PHYSICAL REVIE% B VOLUME 47, NUMBER 15 15 APRIL 1993-I

Vibrational properties of Si/Ge and a-Sn/Ge superlattices with intermixed interfaces

Jian Zi, Kaiming Zhang, and Xide XieChinese Center ofAdvanced Science and Technology (World Laboratory),

P. O. Box 8730, Bejting 100080, People's Repubh cof'Chinaand Department ofPhysics, Fudan University, Shanghai 200433, People's Republic of China

E,'Received 1 October 1992)

It is found that Raman spectra of Si/Cxe and a-Sn/Ge[001j superlattices are drastically modified bythe introduction of interface intermixing. Some new peaks appear due to intermixing. The calculationsclearly show that the peaks around 400 cm ' in Si/Ge and 230 cm ' in o.-Sn/Ge superlattices observedin Raman experiments originate from the alloyed layers formed at the interface. It is suggested that rela-tive frequencies and relative intensities of some Raman peaks could be used as a measurement of thecomposition profiles and the degree of interface perfectness.

Si/Ge superlattices have currently received consider-able interest because of their potential applications in de-vices, especially the hope to create semiconductors with afundamental direct gap. Phonons of Si/Ge superlatticeshave been intensively investigated in recent years, leadingto great advances in the understanding of their basic vi-brational properties. ' Owing to the great advances inepitaxy techniques, short-period strained a-Sn/Ge super-lattices have been successfully grown pseudomorphicallyon a Ge(001) substrate by Wegscheider et al. , althoughthere exists a very large lattice mismatch of 14.7% be-tween a-Sn and Ge. The combination of zero-gap a-Snand indirect-gap Ge may give different band structuresand open attractive possibilities in band-structure en-gineering based on group-IV semiconductors. Most re-cently, phonons of a-Sn/Ge superlattices have been stud-ied by Fasolino et al. and Zi et al.

It is now well established that acoustic- and optical-phonon modes in semiconductor superlattices are affectedby the superlattice periodicity along the growth directionin quite different ways: in the overlapping range of theacoustic branches of the constituent materials, the corre-sponding modes can be explained by the "folding" ofbulk modes; the optical modes are confined to slabs of ei-ther constituent material if the optical branches of theconstituent materials do not overlap. In addition, thereare interface modes which are sharply confined to the in-terface range owing to the fact that neither material cansustain those vibrations.

Recently, effects of interface intermixing have attract-ed considerable attention from both theories' ' and ex-periments, ' ' since it is of both technological andscientific interest to determine the interface profiles and

I

to reduce the intermixing. It is, however, a very difficulttask to get and estimate the degree of intermixing unin-tentionally introduced at each interface during thegrowth. The infIuence of disorder due to interface inter-mixing on Raman spectra and the relaxation of selectionrules have been intensively studied for alloys and amor-phous structures. However, up to now, there exist fewtheoretical studies concerning the disorder effects on pho-non modes of semiconductor superlattices from a micro-scopic point of view. '

For Si/Ge[001] superlattices, there still exists adisagreement between theories and experiments. " Thepeak around 400 cm ' observed by Raman experimentsdoes not appear in theoretical calculations. ' Thisdiscrepancy originates from the unrealistic assumption ofan ideal interface in theoretical treatment whereas, inreality, the interface intermixing might be inevitable dur-ing the growth. In the present work, Raman spectra ofSi/Ge and a-Sn/Ge superlattices with intermixed inter-face are systematically studied and compared with exper-iments. To account for the alloyed layers formed at theinterface due to intermixing, a supercell technique isused. The superlattice with intermixed planes near theinterface is modeled by a tetragonal supercell whose in-plane lattice constant is 2a, thus consisting of eight atomsper two-dimensional unit cell. The total number of atomscontained in a supercell for an A /B„superlattice is8(m +n), where A and 8 are the group-IV semiconduc-tors. For simplicity, only atoms in layers nearest to theinterface are allowed to exchange to form alloyed layers.Therefore, a nominal A /B„superlattice becomes (forsimplicity, the degree of intermixing is assumed to beidentical at every interface)

(A, 8„),(A) ~(A, „8 ), /(A 8, „),(B)„2(A 8, ),

after intermixing, where x is the degree of interface inter-mixing. In the alloyed planes the A (or 8) atom distribu-tion is chosen at random in order to obtain the desired in-termixing. The calculated Raman spectra are averaged

I

over five distinct random configurations. The choice offive seems reasonable, since it is found that a good con-vergence can be obtained by using about fiveconfigurations.

