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Transmission of high-frequency phonons through thin glass films
Solid State Communications, Vol.37, pp. 17 1—174. Pergamon Press Ltd. 1981. Printed in Great Britain. TRANSMISSION OF HIGH-FREQUENCY PHONONS THROUGH THIN GLASS FILMS J. Wolter and R.E. Horstman Philips Research Laboratories, Eindhoven, The Netherlands (Received 7 August 1980 by AR. Miedema) By means of phonon spectroscopy we measured the transmission of highfrequency phonons through thin glass films in the frequency range from 100 to 300 GHz. The films were prepared by thermal oxydation of silicon single crystals. Our data obtained from films with different thicknesses suggest that the observed phonon attenuation is due to scattering processes at the silicon-glass interface and not to a bulk effect in the glass film. The phonon mean free path at 300 GHz turns out to be larger than 4pm. We find evidence for the absence of inelastic scattering processes. 1. INTRODUCTION
amorphous glass films, which have not been prepared by
AT LOW TEMPERATURES amorphous dielectrics have revealed a number of unexpected thermal and acoustic properties [1]. Most of these are well descnbed by the “two-level tunnelingmodel” [2]. In particular, this model explains the linear temperature dependence of the specific heat observed at temperatures below 1 K and it accounts for the observed saturation of the ultrasonic attenuation at high power levels. Also thermal conductivity data below 1 K are adequately described by the tunneling model assuming resonant scattering of the phonons by the two-level systems. On the other hand, in the region between 5 and 12K the thermal conductivity shows a “plateau”, which at present is not understood. Thermal conductivity measurements are not able to yield detailed information on the phonon scattering processes which lead to this plateau. These processes can be
evaporation or by sputtering but by thermal oxydation of silicon smgle crystals. We measured the transmission for phonon frequencies between 100 and 300 GHz.
investigated more specifically by means of highfrequency phonon techniques [3, 4]. Recently experiments using this technique have been carried out on thin amorphous films [5, 61, which were prepared by evaporation or sputtering. For these films it was found that the dominant scattering process for phonons is inelastic in the frequency range between 100 and 300 GHz. It has been suggested that this result is inherent to the amorphous nature of the films and does also apply to other glasses, which may be prepared quite differently. On the other hand, it is well-known that the structural properties of amorphous SiO2 films strongly depend on the preparation conditions [7]. Furthermore, for amorphous Si-films experimental evidence has been obtained recently [8] that strong differences exist in the acoustic properties of Si-films prepared by different methods. In this paper we report on experiments on the transmission of high-frequency phonons through thin
locally removed by means of standard photolithographic techniques in order to obtain the desired geometry (inset of Fig. I). The procedure of thermal oxydation in a highpurity atmosphere yields high-quality SiO2 films, which are free from metal impurities. As is known from IC-technology these films are also very dense and stable in comparison with evaporated and sputtered films, which are rather porous [9]. Furthermore, the interface between the silicon and the glass film is very clean. We therefore expect to avoid to a large extent phonon scattering processes due to impurities at the interface. The thicknesses of the glass films we investigated were 1.1 pm and 4.2 pm. X-ray diffraction measurements proved that the films were amorphous. After the glass films had been prepared, aluminium tunnel junctions were fabricated to generate and to detect high-frequency phonons. The generator junction was made on the glass-free surface of the silicon crystal.
