Si1-xGex superlattices

.:.:....‘j:‘.:,.:. .,.....,..

,, :,~~,.;‘.:::,(..~~....... :_,:,..;./.

Applied Surface North-Holland

Science 65/66

High precision J.-M.

Baribeau

Institute

for Microstructural

Received

29 June

(1993) 494-500

.

structural

*, D.J.

Lockwood

study of Si/Si, _,Ge, and

P.X.

Sciences, National Research

1992; accepted

for publication

:..

..‘.

..(:

“.

., .. .)

..:,.

..

;.,

,,..

‘-;

applied surface science

superlattices

Zhang

Council Canada,

Ottawa.

Canada KIA OR6

16 July 1992

We report on a structural study of molecular-beam epitaxy grown Si/Si,_,Ge, superlattices by grazing incidence X-ray reflectometry and Raman spectroscopy. X-ray reflectometry proved to be very sensitive to superlattice stacking anomalies and modeling of the reflectivity profiles has allowed estimation of the period length fluctuations and the sharpness of the interfaces. The results of simulations are consistent with thickness fluctuations of the order of I-257 and symmetrical interfaces with a roughness of about two monolayers. Perfection of the superlattices was also assessed by high resolution ( - 0.1 cm ‘) Raman spectroscopy of folded longitudinal acoustic phonons. In the best samples the recorded spectrum exhibited a rich low-frequency phonon structure with a well-resolved Brillouin peak and sharp-folded acoustic phonons extending up to 00 cm ‘_ Measurement of the dispersion relation of the folded phonons allowed accurate determination of the superlattice parameters. The line shapes and widths of the folded phonon peaks are also sensitive to thickness variations. as is demonstrated in a study of a superlattice which contains intentionally built-in thickness inhomogeneities.

1. Introduction Heteroepitaxy of Si/Si I _,Ge, heterostructures has recently attracted much attention due to potential new device applications in Si-based electronics [l]. During growth, the Si, -.Ge, layer adopts the in-plane substrate (Si) lattice parameter causing a tetragonal distortion of the unit cell. Pseudomorphic growth can proceed up to a critical thickness above which it becomes energetically favorable to relieve the stress by nucleation of misfit dislocations or island formation. Multilayers, and in particular superlattices made of repeats of identical Si, _,Ge,/Si bilayers, are of special interest because they allow growth of reasonably thick structures whilst preserving pseudomorphicity. This is an essential feature in most Si-Ge device structures where the resulting bandgap narrowing in the Si, _xGe, alloy and band offsets at the Si-Ge hetero-interfaces are exploited to improve device performance. Strain relaxation is highly undesirable because of the loss of crystallinity that results, and of the detri-

* To whom correspondence Elsevier

Science

Publishers

should B.V.

be addressed.

mental effect it has on the band offset at the heterointerfaces. This latter aspect is also of concern in coherent structures where random potential fluctuations caused by interfacial mixing or ordering may also affect band discontinuity. Clearly there is a need to develop characterization tools to probe the perfection of these heterostructures. Structural properties of semiconductor superlattices are routinely studied by high resolution X-ray techniques such as double-crystal diffractometry which can provide accurate values for the composition, thickness and strain partition. This technique is, however, not well suited to study growth anomalies such as thickness or composition fluctuations, because these only have small effects on the superlattice satellite peaks. Alternatively, X-ray reflectometry is a technique far more sensitive to stacking anomalies. This probe has a shorter penetration distance and the reflectivity from a multilayer is strongly dependent on the vertical chemical modulation in the sample. Moreover, the reflectivity is hardly affected by threading dislocations, which allows investigation of strain-relaxed superlattices. The analysis of the reflectivity curves is straightforward and can pro-

