier flow.

Though complexities are incurred in the composition andtechnology for heterostructures, their compelling advantagesforced communities to use them in most of the devicescurrently used in our daily life. This report is limited onlyto the introduction of physics and electrical characteristics ofheterostructures. The advanced stuff on this subject shall comein the next version of this report.

The physics and materials are discussed in section II.The different kinds of heterostructures and their combinationsalong with physical phenomenon are discussed in section III.The widely used devices such as LED, laser and solar cell arecovered in section IV.

II. PHYSICS AND MATERIAL COMPOSITION

A. At Microscopic Level

A perfect crystal has translational invariance property ofa unit cell which has a set of lattice vectors. Translationalinvariance means that the lattices vectors for two points in acrystal differ by three dimensional translation. In an non-idealcase, a heterojunction has no definite plane which separates thetwo different semiconductor materials. Thus, heterojunctions

have abrupt interface. The physics and electrical propertiesdepend on the crystal structure.

The lattice constants of two semiconductor materials, form-ing the heterostructure, should match closely. A large numberof crystalline defects (traps) on the epitaxial layer is one ofthe side effects of lattice mismatch. This affects the density ofelectronic charge which is a periodic function on the crystallattice. For example, the lifetime of light emitting devices withthis defect is shortened and its performance also degrades.Nevertheless, devices with heterojunctions are useful in thesense that the carrier transport phenomenon due to variationsof bandgap across the interface are exploited in photonicdevices.

The materials with matching lattice constants, for exampleGaAs and AlAs, are mostly used in photonic devices. Recentadvancements showed that materials with different latticeconstants could also be used to form high-quality devices(T. P. Pearsall, editor, Strained-Layer Superlattices: MaterialsScience and Technology). The key point is that one of thesemiconductor material should have thin layer such that thedeformation should exactly accommodate the strained-layer.The Si-GexSi1x is one of the example of such case. Thestrains in the material affect electrical properties.

The elements from the same column of periodic table arecalled chemically similar. The junction formed by chemicallydissimilar materials may have high density of localized traps.The electrical properties at the junctions are affected andundesired behavior crop up after adding the dopant atoms. Theresearch 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 formheterostructures 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 regionand substrate. We generally use graded composition layer incompound semiconductor materials, for example by control-ling mole fraction x in AlxGa1xAs, in between active regionand 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 AlxGa1xAs-GaAs heterojunction, As is common anionelement. It is a fact that conduction band and valence bandwave functions are derived from atomic wave functions ofcations and anions (Harrison 1980).

B. Band Diagram

The first step in modeling a semiconductor device is todraw the band diagram. The energy band diagram is usedto compute the electrostatic potential, electric field in thejunction and charge densities at various sites of the device. Theenergy levels in the band diagram are measured with respectto the reference vacuum level (E0). Electron affinity (s) isthe energy required to raise an electron from conduction bandto the vacuum level. So, the conduction band edge is given by

Fig. 2. Energy Band Diagram of Uniform Semiconductor Junction

EC = E0 s (1)The work function (s) of a semiconductor is the difference

between vacuum level and Fermi level (Ef ). The differencebetween the conduction band minimum edge and valenceband maximum edge is termed as energy band gap (Eg). Thevalence band edge can be expressed as follows

EV = EC Eg = E0 s Eg (2)A homojunction has zero conduction and zero valence

band offset. Therefore, understanding the band diagram of ahomojunction is prerequisite for that of heterostructure whichhas non-zero band offset.

1) Homojunction: For a uniform semiconductor junction,the three electrical quantities - electrostatic potential, electricfield and charge density - are computed using the followingtechniques,

1) The gradient in the conduction band, valence band orintrinsic Fermi level is used to compute the electrostaticpotential.

2) Slope of conduction band, valence band or Fermi levelis proportional to the electric field. The constant ofproportionality is 1q .

3) The second derivative of EC , EV or Ei is proportionalthe charge density. The constant of proportionality is qs .

