Real-time nanomechanical property modulation as a framework for tunable NEMS

Phase-change materials (PCMs) can switch between amorphous and crystalline states permanently yet reversibly. However, the change in their mechanical properties has largely gone unexploited. The most practical configuration using suspended thin-films suffer from filamentation and melt-quenching. Here, we overcome these limitations using nanowires as active nanoelectromechanical systems (NEMS). We achieve active modulation of the Young’s modulus in GeTe nanowires by exploiting a unique dislocation-based route for amorphization. These nanowire NEMS enable power-free tuning of the resonance frequency over a range of 30%. Furthermore, their high quality factors (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q$$\end{document}Q > 104) are retained after phase transformation. We utilize their intrinsic piezoresistivity with unprecedented gauge factors (up to 1100) to facilitate monolithic integration. Our NEMS demonstrate real-time frequency tuning in a frequency-hopping spread spectrum radio prototype. This work not only opens up an entirely new area of phase-change NEMS but also provides a novel framework for utilizing functional nanowires in active mechanical systems.


Device fabrication
Fabrication of the electrodes: To manufacture the electrical platform for the testing of freestanding GeTe nanowires, we used a 10×10 mm 2 piece diced from a Si wafer with a thin layer of Si3N4 (0.33 µm) on top of a 3 µm-thick oxide layer. The Au electrodes (95 nm) were patterned using electron beam lithography (JEOL 5500FS) and deposited by thermal evaporation with a 5 nm of Cr adhesion layer. With the electrodes acting as a hard-mask, the Si3N4 thin-film was anisotropically etched by reactive ion etching (RIE, Oxford 80 Plasmalab).
Thus, we formed trenches deeper than 0.4 µm in total by fully removing the Si3N4 layer.
Growth of GeTe nanowires: Germanium telluride (GeTe) nanowires were synthesized by a catalyst-assisted vapor-liquid-solid (VLS) growth mechanism 1,2 . As the catalyst, a thin film of Au-Pd (~5 nm) was sputtered on silicon substrate. The synthesis was carried out in a 1-inch tube furnace (Lindberg/Blue M) where a few milligrams of GeTe powder (Alfa Aesar, 99.999% purity) was placed in the centre while the substrate was placed at ~5 inches upstream from the centre. Before heating up the furnace, Ar gas was purged into the chamber several times to remove any residual oxygen until reaching a pressure of 30 mTorr. The base pressure in the furnace was then stabilized at 100 Torr while keeping the argon flow rate at 100 sccm.
Subsequently, the temperature of the furnace was ramped up to 650 ℃ and the nanowire synthesis was carried out for an hour. After completion of the growth, the furnace was gradually cooled down to room temperature. The scanning electron microscope (SEM) image of the fabricated nanowires is given in Fig. S1.
Deposition of the nanowires over the electrodes: We mechanically transferred the nanowires over the electrodes using a bottom-up approach by utilising polydimethylsiloxane (PDMS) stamps. The steps regarding the method can be found elsewhere 3 .

Experimental setup for resonance testing and tuning
The setup combining both piezoresistive detection and electrical tuning of the resonator is depicted in Fig. S2. Actuation of the device is performed through direct mechanical coupling using a piezoceramic shaker (~780 pF). The chip was electrically isolated and mounted on the actuator. The drive signal ( ) was sourced by the lock-in system (Zurich Instruments HF2LI) and amplified by the high-power amplifier (HPA, Mini Circuits LZY-22+). Note that the drive signal is applied to the bottom plate of the piezo crystal while its top plate is grounded in order to avoid any performance degradation in the NEMS resonator through capacitive coupling.
For the piezoresistive detection, the d.c. bias voltage across the nanowire is supplied by a battery. When the simultaneous monitoring of the electrical resistance is of interest, e.g. in Figs. 2C and 3B of the main article, the d.c. bias was applied by the source measure unit (SMU, Keithley 2410 SourceMeter). The read-out signal (2 ) was coupled into the low-noise Electrical measurement and tuning setup. The lock-in amplifier drives the piezo actuator at a frequency of and detects the frequency response of the resonator at 2 reference. Amplification of the drive and the read-out signals is performed by the HPA and the LNA, respectively. The pulse generator is utilised for both tuning the resonator and controlling the RF switch that efficiently isolates the detection and the tuning circuitry. amplifier (LNA, MITEQ AU-1442) using a coupling capacitor (Crystek DC Block 300 kHz -3 GHz). The amplified signal was routed into the lock-in amplifier with its demodulation reference set to 2 .
The tuning of the device was performed by electrical pulses, which were generated by the arbitrary function generator (AFG, Tektronix AFG3151C). It is important to mention that the RF switch (Mini Circuits ZFSWA-2-46) isolates the detection and the tuning circuitry for energy efficiency and is controlled by another AFG (Tektronix AFG3102C). When the switch is in sate '1', the piezoresistive detection is activated. For the electrical tuning, the switch is transiently brought to state '2' connecting the AFG directly to the nanowire. Finally, frequency response of the resonator was acquired by the data acquisition (DAQ) software of the lock-in amplifier through universal serial bus (USB) interface.

