P-type cold-source field-effect transistors with TcX2 and ReX2(X =S,Se)cold source electrodes: A computational study

Qianwen Wang(汪倩文), Jixuan Wu(武继璇), Xuepeng Zhan(詹学鹏),Pengpeng Sang(桑鹏鹏),†, and Jiezhi Chen(陈杰智),‡

1School of Information Science&Technology,Qingdao University of Science&Technology,Qingdao 266000,China

2School of Information Science and Engineering,Shandong University,Qingdao 266000,China

Keywords: cold metal,steep-slope transistor,subthreshold swing,quantum device simulations

1.Introduction

With the intensely increasing demands for miniaturization and integration of field-effect transistors (FETs), power dissipation has been one of the major challenges limiting the performance of modern nanoelectronics circuits.[1,2]Power consumption mainly includes dynamic switching dissipation and static leakage consumption.[3]Both dynamic and static power consumption are related to the supply voltage.[4,5]Consequently, reducing the supply voltage, while simultaneously ensuring a low off-state current(Ioff),is an effective way to relieve the consumption issue.Therefore, it is highly desired for the steep-slope from off-state to on-state.Researchers have made tremendous efforts on the aspects of materials and device principles.On the one hand, numerous twodimensional (2D) materials have emerged as promising candidates because of their atomically thin thickness and smooth surface, such as transition metal dichalcogenides (TMD),[6,7]group-VA semiconductors,[8,9]and recent emerging MA2Z4family.[10-13]On the other hand, many novel device models have been proposed to achieve steep-slope FETs with the ultra-steep subthreshold swing (SS).SS is the key parameter to evaluate the switching slope of devices and plays a crucial role in power optimization.However, there is a limitation for the SS in conventional MOSFETs, which cannot be lower than 60 mV/dec at room temperature because of the Boltzmann thermal distribution of carriers.Steep-slope devices with sub-60 mV/dec SS have attracted much attention.Tunneling FETs (T-FETs)[14-20]and negative capacitance FETs(NC-FETs)[21-24]have been proposed to break the SS limitation.However,T-FETs and NC-FETs usually suffer from some issues of small drive currents and large hysteresis,respectively.By modulating the density of states (DOS) of the source electrode, the recently proposed cold source FETs(CS-FETs) can realize the steep switching and high on-state current(Ion)simultaneously.[25-28]Structures including Dirac semimetals,[25]semiconductors,[29]isolated states,[30,31]and tunneling junctions[32]have been proposed as the source electrodes of CS-FETs.However,these structures have to be artificially doped,which is challenging for two-dimensional semiconductors.

Recently, a type of cold metal material was discovered,[33,34]which is intrinsic metal but possesses a gap in the conduction band(CB)or valence band(VB)around the Fermi level(EF).It can effectively filter out the carriers’thermal tails(high-energy electrons or holes)and thereby achieve the sub-60 mV/dec SS.Cold metals can directly serve as injection electrodes without artificial doping.Typical cold metals NbX2and TaX2(X=S, Se, Te) feature an energy gap aboveEFdue to one fewer electron than semiconducting MoX2and WX2,and are similar to p-type doped semiconductors.Hence,NbX2and TaX2can filter the high-energy electrons aboveEFand are suited for n-type CS-FETs(CS-nFETs).[33]Our prior research has revealed that the energy gap belowEFor the decreasing DOS with lower energy is necessary to cut-off or suppress hole tails and realizes p-type CS-FETs(CS-pFETs).[29]Hence,it is important to explore and design the potential cold metals for CS-pFETs.

In this work, regarding the CS-pFETs, we theoretically propose TcX2and ReX2(X=S,Se)as cold metals aiming at the steeper switching for hole transports.Different from prior NbX2(TaX2),TcX2and ReX2possess one more electron than that of the typical MoX2and WX2semiconductors.The desired energy gap for CS-pFETs can be expected in TcX2and ReX2, which can effectively filter out the high-energy holes and achieve sub-60 mV/dec SS.Based on the first-principles calculations, the electronic properties of TcX2and ReX2are systemically analyzed and their cold-metal characteristics are revealed.Moreover, taking WSe2pFET as an example, the steep switching performance is demonstrated by using TcX2and ReX2as injection sources,systemically verifying the coldmetal effects in device switching.Besides,the thickness influences of cold metals on the switching properties of CS-FETs are also discussed.

2.Methodology

The geometric and electronic properties were computed in the framework of density functional theory (DFT) implemented in the QuantumATK package.[35]The ion-electron interactions were treated by using the PseudoDojo normconserving pseudopotential.[36]The exchange-correlation functional was treated by the Perdew Burke Ernzerhof within generalized gradient approximation (GGA).[37]Geometric structures were fully relaxed with a force tolerance of less than 0.01 eV/˚A.The Brillouin zone sampling of 12×12×1 Monkhorst-Packk-points was employed.The vacuum space was set to be 20 ˚A to avoid the interactions between material and its periodic images.