Fig. 3. Energy Band Diagram of Uniform Semiconductor Homojunction

These three techniques, as is, do not work for a heterojunc-tion. Once, the understanding of the band diagram for uniformsemiconductor junction is clear, same is easily modified forthe heterojunctions. In the presence of electrostatic potential,V (x), the energy of charge particle changes, say, by amount4E,

4E = qV (x) (3)Conduction band edge is a function of x

EC(x) = E0 s qV (x) (4)Similarly, valence band would also be a function of x in thejunction

EV (x) = E0 s Eg qV (x) (5)Let us consider a PN-junction with uniform semiconductor

as shown in the Fig. 3. The difference between Fermi level,EFP , and valence band of a p-type semiconductor is P =EFP EV . Similarly, for n-type semiconductor, N = EC EFN . The difference between Fermi levels is given by

EFN EFP = Eg N P (6)After contact, the electron would transfer from Fermi level

to lower Fermi level until a build-in potential (Vbi) is estab-lished. The build in potential is give by the difference betweenthe Fermi energy levels of p-type and n-type semiconductors.

qVbi = EFN EFP = kT logNANDn2i

(7)

where ND and NA 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 conductionand valence bands. Therefore, electrons and holes possessequal but opposite force and move across the metallurgicaljunction as shown in Fig. 4(a). For non-uniform semiconductorstructures, there can be different possibilities of changes in theconduction and valence band edges at the junction. Two ofsuch cases are given in Fig. 4(b) and Fig. 4(c). Electric forcein 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, letus consider the high level steps to draw the band diagram ofa 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 iscontinuous every where.

3) The discontinuities are present at conduction and valenceband edge at the junction. The discontinuities in conduc-tion band edge (4EC) and valence band edge (4EV )are not function of doping in case of non-degeneratesemiconductor.

4) To draw the band diagram, the signed conduction band-offset (4EC) and signed valence band-offset (4EV )are added at the metallurgical junction point.

For a heterostruture, small and capital letters are usedfor materials with smaller bandgap and wider bandgap. Thedetailed band diagrams of a nP-heterojunction before contact isshown in figure 5(a) [2]. After contact, the band diagram underthermal equilibrium is shown in figure 5(b). The total build-inpotential 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.

Vbi = V b1 + V b2 (8)

The expression for depletion widths on two sides and capaci-tance are obtained as follows [2]:

x1 =

[2NA2 12(Vbi V )

q ND1(1ND1 + 2NA2)

]1/2(9)

x2 =

[2ND1 12(Vbi V )

q NA2(1ND1 + 2NA2)

]1/2(10)

C =

[qND1NA212

2(1ND1 + 2NA2)(Vbi V )]

(11)

In each of the semiconductors, the relative voltages V1 and V2in terms of doping concentrations are given by the followingexpression [2],

Vb1 VVb2 V =

NA22ND11

(12)

where V = V1 + V2.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 differencesbetween energy levels is not enough. It is important howenergy bands are lined up at the junction. The device designeruse band discontinuities at the junction to alter the motion andconfinement of charge carriers. Therefore, heterojunctions areclassified 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 theband gap of second semiconductor. It means that conductionband of first semiconductor is above the conduction band ofsecond semiconductor and valence band of first semiconductoris below the valence band of second semiconductor. This typeof configuration is called straddling heterojunction as shownin figure (7). For this kind of heterojunctions

4EC = 2 1 (13)This is called electron affinity rule. The difference betweenenergy band gap is equal to the sun of the difference be-tween conduction band and difference between valence band(4EG = 4EC + 4EV ). The AlAs-GaAs, GaP-GaAs andAlxGa1xAs-GaAs are examples of type-I heterojunction.

2) Type-II: Both the conduction band and valence bandof first semiconductor are above or below the conductionband of second semiconductor with some overlap in thebandgap. This type of configuration is also called staggeredheterojunction. The examples of type-II heterojunction areInxGa1xAs-GaxSb1xAs and AlxIn1xAs-InP.

3) Type-III: Both the conduction band and valence band offirst semiconductor are above or below the conduction bandof second semiconductor with no overlap in their bandgapsas shown in Fig. 8. The example of type-III heterojunction isGaSb-InAs.

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

D. Flow of Charge Carriers

When two semiconductors form a heterojunction, the flowof charge carriers at the junction is slightly different fromthat of uniform semiconductor junction. The figure 9 showsan example of N-p junction. Before contact the Fermi levelof N-type semiconctor is above the Fermi level of p-typesemiconductor. 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) andaccumulation region is formed. Also, the electron from lowerFermi level to higher Fermi level would see a potential barrierand depletion region is formed. Conversely, holes would flowfrom lower Fermi level to higher Fermi level (p-to-N). There ispotential barrier due to difference between the valence bandsof N-type and p-type semiconductors.

Under equilibrium, the net potential barrier is created dueto electric field in the depletion region at the junction. The netpotential barrier is the sum of potential barriers due to slopein conduction and valence bands. Another example to depictthis case is also shown in Fig. 5.