J.-M. Baribeau et al. / High precision structural study of Si /Si,

vide estimates of the surface and interface abruptness or of thickness errors in multilayer structures. The phonon spectra of semiconductor superlattices have been studied extensively, especially by Raman scattering [2]. The most attractive feature of the physical properties in the new periodic structures is the folding of the Brillouin zone. Measurement of the folded longitudinal acoustic (FLA) mode frequencies can be used to obtain accurate values of the layer thicknesses in a superlattice period. High-resolution measurements of the dispersion relation of FLA phonons, especially in the vicinity of the minizone boundary can provide a precise determination of the physical parameters of the superlattice, such as the sound velocity and the density of the component layers [3]. Besides the main FLA phonon peaks, additional weak features in the low frequency Raman spectrum are observed, which may provide further information on the intrinsic or inhomogeneous microstructure. In this paper we present an X-ray reflectometry and Raman-scattering investigation of several The techniques are Si/Si, _xGex superlattices. used to obtain precise dimension and composition information about the samples and to estimate their structural perfection. The usefulness of both techniques to detect thickness anomalies is illustrated in the case of a superlattice which contains intentionally built-in thickness variations.

2. Experimental

details

The epitaxial layers were produced in a VG Semicon V80 molecular-beam-epitaxy system using a methodology described elsewhere [4]. The samples were grown on Si(100) in a temperature range of 450-500°C and at a growth rate of N 0.4 rim/s.. The shutter operation during synthesis of the superlattices was computer-controlled (0.1 s time resolution) and the deposition rates were stabilized using a Inficon III rate monitor. This set-up allowed fabrication of structures containing intentionally built-in thickness variations (see below).

,Ge, superlattices

495

X-ray reflectometry was performed with a Philips 1820 0-20 vertical goniometer using a 1.5 kW generator and CuKa radiation. The instrumental 28 resolution is estimated to be 0.02” and the background signal corresponds to a reflectivcrystal diffracity of - (5-10) x 10p7. Double tometry was performed on a BEDE 150 system using CuKo radiation to determine the Ge fraction x in the superlattice. Raman spectra of the samples were first recorded at low resolution (0.8 cm-‘> with a Spex 14018 double monochromator. Peak line shapes and other fine structures in the spectra were measured at high resolution (0.1 cm-‘) and with wave-number accuracy of 0.05 cm- ’ using a SOPRA DMDP2000 double monochromator. The measurements were performed at room temperature and in a Brewster-angle pseudo-backscattering geometry, where the phonon wave vector was nearly perpendicular to the layers. The Raman spectra were recorded with different excitation wavelengths (of 300 mW power) to obtain the dispersion relation of the FLA phonons.

3. Theoretical

background

3.1. X-ray rejlectometry The reflection amplitude from a multilayer can be calculated using a recurrence relationship to evaluate the reflection amplitude R,+l at an interface n + 1 in terms of the Fresnel coefficient r n+ 1 and the amplitude R, from the layer below. Starting from the substrate for which R, = 1, R n+1 is given by [5] r n+l

e-ik,d,

R n+1=

+R,

1 +m+*hI

’

with rn+1=

k, =

k

n+l

-kl

k

n+l

+kI

(4

’

T(B’- 26, -

Zp,)“‘,

where 8 is the angle of incidence, d, is the thickness of layer n and (1 - 6, - ip,> its index

J.-M. Baribenu et ul. / High precision .structurrtl study

496

of Si / Si,

I G‘c, .superluttice.v

of refraction. At X-ray wavelengths, the latter is less than unity and is a function of the electron density near the solid-vacuum interface. Typically 6 = 1 x lo-” and at grazing incidence, Xrays are totally reflected up to a critical angle tic = &S. The interface roughness v,~,,,+ , between layers n and II + 1 may be taken into account by multiplying the Fresnel coefficient r ,,+, in eq. (1) by a Debye-Waller type roughness factor [6] r n+l= r r1+l e ~;k,,+,k,,6,+1

(4)

