Probing of oscillating surfaces by a scanning acoustic tunneling microscope

Thin

Solid Films 264 (1995) 226-229

Probing of oscillating surfaces by a scanning acoustic tunneling microscope T. Hesjedal,

E. Chilla, H.-J. Frijhlich

Paul-Drude-lnstitut f iir Festkiirperelektronik,

Hausvogteiplatz 5- 7, D-101 17 Berlin, Germany

Abstract The scanning acoustic tunneling microscope (SATM) which is based on a scanning tunneling microscope, is capable of detecting the amplitude and the phase of high-frequency surface acoustic waves (SAWS) as well as the surface topography. For our experiments the SAWS have been excited by interdigital transducers on YZ-LiNbO, samples. A thin gold film with a thickness of about 100 nm has been deposited on its surface. The read-out of the high-frequency acoustic wave field is performed by a mixing technique. Owing to the non-linear dependence of the tunneling current on the tip-to-sample distance an additional slightly-shifted high-frequency modulation of the gap voltage leads to an increase of the d.c. tunneling current and to a low frequency signal at the difference frequency. The a.c. tunneling current contains the information on the elastic properties of the solid. Thin films deposited on the surface cause a dispersion of the phase velocity, which then reveals the elastic parameters. By measuring the phase and the amplitude of an acoustic wave field with high spatial resolution the SATM technique allows the mapping of the acoustic wave field and thereby the investigation of the elastic properties of thin films. Keywords:

Surface acoustic waves; Scanning tunnelling

microscopy

1. Introduction Ultrasonic methods are widely used in solid-state physics in the field of non-destructive testing and material characterization [ 11. Integral physical properties of solids can be studied by the measurement of the velocity and the attenuation of acoustic waves. This leads to the understanding of the intrinsic physical mechanism of energy loss, e.g. by absorption and scattering. The elastic moduli can be determined from velocity measurements in various crystal directions. With surface acoustic waves (SAWS) the integral properties of surfaces and layered structures are studied. Contrary to bulk acoustic waves, SAWS are modes with a wave-like behavior parallel to the surface and an exponential decay perpendicular to it, at which the decay length is of the same order as the wavelength. The probing of SAW fields has been carried out in several ways. Light wave diffraction [2], X-ray scattering [3], or electron reflection methods [4] have the disadvantage of limited spatial resolution. For example, for the widely applied laser optical probing a 0040-6090/95/$09.50 0 1995 Elsevier SSDZ 0040-6090(95)005820-6

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resolution of about 1 km can be obtained. With the need of characterizing quantum wells and ultrathin films with typical dimensions in the nanometer scale, higher spatial resolution of the acoustic wave field is demanded. The modified scanning probe microscopes, namely the scanning acoustic force microscope (SAFM) [5,6] and the scanning acoustic tunneling microscope (SATM) [7-91 are capable of measuring simultaneously the amplitude and the phase of the SAW as well as the surface topography. The SAFM detects the amplitude of the SAW by an effective shift of the average position of the tip owing to the non-linear dependence of the force on the tip-to-sample distance. The SATM is able to detect both the amplitude and phase of SAWS. For that purpose, the non-linearity of the tunneling process, which works as a frequency mixer, is utilized. When a travelling SAW passes the probe, the tip-to-sample distance is modulated with the SAW frequency. In order to use conventional STM electronics with its limited bandwidth, an additional slightly detuned high-frequency signal is applied to the tunneling gap.

T. Hesjedal et al.

Consequently the full wave information appears in the difference frequency signal resulting from the mixing process. Here, we present experimental results on the amplitude and phase of surface oscillation as well as surface topography measured simultaneously by a multichannel SATM.