E. Role of Band Offset

The optical and electrical properties of a heterojunctiondepend on how the bands of two dissimilar semiconductorsare lined up. The quantum mechanical barrier for electronpropagation is determined by these band offsets. There aremultiple techniques to compute the band offsets. As perthe Andersons rule for the bands alignment, the differencebetween the two band gaps E2g E1g is 4Ec +4Ev , where4Ec and 4Ev are conduction and valence band offsets [3].This is also known as electron-affinity rule. The electronaffinity rule is not proven to be reliable to compute the bandoffset. The electron affinity depends on the surface changesand dipoles. But, we know that band offset should not dependon the surface properties. Later, electron affinity rule wasoverridden by the common anion rule. Other theories are alsocame up including Tersoffs Quantum Dipole Theory, bandoffset 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 heterostructurewith ternary alloy is InxGa1xAs-InP. For achieving bettercontrol over the bandgap energy, quaternary alloys are usedsuch as GaxIn1xAsyP1y and In1xyAlxGayAs. Thoughlattice matching is important for heterojunction but very thinlayers are useful for making high performance lasers evenwhen there is substantial mismatch in lattice constants.

For photonic devices, the recombination process is impor-tant. The type of semiconductor material - direct bandgapand indirect bandgap - is important for absorption and emis-sion of photons. In direct bandgap material the electrons inminimum conduction band have same momentum as electronin maximum valence band. This is not the case for indirectbandgap materials as shown in the E-k digram in figure(10). For indirect bandgap material, one or more phononsare required to conserve the momentum. The interaction ofelectron, hole, photon and phonon particles is required. Theinvolvement of multiple particles lessens the recombinationefficiency. Therefore, direct bandgap materials are appropriatefor efficient radiative recombination which is required for LEDand laser diodes.

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

For radiative recombination, composition of materials isimportant. 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-VIcompounds are all direct semiconductor. The most commonelements used to form compound semiconductors are shownin table I.

TABLE ISHORT PERIODIC 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 dependson the bandgap energy and type of bandgap direct or indirect

bandgap. The wavelength () and bandgap (Eg) are related asfollows,

Eg = h =h c

= h c

Eg=

1.24

Eg(14)

where Eg is bandgap energy in eV.In case of compound semiconductor the type of bandgap

and properties of resultant materials are controlled by thecomposition of elements. For example specific properties ofAlxGa1xAs depend on mole fraction x. This is shownin figure 11. If 0 < x < 0.45, the resultant material isdirect bandgap otherwise it has indirect bandgap which is notsuitable for photonic devices. By changing the bandgap, thewavelength of photon in case of radiative emission is altered.

Fig. 11. Bandgap energy of AlxGa1xAs as a function of mole fraction x[2]

Another compound semiconductor, whose bandgap canbe controlled by mole fraction of constituent elements, isGaAs1xPx. For 0 < x < 0.45, alloy is direct bandgap andbecomes indirect bandgap for x > 0.45. It means that GaP isindirect bandgap with x = 1 and GaAs with x = 0 is directbandgap.

III. CLASSIFICATION OF HETEROSTRUCTURES

The first patent filed by W. Shockley in 1951 has descriptionof p n junction transistor with wide-gap emitter to haveone-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 usingdouble heterostructures so that more carriers would confine inthe active region. This is the most desired change for laserdevices [1].

1) Initially, heterojunctions were popular due to superinjection of carriers, optical confinement and electronconfinement.

2) Stimulated emission for optical devices is achieved bydouble injection in double heterostructures with havinghighly doped or degenerate middle layer. This leads tothe high concentration of light in the middle layer thoughthere are optical losses in outer emitter layers.

Let us consider the case of photon emission to under-stand the behavior of altering carrier concentrations overthe junctions under thermal equilibrium and non-equilibriumconditions. There are three ways a photon and charge carrierscan 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 bandabsorbs incident photon and raised to conduction band,this process is called induced absorption, as shown infigure 12(a).

2) Spontaneous emission: If an electron spontaneouslymakes the transition from conduction band to valenceband, this is called spontaneous emission process asshown in figure 12(b). This is the basis for light emittingdiode.

3) Stimulated or induced emission: When an incident pho-ton interact with an electron in conduction band andcauses electron transition to the valence band. Thistransition from higher energy band to lower energy bandproduces a photon. Since, this process was initiated bythe incident photon, this is called stimulated emission.The result is two coherent photons and optical gain. Thisemission is the basis for laser devices.