The device transport performance was simulated by using DFT coupled with the nonequilibrium Green’s function(NEGF)method.Thek-points were chosen as 1×1×150 for device self-consistent calculations.The current was calculated by using the Landauer-B¨uttiker formula[38]

wheref(E) is the Fermi-Dirac distribution function;µs/dis the Fermi level of the source/drain electrode;andT(E)is the transmission coefficient from the source to drain.The electrode temperature was set to 300 K.

3.Results and discussion

Fig.1.Band structures and DOSs of monolayer TcX2 and ReX2 (X =S,Se,Te).The Fermi level is set to zero.

As shown in Fig.1,the calculated band structures of TcX2and ReX2present similar shapes to those of NbX2and TaX2.However,the Fermi level crosses through the CB of TcX2and ReX2,which is different from NbX2and TaX2with the Fermi level crossing through the VB.This is related to the electron numbers in the outmost shells of transition metal atoms.In comparison to semiconducting MoX2and WX2, TcX2and ReX2can be seen as naturally n-doped semiconductors.There is an energy gap below the Fermi level,which is referred to as the sub-gap as marked in Fig.1.It is the sub-gap that breaks up the continuous DOS distributions aroundEFand can filter out the holes with energies in the sub-gap.The energy difference betweenEFand the conduction band minimum (CBM)is denoted by ∆E.It should be pointed out that the ∆Edetermines the number of carrier thermal tails involved in device transport,whereas the sub-gap determines the number of thermal tails that are cut off.Hence, the larger sub-gap and smaller ∆Eare desired for effectively cut off thermal tails.As shown in Fig.1, the ∆E(sub-gaps) are calculated to be 1.08(0.63 eV),0.79(0.68 eV),0.46(1.35 eV),0.59(1.01 eV),0.46(0.80 eV) and 0.55 (0.65 eV) for ReS2, TcS2, ReSe2, TcSe2,ReTe2and TcTe2, respectively.It is found that the Se- and Te-series possess smaller ∆Ethan the S-series, besides, the Se-series possesses larger sub-gaps than the S-and Te-series.Hence, the Se-series exhibits more advantages in cutting off the hole tails.Although the ∆Eof 0.79-1.08 eV is slightly too large for ReS2and TcS2to directly cut off thermal tails, the significantly decreasing DOS below the Fermi level can also effectively suppress the spread of hole tails.Given the coldmetal characteristics with a sub-gap or decreasing DOS below the Fermi level, TcX2and ReX2are expected to serve as the injection source of p-type FETs (pFETs)and realize the cold source effects.Moreover,the calculated band structures in the presence of spin-orbital coupling(SOC)are shown in Fig.S1 of the supporting information.The SOC impacts can be ignored for TcX2.Although the SOC induces obvious splitting at thek-point of valence bands for ReX2, the critical sub-gap and ∆Eare slightly affected for ReS2and ReSe2.Hence, the SOC is predicted to be free of influence on transport properties when TcX2,ReS2,and ReSe2serve as the injection source.Although ∆Eis going to vanish,ReTe2shows cold-metal characteristics with a decreasing DOS.

Fig.2.(a)Schematic device structure of ReSe2-WSe2 heterojunction CSFETs with ReSe2 acting as injection source.(b) Comparisons of transfer characteristics between ReSe2-WSe2 CS-FET (red lines) and WSe2 MOSFET(black lines);the solid and open points represent the ReS2 electrode and WSe2 channel undergoing the mismatch strain,respectively.