2. The principle The essential non-linear dependence of the tunneling current on the tip-to-sample spacing is the key for the effective mixing of high-frequency signals. When modulating the gap distance by a SAW with an angular frequency o1 and when supplying an additional voltage at a high frequency o2 to the gap, the mixing leads to a frequency spectrum for the tunneling current I:

+ P,,,sin (~,t + 9) + PF, cos[(w, ? ~*)t + ‘p] + P,,, cos(20, t + 2~) + Ptlsin [(20, IfIW& + 24471 + P,,, sin(3w,t + 3~) + P-T, cos[(3w, * W& + 3~1 f ...

(1)

with f’,, dependent on the tip-to-sample spacing d,,, the SAW amplitude d,, and the reciprocal decay length of the electron wave function in the tunneling gap k. and in some cases also on the superimposed a.c. voltage V, and the gap voltage V,. For small acoustic wave amplitudes compared with d, one obtains in linear approximation for the a.c. component of the tunneling current at the lowest difference frequency 10, - 0~1

with the local phase cp of the SAW linearly dependent on the propagation length. Besides the a.c. frequency terms there is a contribution to the d.c. tunneling current as ‘((2kd,)‘+

1) +

227

I Thin Solid Films 264 (1995) 226-229

a.c. tunneling current caused by the normal component of the displacement vector. If one is interested in the elastic properties of thin films a further important property of SAWS can be exploited. A Rayleigh wave travelling along an unloaded surface usually shows no dependence of the phase velocity on the frequency. With a thin film deposited on the bulk material the waves become dispersive. From the measurement of the dispersion relation the elastic constants of the film and of the bulk material can be obtained by numerically solving the inverse problem of the surface wave dispersion relation. The precision of the elastic constants calculated in this way can be increased by the utilization of different surface acoustic modes [lo]. Local mapping of the material parameters of thin films can be performed by the evaluation of the dispersion relation, i.e. the functional dependence of the phase velocity on h/A with h the film thickness and A the wavelength of the SAW. For that purpose the phase difference between two topographic points parallel to the propagation direction has to be measured varying either h or A. The direct determination of the SAW velocity requires the phase of the difference frequency signal upon two topographically extremal points, where only the normal component of the tunneling current contributes

[Ill. 3. Experimental

results and discussion

The counter electrode of the SATM was a Au film with an average thickness of 100 nm which was evaporated on a YZ-LiNbO, crystal cut. A schematic diagram of the set-up is presented in Fig. 1. The SAW was excited by a conventional IDT with a center frequency of 39.5 MHz. The a.c. tip voltage frequency was detuned by 50 kHz from the SAW frequency. The

rf

generators

attenuators

mixer

phase

amplitude

..

which is negligible for small wave amplitudes d, compared with the unmodulated tip-to-sample distance d,,. For samples with non-ideally flat surfaces the tunneling geometry has to be described in three dimensions 191. This will lead to a tunneling current consisting of three components each affected by the surface oscillation amplitudes. Therefore, the a.c. components contain the information on the elastic constants of the solid. Then Eq. (2) describes the component of the

particle

Fig. 1. Schematic

diagram

displacement

of the measuring

damping

arrangement

mass

228

T. Hesjedal et al. I Thin Solid Films 264 (1995) 226-229

Fig. 2. SATM topographic image of a Au film (100 nm thick) on a YZ-LiNbO, crystal cut.

Fig. 4. Amplitude mapping of the a.c. tunneling current of the area imaged in Fig. 2.

scan direction of the SATM was perpendicular to the propagation direction of the SAWS. Fig. 2 shows a 50 x 50 nm2 grey scale image of the topography measured in the constant current mode. The step width was 1 8, in both directions. The grains have a typical scale of some ten nanometers. Figs. 3 and 4 present the phase and the amplitude images of the a.c. tunneling current measured simultaneously. By locking at the mixing frequency, they can be seen as a stroboscopic view of the oscillating surface. The propagation direction of the acoustic wave was almost parallel to the y axis of the figure, the scan direction perpendicular to it. The phase (amplitude) of the a.c. tunneling current shows the maximum con-