Non-zero phase Lorentzian fitting of resonance peaks
The motion of a damped harmonic oscillator, e.g. spring-mass system, driven by a sinusoidal force is governed by the following differential equation where is the displacement, is the mass, is the linear damping coefficient, is the spring constant while 0 and are the amplitude and the angular frequency of the driving force, respectively. In steady sinusoidal state, the solution to equation (S1) can be written as where the frequency dependent amplitude | 0 | and phase 0 of the displacement are: Here, = 0 ⁄ is the quality factor and 0 = √ ⁄ is the resonance frequency of the mechanical system for 2 ≪ 4 . As discussed in the main article, the piezoresistive readout signal pz ( ) in our case varies linearly with the square of the displacement ( 2 ) unlike the traditional piezoresistive transduction schemes. As given in equation (S4), | pz ( )| follows the Lorentzian lineshape.
Apart from pz ( ), there is also a constant and frequency dependent electrical background response of the experimental setup, bg ( ), regardless of the resonance condition. Hence, the overall lock-in read-out ( ) is simply the addition of these two physical quantities, i.e.
( ) = bg ( ) + pz ( ). However, it should be noted that due to non-zero delays within the experiment, e.g. non-ideal cables and device parasitics, the coupling between mechanical and electrical domains will not happen instantaneously but with an inevitable phase shift ∆ . In that case, to model the overall frequency response of the device, one should add these two terms considering the ∆ . Within a small frequency interval ( ≫ 1), | bg ( )| can be linearized as + , where and are the fitting parameters. By following a similar procedure that was previously described by Sazonova 4 , the resulting amplitude response of the overall electrical read-out can be written as: Here, abs{•} operator is the same as |•| operator, and it denotes the magnitude of the complex quantity. For | | ≫ , where is the peak height, | ( )| can be further simplified as: In Fig. S3 are depicted two sets of experimental data and best fits to them. As seen, the modified non-zero phase Lorentzian model | ( )| fits well to the data while the generic nonzero phase square root Lorentzian model 4 clearly diverges from the detected signal for the same value. This further verifies our assumption of squaring effect made in the main article.
The goodness of the fits is quantitated in terms of normalised root-mean-square-error. The  1% tuning) with a superior tuning efficiency. It can also be seen that the mode shape is dramatically altered in the case of unidirectional pulsing.

A note on phase-locked loop (PLL) measurements and the FHSS radio
PLLs are based on a negative frequency feedback loop that tries to match the phase and frequency of the loop oscillator with the phase and frequency of the input signal. Fig. S7 depicts the logical block diagram of the internal PLL circuitry within the lock-in system. Here, the loop oscillator is a numerically controlled oscillator (NCO) and the piezoresistive read-out signal is demodulated at the 2 nd harmonic of the NCO frequency to compensate for the frequency-doubling effect (subharmonic detection). The PID controller within the loop ensures the phase of the demodulated signal stably matches the setpoint ( 0 ).
Note that the NCO output directly drives the resonator in Fig. S7. We use this configuration for the FHSS radio implementation (Fig. 5A), where we form a local oscillator (LO) using the NEMS resonator. However, in the case of phase noise measurements 10 (Fig. 4), we perform open-loop frequency tracking, i.e. drive signal is disconnected from the NCO within the PLL and manually set using a separate internal NCO of the lock-in amplifier. This allows for the true phase characteristics of the NEMS device to be captured 11 . Further we select 500 Hz as the PLL bandwidth during phase noise measurements since the theoretical phase noise of the resonator is better than -110 dBc Hz -1 at 500 Hz offset. The relevant PID parameters for the desired loop bandwidth are automatically calculated by the lock-in software. The bandwidth of the low-pass filter (LPF) in IQ demodulator is set to 4 kHz for stability purposes.

Fig. S7
Interfacing of the NEMS setup with the internal PLL of the lock-in amplifier. The PLL is composed of an IQ demodulator, a PID controller, and a numerically controlled oscillator (NCO). The loop is forced to lock into the subharmonic of the read-out signal to compensate for the frequency-doubling effect caused by the transduction method. This is done via changing the harmonic settings of the phase detector to '2', which logically adds a frequency doubler on the feedback path.
For the FHSS radio experiments, the audio signal was produced with a sampling rate of 8 kHz.

Effect of growth direction on quality factors
The reason why phase-change tuning does not affect the factors in this work is actually the non-changing surface states between two phases. Here, the growth direction of these nanowires plays a significant role and causes the defects to propagate along the growth axis, i.e. along 〈110〉 crystalline orientation 12 . This behaviour is dissimilar to other nanowire systems experiencing stress, e.g. the work by Greer and Nix 13 , where the defects are pushed towards the surface. Since no new defects (or dangling bonds) are created on the surface, the factors remain almost intact.