To verify the role of cold metals (TcX2and ReX2) for p-type CS-FETs, we construct heterojunction FETs with monolayer ReSe2acting as the injection source, as shown in Fig.2(a).The lateral heterostructures are experimentally feasible and can be obtained by edge-epitaxial growth in experiments.[39]The intrinsic and p-type doped WSe2monolayer serves as the channel and drain electrode, respectively.The intrinsic WSe2channel is sandwiched between two 0.41 nm SiO2(with a dielectric constant of 3.9) layers,with a gate length (Lg) of 6.6 nm.The drain electrode is doped with a hole concentration of 0.02 per atom to ensure the Fermi level aligns with or down to the valence band maximum(VBM) of WSe2.Due to the lattice mismatch, two different contact models are considered: (i) the biaxial compressive strain of-1.1% is applied on monolayer ReSe2, while the contacted WSe2is free of strain to preserve its intrinsic transport properties for comparison; (ii) the tensile strain of 1.1%is applied on WSe2channel, while the ReS2metal is free of strain to verify its intrinsic cold-metal characteristic.The ballistic transports of the ReSe2-WSe2FET are simulated under the drain-source voltageVdsof-0.5 V.The results are presented in Fig.2(b)(see the red lines).For comparisons,the conventional WSe2MOSFET is also simulated with the p-doped WSe2serving as the injection source, and the results are also listed in Fig.2(b) (see the black lines).The solid points represent the pristine WSe2channel (contacting the strained ReS2electrode), while the open points represent the strained WSe2channel(contacting the pristine ReS2electrode).It is found that the SS as steep as 32-44 mV/dec is achieved for ReSe2-WSe2FET with ReSe2cold source,which breaks the thermal limitation of 60 mV/dec and is much lower than the result of WSe2MOSFET with p-doped WSe2source(62-64 mV/dec).The sub-60 mV/dec SS is obtained over eight decades of currents from 10-6µA/µm to 102µA/µm.Moreover, the off-state currents (Ioff) are defined around 10-6µA/µm and extracted at the gate voltageVg=0 V, and then the on-state currents (Ion) are obtained atVon=Voff-Vds.By using the constant current definition, the steeper SS results in a largerIonat a finite gate voltage range.However, the largerIondoes not mean larger saturation currents.By employing the cold metal ReSe2as the injection source, theIonof the WSe2FET is improved by one order of magnitude from 3-6µA/µm to 32-75µA/µm.It is found that the tensile strain degenerates WSe2transport properties and the slight compressive strain can promote the cold-source effects of ReS2metal.

To uncover the physical mechanism of cold metal injection,we further present the source DOS and calculate the corresponding hole densityn(h)distribution by using the Fermi-Dirac functionf(E),n(h)=f(E)×DOS(E).The spectrum currents dIand energy-resolved current density, are also calculated at the on-/off-state.The results are shown in Fig.3,where the source Fermi level (EFS) was set to 0 eV.Benefitting from the sub-gap belowEFin ReSe2, the hole tails with energy lower than 0.35 eV are effectively cut off (see Fig.3(a)).Consequently, the transmission currents from offstate to on-state are mainly from the holes located around theEFS.The thermal leakage currents are abruptly cut off at the energy range lower than 0.35 eV, which is the origin of the sub-60 mV/dec SS.While for the p-doped WSe2source, the continuous DOS belowEFresults in the continuous hole tails spreading to-0.75 eV and below(see Fig.3(b)).The spread tails usually lead to hole leakages from the source to the drain and are not conducive to gate modulation.As a result, the transmission currents from off-state to on-state possess a wide range spreading to-0.61 eV and below,which is quite different from the results of cold-metal sources.

We proceed to study the other cold metals when applied to an injection source for WSe2pFETs.The ReTe2and TcTe2metals are not further considered as the source because of the large lattice mismatch of over 11% with the WSe2channel.The device structure shown in Fig.2(a)is employed with the ReSe2monolayer replaced by ReS2, TcS2, and TcSe2monolayers,respectively.To avoid the strain influences on the WSe2channel and facilitate direct comparison between the results,we mainly discuss the contact model where the lattice mismatch at the interface is entirely applied on cold metals with a biaxial strain of-0.3%, 0.4%, and-3.4%for ReS2, TcS2,and TcSe2monolayers,respectively.It notes that experimental measurements have shown that 2D TMDs can withstand very large deformations of about 10%effective in-plane strain.[40]The simulatedId-Vgcurves are shown in Fig.4(a).The studied ReX2and TcX2(X=S,Se)injection sources all enable steeper slopes than the p-doped WSe2source and lift the currents from∼10-6µA/µm approaching 102µA/µm withinVgof-0.5 V.We further extract the current on/off ratio(Ion/Ioff)and the SS,as listed in Fig.4(b).It is found that the sub-thermal switches were all achieved with the SS of 38 mV/dec, 33 mV/dec,32 mV/dec,and 29 mV/dec for ReS2,TcS2,ReSe2,and TcSe2monolayer source, respectively.Benefitting from the steep slope, theIon/Ioffas large as 2.3×107, 2.5×107, 5.6×107,and 5.1×107are obtained for WSe2pFETs with ReS2,TcS2,ReSe2, and TcSe2monolayer source, respectively.The results are five or ten times higher than that of the normal WSe2MOSFET (4.1×106).Moreover, we also simulate the contact model where the interfacial mismatch is entirely applied on the WSe2channel,and the results can be found in Fig.S1 of the supporting information.The strain-free ReX2and TcX2both can break the thermal limitation and promote the steep SS with values of 33-44 mV/dec.The correspondingIon/Ioffis as high as(2-8)×107.

Fig.3.Comparisons of injection mechanism between (a) ReSe2 coldsource and(b)p-type doped WSe2 source.The panels from left to right are respectively the DOS of the injection source,corresponding hole density n(h),and the spectral current dI at the on/off state.

