The physics of mesoscopic electronic systems has been explored for more than 15 years. Mesoscopic phenomena in transport processes occur when the wavelength or the coherence length of the carriers becomes comparable to, or larger than, the sample dimensions. One striking result in this domain is the quantization of electrical conduction, observed in a quasi-one-dimensional constriction formed between reservoirs of two-dimensional electron gas. The conductance of this system is determined by the number of participating quantum states or 'channels' within the constriction; in the ideal case, each spin-degenerate channel contributes a quantized unit of 2e(2)/h to the electrical conductance. It has been speculated that similar behaviour should be observable for thermal transport in mesoscopic phonon systems. But experiments attempted in this regime have so far yielded inconclusive results. Here we report the observation of a quantized limiting value for the thermal conductance, Gth, in suspended insulating nanostructures at very low temperatures. The behaviour we observe is consistent with predictions for phonon transport in a ballistic, one-dimensional channel: at low temperatures, Gth approaches a maximum value of g0 = pi2kB2T/3h, the universal quantum of thermal conductance.

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In their paraelectric phases, SrTi03 and KTa0 3 crystallize in the cubic perovskite structure (space group Oh 1 ) in which the first-order Raman effect is forbidden. We discuss here experiments in which firstorder Raman scattering has been induced by the application of an external electric field that serves to remove the center of inversion symmetry of the crystals. An electric field applied along a (001) direction induces a C^v symmetry in the crystal and renders all the phonons first-order Raman-active. We have studied induced scattering from all four TO phonons in SrTi03 and from three TO phonons in KTa03 at temperatures between 8 and 300°K and with electric fields between 0.2 to 15 kV/cm. Most attention was given to the lowest-frequency TO phonon-the "soft" or "ferroelectric" mode-whose striking decrease in frequency as the temperature is lowered signals the lattice instability associated with the ferroelectric phase transition. Detailed investigations were also made of the electric field dependence of the soft-mode frequencies in both materials. At 8°K this frequency in SrTiOs increases from 10 cm -1 at zero field to 45 cm -1 at 12 kV/cm. Similar behavior is observed in KTa0 3 . From this behavior we infer values for the nonlinear dielectric response coefficients of the crystals. Some discussion is given of the large discrepancies between the soft-mode linewidths that we observe and those previously obtained from infrared (IR) reflectivity experiments. At 80°K in SrTi03 the Raman and IR measurements yield values of 3 and 61.7 cm -1 , respectively. Additional topics considered include relative electric-field-induced scattering cross sections for the various phonon modes, and the temperature dependence of the soft-mode linewidth. Finally, the question of anomalous first-order Raman scattering in the intrinsic spectrum of SrTi03, recently reported by several authors, is considered in the light of the field-induced first-order Raman scattering.

We describe and demonstrate a new class of devices that enable direct thermal conductance measurements on monocrystalline nanostructures. These are possible through our newly developed techniques for three-dimensional, successive surface nanomachining of GaAs-based heterostructures. Our methods allow the patterning of complex devices comprising electrically insulating, mesoscopic thermal conductors with separate, thermal transducers in situ. Intimate thermal contact between these elements is provided by their epitaxial registry. Low-temperature thermal conductance measurements indicate that phonon boundary scattering in these initial nanometer is scale structures is partially specular. These devices offer promise for ultrasensitive bolometry and calorimetry.

We have developed specially designed semiconductor devices for the measurement of thermal conductance in suspended nanostructures. By means of a novel subtractive comparison, we are able to deduce the phonon thermal conductance of individual nanoscale beams of different geometry and dopant profiles. The separate roles of important phonon scattering mechanisms are analyzed and a quantitative estimation of their respective scattering rates is obtained using the Callaway model. Diffuse surface scattering proves to be particularly important in the temperature range from 4 to 40 K. The rates of other scattering mechanisms, arising from phonon-phonon, phonon-electron, and phonon-point defect interactions, also appear to be significantly higher in nanostructures than in bulk samples.

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We have studied the photoluminescence and photoexcitation spectra of ultrasmall structures, of approximately 500 Å in dimension, which we refer to as quantum ribbons and quantum disks. These are fabricated from GaAs-AlGaAs quantum wells grown by molecular beam epitaxy and patterned by electron beam lithography. Contrary to our expectation, photoluminescence from these structures is extremely efficient. The excitation spectra of the two types of small structures differ greatly from each other and from that of the as-grown quantum wells. These differences may be a result of the confinement of the carriers in these small structures.

In Cochran's theory of ferroelectricity, 1 softphonon modes are of central importance. As the transition temperature is approached from above (in the paraelectric phase) the phonon frequency tends toward zero. We have previously reported studies of the soft-phonon modes in KTa0 3 2 and SrTi0 3 3 in which an electric field was employed to induce Raman scattering from these odd-parity phonons. In this Letter we report the observation of striking electric field dependence of some optical-phonon frequencies in SrTi0 3 . In particular, the lowest lying transverse optical phonon has been observed to shift in frequency by 400 % and to split into two components polarized parallel and perpendicular to the applied field. Schaufele, Weber, and Silverman 4 have recently observed a small electric-field shift in the soft mode frequency at 77°K. We have examined the induced Raman scattering at a variety of electric fields (between 0.2 and 12 kV/cm) and at temperatures between 8 and 250°K with the following general results:(1) With very small applied fields the soft-mode frequency varies with temperature from 11 cm" 1 at 8°K to 85 cm"" 1 at 250°K, in good agreement with the predictions of the Lyddane-Sachs -Teller (LST) relation inserting Weaver's values of the dielectric constant. 5 (2) At low temperatures (<55°K) the spectrum of the fieldinduced scattering exhibits a field-dependent structure. Figure 1, taken at 8°K, shows that as the field is increased not only does the frequency of the soft mode shift from 11 to 45 cm"" 1 , but also three additional peaks become visible. Those labeled B and C are identified as components of the soft TO mode, polarized perpendicular and parallel to the applied field, respectively. Peaks A and D are not components of the soft mode, and appear as well in the intrinsic spectrum of SrTiO s [see Fig. 1(b)]. (3) The effects of electric field become increasingly strong as the temperature is lowered. This is true for the efficiency of the induced Raman scattering as well as for the shifting and splitting of phonon frequencies. (4) In contrast to the case of KTaO s , we have observed in SrTi0 3 induced Raman scattering from the other TO modes at 170 and 550 cm"" 1 . We shall not discuss these results here except to say that these In electric-field-induced Raman-scattering experiments on the cubic perovskite SrTi0 3 , a striking electric field shift and splitting of the "soft" optical phonon mode is observed. Experiments were done at temperatures ranging from 8 to 250°K and for electric fields between 0.2 and 12 kV/cm. We interpret the temperature and electric field dependence of the phonon frequency using Devonshire model of ferroelectricity and the Lyddane-Sachs-Teller relation. 1176