Energy bandgap largely determines the optical and electronic properties of a semiconductor. Variable bandgap therefore makes versatile functionality possible in a single material. In layered material black phosphorus 1 5 , the bandgap can be modulated by the number of layers; as a result, few-layer black phosphorus has discrete bandgap values that are relevant for opto-electronic applications in the spectral range from red, in monolayer, to mid-infrared in the bulk limit 3,6 8 . Here, we further demonstrate continuous bandgap modulation by mechanical strain applied through flexible substrates. The strain-modulated bandgap significantly alters the charge transport in black phosphorus at room temperature; we for the first time observe a large piezo-resistive effect in black phosphorus field-effect transistors (FETs). The effect opens up opportunities for future development of electro-mechanical transducers based on black phosphorus, and we demonstrate strain gauges constructed from black phosphorus thin crystals.Under mechanical strain, the deformation of the atomic lattice is able to induce profound changes in the electronic structure of a crystalline material. This is best exemplified in doped silicon, where strain alters the energy bands of electron or hole carriers; the transfer of carriers to bands with small effective mass leads to drastic enhancement of carrier mobility (and thus conductivity) 9 13 . Strained silicon is, therefore, able to provide improved switching performance as the transistor dimension is aggressively scaled down in modern electronics 14,15 . Meanwhile, the large resistance response under strain has enabled the development of a myriad of silicon-based transducers 16 , such as strain and torque gauges, that are widely used in industrial applications.
Page 3 of 17Black phosphorus, a two-dimensional (2D) material with a puckered honeycomb lattice, offers new possibilities. The puckered lattice in a monolayer, shown in Fig. 1a, can be viewed as rows of two orthogonally coupled hinges along the zigzag direction 17 . The structure makes black phosphorus a soft, and yet mechanically resilient, material that can withstand large strain modulation 18 . More importantly, deformation of the puckers under strain changes the configuration of pz orbitals near the band edges 19 ; modulating the black phosphorus bandgap (and therefore its material properties) via strain becomes a possibility. Indeed, it has been shown that a moderate high pressure of ~1.2 GPa can close the bandgap, and raise the conductance by one order of magnitude at room temperature 20 ; modulation of the optical properties was also observed in corrugated black phosphorus sheets 21 . Those studies hinted at strain as a powerful tool to modulate the electronic and optical properties of black phosphorus.Here, we observe a large piezo-resistive effect in black phosphorus FETs at room temperature. The piezo-resistive response (defined as the relative change in sample resistance, , at a given strain, ) varies with the gate doping, and reac...