Photoreflectance and X-ray studies of silicon films on sapphire

Volume 8, number I,2

PHO~~F~~~CE

MATERIALS LETTERS

April 1989

AND X-RAY STUDIES OF SILICON FILMS ON SAPPHIRE

Adriana GIORDANA, R. GLOSSER PhysicsPrograms, The Universityof Texas at Dallas,Richardcan. TX 75083, USA

Joseph G. PELLEGRINO i, Syed QADRI and Eliezer Dovid RICHMOND NavalResearch Laboratories,Washington,DC 20375, USA Received 11 October 1988; in final form 11 January 1989

Photoreflectance was used for the first time to study silicon films on sapphire (SOS). The film thicknesses ranged from 150 to 40000 A. The 3.4 eV structure was monitored with bulk silicon as a standard. A shift of this structure toward lower energies was observed for the thinner films. As the film thickness increased from 1000 to 40000 A, the energy shift appeared to oscillate about the energy value associated with the bulk silicon sample. The energy shift with thickness of the photoreflectance structure is consistent with that calculated from the X-ray measured strain for the thicker films. The short optical penetration depth at 3.4 eV ( = 100 A) is essential to allowing photore~ectance inv~ti~tion of films of this order of thickness.

Silicon films on sapphire (SOS) have been studied for more than twenty years [ l-31 as an alternative to bulk silicon substrates for the construction of high-density, low-power electronic devices and, more recently, of three~mensional structures. SOS films also possess inherent radiation hardness to single-event upsets. Several techniques, including X-ray diffraction and optical absorption, have been used to study SOS films. We report here the first successful application to SOS of photoreflectance ( PR ) , a non-destructive contactless method of optical characterization [ 45 1. Due to its ability to measure the energy associated with interband transitions in semiconductors, PR is a promising method for detection and measurement of strain in the SOS films. It also allows determination of the crystalline quality of the silicon layer. The limited penetration depth of the probe beam (less than 100 A at 3.4 eV, the first direct gap of silicon) is also a very desirable feature, since it allows studying just the upper layers of a film and obtaining a signal from films of thickness of the order of 100 A. It is worth noting that typically the results obtained by other conventional techniques, such as X’ Present address: NIST, Gaithersburg, MD 20879, USA.

64

ray diffraction and Raman spectroscopy, represent an average over a much greater depth of material, and that SOS films thinner than 1000 8, cannot be easily examined by X-ray diffraction. The silicon films were deposited via molecular beam epitaxy (MBE) on sapphire substrates annealed at 1450°C for 30 min. The temperature of the substrate during the deposition was 750°C. The sapphire substrates were oriented to within 2” of the ( 1i02) plane; consequently, the silicon films have a [OOl ] orientation [6]. The thickness of the silicon films ranged from 150 to 40000 A. We used PR to scan the energy range 3-4 eV to study the variation of the position of the 3.4 eV Si structure [ 71 as a function of the film thickness. This response was compared with that of a bulk reference sample (a Czochralski grown 60 R cm p-Si sample). The PR instrumentation has been described in detail elsewhere [ 8 1. In our case the SOS signal modulation was achieved with the 5 145 8, line of an argon ion laser, chopped at a frequency of 500 Hz; the power density at the sample was approximately 250 mW/cm’. The probing light source was a 75 W xenon lamp, placed at the entrance slit of a 30 cm focal length Czerny-Turner monochromator. Photoluminescence and scattered laser light were minimized

0 167-577~89/$03.50 0 Elsevier Science Publishers B.V. (Noah-Holland Physics Publishing Division)

MATERIALS LETTERS

Volume 8, number 1,2

of glass filters. The detector was a UV-enhanced Si photocell. All the measurements were performed at room temperature and atmospheric pressure. In order to significantly increase the signal-to-noise ratio, several spectra from the same sample were averaged. We observed that for a modulation power of 250 mW/cm2 the fractional change in reflectance for the Si reference was approximately 2 x 10e3 while the fractional changes for the films were typically 50 times smaller. This effect is possibly due to the thinner films possessing a weak surface field; we are currently investigating this problem. Fig. 1 compares the spectra from the Si reference with that from the 150 8, sample. The latter spectrum is the average of 11 individual spectral scans, and it has been magnified 25 times. Note the spectral shift to lower energies compared to the reference sample. The PR experimental data (triangles) indicated in fig. 2 show the shifting of the 3.4 eV structure with respect to the Si reference position as a function of the SOS film thickness. The energy gap associated with the structure at each thickness was calculated with Aspnes’ three-point method [ 91; the position of the structure in our Si reference sample was determined to be 3.363 + 0.005 eV. Later in the article we

April 1989

with a combination

-

SI standard 150 a SOS

Energy (eV)

Fig. 1. The PR spectra from bulk silicon (p) and 150 A SOS film (A ) are superposed. The latter spectrum has been magnified 25 times and is an average of 11 spectra.

