ELECTRONIC STRUCTURE OF Si-Ge STRAINED SUPERLATTICES

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ELECTRONIC STRUCTURE OF Si-Ge STRAINED SUPERLATTICES

C. Tejedor, L. Brey

To cite this version:

C. Tejedor, L. Brey. ELECTRONIC STRUCTURE OF Si-Ge STRAINED SUPERLATTICES. Jour- nal de Physique Colloques, 1987, 48 (C5), pp.C5-557-C5-560. �10.1051/jphyscol:19875120�. �jpa- 00226704�

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JOURNAL DE PHYSIQUE

Colloque C5, supplement au noll, Tome 48, novembre 1987

ELECTRONIC STRUCTURE OF Si-Ge STRAINED SUPERLATTICES

C. T E J E D O R and L . BREY

Departamento de Fisica de la Materia Condensada, Universidad Autonoma, Cantoblanco, E-Madrid 28049, Spain

Abstract.- We present a calculation of both electronic energy levels and intensities of optical transitions in (Si)n-(Ge)n strained superlattices. Strain effects are analyzed by considering cases where either Si or Ge is the substrate determining the lattice parameter.

The results are in qualitative agreement with the available experimental information.

Recent developments in strained layer epitaxy have made possible the growth of (SiIn-(Ge), superlattices (SL) on (001) Si substrates[l].

The main consequence of the ordering of Si and Ge layers is the appea- rance of direct optical transitions in the range between 0.7eV and 2.4eV which do not exist in SiGe alloys~l]

.

We present theoretical calculations of the electronic structure of (Si),-(Ge), (n=4,6,8,10 and 12) SL grown in the (001) direction.

The very large latkice mismatch implies an enormous strain on the layers of the SL. In order to analyze strain effects, we compute the electronic band structures when the SL has its lattice accommodated elastically either to a Si or to a Ge substrate. Since we are concer- ned with ultrathin layers of indirect materials, effects coming from the folding of the Brillouin zone are expected to be important.

Therefore,we use a tight-binding approach[21 including all the folding effects.-The Hamiltonian H with spin-orbit terms is represented in an sp3s* basis. We start by testing the ability of our method for compu- ting changes induced by strain on the electronic structure, i.e.

hydrostatic and uniaxial deformation potentials. This is performed by scaling the tight-binding parameters as a function of the interatomic distance d. We make use of the scaling behaviour selfconsistently computed for Si and ~ e r 3 J . Off-diagonal interactions have a dependence d-2, the diagonal terms ( s*I HI S*> scale as d3 while <S l H l S) and

< p J H \ p > behave as d0.36 for Si and d1-09 for ~e[3]. Table I shows our results for deformation potentials together with experimental values[4]

for comparison. The agreement is satisfactory enough to use our strained Hamiltonian in the study of (Si)n-(Ge)n strained SL.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19875120

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C5-558 JOURNAL DE PHYSIQUE

...

Theory E X ~ . l 4 1 Theory ExP- l41 ...

(ac-av) -7.8 --- -8.5 -9.4

...

Table I.- Theoretical and experimental values (in eV) of selected deformation potentials of the

r8

valence bands and

r 7

and A 1 conduc- tion bands in Si and Ge.

n n

Figure l.-Energy levels atr'point of (Si),-(Ge), SL grown on Si(a) or Ge(b).O States coming from the point of bulk semiconductors.0 States with other l<-vectors folded onto the SL

r

point. The origin of energies is taken at the top of the valence band of unstrained Si.

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The supercell of our SL has n atoms of one of the semiconductors (that forming the substrate) at their ideal bulk positions and n atoms of the other semiconductor displaced to fit the substrate lattice parameter in the xy plane while its interplane distance in the z direction varies according to the Poisson ratio. We borrow the valence band offsetAE, from selfconsistent calculations~51 being DE,=o.~~~v for a Si substrate and A E , = o . ~ ~ ~ v for a Ge substrate (in both cases the Ge valence band edge is higher than the Si one). Figure 1 shows energy levels at the

r

point as a function of n for SL having their parallel lattice parameter equal to either that of Si (fig. la) or Ge(fig. lb).

SL states originating from states at the

r

point of bulk semiconductors are depicted by open circles, while states coming from other k-vectors folded onto the SL point are given by dots. One would expect that the k-character of the states should have implications on the intensity of optical transitions. In

order to clarify this point, we have calculated transition probabilities by means of a simple approximation for the matrix

elements of the momentum opera- ;;

tor 121

.

Our results for a SL on

C,

a Si substrate are given in fi- ?

gure 2 for different values of ^I?h m n. There, it is shown that for

n=4 three sets of transitions V) W

H

appear roughly at 1.1, 1.5 and 5-

H 2.2eV no far from the experi-

mental values 0.76, 1.25 and 2.31 eV. The higher intensity is that of transitions between r-like states. For increasing values of n the transitions evolve both in energy and intensity. When going from n=4 to n=6 the two lowest sets of transitions decrease signifi- cantly in intensity with respect

to the higest one. This is in ^h-(eV)

qualitative agreement with the Figure 2.- Transition probabilities experimental results ill

.

(in arb. units) conputed at the

point of (Si),-(Ge), SL grown on Si.

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C5-560 J O U R N A L DE PHYSIQUE

In summary, we have computed the electronic structure of

(Si),-(Ge), strained SL by means of a tight-binding approach. The new transitions observed by electroreflectance[l~ and their dependence on n are well accounted for by strain and folding arguments.

This work has been supported in part by the Comision Asesora d.e Ciencia y Tecnologia of Spain.

01 T.P.Pearsal1, J-Bevk, L.C.Feldman, J.M.Bonar, J.P.Mannaerts and A.Ourmazd, Phys.Rev.Lett. 58 729 (1987); J-Bevk, A-Ourmazd, L.C.Felman, T.P.Pearsal1, J.M.Bonar, B.A.Davidson and J.P.Mannaerts, Appl-Phys.

Lett. 50 760 (1987).

C21 L.Brey and C.Tejedor, Phys.Rev.B in press.

131 L.Brey, C.Tejedor and J.A.Veryes, Phys.Rev.B 2 6840 (1984).

141 LandBlt-Borstein "Numerical data and functional relationships in Science ang Technology", 0-Madelung ed. (Spriger. Berlin) 1982, ~01.17-

B]

C.G.Van de Walle and R.M.Martin, Phys.Rev.B 2 5621 (1986).