2. EXPERIMENTAL TECFINIQUE The glass films were prepared as follows. Undoped silicon single crystal bars (1 inch diameter), dislocation free grown along the [111] crystallographic direction, were cut into disks (8 mm thick). The {1 11 } end faces were polished by means of a combined mechanical and chemical polishing technique ensuring damage free surfaces. The silicon samples were oxydized at 1100°C. High-purity nitrogen gas was saturated with water vapour at 95°Cand was then passed along the sample for several hours. After this procedure the Si02 film was
171
172
TRANSMISSION OF HIGH-FREQUENCY PHONONS THROUGH THIN GLASS FILMS Vol. 37, No.2 d.c. current is sent through the generator junction. By
_________
C)
~
I
Si
d1
~ s102
2
means of a lock-in technique the rate of phonons phonon frequency by slowly increasing the d.c. current. arriving Ouratmeasuring thebasic detector technique is recorded is somewhat a function different, of the although the principles are theassame. With the help
z
d2
u U-
0
of signal signal 100 200
300 / 0Hz Fig. 1. Differential phonon rate as a function of phonon frequency. Reference detector d1, “glass” detector d2. The underground of the recombination phonons is extrapolated by the dashed line. For the dotted lines see text. The glass film is 1 .1 pm thick. The ambient ternperature is 280mK. The inset shows a sketch of the experimental set-up. The frequency resolution ~f is 12GHz. —~
Opposite to the generator two detector junctions were simultaneously evaporated, one (d2) onto the glass film, the other (d1) onto the free silicon surface. The electrical characteristics of the detector junctions were almost identical. This arrangement enables us to investigate the phonon transmission through the glass film by comparing the phonon signals received by the two detectors d1 and d2. In [SI a similar configuration was used. The role of the junctions, however, was interchanged. Junction g was the detector, while the junctions d1 and d2 worked as phonon generators. In this case, however, phonon backscattering in the glass film and subsequent reabsorption of these phonons in the generator d2 may modify the phonon spectrum which is emitted under steadystate conditions. Our configuration avoids this problem. The dimensions of the tunnel junctions are as follows: the generator is about 39 nm thick with lateral dimensions of 1 x 1mm; the detector junctions, which are separated by about 0.3 mm, are 300nm thick with lateral dimensions of 0.35 x 1mm. i’his geometry ensures that both detectors lie within the [111] focusing channel. We note that the thickness of the generator junction is much less than the mean free path for reabsorption of the generated phonons. Experimental values for the mean free path are 540 nm at 100 GHz and 200nm at 300GHz [10]. Therefore a large fraction of the phonons escapes the generator and enters the substrate without frequency conversion, The phonons generated in junction g by the relaxation of quasiparticles are used for phonon spectroscopy. This technique is based on the feature that the relaxation spectrum has a sharp cut-off at the high-frequency end [4]. Usually a small a.c. current superimposed on a
a gate module we measure the transverse phonon arising from a short (lps) current pulse through the generator junction. Thus only the direct phonon (without any contributions from multiple phonon reflections at the crystal surfaces) is recorded. The phonon signal V~(IG) is stored in the memory of a Nicolet 1170 signal averager as a function of the slowly increasing generator current (i.e. pulse amplitude). A few hundred sweeps are usually taken to achieve a good signal to noise ratio. We also stored the current-voltage characteristic VG(IG) of the generator junction in the Nicolet memory. Furthermore, we calibrated both detectors in the same experiment in order to be able to compare the absolute values of the current increase in the two detectors. To this end a small current pulse I~was superimposed on the detector bias [31and was slowly varied to yield detector signals Vs(Is) with the same absolute amplitudes as those originating from the phonon pulses. All measurements were transferred to an APPLE II computer system which we use for digital data handling. Here we calculate I~(V0)and the physically relevant quantity dls/d VG( VG), which is proportional to the differential phonon rate. This procedure, which was proposed in [3], also avoids that nonlinearities in the I/V characteristics of the detector junctions enter the experimental results. Furthermore, by suitable selection of the differentiation interval ~ VG we adjust the optimum frequency resolution ~f (z~ VG) of the spectrometer after the measurement has been done, making a compromise between resolution and signal to noise ratio. The detector currents are proportional [11] to the values of TeffI(Roo *d), with Teff being the life time of the quasiparticles in the tunnel junction, R,,being its normal state resistance, and d being the thickness of the junction. These quantities together with d18/d VG(VG) provide a measurement of the phonon intensity [3] absorbed in each of the two detectors. The experiments were carried out in a He3—He4 dilution refrigerator. The silicon sample was attached with its cylindrical sidewall to the mixing chamber. We used G.E. varnish for good thermal contact. The experiments were done in vacuum, because helium introduces all kinds of spurious effects [12]. Most data were taken at a temperature of 280 mK. We also investigated whether there was any temperature dependent effect on the phonon transmission through the glass films in the temperature range between 45 and 450 mK. ~