The interface roughness extracted from the analysis can be viewed as a phenomenological parameter which combines interdiffusion and corrugation and represents an average over the whole superlattice structure. Nevertheless, interesting conclusions can be drawn from a comparative study of various samples. Period fluctuation was included here by allowing the individual layer thicknesses to vary randomly according to a Gaussian distribution of half-width 3, expressed as a percentage of the nominal layer thicknesses. 3.2. Raman scattering from folded acoustic phonons In the low-frequency or long-wavelength limit the superlattice can be modeled by a periodic structure with two layers each characterized by a thickness d,, a sound velocity I:,, and a density p, (i = 1,2). In the elastic continuum approximation the acoustic phonons are described by means of elasticity theory by solving the wave equation in each layer and applying periodic boundary conditions. The dispersion relation for the acoustic phonon is given by (ref. [7]) cos(qd)

= cos( :)cos(:)

- i[R+

k]sin(%]sin($],

0

2

4

a

6

28 (degree) Fig. I. Measured curves

from

(a) and calculated

a 15 period

was obtained

Si/Si,

(h and c) X-ray _,Ge,

supcrlattice.

for x = 0.48, tl,, = 20.5 nm and d,,,,,

and a uniform

interface

was calculated

with

cluded

roughness the

same

CT,,,,,+ ,

physical

a A = 25% thickness

= 0.3 nm. parameters

reflectivity Curve

c

= 4.0 nm C‘urve (h) but

in-

variation.

predicts two important differences between superlattices and bulk materials. Firstly, the Brillouin zone is folded into a mini-zone delimited by H = 0 and q,,, = r/d. Secondly, phonon-energy gaps are opened at the mini-zone boundary giving rise to phonon doublets near q = 0 and y = q,,,. Here m is an integer and refers to the folding index of the FLA modes. The dimension and composition of the superlattice can be obtained from a fit of the measured dispersion relation using eq. (5). Alternatively, if the superlatticc dimensions are known from other measurements, the acoustic impedance and sound velocity in the two media can be inferred from eq. (5).

4. Results

(5) where R is the ratio of the acoustic impedance p,~:, of the two component layers, d = d, + d, is the period length, and o and 9 are respectively the phonon frequency and wave vector. Eq. (5)

4.1. Typical Si,

,Ge 1/ Si superlu ttice

Fig. 1 displays experimental (a) and calculated (b and c) X-ray reflectivity curves from a 15 period Si/Si, _.,Ge., superlattice. The spacing and

J.-M. Baribeau et al. / High precision structural study

intensity modulation of the satellite peaks is well reproduced by a structure consisting of alternating layers of Si and Si, _xGe, of respective thickness d, = dsi and d, = dSiGe of 20.5 and 4.9 nm and with x = 0.48 (curve c>. The features between satellites and the gradual peak broadening with increasing angle of incidence in the experiment are due to a non-precise period definition and are consistent with a random (non accumulating error) thickness fluctuation A = 2% across the superlattice (curve b). The intensity of higherorder satellites is well reproduced by introducing an interfacial roughness of 0.3 nm corresponding to about two atomic monolayers. Other superlattices were examined by X-ray reflectometry and corresponding thickness variations were clearly evidenced. For example, gradual increase in the deposition rates gives rise to a continuous period-length increase (accumulating error) that could easily be detected from the asymmetric shape of high-order satellites. DisCrete thickness variations (i.e., sudden change in the period length) caused the splitting of highorder satellites. In all the structures investigated, the interfacial roughness varied from 0.25 to 0.4 nm. This seemed to be independent of the composition or growth rate and no difference in the sharpness of Si on Sir _xGe, and Si, PxGex on Si interfaces could be found. Better experimental data extending to higher incidence angles and a more sophisticated treatment of boundary imperfection that includes possible correlation effects may be needed to fully characterize the interfaces

