We demonstrate the continuous and reversible tuning of the optical band gap of suspended monolayer MoS 2 membranes by as much as 500 meV by applying very large biaxial strains. By using chemical vapor deposition (CVD) to grow crystals that are highly impermeable to gas, we are able to apply a pressure difference across suspended membranes to induce biaxial strains. We observe the effect of strain on the energy and intensity of the peaks in the photoluminescence (PL) spectrum, and find a linear tuning rate of the optical band gap of 99 meV/%. This method is then used to study the PL spectra of bilayer and trilayer devices under strain, and to find the shift rates and Grüneisen parameters of two Raman modes in monolayer MoS 2 . Finally, we use this result to show that we can apply biaxial strains as large as 5.6% across micron sized areas, and report evidence for the strain tuning of higher level optical transitions.KEYWORDS: Strain engineering, MoS 2 , photoluminescence, bandgap, Raman spectroscopy, biaxial strain 3 The ability to produce materials of truly nanoscale dimensions has revolutionized the potential for modulating or enhancing the physical properties of semiconductors by mechanical strain 1 . Strain engineering is routinely used in semiconductor manufacturing, with essential electrical components such as the silicon transistor or quantum well laser using strain to improve efficiency and performance 2,3 . Nano-structured materials are particularly suited to this technique, as they are often able to remain elastic when subject to strains many times larger than their bulk counterparts can withstand 4 . For instance, bulk silicon fractures when strained to just 1.2%, whereas silicon nanowires can reach strains of as much as 3.5% 5 . Parameters such as the band gap energy or carrier mobility of a semiconductor, which are often crucial to the electronic or photonic device performance, can be highly sensitive to the application of only small strains. The combination of this sensitivity with the ultra-high strains possible at the nanoscale could lead to an unprecedented ability to modify the electrical or photonic properties of materials in a continuous and reversible manner.Monolayer MoS 2, a 2D atomic crystal, has been shown in both theory 6,7 and experiment [8][9][10][11][12] to be an ideal candidate for strain engineering. It belongs to the class of 2D transition metal dichalcogonides (TMD's), and as a direct-gap semiconductor 13 has received significant interest as a channel material in transistors 14 , photovoltaics 15 and photodetection 16 devices. It has a breaking strain of 6-11% as measured by nanoindentation, which approaches its maximum theoretical strain limit 17 and classifies it as an ultra-strength material. Its electronic structure has also proven to be highly sensitive to strain, with experiments showing that the optical band gap reduces by ~50 meV/% for 4 uniaxial strain 8,11 , and is predicted to reduce by ~100 meV/% for biaxial strain 18,19 . This reversible modulation of the band...

Monolayer molybdenum disulfide (MoS2) has emerged as a model system for studying many-body physics because the low dimensionality reduces screening leading to tightly bound states stable at room temperature. Further, the many-body states possess a pseudo-spin degree of freedom that corresponds with the two direct-gap valleys of the band structure, which can be optically manipulated. Here we focus on one bound state, the negatively charged trion. Unlike excitons, trions can radiatively decay with non-zero momentum by kicking out an electron, resulting in an asymmetric trion photoluminescence (PL) peak with a long low-energy tail and peak position that differs from the zero momentum trion energy. The asymmetry of the trion PL peak and resulting peak red-shift depends both on the trion size and a temperature-dependent contribution. Ignoring the trion asymmetry will result in over estimating the trion binding energy by nearly 20 meV at room temperature. We analyze the temperature-dependent PL to reveal the effective trion size, consistent with the literature, and the temperature dependence of the band gap and spin-orbit splitting of the valence band. This is the first time the temperature-dependence of the trion PL has been analyzed with such detail in any system.

We report on a modified transfer technique for atomically thin materials integrated into microelectromechanical systems (MEMS) for studying strain physics and creating strainbased devices. Our method tolerates the non-planar structures and fragility of MEMS while still providing precise positioning and crack-free transfer of flakes. Furthermore, our method used the transfer polymer to anchor the 2D crystal to the MEMS, which reduces the fabrication time and increases the yield, and allowed us to exploit the strong mechanical coupling between the 2D crystal and polymer to strain the atomically thin system. We successfully strained single atomic layers of molybdenum disulfide (MoS 2) with MEMS devices for the first time and achieved greater than 1.3% strain, marking a major milestone for incorporating 2D materials with MEMS. We used the established strain response of MoS 2 Raman and photoluminescence spectra to deduce the strain in our crystals and provide a consistency check. We found good comparison between our experiment and the literature.

Pristine graphene encapsulated in hexagonal boron nitride has transport properties rivalling suspended graphene, while being protected from contamination and mechanical damage. For high quality devices, it is important to avoid and monitor accidental doping and charge fluctuations. The 2D Raman double peak in intrinsic graphene can be used to optically determine charge density, with decreasing peak split corresponding to increasing charge density. We find strong correlations between the 2D 1 and 2D 2 split vs 2D line widths, intensities, and peak positions. Charge density fluctuations can be measured with orders of magnitude higher precision than previously accomplished using the G-band shift with charge. The two 2D intrinsic peaks can be associated with the “inner” and “outer” Raman scattering processes, with the counterintuitive assignment of the phonon closer to the K point in the KM direction (outer process) as the higher energy peak. Even low charge screening lifts the phonon Kohn anomaly near the K point for graphene encapsulated in hBN, and shifts the dominant intensity from the lower to the higher energy peak.

Graphene is a promising material for strain engineering based on its excellent flexibility and elastic properties, coupled with very high electrical mobility. In order to implement strain devices, it is important to understand and control the clamping of graphene to its support. Here, we investigate the limits of the strong van der Waals interaction on friction clamping. We find that the friction of graphene on a SiO2 substrate can support a maximum local strain gradient and that higher strain gradients result in sliding and strain redistribution. Furthermore, the friction decreases with increasing strain. The system used is graphene placed over a nanoscale SiO2 grating, causing strain and local strain variations. We use a combination of atomic force microscopy and Raman scattering to determine the friction coefficient, after accounting for compression and accidental charge doping, and model the local strain variation within the laser spot size. By using uniaxial strain aligned to a high crystal symmetry direction, we also determine the 2D Raman Grüneisen parameter and deformation potential in the zigzag direction.