Vol. 37, No.2
TRANSMISSION OF HIGH-FREQUENCY PHONONS THROUGH THIN GLASS FILMS
3. EXPERIMENTAL RESULTS A typical phonon spectrum obtained for a 1 .lpm thick SiO2 film is given in Fig. 1 together with the corresponding reference spectrum (without glass). Note that both spectra are plotted with the same vertical scale. The total phonon intensity arriving at the “glass” detector is about 0.85 times that of the reference signal. The “glass” and the reference spectrum are very similar to each other. Below 90 GHz only the recombination phonons of the generator are detected. At 90 GHz there is a sharp onset in the spectra, where the relaxation phonons become detectable. Above 90 GHz both kinds of phonons are detected. In order to separate the contribution of the relaxation phonons, we have extrapolated [13] the underground of the recombination phonons (see the dashed line in Fig. In both spectra an additional signal rise occurs at 200 GHz, where the relaxation phonons emitted by the generator are able to break up two Cooper pairs in the detector (see the dotted lines in Fig. 1). This feature proves that phonons with frequencies larger than 200 GHz are arriving at the detector. Between 100 and 200 GHz oscillations of the phonon intensity can be seen. We found this structure to be due to thickness resonances of longitudinal phonons in the generator leading to a modulation of the emitted phonon intensity as a function of frequency [13]. A further analysis of the “glass” and the reference spectrum (Fig. 1) now leads to the following observations and conclusions. There is an overall decrease in the phonon intensity due to the glass film, but the phonon spectrum has not changed essentially. In particular, within experimental error, for frequencies up to 300 GHz there is no decrease in the rate of relaxation phonons arriving at the detector. It proves that the glass film has not caused inelastic phonon scattering processes in this frequency range. This behaviour is entirely different from the results Dietsche and Kinder [5] obtained from evaporated glass films. They observed a considerable decrease of the phonon signal as a function of the phonon frequency. In order to investigate whether the overall decrease in intensity is due to phonon scattering in the bulk of the glass film or at the interfaces we carried out a similar experiment with a 4.2 pm thick glass film. Within experimental error the spectra we obtained for frequencies up to 300 GHz are identical to those obtained for the 1.1 pm thick film. In particular, there is again no frequency dependent decrease in the detected phonon rate between 100 and 300 GHz. In this experiment we determined the absolute intensity of the phonon flux incident on the two detectors by means of a reverberation method [11]. Generator current pulses with 40 ps duration were used. The advantage over a “ballistic ~.
173
experiment” is that phonon focusing is eliminated in the calibration and thus a small misalignment of the two detectors with respect to the [Ill] focusing channel in silicon does not enter the measurement. With this procedure we determined the phonon flux at 100 GHz mcident on the “glass” detector to be 0.80 times that of the reference detector. We thus obtain within experimental error the same phonon attenuation for a four times thicker glass film. These results imply that the phonon attenuation introduced by the glass film for the most part is not due to a bulk effect in the glass, but must be attributed to phonon scattering at one of the glass interfaces. From the reverberation measurements we determined the absolute phonon yield to be 30% at 300 GHz. Changing the ambient temperature between 450 and 45 mK had no systematic influence on this number. Approximately the same low phonon yield has been obtained by Trumpp et aL [11]. They found the interfaces between the tunnel junctions and the substrate to be responsible for the phonon loss. In view of their results it is not surprising that the extra interface siliconglass introduces an additional phonon loss of about 20%.
4. CONCLUSIONS From our experiments we conclude that for thermally grown amorphous Si02 films the phonon mean free path at 300 GHz is larger than 4pm. From evaporated amorphous glass films a mean free path of 0.5 pm at 300 GHz was obtained [5]. These results suggest that there is a relationship between the preparation conditions of the glass and the phonon mean free path. Probably the density of the glass and the occurrence of voids are relevant parameters. Our thermally grown films are expected [9] to have a larger density than evaporated films. They also have a larger phonon mean free path. Taking ultrasound measurements on bulk samples at 1GHz [1] extrapolation to 300 GHz yields a mean free path of the same order of magnitude (1.4 pm), when we assume the model of resonant phonon scattering at two-level systems. On the contrary, from measurements of the thermal conductivity on bulk samples a phonon mean free path of only 20 nm is deduced at 5 K, where the dominant phonon frequency is about 300 GHz. The reason for this discrepancy is unknown. For our thermally grown SiO2 films we found evidence for the absence of inelastic phonon scattering processes in the frequency range between 100 and 300 GHz. This is in contrast to experimental results obtained for evaporated and sputtered glass films [5, 6]. We find the phonon attenuation in our films to be due to phonon scatteringat the glass—silicon interface.
