Compact conduction band model for transition-metal dichalcogenide alloys

Abstract

Monolayer transition metal dichalcogenide (TMD) alloys, such as Mo_1 − xW_xS₂, owing to the unique electronic properties of the atomically thin two-dimensional layered structure, can be made into high performance metal–oxide–semiconductor field-effect transistors. The compact conduction band model of effective mass approximation (EMA) with the second nonparabolic correction is proposed for monolayer Mo_1 − xW_xS₂. The three band tight-binding (TB) method is used for calculating the band structure for monolayer TMD alloys such as Mo_1 − xW_xS₂, and a compact conduction band model is precisely developed to fit the band structures of TMD alloys calculated with tight-binding methods for the calculation of electron mobility. The impact of alloys on electron mobility of monolayer Mo_1 − xW_xS₂ is discussed in this study.

Introduction

Transition-Metal Dichalcogenides (TMD) and its alloy present great potential on the application to future transistor technology. TMD alloys, with the advantage of adjustable band gap, show the potential on the application to band gap engineering and could be applied to nanoscale Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) devices. The effects of alloy concentration on TMD alloy band structure and the correspondent carrier mobility are very important in new MOSFET device development. There are two types of Transition metal dichalcogenide alloy (TMD alloy) monolayer. For the first type monolayer TMD alloys, they are atomically thin semiconductors of type M″X₂, with M″ = M_1 − xM′_x a transition metal atom (M(M′) = Mo, W, etc.) and X a chalcogen atom (S, Se, etc.). One layer of M″ alloy atoms is sandwiched between two layers of X atoms. For the second type of monolayer TMD alloys, they are atomically thin semiconductors of type MX″₂, with X″ = X_1 − xX′_x a chalcogen atom (X(X′) = S, Se, etc.) and M a transition metal atom (Mo, W, etc.). One layer of M atoms is sandwiched between two layers of X_1 − xX_x′ alloy atoms. The first type of monolayer TMD alloys, such as Mo_1 − xW_xS₂, is a very promising two-dimensional material for future transistor technology. The Mo_1 − xW_xS₂ layer structure exhibits similar performance to graphite, such that Mo_1 − xW_xS₂ could be used for a high performance transistor device. Mo_1 − xW_xS₂, with its two-dimensional super-thin atomic structure and uniquely optical and electronic properties, has been broadly studied in past years. Experimental effort has been made on TMD alloys. The 2D layered transition-metal dichalcogenide alloys may have better inter miscibility and are predicted to be stable [1]. Several layered TMD bulk alloys, such as Mo_1 − xW_xS₂ and Mo_1 − xW_xSe₂, have been synthesized [2], suggesting good thermodynamic stability for the corresponding TMD alloys.

In 2012, Prof. Ying-Sheng Huang's research team [3] from Taiwan obtained the statistics of the homo- and heteroatomic coordinates in monolayer Mo_1 − xW_xS₂ from the atomically resolved scanning transmission electron microscope images and successfully quantified the degree of alloying for the transition metal elements (Mo or W). In their work, they performed the direct visualization of the atomic species Mo and W in the Mo_1 − xW_xS₂ compounds, clearly showing how the two elements could be mixed in a monolayer [3]. Recently, Dr. Liming Xie's group from China exfoliated the first family of atomic monolayer Mo_1 − xW_xS₂ and observed the composition-dependent photoluminescence from the monolayer Mo_1 − xW_xS₂ (1.82 to 1.99 eV) [4]. Prof. Zigang Shuai's research group [5] investigated the composition-dependent electronic properties of monolayer Mo_1 − xW_xS₂ based on first-principles calculations by applying the supercell method and effective band structure (EBS) approximation [6]. Their results released that the tunable electronic properties of monolayer TMD alloys made them attractive for electronic and optoelectronic applications. Above are the motivations of this work. To our knowledge, current effective mass approximation (EMA) band model could not accurately fit the band structure of monolayer TMD and its alloys. For this reason, it is necessary to develop the correct compact band model of monolayer TMD alloys for carrier mobility calculation. The compact conduction band structure and electron mobility of monolayer Mo_1 − xW_xS₂ as a potential channel material in future transistor devices are investigated in this study. In Section 2, calculation method for band structure from TB method and compact model and electron mobility calculations of monolayer Mo_1 − xW_xS₂ are presented. The results of this work are discussed in Section 3. Section 4 presents a conclusion of this work.