tance R$_{dc}$ = R$_{beam}$ + R$_{0}$ =794 Ω, bias and cable capac- itances C$_{0}$ = 54 nF and C$_{1}$ = 70 pF were measured using an impedance analyser at 1 . 26 MHz. Terminals T3 and T4 are grounded. A 1 MΩ input impedance voltage buffer amplifier is used to minimize the effects of cables and spectrum analyser on the engine opera- tion. In Fig. 3b DC resistive heating can lead to a tem- perature increase of the beam which opposes the refrig- eration mechanism. It is estimated from the tempera- ture dependence of the resistance and from FEM sim- ulations that the maximum temperature of the engine beam is 370 ± 20 K at I$_{dc}$ = 3 mA (see Supplementary Fig. C). This temperature increase of 17% by DC re- sistive heating is relatively small compared to the factor 5 decrease in T$_{eff}$ as a result of the reduction of Q$_{eff}$ . We thank J.J.M. Ruigrok, C.S. Vaucher, K. Reimann, R. Woltjer and E.P.A.M. Bakkers for discussions and sug- gestions and thank J. v. Wingerden for his assistance with the SEM measurements. The authors declare that they have no competing financial interests. Author Con- tributions: K.L.P., P.G.S., J.T.M.v.B. and M.J.G. in- vented and designed the device. P.G.S., K.L.P., M.J.G. and C.v.d.A. performed the experiments. P.G.S. devel- oped the theory, analysed the experiments and wrote the article. J.T.M.v.B., G.E.J.K. and G.J.A.M.V. de- veloped the process technology and manufactured the de- vice.Correspondence and requests for materials should be addressed to P.G.S. (peter.steeneken@nxp.com). 8 1 Epstein, A. H. Millimeter-scale, micro-electro-mechanical systems gas turbine engines. J. Eng. Gas Turbines Power 126 , 205–226 (2004). 2 Jacobson, S. A. & Epstein, A. H. An informal survey of power MEMS . Int. Symp. Micro-Mech. Eng. (ISMME) pK18 (2003). 3 Spadaccini, C. M. & Waitz, I. A. Comprehensive Microsys- tems , chap. 3.15 Micro-Combustion (Elsevier, Amsterdam, 2008). 4 Peterson, R. B. Size limits for regenerative heat engines. Nanoscale and Microscale Thermophysical Engineering 2 , 121–131 (1998). 5 Wilfinger, R. J., Bardell, P. H. & Chhabra, D. S. The resonistor: a frequency selective device utilizing the me- chanical resonance of a silicon substrate. IBM J. Res. Dev. 12 , 113–117 (1968). 6 Elwenspoek, M. et al. Transduction mechanisms and their applications in micromechanical devices. Proc. IEEE MEMS 126–132 (1989). 7 Lammerink, T., Elwenspoek, M. & Fluitman, J. Frequency dependence of thermal excitation of micromechanical res- onators. Sens. Act. A 25–27 , 685–689 (1991). 8 Guckel, H. et al. Thermo-magnetic metal flexure actuators. IEEE Solid-State Sensor and Actuator Workshop 5 , 73–75 (1992). 9 Reichenbach, R. B., Zalalutdinov, M., Parpia, J. M. & Craighead, H. G. RF MEMS oscillator with integrated resistive transduction. IEEE Electr. Dev. L. 27 , 805–807 (2006). 10 Seo, J. H. & Brand, O. High q -factor in-plane-mode reso- nant microsensor platform for gaseous/liquid environment. J. MEMS 17 , 483–493 (2008). 11 Cohadon, P., Heidmann, A. & Pinard, M. Cooling of a mirror by radiation pressure. Phys. Rev. Lett. 83 , 3174– 3177 (1999). 12 Metzger, C. H. & Karrai, K. Cavity cooling of a microlever. Nature 432 , 1002–1005 (2004). 13 Arcizet, O., Cohadon, P.-F., Briant, T., Pinard, M. & Hei- dmann, A. Radiation-pressure cooling and optomechanical instability of a micromirror. Nature 444 , 71–74 (2006). 14 Kleckner, D. & Bouwmeester, D. Sub-kelvin optical cooling of a micromechanical resonator. Nature 444 , 75–78 (2006). 15 Schliesser, A., Del’Haye, P., Nooshi, N., Vahala, K. J. & Kippenberg, T. J. Radiation pressure cooling of a microme- 28 Bullis, W. M., Brewer, F. H., Kolstad, C. D. & Swartzen- druber, L. J. Temperature coefficient of resistivity of sil- icon and germanium near room temperature. Solid-State Electronics 11 , 639–646 (1968). 27 Burg, T. P. et al. Weighing of biomolecules, single cells and single nanoparticles in fluid. Nature 446 , 1066 (2007). 26 Ebefors, T. & Stemme, G. The MEMS Handbook: MEMS Applications , chap. Microrobotics (CRC Press, Boca Ra- ton, 2006). 25 Weldon, J. A., Alem´ an, B., Sussman, A., Gannett, W. & Zettl, A. K. Sustained mechanical self-oscillations in carbon nanotubes. Nano Lett. 10 , 1728–1733 (2010). 24 Ayari, A. et al. Self-oscillations in field emission nanowire mechanical resonators: A nanometric dc-ac conversion. Nano Lett. 7 , 2252–2257 (2007). 23 Fan, D. L., Zhu, F. Q., Cammarata, R. C. & Chien, C. L. Controllable high-speed rotation of nanowires. Phys. Rev. Lett. 94 , 247208 (2005). 22 Fennimore, A. M. et al. Rotational actuators based on carbon nanotubes. Nature 424 , 408–410 (2003). 21 K¨ oser, H. & Lang, J. Modeling a high power density mems magnetic induction machine. Proc. MSM Nanotech (2001). 20 Spadaccini, C. et al. High power density silicon combustion systems for micro gas turbine engines. Proc. ASME/IGTI Turbo Expo GT–2002–30082 (2002). 19 Feynman, R. P., Leighton, R. B. & Sands, M. The Feyn- man Lectures on Physics , vol. I, ch. 46 (Addison-Wesley, Reading, 1963). 18 Teufel, J., Donner, T., Castellanos-Beltran, M. A., Harlow, J. & Lehnert, W. Nanomechanical motion measured with an imprecision below that at the standard quantum limit. Nature Nanotech. 4 , 820–823 (2009). 17 Metzger, C., Favero, I., Ortlieb, A. & Karrai, K. Opti- cal self cooling of a deformable F abry- P erot cavity in the classical limit. Phys. Rev. B 78 , 035309 (2008). 16 Brown, K. R. et al. Passive cooling of a micromechanical oscillator with a resonant electric circuit. Phys. Rev. Lett. 99 , 137205 (2007). chanical oscillator using dynamical backaction. Phys. Rev. Lett. 97 , 243905 (2006).