47 9937 1993 The American Physical Society

9938 BRIEF REPORTS 47

x=3/8

x=3/8

x= 1/8

x=0

250 350I

450

Frequency (cm i)

550 i00 200 300 400 500 600

Frequency (cm i)

FIG. 1. Calculated Raman spectra of a Si4/Ge4 superlatticegrown on Si(001) for different interface intermixing in thez (x,y)z scattering configuration.

FIG. 2. Calculated Raman spectra of a Si6/Ge2 superlatticegrown on Si(001) for different interface intermixing in thez (x,y)z scattering configuration.

A generalized Keating model presented elsewhere ' '

is adopted to calculate the frequencies and eigenvectorsfor Si/Ge superlattices grown on Si(001) and a-Sn/Ge su-perlattices grown on Ge(001). In the framework of thismodel, the strain effects can be properly accounted for.In addition, the geometrical structures of strained Si/Geand cx-Sn/Ge superlattices can also be predicted; the re-sults are in quite good agreement with both ab initio cal-culations and experiments. ' ' ' The Raman spectra areobtained from the calculated eigenvectors with a bondpolarizability model. '

In Fig. 1 the calculated Raman spectra of a Si4/Ge4 su-

perlattice grown on Si(001) are shown for difFerent inter-face intermixing in the z(x,y)z scattering configuration.For an ideal interface, the spectrum is dominated bythree peaks, corresponding to, in the order of increasingfrequency, Ge-like LO, Si-like LA, and Si-like LO modes,respectively. The Raman spectra are considerablymodified by the formation of alloyed layers at the inter-face, particularly in the frequency range between Ge-Geand Si-Si peaks. With interface intermixing, the intensityof the peak around 360 cm ' decreases, while the intensi-ty of the peak around 400 cm ' increases. An inspectionof the longitudinal density of states projected ontodifferent layers reveals that the peak around 400 cmoriginates from the alloyed layers and its intensity isroughly proportional to the degree of intermixing, inagreement with the experimental results. ' ' It isworthwhile to note that in the Si Ge, alloy, there ex-ists also a peak around 400 cm ' which arises from the

local Si-Ge vibrations. Comparing the 400-cm peakboth in alloy and in superlattice, it is obvious that the ori-gin of the 400-cm peak in Si/Ge superlattices is similarto that of the Si-Ge peak in the alloy.

In addition, the interface intermixing also affects thefrequencies of Si-Si peaks which decrease with increasingintermixing. The variation of the frequency of the Si-Sipeak in a Si4/Ge4 superlattice with respect to intermixingis given in Table I. The Si-like LO modes can be wellmapped onto the corresponding bulk LO dispersions byan effective confinement wave vector k =4vrj /(n, fr+1)a,where j is the order of a confined mode and n,~ theeffective number of Si layers involved in vibrations.With the increasing intermixing, n, ff decreases, leading toa larger confinement wave vector, corresponding to lowerfrequency. Table I also gives n,z versus the degree of in-termixing. Variation of the Ge-like LO peak with respectto intermixing is somewhat complex due to both thestrain and confinement effects. For small intermixing(x (3/g), the frequency of the Ge-Ge peak slightly in-creases with the increased intermixing and then decreaseswith intermixing for x )3/8. The Si-Ge alloy peak in su-perlattices is found to slightly increase in energy with theincreased intermixing.

For investigating the intermixing effects on high-orderSi-like LO modes and folded LA modes, the Raman spec-tra of the Si6/Ge2 superlattice grown on Si(001) substrateare also studied and shown in Fig. 2 in the z(x,y)zscattering configuration. Four Raman peaks appear in

TABLE I. Frequency of the Si-like LQ mode and n, ff vs the degree of intermixing for a Si&/Ge4 su-

perlattice grown on Si(001).

co (cm ')n,z

5024

0.13

5013.09

0.25

5003.8

0.38

4993.7

0.5

4983.5

0.63

4973.4

0.75

4933.1

0.88

4892.8

4722

47 BRIEF REPORTS 9939

the case of an ideal interface. The two peaks at 510 and439 cm ' correspond to the first- and third-order Si-likeLO modes (in this case only odd-order modes are Ramanactive). The Ge-Ge peak appears around 300 cm '. Thelow-frequency peak at 209 cm ' corresponds to the fold-ed LA mode. It is found that both the high-order Si-likeLO mode and the folded LA mode are quite sensitive tothe interface intermixing. Their intensities drastically de-crease with the increased intermixing. This result can ex-plain the experimental observations' ' which show thatthe intensities of those peaks decrease with increased an-nealing temperature. The appearance of the Raman peakaround 400 cm ' clearly indicates the formation of al-loyed layers at the interface.

