# Piezoresistive heat engine and refrigerator 

P.G. Steeneken, K. Le Phan, M.J. Goossens, G.E.J. Koops, G.J.A.M. Brom, C. van der Avoort and J.T.M. van Beek 

NXP-TSMC Research Center, NXP Semiconductors, HTC 4, 5656 AE Eindhoven, the Netherlands. 

Heat engines provide most of our mechanical power and are essential for transportation on macro- scopic scale. However, although significant progress has been made in the miniaturization of elec- trostatic engines, it has proven difficult to reduce the size of liquid or gas driven heat engines below 10 $^{7}$µ m $^{3}$. 

Here we demonstrate that a crystalline silicon structure operates as a cyclic piezoresistive heat engine when it is driven by a sufficiently high DC current. A 0.34 µ m 3 engine beam draws heat from the DC current using the piezoresistive effect and converts it into mechanical work by expansion and contraction at different temperatures. This mechanical power drives a silicon resonator of 1.1 × 10 3 µ m 3 into sustained oscillation. Even below the oscillation threshold the engine beam continues to amplify the resonator’s Brownian motion. When its thermodynamic cycle is inverted, the structure is shown to reduce these thermal fluctuations, therefore operating as a refrigerator. 

Most heat engines operate by the cyclic expansion and contraction of a gas at different temperatures. Much ef- fort has gone into miniaturizing these conventional heat engine concepts $^{1–3}$. However this downscaling is diffi- cult, because the efficiency and power density of these engines reduce strongly with its size $^{4}$. A promising route for the miniaturization of heat engines is the use of an electrically heated solid as a working substance, because the large heat capacitance of solids allows much higher power densities and electrical interconnect facilitates en- ergy transport and localized heat generation at the mi- croscale. This concept has often been applied in elec- trothermal actuators for microscopic devices $^{5–10}$, how- ever the similarity between thermal expansion actuators and heat engines has received little attention. 

In order to operate as a cyclic heat engine, a thermal actuator needs to be supplemented with a mechanism that regulates the thermodynamic cycle of heating, ex- pansion, cooling and compression. This cycle can be reg- ulated by an external AC frequency synthesizer 7 or by a feedback loop, where a sustained reciprocating motion is generated from a DC power $^{5,9,10}$. In previous reports of electrothermal engines, the thermodynamic cycle was always regulated by external electronic transistor circuits and amplifiers. 

Here it is shown that a well-dimensioned silicon crystal of uniform composition operates as a cyclic heat engine when driven by a DC current. It is demonstrated that a silicon engine beam can drive a silicon resonator into sustained oscillation. In contrast to earlier work $^{5,9,10}$, no external transistors or amplifiers are needed to regulate the heat engine, because a mechanism based on the in- trinsic piezoresistive heating and thermal expansion of silicon provides the required feedback. The engine dis- placement volume of the heat engine, which similar to car engines is defined by the space occupied by the working substance, is 0.34 µ m $^{3}$. Despite its low efficiency, the en- gine’s power density is almost a factor 1000 higher than that of modern car engines. 

Like any other reciprocating heat engine, this piezore- sistive heat engine requires a minimum threshold power P$_{t}$ to compensate its internal dissipation and sustain its 

cyclic motion. In the first part of this article the opera- tion of the piezoresistive heat engine above this threshold power P$_{t}$ is demonstrated by driving a resonator into sus- tained oscillation. In the second part the motion of the device at driving powers below P$_{t}$ is investigated. Mea- surements show that the engine beam continues to in- crease the thermal energy stored in the resonance mode like a heat pump. When the thermodynamic cycle of the engine is reversed, it is shown to reduce the stored thermal energy in the resonant mode, similar to recently developed optical and RF refrigerators $^{11–18}$. In contrast to conventional refrigerators, which simultaneously re- move thermal energy from many degrees of freedom of a substance, this type of refrigerators cools by removing thermal energy from only a single mechanical resonance mode. This piezoresistive refrigerator provides an alter- native way to reduce undesirable Brownian fluctuations in micromechanical sensors and mirrors. 

Experiments are performed on the homogeneous crys- talline silicon structure shown in Fig. 1a. The struc- ture consists of a mass measuring 12.5 × 60.0 × 1.5 µ m $^{3}$, which is suspended by a 3 µ m wide spring beam and a 280 nm narrow engine beam. Both beams have a length of 800 nm. Before discussing the stand-alone operation of the heat engine, its in-plane mechanical resonance at 1.26 MHz (Fig. 2a) is characterized by actuating it via terminal T3 with an AC electrostatic force and detect- ing the strain variations in the engine beam using the piezoresistive effect (see Methods). To operate the de- vice as a piezoresistive heat engine, the external AC ac- tuation voltage is disconnected from terminal T3. Thus, as shown in Fig. 1b the device is only connected at ter- minal T1 to a DC current source I$_{dc}$ and to a capacitively coupled oscilloscope. All other terminals are grounded. At low values of I$_{dc}$ only noise is observed on the oscil- loscope. However, if the DC current is increased above a threshold I$_{t}$ =1.19 mA a remarkable effect occurs: the device spontaneously starts to oscillate and generates a 

## Piezoresistive heat engine 

