DefectsDefects in in semiconductors semiconductors

From: P.Y. Yu and M. Cardona, Fundamental of Semiconductors, Springer Verlag

The semiconductors are so useful for device applications while their electricalproperties can be modified significantly by the incorporation of small amountsof impurities (doping) or other kinds of defects.

However, while one type of defect, the doping impurities, can make asemiconductor useful for fabricating a device, another type, crystal defects,can have undesirable effects which render the device useless.

The defects can be separated into broad categories:shallow or hydrogen impurities have energy levels close to the Ec and Ev andelectron wave functions typically extend over many lattice constant,

deep centers are defects whose electronic levels are located near the middleof the band gap and the wave functions are localized.

SurfacesSurfaces

The surface which terminates a 3D crystalcan also be considered as a 2D ‘defect’.The qualitative effect of creating a surfaceis to introduce surface states whoseenergies lie in the forbidden gaps of theperfect crystal.The wave functions associated withsurface states have amplitudes that arelarger at or near the surface and decay toessentially zero in the interior of thecrystal. The surface states may formsurface energy bands.The nature of the atomic arrangement atand near the surface can vary widely fromone type of crystal to another.

Surface RelaxationSurface Relaxation

In the simplest situation, the spacing between adjacent atomic layers retainsits bulk value right up to the surface layer, and the atomic arrangement withinthe surface layer is the same as that in the corresponding interior layers.

More generally the interlayerspacing may change as thesurface is approached, givingrise to surface relaxation.

Surface RelaxationSurface Relaxation

Surface ReconstructionSurface Reconstruction

Furthermore, the atomic arrangement within the surface layer may differ fromthat of a corresponding layer in the bulk as a result of a surface recostruction.

ExampleExample:: GaAs GaAs(001) 2x4(001) 2x4 reconstruction reconstruction

GaAs(001) (2x4) units cellconsists of three As dimers andone dimer vacancy

Top As layer

2nd As layer

Top Ga layer

Crystal defectsCrystal defects

The defects are classified into point defects and line defects.

Point defects involved isolated atoms in localized regions of a hostcrystal.

Line defects involve rows of atoms (ex: dislocations).

Line defects are always detrimental to devices.

In addition there are defects which are composed of a small numberof point defects called complexes.

Point defectsPoint defects

Vacancy: the vacancy created by a missingatoms A is denoted VA.

Substitutional: an atom C replacing a hostatom A is denoted by CA.

Interstitial: an atom A occupying an interstialsite is denoted by IA.

Frenkel defect pair: a complex VA- IA formedby an atom A displaced from a lattice site tonearby interstitial site.

Points defects are often classified into the following kinds with specialnomenclature and notations:

AntisiteAntisite defects defects

Antisite: a special kind of substitutional defect in which a host atom B occupiesthe site of another host atom A.

Example: group V atoms occupying group III lattice sites or vice versa incompound III-V semiconductors.In its neutral charge state As0(Ga) should be a double donor as there are twoexcess electrons.

AntisiteAntisite domain boundaries domain boundaries in in InAlAs alloys InAlAs alloys

Intrinsic vs ExtrinsicIntrinsic vs Extrinsic

Vacancies and antisites defects are intrinsic (native) defects since they do notinvolve foreign atoms.

Defects involving foreign atoms (i.e. impurity: donors and acceptors) arereferred to as extrinsic defects.

Shallow or Hydrogen impuritiesExample: SiliconDonorsGroup V atoms: P, As, and Sb (substitutional atoms)Li, Na (interstitial).Double donors (can contribute up to two conduction electrons)Group VI atoms: S,Se, and Te (substitutional atoms).

AcceptorsGroup III atoms: B,Al,Ga, and In (substitutional atoms)Double acceptors (can contribute up to two valence holes)Group II atoms: Be and Zn

Ionization energiesIonization energies in in Ge Ge, Si, and, Si, and GaAs GaAs

shallow impurities versus deep centers

VacancyVacancy

A vacancy in a covalent semiconductor produces four unpaired danglingbonds. The four dangling bonds can repair the problem by forming two pairsof bonds among neighboring dangling bonds.

Since originally the distances between atoms with dangling bons are largerthan the bond lengths in the perfect crystal, atoms with dangling bonds haveto move closer to each other in order to form new bonds.This displacement of neighboring atoms involves an elastic energy, which iscompensated for by the lowering of the energy of the four electrons originallyin the dangling bonds.

VacancyVacancy

As another example of lattice relaxation in deep centers we consider avacancy in a group-IV semiconductor (Si).

Fig. 4.5 Yu

The removal of an atom results in a loss of four electrons. This is equivalentto adding four positive charges to the otherwise neutral semiconductor.

Deep centersDeep centers

The reason why lattice displacements are important in deep centers can beseen from the following example.

Suppose an impurity atom in a semiconductor has a choice of becomingeither shallow donor on a substitutional site or a deep level via a latticedistortion.E0 (thermal ionization energy) is the energy associated to the deep level andis located close to the center of the band gap.On the other hand, as a shallow donor its energy will be near the conductionband edge. The impurity atom in order to lower its energy and becoming adeep center, it requires a lattice relaxation energy (Ed) to produce the latticedistortion. If E0 is larger then Ed it is energetically favorable for the impurityatom to distort spontaneously and become a deep center.It is necessary to know both E0 and Ed in order to predict whether thisimpurity will be deep or shallow.

Deep centersDeep centers

Deep centers have localized wave functions and they present highlylocalized potentials.

Such localized potentials can be caused by broken bonds, strain associatedwith displacement atoms, and difference in electronegativity or corepotential between the impurity and host atoms.

To calculate the energies of deep levels one needs to know the defectpotential and then find a way to solve the corresponding Schrödingerequation.

In general, it is very difficult to deduce the defect potential for deep centersbecause displacements of atoms (or lattice relaxation) can occur.Both impurity atom and atoms surrounding it can be involved in therelaxation.

DXDX centers centers in in AlGaAs alloys AlGaAs alloys

Lattice displacements are responsible for the shallow-to-deep instabilitywhich converts shallow donors in AlxGa1-xAs (x<0.22) to the DX center inAlxGa1-xAs alloy (x>0.22).

Shallow impurity E0=7 meV DX centers E0≈ 160meV

Lattice Lattice ConstantConstant