[a.Fig. 2 displays the low-frequency Raman spectrum from the x = 0.48 superlattice measured with two different excitation wavelengths. Curve (a> was obtained using the Ar 514.5 nm laser light, which, in the Brewster-angle pseudo-backscattering geometry used, corresponds to a normalized phonon wave vector (given here by q/qm = 4dv/A = 0.855, where 77 is the index of refraction) well inside the folded Brillouin zone. The spectrum exhibits well-resolved FLA doublets. The sharpness and the number of peaks observed (folded modes could be measured up to 90 cmP’> show that the sample is of high quality with well-defined interfaces. Curve (b) was recorded at

0

ofSi/Si,

497

*Ge, superlattices

IO Frequency

20

30

40

Shift (cm~‘)

Fig. 2. Room-temperature Raman spectra of folded phonons in the Si/Si,,,,Ge,,s superlattice excited 514.5 and (b) 457.9 nm light.

acoustic with (a)

a wavelength corresponding to a normalized phonon wave vector q/q, = 1.05 which is close to the Brillouin zone boundary. Under these conditions the phonon lines are much sharper and the intensity ratio in the doublets is much different from that of curve (a). Several authors have pointed out that the phonon line width is proportional to the group velocity II, in the superlattice. When approaching the mini-zone boundary, the dispersion curve becomes flat and cg approaches 0. This qualitatively explains the narrowing of the phonon lines. A detailed interpretation of the intensity variations across the mini-zone boundary may require an improved theory of Raman scattering. The measured and calculated phonon frequencies obtained using the superlattice dimensions as determined from the reflectivity analysis, are listed in table 1. As can be seen, good agreement (typically 0.5%) is obtained, although small discrepancies exceeding the experimental uncertainties are seen for high-order FLA phonons. To fit the measured FLA phonon dispersion relation, especially near the mini-zone boundary, we have to treat the densities and sound veloci-

498

J.-M. Baribeau et al. / High precision structural study of Si/Si,

xGex superlattices

Table 1 Experimental and calculated Raman frequencies of FLA phonons at two excitation wavelengths with their folding index Cm) assignments 514.5 nm (q/q,, = 0.855) *exrl (cm-‘)

Wcalc (cm-‘)

4.35 6.04 14.67 16.44 25.00 26.68 35.23 _

4.32 5.96 14.64 16.40 25.04 26.58 35.25 37.08 45.74 47.22 55.89 57.13

45.58 57.23

m

Brillouin -1 +1 -2 +2 -3 +3 -4 +4 -5 +5 -6

457.9 nm (q/q, = 1.05) wcxp (cm-‘)

Wcnlc (cm-‘)

5.79 4.51 16.21 15.08 26.30 25.40 36.2 35.6 46.69

5.58 4.70 16.06 14.9’) 26.14 25.48 36.76 35.58 46.74 46.23 51.42 56.21

56.94 _

ties as adjustable parameters. In this way a more precise determination of the superlattice physical parameters is obtained. Table 2 lists the parameter values used for the fitting and the values reported earlier in the literature [9,10]. The parameters in early works were deduced from somewhat limited FLA phonon measurements and were good only for the lower-frequency FLA phonons at wave vectors far away from the minizone center and boundary. The fact that the best fit parameters obtained here are different from the expected bulk values (especially the Si density) may indicate a departure from Rytov’s theory at the mini-zone boundary. Finally, it is interesting to note that the phonon peaks demonstrate peculiar line shapes, and sometimes show double peaks. These fine structures and other small peaks

Table 2 Superlattice physical parameters as determined from high-resolution Raman scattering of FLA phonons in the vicinity of the mini-zone boundary

This work Refs. [9,10]

PS,Ge

us,

L’S~Ge

r$crn3,

(g/cm3)

(x105 cm/s)

(x105 cm/s)

2.23kO.05 2.33

3.79kO.05 3.61

8.19kO.04 8.43

6.75kO.04 7.3-1.5

, 0

2

4

6

8

10

28 (degree) Fig. 3. Measured (c) and calculated (a and b) double-crystal 400 X-ray rocking curves from a 40 period Si/Si, _,Cie, superlattice with built-in thickness fluctuations. Curve (a) corresponds to the reflectivity from an ar’erage structure with d,, = 11.6 nm and d,, = 3.0 nm. Curve (b) is a calculation based on the actual growth conditions.