I 100

1000 THICKNESS

10000

100000

(AI

Fig. 2. The PR experimental values ( A ) and calculations from the Kondo and Moritani expression ( 0, 0 ) of the energy shift of the direct gap structure with respect to its bulk position are plotted versus the film thickness. The squares correspond to the - sign and the circles to the + sign in the Kondo and Moritani expression for the energy shift (eq. (2) ). The two data points corresponding to the 12600 A thickness were obtained from two samples of the same nominal thickness.

will discuss the other points in the figure. The uncertainty associated with each point is related to the quality of the signal produced by the corresponding film. Although the uncertainty on some of the measurements is quite large, the shift toward lower energies of the structure for the thinnest films is unmistakeable. This shift decreases with increasing thickness. For films of thicknesses ranging between 1000 and 40000 A, the 3.4 eV structure seems to oscillate around its position in the bulk. We believe that this erratic behavior is due to the effective strain produced by lattice mismatch and differences in thermal expansion coefficients between silicon and sapphire. Formation of misfit dislocations and microtwins could relieve the strain in different ways in the different films, and therefore cause the oscillations [lo]. Although SOS has been studied for over twenty years, there is not a clear understanding of how the accommodation of the strain related to the lattice mismatch is connected to the existence of defects at the interface and in the silicon film. The crystallographic structures of silicon and sapphire are very different: sapphire has a rhombohedral structure with dimensions a=4.75 8, and c= 12.97 A, while silicon has a diamond structure with lattice parameter ao= 5.4301 A. 65

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The plane ( 1f02) of sapphire, on which our films were deposited, is structurally ‘equivalent to the ( i012) plane. It has been shown [ 111 that silicon deposited on this surface is oriented along the [001] direction. In the model of Nolder and Cadoff [ 111 the silicon atoms of the first layer are assumed to be positioned at the locations of the aluminum atoms at the interface. In the ( 1i02) plane the Al-Al distance along the [ 12 lo] direction is 4.75 A, while the distance along the perpendicular direction [ 1Oi 1 ] is 5.2 A. According to this picture then the silicon is compressed at the interface, experiencing different stresses along two perpendicular directions. It is well known that the 3.4 eV silicon structure is the result of contributions from transitions along the ,4 and A directions, the dominant structure being along ,4 [ 12 1. We were unable to separate these components. This was probably due at least in part to lack of resolution from our apparatus: in order to obtain a reasonable signal-to-noise ratio, the slits of the monochromator were opened to allow a resolution of about 50 A. While the use of Aspnes’ three-point method is justified with respect to the low-field condition (fiQ
April 1989

0.003 0

;

00 0°% Ezr

E z a 0001 p’ ?? D Oa 5 2 -0.001;

00

A.. ".Ap '..

L

E

0 A.

H -0003 100

0. 0' 1000

10000

.o 0 IOOcm

THICKNESS(AI

Fig. 3. The strain in the plane, t (0 ), and along the [ 0011 direction, t,, (0 ), are plotted as a function of film thickness. The dotted line (from eq. ( 1) ) has been used for extrapolation of the values of 6 for films of thicknesses 1500,400O and 10000 A ( A ).

to estimate Efor those thicknesses where we have experimental values for a, only. This is done by taking the values oft from the measured values of a,,, fitting an exponential curve to these points and extrapolating from this curve the values of c at 1500, 4000 and 10000 A. The equation of the curve was t=608 exp( - 1299e) ,

(1)

t being the sample thickness. The interpolated points are represented by triangles in fig. 3 and are printed between square brackets in table 1. We assume that the stress along [ 1001 is the same as the stress along [ 0101, i.e. that the stress in the plane x-y, parallel to the interface, is the same along the x and y axes. In effect, we are neglecting the asymmetry in the position of the aluminum atoms: this approximation is probably correct for the thicker films, but it may fail for very thin films. In order to further characterize the films as a function of thickness, we computed the Poisson ratio appropriate for biaxial stress, which we take to be the ratio of the strain along the stress direction (parallel to the interface) to the strain perpendicular to the stress direction, namely 1~/t,,l. In bulk the Poisson’s ratio is expected to be C, ,/2Cr2, and using tabulated values [ 141 we found it to be 1.299 for silicon. Table 1 shows this ratio to fall drastically for the thinner films. We now try to correlate our PR measurements with the strain results from Pellegrino and co-workers.

Volume 8, number

MATERIALS

1,2

April 1989

LETTERS

Table 1 Values of the lattice constants in the plane (a,, ) and along the [00 1 ] direction (a I ), the strains in the plane (e ) and in the [00 1 ] direction (c,:), and the Poisson’s ratio ]e/ezz] associated to each SOS film. The values between brackets have been extrapolated using eq. ( 1) as shown in fig. 3 Thickness 1500 4000 5500 7000 10000 12570 15000 30000 40000

(A)

alI (A)