174
TRANSMISSION OF HIGH-FREQUENCY PHONONS THROUGH THIN GLASS FILMS
Acknowledgements The authors thank M.JJ. Theunissen for the preparation of the SiO2 films. They also wish to thank M.C.H.M. Wouters for technical assistance in the experiments. —
4. 5. 6.
REFERENCES 1.
2. 3.
S. Hunklinger & W. Arnold, in PhysicalAcoustics. (Edited by R.N. Thurston and W.P. Mason) Academic Press, New York (1976), and references cited therein. P.W. Anderson., B.I. Halpermn & C.M. Varma, Phil. Mag. 25, 1(1972); W.A. Phillips, J. Low Temp. Phys. 7,351 (1972). W. Eisenmenger, in PhysicalAcoustics (Edited by R.N. Thurston and W.P. Mason) Vol. 12, p. 79—153, Academic Press, New York (1976); and
7. 8. 9. 10. 11. 12. 13.
Vol. 37. No.2
references cited therein. H. Kinder, Phys. Rev. Lett. 28, 1564 (1972). W. Dietsche & H. Kinder, Phys. Rev. Lett. 43, 1413 (1979). A.R. Long, A.F. Cattel & A.M. MacLeod,J. NonCryst. Solids 35 & 36, 1149(1980). K. Hara, Y. Suzuki & Y. Taga,Japan. J. AppL Phys. 18, 2027 (1979). R. Vacher, H. Sussner & M. Schmidt. Solid State Commun. 34, 279 (1980). Shiojiri, M. et aL, Japan. J. Appi. Phys. 18, 1931 (1979). A.R. Long,J. Phys. F. 3,2023; 3,2041(1973). H.J. Trumpp & W. Eisenmenger, Z Physik B28, 159(1977). E.W. Homung, R.A. Fisher, G.E. Brodale & W.F. Giauque,J. Gzem. Phys. 50,4878 (1969). H. Kinder,J. Physique 33, C4, 21(1972).
amorphous glass films, which have not been prepared by
AT LOW TEMPERATURES amorphous dielectrics have revealed a number of unexpected thermal and acoustic properties [1]. Most of these are well descnbed by the “two-level tunnelingmodel” [2]. In particular, this model explains the linear temperature dependence of the specific heat observed at temperatures below 1 K and it accounts for the observed saturation of the ultrasonic attenuation at high power levels. Also thermal conductivity data below 1 K are adequately described by the tunneling model assuming resonant scattering of the phonons by the two-level systems. On the other hand, in the region between 5 and 12K the thermal conductivity shows a “plateau”, which at present is not understood. Thermal conductivity measurements are not able to yield detailed information on the phonon scattering processes which lead to this plateau. These processes can be
evaporation or by sputtering but by thermal oxydation of silicon smgle crystals. We measured the transmission for phonon frequencies between 100 and 300 GHz.
