Monte Carlo Simulation of Joule Heating in Monolayer MoS₂ Devices

Two-dimensional (2D) transition metal dichalcogenides (TMDs) like monolayer MoS₂ have emerged as promising semiconductors for nanoscale transistors and electronics due to their good charge mobilities at small thicknesses compared to ultrathin silicon [1]. However, to engineer high-performance 2D transistors, a detailed understanding of charge scattering and heat generation in TMDs is needed. When electrical current passes through a transistor, heat is generated due to electron-phonon scattering, an effect known as Joule heating. This effect occurs even in nanoscale transistors, where charge transport is partially ballistic [2]. Joule heating leads to increased phonon occupation, causing additional electron-phonon scattering, and thus a degradation of electrical transport; it also causes reliability concerns [2].<br/><br/>Here, we employ Monte Carlo simulations to investigate charge transport in monolayer MoS₂ transistors with Joule heating, inspired by earlier approaches with silicon [3]. We consider intravalley and intervalley electron-phonon scattering using the deformation potentials from [4]. To incorporate Joule heating, we consider the back-gated transistors frequently used in experimental transport studies on 2D semiconductors. The thermal resistance <i>R</i>_th of such a device is estimated as the sum of 1) the thermal boundary resistance of the MoS₂-SiO₂ interface, 2) the thermal resistance of the underlying oxide (SiO₂), and 3) the thermal resistance of the back-gate (Si) [5]. Such a thermal model can be easily modified to include heat loss through a top-gate or gate-all-around geometry for more general device structures [6].<br/><br/>The Monte Carlo approach is advantageous because it provides rich details on the contributions of different phonon modes to heating. With this approach, we simulate electron drift along the MoS₂ channel as the transistor heats up due to Joule heating. At steady-state, the average temperature rise is Δ<i>T = PR</i>_th, where <i>P</i> is the power generated in the MoS₂ channel. This <i>P</i> is computed by summing the heat generated from electron-phonon scattering events and agrees with the expected <i>P = IV</i>, where <i>I</i> is the current and <i>V</i> is the potential across the channel. At 300 K ambient temperature, carrier density of 10¹³ cm^-², and lateral electric fields in the velocity saturation regime (~4-5 V/µm), our simulations show that Joule heating leads to a transistor temperature rise of Δ<i>T</i> ≈ 200-250 K during steady-state operation. This heating decreases the electron saturation velocity by &gt;50% compared to when heating is not considered, indicating that high-field measurements of transistor operation must consider self-heating during analysis [7].<br/><br/>Overall, this work highlights the important consequences of Joule heating on charge transport in monolayer MoS₂ transistors. These simulations can further be extended to other TMDs and transient (i.e. digital) operation to identify design parameters for high-performance TMD devices that minimize Joule heating. This work was in part supported by the NSF Graduate Research Fellowship and Shoucheng Zhang Fellowship (M.A.W.) and by the SRC ASCENT JUMP Center (E.P.).<br/><br/>[1] C. English, et al., <i>Nano Lett.</i> <b>16</b>, 3824-3830 (2016).<br/>[2] E. Pop, et al., <i>Proc. IEEE</i>, <b>94</b>, 1587 (2006).<br/>[3] E. Pop, et al., <i>Appl. Phys. Lett.</i> <b>86</b>, 082101 (2005).<br/>[4] X. Li, et al., <i>Phys. Rev. B</i> <b>87</b>, 115418 (2013).<br/>[5] E. Yalon, et al., <i>Nano Lett.</i> <b>17</b>, 3429-3433 (2017).<br/>[6] A. Daus, et al., <i>Nat. Electron.</i> <b>4</b>, 495-501 (2021).<br/>[7] K. Smithe, et al., <i>Nano Lett.</i> <b>18</b>, 4616-4522 (2018).