trast parallel (perpendicular) to the propagation direction. This behavior can clearly be verified by viewing the marked areas (arrows in Figs. 3 and 4). When comparing local maximum positions on flat grain structures the linear dependence of the phase on the distance becomes evident [ 111. The phase image provides even more information about the surface because it is the convolution of the acoustic wave field signal with the topographic one [9], i.e. the wave field mapping as well as the resolutionenhanced topography can be obtained. The resolution enhancement comes from the fact that the modulation of the tip-to-sample distance is transferring the topographic information to a higher frequency band with smaller noise contributions [12]. It is now possible to use the complete phase-velocity image as an input for the inverse dispersion problem, regarding the local tip area to be three dimensional as described previously ]9,131. Owing to the linear dependence of the phase of the SAW cp = 21rxlA on the propagation length x a SAW with 100 pm wavelength, which corresponds to a frequency of about 35 MHz on YZ-LiNbO,, has a phase difference of some (lo-‘)’ for a propagation distance of 100 nm. This can be measured by the usual lock-in technique with a phase error of about O.OOl”, i.e. lateral resolution in the nanometer range for the determination of elastic constants is reachable.

4. Conclusions

Fig. 3. Phase mapping of the a.c. tunneling current of the area imaged in Fig. 2.

The modified scanning tunneling microscopy technique presented in this paper reveals the possibility of obtaining, besides the surface topography, the phase

T. Hesjedal et al. I Thin Solid Films 264 (1995) 226-229

and the amplitude of surface oscillations owing to a propagating SAW. In a further step the elastic properties of thin films and layered structures up to approximately one SAW wavelength in depth within lateral nanoregions can be obtained out of the phase mapping. Therefore it will be possible to investigate the mechanical properties of nanostructures such as quantum dots and quantum wires as well as layered structures like quantum wells. Thereby, a new field complementary to the spectroscopic methods is opened.

References [l] R. Truell. C. Elbaum and B.B. Chick, Ultrasonic Methods in Solid Stare Physics, Academic Press, New York, 1969. [2] J.P. Monchalin, IEEE Trans. Ultrason. Ferroelectr. Freq. Confrol UFFC-33, IEEE, New York, 1986, p. 485. [3] H. Cerva and W. Graeff, Phys. Stat. Sol. (a), 82 (1984) 35.

[41 H.P. Feuerbaum, Scanning Electron.

PI W. Rohrbeck

229

H.P. Grass],

U. Knauer

and R. Veith,

Microsc.,

1 (1983) 55. and E. Chilla, Phys. Slat. Sol. (a)

, 131 (1992)

69.

b51 E. Chilla, T. Hesjedal and H.-J. Frdhlich, Proc. IEEE Ultrasonics Symposium, Cannes. November, 1994. IEEE Publishing Services, New York, 1994, p. 363. [71 W. Rohrbeck, E. Chilla. H.-J. Friihlich and J. Riedel, Appl. Phys. A, 52 (1991) 344.

PI E. Chilla, W. Rohrbeck, H.-J. Friihlich, R. Koch and K.H. Rieder, Appl. Phys. Len., 61 (1992) 3107. [91 E. Chilla, W. Rohrbeck, H.-J. Friihlich, R. Koch and K.H. Rieder, Annal. Phys., 3 (1994) 21. SW S. Makarov, E. Chilla and H.-J. Frijhlich, in preparation. 1111 E. Chilla, J. SchGnberg and H.-J. Frdhlich, Proc. 20th Conf Advances

in Acoustics-DAGA

94,

Dresden,

March,

1994,

Physik-Verlag, Weinheim, 1994, p. 853. [121 D.W. Abraham, C.C. Williams and H.K. Wickramasinghe, Appl. Phys. Left., 53 (1988) 1503. [I31 E. Chilla and H.-J. Friihlich. Proc. IEEE Ultrasonics Symposium, Cannes, November, 19Y4. IEEE Publishing Services, New York, 1994, p. 355.