A. Physical Phenomena in Heterostructures

1) Population Inversion: Under thermal equilibrium theconcentration of electrons in the higher energy states isinadequate (N2 < N1) to produce coherent and incoher-ent spectral output. For efficient spontaneous and stimulatedemission, the junction should come under non-equilibriumcondition to increase concentration at higher energy levels(N2 > N1). This is called population inversion. The currentrequired to bring semiconductor structure into this stage iscalled threshold current. The population inversion is easilyachieved 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 forwardbias, there is a region in which population inversion occurs.

In p-type region at the junction Fermi level EFn is below theconduction band, that region becomes more n-type. Similarly,there is a region in n-type semiconductor near junction whichbecomes more p-type. This population inversion is requiredfor lasing operation.

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

The population inversion can be achieved by degeneratingthe semiconductor. Also, there are heterojunctions where dou-ble injection solves the population inversion problem withoutusing degenerate semiconductors.

2) Re-absorption: The re-absorption is the problem inhomojunction, the direct bandgap materials. The re-absorptionwould happen when photon energy h is greater than thebandgap energy. For such photons, the absorption coefficient isnot zero. This problem is fixed by using double heterojunctionsin which narrow bandgap material is surrounded by widerbandgap materials as cladding layers. In this case, most ofthe photons have energy less than the bandgap of materialsforming cladding layers. Thus, the absorption coefficient isclose to zero.

3) Other Physical Phenomenon: Following are the mostimportant physical phenomenon in heterostructures as shownin figure 14 [5].

1) One-sided injection2) Superinjection3) Diffusion in build-in electric field4) 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 claddinglayers and another material is used as inner layer. The materialused for cladding layers has wider bandgap as compared tothat 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 layersare doped with acceptor and donor impurity atoms. The innerlayer is formed of intrinsic semiconductor. The energy dis-continuities at the two junctions facilitate the better control ofconcentration of charge carriers. Under forward bias condition,the electrons and holes are confined to the smaller band gapmaterial. These electrons and holes recombine and leads to thegeneration of photons. Thus electron and optical confinementis one of the property of this example of heterostruture, asshown in figure 14(d). The wavelength of photons dependson the material composition of heterostructures. A doubleheterostructure is used to create quantum structures like tunnelbarriers and quantum wells.

2) Tunnel Barriers: In a tunnel barrier, bandgap of claddinglayers 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 semiconductormaterials. The thickness of each layer is of the order ofnanometer. Therefore, superlattice has multiple and alternatelayers of wells and barriers. They are used to filter the electronenergies and to absorb electron to detect infrared radiation. Ifthe barriers between wells are thicker, the tunneling betweenwells is not very effective and properties of superlattice arenot realized.

4) Quantum Well: Unlike double heterostructures, quantumwells have discrete energy values. In double heterostrutures, ifthe width of inner layer is reduced to the order of de Brogliewavelength, the resulting DH becomes quantum well. Thiswidth is of the order few hundred angstroms. The inner layersin DH has continuous energy states whereas the quantum wellhas discrete energy levels. Therefore, quantum confinementphenomenon takes place in this region. The energy levels inthe 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 schematicdiagrams 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 aelectrical conducting wire, it becomes a quantum wire. So, fur-ther lowering the dimensions of quantum well heterostructuresresults in quantum wire and quantum dot. In quantum wire,the electrons move in discrete quantized energy states whenquantum wire is conducting. The conductance of quantum wireis quantized in multiples of 2e

2

h , where h is Plancks constantand e is electron charge. The conventional Ohms law doesnot work.

6) Quantum Dots: The quantum dot is small enough that itsexcitons are confined in all the three spatial directions. Theseare nanocrystals. In quantum dots, the size and bandgap areinversely related. The emission frequencies increases as thesize of quantum dots decreases. Thus by changing the size ofquantum dots the color of emission changes.

Heterostructures are impacted by the reduction in dimen-sional of semiconductor. The most important property isdensity of states, which is shown in figure 17, with respect tothe dimension reduced from single heterostructure to doubleheterostructure, quantum wire and finally quantum dots [5].