5.4220 5.4179 5.4155 5.4167 5.4146 5.4146

5.4441 5.4432 5.4439 5.442 1 5.4422 5.4418 5.4413 5.4413 5.4413

Based on earlier discussion, we only consider the A contribution. Kondo and Moritani [ 12 ] have done an extensive analysis of the electroreflectance response of silicon under uniaxial stress. They obtain expressions for the energy shift under uniaxial stress of the 3.4 eV structure associated with the LI direction (table 2 of ref. [ 121). We recast this in terms of strain, which allows us to apply the expression to our experimental situation. This yields

where 0; is the hydrostatic deformation potential which, following Kondo and Moritani, we take as -9.8 eV, and D:, taken as 4.7 eV, is the intraband parameter for strain along [00 11. The plus sign corresponds to transitions for which polarization both parallel and perpendicular to [00 I] is allowed, while the minus sign corresponds only to polarization perpendicular to [00 11. These two polarization branches refer to the splitting of the valence band. In our geometry both branches are allowed, and we compute the energy shift for both. The results are plotted in fig. 2. The squares correspond to the minus sign, the circles to the plus sign. We see that both branches shift in the same direction as a function of thickness, and that this shift is consistent with our results. An essential feature of our work is the ability to track the behavior of the 3.4 eV structure down to film thicknesses of 150 A and possibly thinner. We believe this stems from the small optical penetration depth (Y-I, with (Y= 3rtk/A, ;i being the wavelength of the incident light and k the extinction coefficient.

[-6.95x 1O-4] [-1.45X10-3] -1.49x lo-3 -2.25x 10m3 [-2.16x 1O-3] -2.69x lo-’ -2.47x 1O-3 -2.85x 1O-3 -2.85x 1O-3

2.58x 2.41 x 2.54x 2.21 x 2.23 x 2.15x 2.06 x 2.06x 2.06x

IO--’ lo-’ lo-’ lo-? 1O-3 10-j 10m3 10-j 10-I

0.27 0.60 0.59 1.02 0.97 1.25 1.20 1.38 1.38

For silicon at 3.4 eV [ 151 k=2.7, and we have CC ‘Z.100 A. We note that while PR samples the top 100 8, and X-ray penetration depths are hundreds of times greater, there is reasonable correlation over the range of thicknesses over which both techniques provide data. This suggests that any strain gradient with respect to film depth is weak. On the other hand, Pellegrino and co-workers [ 13 ] show that even for films 40000 8, thick there is a shift of X-ray spectra with respect to the bulk indicating strain in the silicon film, but PR measurements on film of this thickness yield the bulk value for the position of the 3.4 eV structure, indicating that at least the top 100 8, are unstrained. This apparent discrepancy needs to be examined more closely. Also, while for the thicker films there is good agreement between the energy shift measured by PR and the value calculated from the Kondo and Moritani expression, the large energy shift of the very thin film results need to be examined separately. If we extrapolate E,, and E to 150 8, thickness, which is probably unphysical since e would become positive (i.e. the silicon would be stretched instead of compressed), we still cannot calculate an energy shift as large as the one observed by PR. Several reasons, including the island nature of very thin films and different defect microstructures, may contribute to this behavior that we are, at this moment, unable to explain. Again, we would like to emphasize the great potential of PR as a characterization technique for thin silicon layers, due to the small penetration depth at 67

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MATERIALS LETTERS

3.4 eV, that should allow the application of PR to any silicon on insulator structure, including SIMOX materials. We thank Dr. N. Bottka and Professor R. Chaney for useful discussions.

References [ 11 M.S. Abrahams, C.J. Buiocchi, R.T. Smith, J.F. Corboy Jr., J. Blanc and G.W. Cullen, J. Appl. Phys. 47 (1976) 5139. [2] J. B1ancandM.S. Abrahams, J. Appl. Phys. 47 (1976) 5151. [3] G.W. Cullen and CC. Wang, Heteroepitaxial semiconductors for electronic devices (Springer, Berlin, 1978). [ 41 F.H. Pollak, in: Proceedings of the Society of Photo-Optical Instrumentation Engineers, San Jose, 1981, eds. D.E. Aspnes, S. So and R.F. Potter (SPIE, Bellingham, 1981).

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[ 51O.J. Glembocki, B.V. Shanabrook, N. Bottka, W.T. Beard and J. Comas, Appl. Phys. Letters 46 ( 1985) 970.

[ 61J. Peliegrino, M. Twigg and E. Richmond, Mater. Res. Sot. Symp. Proc. 107 (1988) 383. [7] B.O. Seraphin, Phys. Rev. 140 (1965) A1716. [ 81 N. Bottka, D.K. Gaskill, R.S. Sillmon and R. Glosser, J. Electron. Mater. 17 (1988) 161. [9] D.E. Aspnes, Surface Sci. 37 ( 1973) 418. [ IO] M.E. Twigg, E.D. Richmond and J.G. Pellegrino, submitted for uublication. [ 111 R. Nolder and I. Cadoff, Trans. Met. Sot. AIME 233 ( 1965 ) 549. [ 121 K. Kondo and A. Moritani, Phys. Rev. B 14 (1976) 1577. [ 13 ] J. Pellegrino, S. Qadri, E. Richmond, M. Twigg and C. Vold, Proceedings Heteroepitaxy on Silicon: Fundamentals, Structures, Devices (Materials Research Society) 116 (1988) 395. [ 141 C. Kittel, Introduction to solid state physics, 4th Ed. (Wiley, New York, 1971). [ 151 E.D. Palik, Handbook of optical constants of solids (Academic Press, New York, 1985).