investigated more specifically by means of highfrequency phonon techniques [3, 4]. Recently experiments using this technique have been carried out on thin amorphous films [5, 61, which were prepared by evaporation or sputtering. For these films it was found that the dominant scattering process for phonons is inelastic in the frequency range between 100 and 300 GHz. It has been suggested that this result is inherent to the amorphous nature of the films and does also apply to other glasses, which may be prepared quite differently. On the other hand, it is well-known that the structural properties of amorphous SiO2 films strongly depend on the preparation conditions [7]. Furthermore, for amorphous Si-films experimental evidence has been obtained recently [8] that strong differences exist in the acoustic properties of Si-films prepared by different methods. In this paper we report on experiments on the transmission of high-frequency phonons through thin
locally removed by means of standard photolithographic techniques in order to obtain the desired geometry (inset of Fig. I). The procedure of thermal oxydation in a highpurity atmosphere yields high-quality SiO2 films, which are free from metal impurities. As is known from IC-technology these films are also very dense and stable in comparison with evaporated and sputtered films, which are rather porous [9]. Furthermore, the interface between the silicon and the glass film is very clean. We therefore expect to avoid to a large extent phonon scattering processes due to impurities at the interface. The thicknesses of the glass films we investigated were 1.1 pm and 4.2 pm. X-ray diffraction measurements proved that the films were amorphous. After the glass films had been prepared, aluminium tunnel junctions were fabricated to generate and to detect high-frequency phonons. The generator junction was made on the glass-free surface of the silicon crystal.
2. EXPERIMENTAL TECFINIQUE The glass films were prepared as follows. Undoped silicon single crystal bars (1 inch diameter), dislocation free grown along the [111] crystallographic direction, were cut into disks (8 mm thick). The {1 11 } end faces were polished by means of a combined mechanical and chemical polishing technique ensuring damage free surfaces. The silicon samples were oxydized at 1100°C. High-purity nitrogen gas was saturated with water vapour at 95°Cand was then passed along the sample for several hours. After this procedure the Si02 film was
171
172
TRANSMISSION OF HIGH-FREQUENCY PHONONS THROUGH THIN GLASS FILMS Vol. 37, No.2 d.c. current is sent through the generator junction. By
_________
C)
~
I
Si
d1
~ s102
2
means of a lock-in technique the rate of phonons phonon frequency by slowly increasing the d.c. current. arriving Ouratmeasuring thebasic detector technique is recorded is somewhat a function different, of the although the principles are theassame. With the help
z
d2
u U-
0
of signal signal 100 200
300 / 0Hz Fig. 1. Differential phonon rate as a function of phonon frequency. Reference detector d1, “glass” detector d2. The underground of the recombination phonons is extrapolated by the dashed line. For the dotted lines see text. The glass film is 1 .1 pm thick. The ambient ternperature is 280mK. The inset shows a sketch of the experimental set-up. The frequency resolution ~f is 12GHz. —~
Opposite to the generator two detector junctions were simultaneously evaporated, one (d2) onto the glass film, the other (d1) onto the free silicon surface. The electrical characteristics of the detector junctions were almost identical. This arrangement enables us to investigate the phonon transmission through the glass film by comparing the phonon signals received by the two detectors d1 and d2. In [SI a similar configuration was used. The role of the junctions, however, was interchanged. Junction g was the detector, while the junctions d1 and d2 worked as phonon generators. In this case, however, phonon backscattering in the glass film and subsequent reabsorption of these phonons in the generator d2 may modify the phonon spectrum which is emitted under steadystate conditions. Our configuration avoids this problem. The dimensions of the tunnel junctions are as follows: the generator is about 39 nm thick with lateral dimensions of 1 x 1mm; the detector junctions, which are separated by about 0.3 mm, are 300nm thick with lateral dimensions of 0.35 x 1mm. i’his geometry ensures that both detectors lie within the [111] focusing channel. We note that the thickness of the generator junction is much less than the mean free path for reabsorption of the generated phonons. Experimental values for the mean free path are 540 nm at 100 GHz and 200nm at 300GHz [10]. Therefore a large fraction of the phonons escapes the generator and enters the substrate without frequency conversion, The phonons generated in junction g by the relaxation of quasiparticles are used for phonon spectroscopy. This technique is based on the feature that the relaxation spectrum has a sharp cut-off at the high-frequency end [4]. Usually a small a.c. current superimposed on a
