Materials for Nano - scale displacement sensing based on Van der Waals interaction

We propose the nano-scale displacement sensor with high resolution for weak-force systems could be realized based on vertical stacked two-dimensional (2D) atomic corrugated layer materials bound through Van der Waals (VdW) interaction. Using first-principles calculations, we found the electronic structure of bi-layer blue phosphorus (BLBP) varies appreciably to both the lateral and vertical interlayer displacement. The variation of electronic structure due to the lateral displacement is attributed to the changing of the interlayer distance dz led by atomic layer corrugation, which is in a uniform picture with vertical displacement. Despite different stacking configurations, the change of in-direct band gap is proportional to d−2 z . This stacking configuration independent d−2 z law is found also works for other graphene-like corrugated bi-layer materials, for example MoS2. By measuring the tunable electronic structure using absorption spectroscopy, the nano-scale displacement could be detected. BLBP represents a large family of bi-layer 2D atomic corrugated materials for which the electronic structure is sensitive to the interlayer vertical and lateral displacement, thus could be used for nano-scale displacement sensor. Since this kind of sensor is established on atomic layers coupled through VdW interaction, it provides unique applications in measurements of nano-scale displacement induced by tiny external force. 1 ar X iv :1 41 2. 53 60 v1 [ co nd -m at .m tr lsc i] 1 7 D ec 2 01 4 High-resolution displacement sensing is essential for scientific measurement with a wide range of applications, among which, the nano-scale positioning measurement is becoming increasingly important in ultra-precision manufacturing and metrology in nano-technological applications. On micro-scale level, many micro-sensors such as microphones, accelerometers and pressure sensors, ultimately rely on accurately detecting small displacements with micro-scale resolution [1–3]. With the development of nanotechnology, the transducer fundamental concepts at the micro-scale are extended into the nano-scale region [4]. Nano-scale displacement sensing with high resolution has urgent applications for nano-devices. Conventional displacement sensing are based on optical interferometry [5], capacitance [6], and piezoresistance [7, 8]. For the nano-scale sensing, the conventional methods encounters different drawbacks. The optical methods are limited by the drawbacks of non-linearity, fringe effects, proportionality errors, volume and cost of optical components, and mostly important, the light wavelength. Capacitive sensing suffers from signal loss and is limited by area [6]. Piezoresistors scaled down to nano-scale leads to strongly increased resistance and the resistance noise followed [7, 8]. To achieve the high resolution in nano-scale, new materials, for example nanotubes, have been applied for nano-scale sensing [4, 9–13]. Yet despite these attempts in nano-materials, it is still complex to get high resolution for displacement induced by tiny force. For example, to measure the displacement of a quantum mechanical oscillator, a single electron transistor was applied as a displacement sensor to achieve the quantum-limited sensitivity [1]. Hence the alternative complementary methods of measuring precise displacement for weak-force system have urgent need in both scientific research and practical applications. Vertical stacked two-dimensional (2D) atomic layers formed by Van der Waals (VdW) interaction arouse intense research interest recently. The weak VdW interaction leads to many new physical phenomena including new van Hove singularities [14–17], Fermi velocity renormalization [18, 19] and Hofstadters butterly pattern [20–24] in graphene bi-layer as well as the tunable interlayer coupling in bi-layer semiconducting MoS2 [25]. In this Letter, we propose a new nano-scale displacement sensor based on bi-layer blue phosphorus (BLBP). Blue phosphorus is a new two dimensional (2D) material predicted by first principles calculations [26]. Similar with other 2D layered materials, BLBP is coupled by VdW interaction. Using first-principles calculations within density functional theory (DFT), we found the electronic structure of BLBP is significantly sensitive to the lateral and vertical displacement between