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 double heterostructures,superlattices, quantum wells, quantum dots and quantum wires.Research in heterostructures broadly covers photonic devicesand integrated circuits as well. Heterostructures are compoundsemiconductor materials. The elements from group II to VIshould comply certain criteria, for example matching of latticeconstant, to form a heterostructure material with desired opticaland electrical properties. One way injection, superinjection, elec-tron confinement, optical confinement, wide-gap window effectand diagonal tunneling are physical phenomenon specificallyobserved in heterostructures, which are generally not seen inbulk semiconductors. Array of heterostructures, say quantumdots, which spans new range of energy spectrum, are alsodescribed. We list most widely used devices which primarilyexploit physics and electrical properties of heterostructures.Specifically, highly efficient light emitting diodes, solar cellsand photodetectors based on the wide-gap window effect andheterobipolar transistors with wide-gap emitter are under focusin this survey paper.

I. INTRODUCTION

TBD

II. PHYSICS AND MATERIAL COMPOSITION

[1]

A. At Microscopic Level

At microscopic level, a perfect crystal has translationalinvariance property of a unit cell which has a set of latticevectors. Translational invariance means that the lattices vectorsfor two points are in a crystal differ by three dimensionaltranslation. In an non-ideal case, a heterojunction has nodefinite plane which separates the two different semiconductormaterials. Heterojunctions have abrupt interface. Not onlyphysical properties but electrical properties also depends onthe crystal structure. Therefore, the lattice constants of twosemiconductor materials, forming the heterostructure, shouldmatch closely. A large number of crystalline defects (traps)on the epitaxial layer is one of its side effect. This affects thedensity of electronic charge which is a periodic function onthe crystal lattice. For example, the lifetime of light emittingdevices with this defect shortens due degradation of theperformance. The lattice constants of GaAs and AlAs matchclosely.

The materials with matching lattice are mostly used inoptoelectronic devices. Recent advancements showed that ma-terials with different lattice constants could also be used to

form high-quality devices (T. P. Pearsall, editor, Strained-Leyer Superlattices: Materials Science and Technology). Thekey point is that one of the semiconductor material shouldhave thin layer such that the deformation should exactlyaccommodate the strained-layer. The Si-GexSi1x is one ofthe example of such case.

The elements from the same column of periodic tableare called chemically similar. Otherwise, elements are calledchemically dissimilar. The junction formed by chemical dis-similar materials may have high density of localized traps. Theelectrical effects of at the junction produce undesired behaviorafter adding the dopant atoms. The research in this area is inprogress (A. G. Milnes and D. L. Feucht, Heterojunctions andMetal-Semiconductor Junctions).

Apart from lattice mismatch and strains, dislocations arealso a concern in the materials used to form heterostructures.If strain-energy is larger, strain turns into dislocations. Suchdislocations and high strained regions are, generally, presentbetween active region and substrate. We generally use gratedcomposition layer (by controlling x in XxY1x) in betweenactive region and substrate.

Common Anion Rule: The compound semiconductor ma-terials are used to form the heterojunction. The pair ofsemiconductor generally shares a common anion element. Forexample in AlxGa1xAs-GaAs heterojunction, As is commonanion element. It is a fact that conduction band and valenceband wave functions are derived from atomic wave functionsof cations and anions (Harrison 1980). This is the basis ofcommon anion rule.

Refer [2]

B. Band Diagram

Fig. 1. Energy Band Diagram of Uniform Semiconductor Junction

The energy levels in the band diagram are measured withreference to vacuum level (E0). Electron affinity (s) is theenergy required to raise an electron in conduction to vacuumlevel.

EC = E0 s (1)The work function (s) of semiconductor is the differencebetween vacuum level and Fermi level (Ef ). The differencebetween the conduction band minimum level and valence bandmaximum is terms as energy band gap (Eg).

EV = EC Eg = E0 s Eg (2)The first step in modeling a semiconductor device is to drawthe band diagram. The energy band diagram is used to computethe electrostatic potential, electric field in the junction andcharge density at various sites of the device. For a uniformsemiconductor junction, following steps are used to computethe three quantities,

1) The change in conduction band (4EC), valence band(4EV ) or intrinsic Fermi level (4Ei) is used to com-pute the electrostatic potential.

2) Slope of conduction band (EC), valence band (EV ) orFermi level (Ei) is proportional to the electric field. Theconstant of proportionality is 1q .