a gate module we measure the transverse phonon arising from a short (lps) current pulse through the generator junction. Thus only the direct phonon (without any contributions from multiple phonon reflections at the crystal surfaces) is recorded. The phonon signal V~(IG) is stored in the memory of a Nicolet 1170 signal averager as a function of the slowly increasing generator current (i.e. pulse amplitude). A few hundred sweeps are usually taken to achieve a good signal to noise ratio. We also stored the current-voltage characteristic VG(IG) of the generator junction in the Nicolet memory. Furthermore, we calibrated both detectors in the same experiment in order to be able to compare the absolute values of the current increase in the two detectors. To this end a small current pulse I~was superimposed on the detector bias [31and was slowly varied to yield detector signals Vs(Is) with the same absolute amplitudes as those originating from the phonon pulses. All measurements were transferred to an APPLE II computer system which we use for digital data handling. Here we calculate I~(V0)and the physically relevant quantity dls/d VG( VG), which is proportional to the differential phonon rate. This procedure, which was proposed in [3], also avoids that nonlinearities in the I/V characteristics of the detector junctions enter the experimental results. Furthermore, by suitable selection of the differentiation interval ~ VG we adjust the optimum frequency resolution ~f (z~ VG) of the spectrometer after the measurement has been done, making a compromise between resolution and signal to noise ratio. The detector currents are proportional [11] to the values of TeffI(Roo *d), with Teff being the life time of the quasiparticles in the tunnel junction, R,,being its normal state resistance, and d being the thickness of the junction. These quantities together with d18/d VG(VG) provide a measurement of the phonon intensity [3] absorbed in each of the two detectors. The experiments were carried out in a He3—He4 dilution refrigerator. The silicon sample was attached with its cylindrical sidewall to the mixing chamber. We used G.E. varnish for good thermal contact. The experiments were done in vacuum, because helium introduces all kinds of spurious effects [12]. Most data were taken at a temperature of 280 mK. We also investigated whether there was any temperature dependent effect on the phonon transmission through the glass films in the temperature range between 45 and 450 mK. ~
Vol. 37, No.2
TRANSMISSION OF HIGH-FREQUENCY PHONONS THROUGH THIN GLASS FILMS
3. EXPERIMENTAL RESULTS A typical phonon spectrum obtained for a 1 .lpm thick SiO2 film is given in Fig. 1 together with the corresponding reference spectrum (without glass). Note that both spectra are plotted with the same vertical scale. The total phonon intensity arriving at the “glass” detector is about 0.85 times that of the reference signal. The “glass” and the reference spectrum are very similar to each other. Below 90 GHz only the recombination phonons of the generator are detected. At 90 GHz there is a sharp onset in the spectra, where the relaxation phonons become detectable. Above 90 GHz both kinds of phonons are detected. In order to separate the contribution of the relaxation phonons, we have extrapolated [13] the underground of the recombination phonons (see the dashed line in Fig. In both spectra an additional signal rise occurs at 200 GHz, where the relaxation phonons emitted by the generator are able to break up two Cooper pairs in the detector (see the dotted lines in Fig. 1). This feature proves that phonons with frequencies larger than 200 GHz are arriving at the detector. Between 100 and 200 GHz oscillations of the phonon intensity can be seen. We found this structure to be due to thickness resonances of longitudinal phonons in the generator leading to a modulation of the emitted phonon intensity as a function of frequency [13]. A further analysis of the “glass” and the reference spectrum (Fig. 1) now leads to the following observations and conclusions. There is an overall decrease in the phonon intensity due to the glass film, but the phonon spectrum has not changed essentially. In particular, within experimental error, for frequencies up to 300 GHz there is no decrease in the rate of relaxation phonons arriving at the detector. It proves that the glass film has not caused inelastic phonon scattering processes in this frequency range. This behaviour is entirely different from the results Dietsche and Kinder [5] obtained from evaporated glass films. They observed a considerable decrease of the phonon signal as a function of the phonon frequency. In order to investigate whether the overall decrease in intensity is due to phonon scattering in the bulk of the glass film or at the interfaces we carried out a similar experiment with a 4.2 pm thick glass film. Within experimental error the spectra we obtained for frequencies up to 300 GHz are identical to those obtained for the 1.1 pm thick film. In particular, there is again no frequency dependent decrease in the detected phonon rate between 100 and 300 GHz. In this experiment we determined the absolute intensity of the phonon flux incident on the two detectors by means of a reverberation method [11]. Generator current pulses with 40 ps duration were used. The advantage over a “ballistic ~.
