# Exact Relationship between Black Phosphorus Thickness and Behaviors of Field-Effect Transistors
## 1 Introduction  
Graphene (G) has an absolute advantage in the preparation of high-frequency devices due to its ultra-high electron mobility, but the intrinsic graphene has no band gap, which limits its application in logic devices [1, 2]. The transition metal chalcogenides (TMDs) represented by molybdenum disulfide (MoS\({}_{2}\)) make up for the defect of zero band gap of graphene. The field-effect transistors (FETs) prepared by them show superior switching modulation characteristics, so they have great advantages in low-power devices [3, 4, 5, 6, 7]. However, the intrinsic carrier mobility of two-dimensional TMDs is usually low, much lower than the electron mobility in crystalline silicon [8, 9], which greatly limits their application in semiconductor electronic devices. Of course, there are more and more methods to improve the carrier mobility of TMDs.  
As another important discovery after graphene and transition metal sulfide, black phosphorus (BP), as the only other known monotypic van der Waals crystal, has broad application prospects in nano optoelectronic devices [10, 11, 12, 13, 14, 15, 16, 17, 18, 19]. In 2014, a FET with nanometer thickness two-dimensional BP as channel material was successfully prepared by the research group of [PERSON] et al. [20]. The test results show that the on/off current ratio of the BP transistor could reach 10\({}^{5}\) when the thickness of the two-dimensional BP film is less than 7.5 nm, and the highest electron mobility maybe reaches \(\sim\)1000 cm\({}^{2}\)/Vs when the thicknessof BP film is greater than 10 nm, which is somewhat better than that of molybdenum disulfide (\(\sim\)200 cm\({}^{2}\)/Vs). BP has become another important member of the two-dimensional nanomaterial family following graphene and molybdenum disulfide [21; 22; 23; 24; 25]. In the research of BP materials and their devices, the band structure of BP crystals was found to change with the thickness of the material itself, i.e., the band gap decreases with increasing thickness [22; 26]. [PERSON] et al. derived the band gap of BP samples with different layers (less than 30 layers) [27] by computer theoretical simulation. By measuring the transport characteristics of BP FETs with different thicknesses, they confirmed this conclusion experimentally. [PERSON] et al. report the evolution of the band gap calculated by different methods from 1 layer to \(\infty\) layers, and show the sheet conductivity as a function of gate voltage for devices with different thicknesses (10 nm, 8 nm, and 5 nm) [22]. However, for BP thickness larger than 30 layers or higher (over 20 nm), the precise effect of material thickness on device characteristics or functional relationship between electrical characteristics (output characteristics, transfer characteristics, mobility, etc.) and thickness have not been systematically studied.  
Here, the effects of BP materials with thicknesses ranging from \(\sim\)10 to \(\sim\)100 layers on the transport properties of BP-FETs were precisely investigated. Five BP-FET devices with different BP thicknesses (\(\sim\)50 nm, \(\sim\)40 nm, \(\sim\)30 nm, \(\sim\)20 nm, and \(\sim\)6 nm) were prepared by mechanical exfoliation technology, and their electrical properties were tested in detail. The influence of BP material thickness on device output and transfer characteristics were systematically analyzed. Using plasma etching technology to etch the material thickness of 50 nm to 30 nm again confirmed the effect of thickness on device performance.