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

IV. DEVICES WITH HETEROSTRUCTURE

A. Solar Cells

When light incident upon a semiconductor material, itcomes under non-equilibrium condition. The electrons fromvalence band absorb photons and jump into conduction band.This results in generation of electron-hole pairs. This is calledphotovoltaic effect. The semiconductor structure possessesbuild-in potential and photo current (IL) flows through it. Asa result, optical energy is converted into electrical energy. So,the solar cell is a reversed-biased p-n junction with a resistiveload. The voltage drop across the resistive load tries to bringp-n junction into forward bias with current (IF ) [4]. The netcurrent flows through in reverse-bias direction is given by thefollowing expression,

I = IL IF = IL IS[

exp(eV

kT

) 1

](15)

The conversion efficiency of a solar cell is given by thefollowing expression

=PmPin 100% = ImVm

Pin 100% (16)

where Pin is incident optical power and Pm is maximumsolar power at current Im and voltage Vm. The conversionefficiency depends on the energy bandgap Eg and othernon-ideal effects such as series resistance and reflection oflight from semiconductor material. The conversion efficiencydecreases with lattice temperature. The variation of conversionefficiency with varying energy bandgap and temperature underfixed 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 emissionprocess. The wavelength of light depends on the bandgap ofsemiconductor material. The region of recombination is calledactive region of lasers. This active region should be formedof direct semiconductors. Other regions, also called claddinglayers, 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 doubleheterostructures.

When current is below threshold value, the semiconductorstructure produces incoherent light through spontaneous emis-sion and stimulated emission to produce coherent light startsafter threshold current. The threshold current for transitionfrom spontaneous to stimulated emission is shown in the figure19. The electron confinement and optical confinement are themost desired properties of a laser device and achieved by usingdouble heterostructure.

Fig. 19. Light vs. current relationship

The band diagram, index of refraction and intensity oflight with respect to the distance are shown in figure (20)for a heterostructure laser. The advantages of using doubleheterostructure in laser devices over single heterostructure andhomojunction laser devices are detailed out in figure 21. Thechange in the refractive index from p-GaAs to p-AlxGa1xAs

is 5% while for GaAs PN-homojunction is merely 1%. Theconfinement of light is better in double heterostructure ascompared 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 confinementthe active region is buried inside a higher bandgap and lowerindex material. This is called buried heterostructure (BH) laseras 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 semiconductormaterials have high resistivity and due to large depletion ofcarriers 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 dueto recombination of injected charge carriers at the metallur-gical junction. This effect is called injection electrolumines-cence. Such devices are Light Emitting Diode (LED). LEDswith ordinary homojunction suffer from the following commonproblems,

1) At the junction, high concentration of electrons andholes are not achievable due to diffusion in the bulkregions.

2) The concentration of electrons and holes is controlledby the potential barriers which is same for both chargecarriers. These barriers are a function of only materialdoping.

3) The emitted photons can be reabsorbed. Due to nonzeroabsorption coefficient, efficiency of emitted light is re-duced.

4) The high carrier concentration is achieved by employinghigher doping concentrations. This intern will increasethe probability of absorption.

But, in heterojunctions the potential barriers for electrons andholes are different at the interface due to doping and differencein energy bandgap of two different materials. To increasethe electron confinement, LED with double heterostructureswith 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 carrierconcentrations for homojunction and double heterojunction isshown in the figure 23. The double heterostructure forms aquantum well therefore recombination rate is increased.

Under electric field, the charge carriers in quantum wellshift and, thus, emission is impacted with a shift calledred-shift. This effect can be reduced by decreasing thesize of quantum well thickness. Since, number of discrete

energy states in quantum well are limited due to quantumconfinement, saturation in the optical power occurs. The easiersolution is to increase the thickness of quantum well, But,this would raise red-shift effect. The efficient solution toovercome this problem in a highly efficient LED is to usemultiple quantum wells. Figure 24(a) and 24(b) shows banddiagram of LED with quantum well and multiple quantumwells. Therefore, a heterostructure LED is brighter than ahomojunction 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 TransistorThe heterojunction bipolar transistor (HBT) has wide-gap

emitter. This results in higher value of current gain (= ICIB ) ascompared to bipolar transistor with homojunctions [9]. Figureshows various currents in HBT as described below

1) In, due to electrons injected from emitter into the base2) Ip, due to holes injected from base into the emitter3) Is, due to recombination in the forward biased emitter-

base junction4) Ir, due to recombination of electrons part of In

The net current in the three regions are expressed in terms ofthese four current components

IE = In + Ip + Is (17)

IC = In Ir (18)IB = Ip + Ir + Is (19)

The gain is given by the following expression [9]

Fig. 25. Band diagram of a wide-gap emitter with hole repelling effect ofthe additional energy gap in the emitter [9]

=ICIB

=In Ir

Ip + Ir + Is