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

Fig. 2. Energy Band Diagram of Uniform Semiconductor Homojunction

These three, as is, do not work for a heterojunction. Letus continue to understand the band diagram for uniformsemiconductor junction. Later, it would be helpful to modifiythe same for heterojunction. In the presence of electrostaticpotential, V (x), the energy of charge particle changes, say, byamount 4E,

4E = qV (x) EC(x) = E0 s qV (x) (3)Similarly, valence band would also be a function of x in thejunction

EV (x) = E0 s Eg qV (x) (4)

Let us consider a PN-junction with uniform semiconductor asshown in the Fig. 2. 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 .Before we make contact, the difference between Fermi levelsis given by

EFN EFP = Eg N P (5)

After contact, the electron would transfer from Fermi level tolower Fermi level until a build-in potential (Vbi) is established.The build in potential is give by the difference between theFermi energy levels of p-type and n-type semiconductors.

qVbi = EFN EFP = kT logNANDn2i

(6)

where ND and NA are donor and acceptor impurity concen-tration and ni is intrinsic carrier concentration.

When a heterojunction is formed between a n-type andp-type semiconductors, above equation would not be valid.Before we derive the expression for build-in potential forheterojunction, let us consider the high level steps to drawits energy band diagram (Fig. 3).

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 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) While drawing the band diagram, first assume this ishomojunction and draw the band diagram and, then,add signed conduction band edge (4EC) and signedvalence band edge (4EV ) discontinuities.

The expression for build-in potential in terms of work functionis given by

qVbi = P N = (P + EGP P ) (N + N ) (7)

qVbi = (P N ) + EGP P N (8)

This expression is valid for heterojunctions.

C. Types of Heterostructures Junctions

For heterojunction, merely the knowledge of differencesbetween energy levels are enough. It is important how energybands are lined up in the junction. This is useful and devicespecific because heterojunctions allow device designer to alterthe motion of charge carriers by introducing such junction.Therefore, heterojunction are classified into three basic cate-gories, type-I, type-II and type-III.

Fig. 3. Type-I (From [3])

Fig. 4. Type-I (From [3])

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 also called straddling heterojunction asshown in Fig 3, 4 and 5. For this kind of heterojunctions

4EC = 2 1 (9)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 examples of type-I heterojunction are AlAs-GaAs, GaP-GaAs and AlxGa1xAs-GaAs.

2) Type-II: Both the conduction band and valence band offirst semiconductor is above or below the conduction band

Fig. 5. Type-I (From [3])

of second semiconductor but their band gaps overlap. Thistype of configuration is also called staggered heterojunction.The examples of type-II heterojunction are InxGa1xAs-GaxSb1xAs and AlxIn1xAs-InP.

3) Type-III: Both the conduction band and valence band offirst semiconductor is above or below the conduction band ofsecond semiconductor and their band gaps do not overlap atall as shown in Fig. 6. The example of type-III heterojunctionis GaSb-InAs.

Fig. 6. Ga-Sb : InAs/P-n Type-3 (From [3])

D. Flow of Charge Carriers

When two semiconductors form a heterojunction the flowof charge carriers at the junction is slightly different from thatof uniform semiconductor junction. Let us take an example

Fig. 7. Flow of Charge Carrier in a Hetero N-p junction (From [3])

of N-p junction as shows in the Fig. 7. After contact, theelectrons from N-side would flow from higher Fermi level tolower Fermi level (N-to-p) and accumulation region is formed.Also, the electron from lower Fermi level to higher Fermilevel would see a potential barrier and depletion region isformed. Similarly, holes would flow from lower Fermi levelto higher Fermi level (p-to-N). There is potential barrier dueto difference between the valence bands of N-type and p-type semiconductors. In equilibrium state, the net potentialbarrier is created due to electric field in the depletion regionat the junction. The net potential barrier is the sum of potentialbarriers due to slope in conduction and valence bands. Anotherexample to depict this case is also shown in Fig. 8.

E. Role of Band Offset

TBD

III. MATERIALS FOR HETEROSTRUCTURES

TBD [1]

IV. ELECTRICAL CHARACTERISTICS OFHETEROSTRUCTURES

TBD [1]Refer [4] and other literature to add fine text to kick-off this

section.

A. Double Heterostructure

TBD [5]

B. Superlattices

TBD

C. Quantum Well

TBD

Fig. 8. Energy Band Diagram of Type-I Semiconductor (a) Before and (b)After. (From [3])

D. Quantum Dots

TBD

E. Quantum Wire

TBD

V. DEVICES WITH HETEROSTRUCTURE

TBD

A. Photonics Devices

TBD1) Solar Cells: TBD [6]2) Laser Diode: TBD3) Light Emitting Diodes: TBD

B. Solid State Devices

TBD

VI. SUMMARY

TBD

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