observed in the vicinity of main peaks (indicated by arrows in fig. 2) demonstrate that rich information is provided in the high-resolution Raman spectrum. 4.2. Anomalous

Si , ~ xGex / Si superlattice

To illustrate the effects of thickness variations on the reflectivity and the Raman spectrum of a superlattice, a sample containing intentionally built-in anomalies was prepared. The sample consists of five consecutive eight-period superlattices of increasing periodicity. The nominal Si and Si r _xGex layer thicknesses were increased by 1% steps in the successive superlattices while the Ge fraction was maintained to a constant value of x = 0.30. Fig. 3 compares the X-ray reflectivity curve measured on that sample with calculated curves. The broadening (splitting into multiple peaks) of low- (high-) order satellites in the experimental curve (c) is direct evidence of the existence of more than one periodicity in the sample. Curve (a) is a calculation obtained using

J.-M. Baribeau et al. / High precision structural study of Si /Si, _ xGex superlattices

constant periodicity corresponding to the average period length in the structure. The calculated curve (b) is obtained when the nominal-periodlength variations (based on the shutter timing) are introduced in the calculation. Comparison of the two curves demonstrates convincingly how reflectivity is sensitive to minor thickness fluctuations. The agreement of curve (b) with experiment is good considering that uncontrolled random thickness fluctuations were neglected. It indicates that in this particular sample unintentional thickness fluctuations are probably less than 1%. The Raman spectrum of the same sample is shown in fig. 4. The experimental conditions are the same as those described earlier. A pronounced broadening of the FLA phonon line, which increases with phonon frequency, is observed. This line broadening is believed to be due to the progressive increase of the superlattice period length. The dispersion relation eq. (5) can be written approximately as a

a=“(?

.,),

499

Table 3 Measured and calculated line width broadening due to the variation of the superlattice period length for the sample with intentionally built-in thickness variations Mode

Ao (experiment) (cm-‘)

Ao (calculation) (cm-‘)

Brillouin -1 +1 -2 +2 -3 +3 -4

0.41 0.60 0.77 0.82 0.98 1.3 1.5

0.27 0.55 0.83 1.1 1.38 1.65 1.93 2.2

where u is the sound velocity of the superlattice. The variation of d leads to a change of w can be

(6) 1

d 10

Conclusion

20

30

Frequency

40

50

60

70

Shift (mm’)

Fig. 4. Room-temperature Raman spectrum of folded acoustic phonons in the 40 period non-ideal superlattice of fig. 3 excited with 457.9 nm light. This spectrum demonstrates the progressive line-width broadening of the main peaks with increase in frequency.

In this paper we have shown that X-ray reflectometry and high-resolution Raman scattering are precise means for determining structural parameters in superlattices. Minor thickness variations that could have been difficult to analyze by double crystal diffraction were clearly evidenced in

SO0

J.-M. Baribeau

el al. / High precision structural study of SI / Si,

reflectivity measurements. Fine structures and peak broadening in both the reflectivity curves and in the low-frequency Raman spectra of nonideal superlattices were correlated with thickness variations in the superlattice.

References [l] See for example, K. Eberl and W. Wegscheider. in: Handbook on Semiconductors, Vol 3, Materials, Properties and Preparation, Ed. S. Mahajan, in press, and references therein.

,Gtp, superlatticc~s

[3] P.X. Zhang, D.J. Lockwood. H.J. Labbe and J.M. Baribeau, Phys. Rev. B, in press. [4] D.C. Houghton. D.J. Lockwood. M.W.C. DharmaWardana, E.W. Fenton, J.M. Bariheau and M.W. Denhoff, J. Cryst. Growth 1X (1987) 343. [5] L.G. Parratt. Phys. Rev. 95 (1054) 3SY. [6] P. Croce and L. NCvot, Rev. Phys. Appl. I