纳米机电系统是一个重要的研究领域，它不仅促进了传感器、信号处理、光机械等应用的发展，也是进行介观机械系统量子行为以及声子辅助机械过程等基础问题研究的理想实验平台。高频率与高品质因数的要求对构建纳米机电系统的材料提出了严苛要求，而碳纳米管凭借其优越的机械和电学性能以及长径比在纳米机电系统领域发挥了重要作用。本论文利用碳纳米管的弯曲和扭转振动模式与外界具有较强耦合的特点，对碳纳米管弯曲和扭转振动器件开展了系统的研究。碳纳米管量子点-机械振子耦合系统是研究非线性力学以及机械振动和电子隧穿相耦合的理想实验体系，已有研究缺乏对碳管大振幅弯曲振动情况以及机械振动对电子隧穿影响的研究。本文利用碳纳米管的弯曲振动模式和外电极的耦合构建了一个量子点-机械振子耦合系统，采用库仑整流法在不同的直流栅压和驱动频率下测量经过机械振动调制后的量子点直流隧穿电流，观察到了非线性共振模式的激发以及库仑峰的伞状展宽和交叠图像。通过有限元分析和欧拉梁方程计算，获得了碳纳米管机械振子的面内和面外振动模式的空间形态、共振频率和非线性系数，发现了该系统中的达芬非线性、倍频激励、分频激励和混频激励等非线性现象。提出了机械振动对电子隧穿的调制模型，建立了量子点直流隧穿电流库仑峰沿直流栅压展宽的边缘与机械振子幅频响应曲线的对应关系。为了验证模型和深入理解，推导了机械振动存在时普适的直流隧穿电流表达式并准确复现了实验结果。这些成果为进一步研究和理解纳米机械系统的非线性振动及其与电子输运的相互耦合奠定了基础。作为一种古老的精密测量仪器，扭秤也是一种桨振荡器机电系统。现有扭秤灵敏度的进一步提高受困于传统材料的加工难度和表面效应。本论文利用碳纳米管的扭转振动模式，以单根碳纳米管为悬丝，以石墨烯-超顺排碳纳米管复合膜双面镀10纳米铝膜为镜子，制作了超灵敏扭秤。通过测量微瓦级功率的光压，证明了碳纳米管扭秤具有fN级力的分辨率，与传统材料扭秤相比，灵敏度取得了几个数量级的进步。在不同气压下测量了扭秤的扭转振动行为，研究了简谐势场的一维布朗运动，并分析了布朗噪声决定的测力极限。该研究成果为进一步提高测力灵敏度，精确控制碳纳米管扭转角度以便研究扭转振动和电信号的耦合，以及简谐势场的一维布朗运动提供了一个新的研究平台。
Nanoelectromechanical system (NEMS) is an important area of research, which not only promotes the development and application of sensors, signal processing, optical machinery, etc., but is also an ideal experimental platform for basic research on the quantum behavior of mesoscopic mechanical systems and phonon-assisted mechanical processes. The requirements of high frequency and high quality factor put forward strict requirements on the materials used to construct NEMS. Carbon nanotubes have played an important role in the field of NEMS due to their superior mechanical and electrical properties and high aspect ratio. Taking advantage of the strong coupling between the bending and torsional vibration modes of carbon nanotubes and the environment, this paper conducts systematic studies on carbon nanotube bending and torsional vibration devices. CNT quantum dot mechanical resonator coupling system is an ideal experimental platform for studying nonlinear mechanics and the coupling between mechanical vibration and electron tunneling. However, the existing studies do not touch on the problems of large amplitude bending vibration of CNT and the modulating effect of mechanical vibration on electron tunneling. In this thesis, a quantum dot mechanical resonator coupling system is constructed by utilizing the coupling between the bending vibration mode of CNT and external electrodes. Coulomb rectification method is used to measure the vibration-modulated DC tunneling current of the quantum dot at different DC gate voltage and driving frequency. The excitation of nonlinear resonance modes and the umbrella-shaped broadening and overlapping images of the Coulomb peaks are observed. By using finite element analysis and Euler beam equation calculations, the spatial shape, resonance frequency and nonlinear coefficients of the in-plane and out of plane vibration modes of CNT resonator are obtained, which reveals nonlinear phenomena such as Duffing nonlinearity, double-, fractional-, and mixed frequency excitations. A modulation model of mechanical vibration on electron tunneling is proposed, and the relationship between the broadened edge of the Coulomb peak along the DC gate voltage and the amplitude-frequency response curve of the resonator is established. To verify the model and deepen the understanding, the universal DC tunneling current expression when mechanical vibration exists is deduced and the experimental results are accurately reproduced. The study on the carbon nanotube quantum dot-mechanical resonator coupling system opens burgeoning opportunities for investigating and understanding the nonlinear motion of a NEMS and its interactions with electron transport in quantum regimes.As an ancient scientific instrument with high precision, torsion balance is also a paddle oscillator NEMS. The further improvement of the sensitivity of the existing torsion balances is limited by the difficulties in fabrication and surface effects of traditional materials. In this thesis, by taking advantage of the torsional vibration mode of CNT, a ultra-sensitive torsion balance is made with a single CNT as the suspended fiber and a graphene-SACNT membrane deposited by 10 nm Al on both sides as the mirror. By measuring the light pressure of microwatt laser, it is proved that the CNT torsion balance has a force resolution of femtonewton. Compared with the traditional torsion balance, the sensitivity has been improved by several orders of magnitude. The torsional vibration behavior of the torsion balance is measured under different air pressures, the one-dimensional Brownian motion in a harmonic potential field is studied, and the thermal noise limit on the measurement of static force is analyzed. The study provides a new platform for improving the sensitivity of measuring force, precisely controlling the torsion angle of CNT in order to study the coupling of torsional vibration and electron transport, as well as the one-dimensional Brownian motion in a harmonic potential field.