Figure 3 gives the calculated Raman spectra of an 0,-

Sn2/Ge6 superlattice grown on Ge(001) with an ideal andintermixed (x =—,') interface in the z(x,y)z scatteringconfiguration. For an intermixed interface the curve often times the intensity below 300 cm ' is also given inFig. 3. The frequency of the Sn-Sn mode is drasticallyshifted downwards after the occurrence of intermixing,which is due to the decrease in the effective thickness ofSn layers. An inspection of the longitudinal density ofstates projected onto the different layers indicates thatthe broad peak around 230 cm ' originates from the lo-cal Sn-Ge vibrations in the alloyed layers. This mightprovide evidence to the suggestion of such a peak ob-served in Raman experiment.

From the above discussions, it might be concluded thatthe presence of around 400 cm ' in Si/Ge superlattice isan indication of the existence of alloyed layers formed atthe interface. The peak around 230 cm ' in the a-Sn/Czesuperlattice might indicate the existence of intermixing atthe interface. The degree of intermixing is roughly pro-portional to the relative intensity of these peaks. In theSi/Ge superlattice the high-order confined LO and foldedLA modes are very sensitive to intermixing. Small inter-

ideal interf ace

intermixed int. erface

x10

I I I 1 I I

100 150 200 250 300 350

Frequency (cm ~)

FIG. 3. Calculated Raman spectra of an a-Sn2/Ge6 superlat-tice grown on G(001) for an ideal and intermixed (x =

—, ) inter-face in the z (x,y)z scattering configuration.

mixing can cause a large decrease in intensities of thesemodes. Therefore, the appearance of high-order confinedLO modes and folded LA modes might indicate the ex-istence of high-quality superlattice interfaces. It is seenthat much information about composition profiles and in-terface roughness could be obtained from the frequenciesof Raman peaks, relative intensities of the alloyed peak,high-order confined LO modes, and folded LA modes. Inother words, information obtained from Raman spectracould be used to characterize the quality of superlatticeinterfaces.

The present work systematically determined the vibra-tional properties of strain layer superlattices with inter-mixed layers. Although the model adopted is rathercrude and the calculation method is not very accurate,the results obtained can explain some experimental obser-vations quite well.

Mailing address.E. Molinari and A. Fasolino, Appl. Phys. Lett. 54, 1220 (1989).

2M. I. Alonso et al. , Solid State Commun. 69, 479 (1989).Zi Jian et al. , Phys. Rev. B 41, 12 862 (1990).

4J. Zi et al. , J. Phys. Condens. Matter 3, 6239 (1991).5R. A. Ghanbari and G. Fasol, Solid State Commun. 70, 1025

(1989).W. Wegscheider et al. , Appl. Phys. Lett. 57, 875 (1990).

7W. Wegscheider et al. , in Proceedings of the 20th InternationalConference on the Physics of Semiconductors, edited by E. M.Anastassakis and J. D. Joannopoulos (World Scientific, Singa-pore, 1990), p. 1685.

sA. Fasolino et al. , in Condensed Systems of Low Dimensionality, edited by J. L. Beeby (Plenum, New York, 1991),p. 495.

J. Zi et al. , Phys. Rev. B 45, 8397 (1992).' S. Wike, Superlatt. Microstruct. 9, 267 (1991).

M. I. Alonso et al. , J. Appl. Phys. 66, 5645 (1990).J. Menendez et al. , J. Vac. Sci. Technol. B 6, 1306 (1988).S. M. Prokes and K. L. Wang, Appl. Phys. Lett. 56, 2628(1990).H. Brugger et al. , Sernicond. Sci. Technol. 3, 1166 (1988).R. Schorer et al. , Phys. Rev. B 44, 1772 (1991).J. Zi et al. , Appl. Phys. Lett. 57, 165 (1990).S. Go et al. , Phys. Rev. Lett. 34, 580 (1975).

' Jian Zi, Kaiming Zhang, and Xide Xie, Phys. Rev. B 45, 9447(1992).C. G. van de Walle and R. M. Mratin, Phys. Rev. B 34, 5621(1986).