173
experiment” is that phonon focusing is eliminated in the calibration and thus a small misalignment of the two detectors with respect to the [Ill] focusing channel in silicon does not enter the measurement. With this procedure we determined the phonon flux at 100 GHz mcident on the “glass” detector to be 0.80 times that of the reference detector. We thus obtain within experimental error the same phonon attenuation for a four times thicker glass film. These results imply that the phonon attenuation introduced by the glass film for the most part is not due to a bulk effect in the glass, but must be attributed to phonon scattering at one of the glass interfaces. From the reverberation measurements we determined the absolute phonon yield to be 30% at 300 GHz. Changing the ambient temperature between 450 and 45 mK had no systematic influence on this number. Approximately the same low phonon yield has been obtained by Trumpp et aL [11]. They found the interfaces between the tunnel junctions and the substrate to be responsible for the phonon loss. In view of their results it is not surprising that the extra interface siliconglass introduces an additional phonon loss of about 20%.
4. CONCLUSIONS From our experiments we conclude that for thermally grown amorphous Si02 films the phonon mean free path at 300 GHz is larger than 4pm. From evaporated amorphous glass films a mean free path of 0.5 pm at 300 GHz was obtained [5]. These results suggest that there is a relationship between the preparation conditions of the glass and the phonon mean free path. Probably the density of the glass and the occurrence of voids are relevant parameters. Our thermally grown films are expected [9] to have a larger density than evaporated films. They also have a larger phonon mean free path. Taking ultrasound measurements on bulk samples at 1GHz [1] extrapolation to 300 GHz yields a mean free path of the same order of magnitude (1.4 pm), when we assume the model of resonant phonon scattering at two-level systems. On the contrary, from measurements of the thermal conductivity on bulk samples a phonon mean free path of only 20 nm is deduced at 5 K, where the dominant phonon frequency is about 300 GHz. The reason for this discrepancy is unknown. For our thermally grown SiO2 films we found evidence for the absence of inelastic phonon scattering processes in the frequency range between 100 and 300 GHz. This is in contrast to experimental results obtained for evaporated and sputtered glass films [5, 6]. We find the phonon attenuation in our films to be due to phonon scatteringat the glass—silicon interface.
174
TRANSMISSION OF HIGH-FREQUENCY PHONONS THROUGH THIN GLASS FILMS
Acknowledgements The authors thank M.JJ. Theunissen for the preparation of the SiO2 films. They also wish to thank M.C.H.M. Wouters for technical assistance in the experiments. —
4. 5. 6.
REFERENCES 1.
2. 3.
S. Hunklinger & W. Arnold, in PhysicalAcoustics. (Edited by R.N. Thurston and W.P. Mason) Academic Press, New York (1976), and references cited therein. P.W. Anderson., B.I. Halpermn & C.M. Varma, Phil. Mag. 25, 1(1972); W.A. Phillips, J. Low Temp. Phys. 7,351 (1972). W. Eisenmenger, in PhysicalAcoustics (Edited by R.N. Thurston and W.P. Mason) Vol. 12, p. 79—153, Academic Press, New York (1976); and
7. 8. 9. 10. 11. 12. 13.
Vol. 37. No.2
references cited therein. H. Kinder, Phys. Rev. Lett. 28, 1564 (1972). W. Dietsche & H. Kinder, Phys. Rev. Lett. 43, 1413 (1979). A.R. Long, A.F. Cattel & A.M. MacLeod,J. NonCryst. Solids 35 & 36, 1149(1980). K. Hara, Y. Suzuki & Y. Taga,Japan. J. AppL Phys. 18, 2027 (1979). R. Vacher, H. Sussner & M. Schmidt. Solid State Commun. 34, 279 (1980). Shiojiri, M. et aL, Japan. J. Appi. Phys. 18, 1931 (1979). A.R. Long,J. Phys. F. 3,2023; 3,2041(1973). H.J. Trumpp & W. Eisenmenger, Z Physik B28, 159(1977). E.W. Homung, R.A. Fisher, G.E. Brodale & W.F. Giauque,J. Gzem. Phys. 50,4878 (1969). H. Kinder,J. Physique 33, C4, 21(1972).