Band Gap Engineering of Nitrogen-Doped Monolayer WSe$_2$ Superlattice and its application to Field Effect Transistor

TL;DR

This work addresses band-gap engineering for 2D FETs by introducing periodic nitrogen doping to form WSe$_2$ monolayer superlattices. It combines first-principles DFT with NEGF-DFT transport calculations under a gate architecture to reveal that periodic N substitution cleanly tunes the band gap, shrinking $E_g$ from about $1.50\,\text{eV}$ in pristine cases to as low as $0.66\,\text{eV}$ in the 4-row structure, while maintaining or adjusting the band-edge positions between $\Gamma$ and $X$ points. Transmission and electrostatic analyses show that the doped structures develop periodic barriers that segmentation into quantum wells alters $\tau(E)$, leading to gate-controllable current with temperature-dependent behavior: $J$ rises with $T$ due to thermionic leakage in the doped cases, while the subthreshold swing can exceed the Boltzmann limit in some regimes. Practically, the 6-row and 8-row configurations offer favorable $V_g^{OFF}$ values around $0.75$ V with stable operating windows, whereas the 4-row configuration performs poorly due to large OFF currents and a narrow working range, guiding design choices for thermally robust 2D WSe$_2$ FETs.

Abstract

We systematically investigate the electronic structures of pristine monolayer WSe$_2$ and WSe$_2$ superlattices with periodic nitrogen substitution. Unlike random doping, which often introduces in-gap impurity states, periodic nitrogen doping primarily modulates the band gap, thereby facilitating effective band gap engineering for electronic and optoelectronic applications. The gap narrows monotonically with increasing dopant density (pristine $>$ 8-row $>$ 6-row $>$ 4-row), directly influencing device switching. We also evaluate the FET performance of nanojunctions created by these configurations by examining the contour plot of current density as a function of temperature and gate voltage, which quantifies how bandgap engineering affects switching characteristics. Our calculations clarify the classical-quantum crossover in sub-10 nm 2D FETs: as $T$ rises, $J$ approaches the thermionic current; as $T$ falls, quantum tunneling dominates, and the steep energy dependence of $τ(E)$ may break the classical limit of subthreshold swing imposed by the Boltzmann tyranny. The optimal gating range ($V_g^\mathrm{ON}$, $V_g^\mathrm{OFF}$) is investigated for each temperature, insensitive to temperature in the high-temperature regime, confirming the good thermal stability of the FET devices. A comparison study demonstrates that the 4-row structure, with large $J_\mathrm{OFF}$ and restricted operation range, is inappropriate for realistic FET applications. The pristine structure has a high $V_g^\mathrm{OFF}$ ($\sim$1.1 V) makes it less practical, since such a large threshold voltage may promote time-dependent dielectric breakdown (TDDB) of the oxide layer, reducing device dependability. The 6-row and 8-row structures exhibit more favorable $V_g^\mathrm{OFF}$ values ($\sim$0.75 V), achieving compromise, making them more promising candidates for future FET integration.

Figures (8)

• Figure 1: a) Schematic of the four representative junction configurations: pristine WSe$_2$ and nitrogen-doped WSe$_2$ superlattices with 8-row, 6-row, and 4-row doping periodicities (from top to bottom), bridged between two platinum electrodes to form nanojunctions with a channel length of around 10 nm. b) Schematic of the gate architecture for the four junctions configured as field-effect transistors (FETs) in DFT–NEGF (NanoDCAL) simulations. The gate is modeled with an equivalent oxide thickness (EOT) of 8 Å and a dielectric constant of 3.9.
• Figure 2: Right panels: band structures. Left panels: total density of states (DOS; black) and atom-projected DOS (PDOS) on W (red), Se (blue), and N (green) for a) pristine WSe$_2$ monolayer and nitrogen-doped superlattices with b) 8-row, c) 6-row, and d) 4-row periodicity. The corresponding band gaps are a) 1.50 eV, b) 1.10 eV, c) 1.07 eV, and d) 0.66 eV.
• Figure 3: Transmission spectra for the four configurations depicted in Figure \ref{['fig:scheme']}$\bf{a}$ at $V_{ds} = 50$ mV, presented on a) linear and b) logarithmic scales. The VBM positions consistent across all instances, but the CBM positions vary considerably, resulting in a decrease in the transmission band gap as nitrogen concentration increases. The minimum values of $\tau(E)$ exhibit minimal sensitivity to doping, demonstrating just a marginal further suppression with increasing nitrogen concentration.
• Figure 4: Electrostatic potential profiles of the four nanojunction structures: a) pristine, b) 8-row, c) 6-row, and d) 4-row configurations depicted in Figure \ref{['fig:scheme']}$\bf{a}$. In the channel region, the pristine junction exhibits a uniform potential landscape, whereas the 8-row, 6-row, and 4-row configurations display equally spaced potential barriers arising from periodic nitrogen doping.
• Figure 5: Log($J$)–$V_{\mathrm{g}}$ characteristics of the four structures at room temperature. As $V_{\mathrm{g}}$ increases, a negatively sloped linear region appears, corresponding to the operational range of each structure. The differential subthreshold swing, defined as $S.S. = d(V_{\mathrm{g}})/d(\log_{10} J)$ and normalized by the Boltzmann tyranny, is also plotted. The pristine structure exhibits the widest range ing within the classical limit ($S.S./B.T. = 1$). In contrast, the ranges for the 6-row and 8-row structures are notably reduced, though they preserve partial linearity, whereas the 4-row structure shows only a very limited sloped region. Quantitatively, the minimum normalized values are $S.S./B.T._\text{min} = 0.96$ (6 rows), 0.85 (8 rows), and 0.84 (4 rows), all surpassing the classical limit of $S.S./B.T. = 1$.