The DOSs and hole distributionsn(h) of the ReX2and TcX2monolayers are presented in Fig.4(c).The exponentially decaying hole density in traditional metals is plotted in blue lines for comparison.For TcSe2(ReSe2)monolayer,the hole tails with energy lower than 0.24(0.35)eV are effectively cut off by the sub-gap below the Fermi level,exhibiting a typical cold metal characteristic like the role of NbTe2in CSnFETs.[33]While for the TcS2(ReS2) monolayer, the overall decaying DOSs with energy result in the superexponentially decreasingn(h) and further the suppression of thermal tail contribution to the off-state, exhibiting a Dirac source characteristic similar to n-doped graphene.[25]It is the suppression or cut-off of the hole tails that breaks the SS limitation in traditional MOSFETs and obtains the sub-thermal switches in CSFETs.

To benchmark the studied device performance against the international technology roadmap for semiconductors(ITRS),[41]we set off-state currents around 5×10-5µA/µm according to the low-power applications in ITRS requirements.We re-extracted the on-state currents and current on/off ratio.Moreover,we calculated the intrinsic delay time(τ), and power dissipation (PDP), which reflect the switching speed and energy consumption, respectively.τis calculated byτ=(Qon-Qoff)/Ion, and PDP is defined by PDP=(Qon-Qoff)·Vds/W,in whichQon/offis the charges at on/offstate andWis channel width.The calculated results are all listed in Table 1.When employing ReX2and TcX2as sources, the WSe2-CSFETs exhibit higherIon/Ioff, smallerτ,and lower PDP than the normal WSe2-FET.Although theIonof WSe2-CSFETs cannot reach the ITRS requirements, theτand PDP both can fulfill the ITRS standard, exhibiting fast speed and lower consumption.Besides, we further compare the WSe2-CSFETs with some other 2D p-type FETs reported in the paper,including silicane,[42]Bi2O2Se,[43]InSe,[44]and MoSi2N4[45]monolayers.It is found that the studied WSe2-CSFETs possess much higherIon, smallerτ, and lower PDP than the silicane- and Bi2O2Se-based pFETs.Although the ions of WSe2-CSFETs are smaller than the reported MoSi2N4-and InSe-based pFETs, theτand PDP are lower than the MoSi2N4FET and the PDP is comparable with the InSe FET.In conclusion, the ReX2and TcX2metals can effectively improve the WSe2FET performance and enhance the competitiveness of the emerging 2D FETs in future low-power transistor applications.

Table 1.Performance comparisons of the WSe2 MOSFET and CS-FETs against ITRS requirements for the low-power transistors and with other 2D p-type FETs.

Fig.4.Transfer characteristics of WSe2 FETs with different cold metals and p-doped WSe2 as the injection source.(b)Switching performance(Ion/Ioff and SS)comparisons of WSe2 FETs with different injection sources.(c)The cold metal DOS and corresponding hole density n(h),EF is set to 0 eV.The exponentially decaying hole distribution nexp is shown in the blue line.

Fig.5.(a)and(b)Transfer characteristics of WSe2 FETs with different thicknesses ReS2 layers(1L-4L)as injection sources: (a)logarithm and(b)linear coordinates.Inset is the FET schematic structure.(c)DOS of ReS2 layers with different thicknesses(1L-4L).

We have revealed the cold source effects of the monolayer ReX2and TcX2.However, accessing singlelayer TMDs remains challenging in practical 2D device fabrications.Taking ReS2as an example,we proceed to study the FET’s performance based on multilayer 2D cold metals.The single-layered(1L),bi-layered(2L),tri-layered(3L),and quad-layered(4L)ReS2are respectively used as the injection source of WSe2pFETs (see the inset of Fig.5(b)).The simulated switching performances are shown in Figs.5(a)-5(b).It is found that for the 1L-4L ReS2injection sources,the WSe2pFETs show similarId-Vgcurves, which all can break the thermal limitation and achieve the steep SS with values of 29-33 mV/dec.The correspondingIon/Ioffis as high as (4-5)×107.Besides,as shown in the linear coordinate(Fig.5(b)),theIonincreases gradually from 38 µA/µm to 60 µA/µm with the increasing layers of the ReS2source.This relates to the carrier concentration in the source electrode.Figure 5(c) further presents the calculated DOS of the 1L-4L ReS2injection sources.The DOS decreasing tendency is preserved for various ReS2layers,which leads to the localization of hole distribution around theEFand is conducive to obtaining the steep switches.Besides,we further analyze the DOS of the other three cold metals with different thicknesses (see Fig.S3 of the supporting information).The multilayer ReX2and TcX2all preserve their cold-metal characteristics,and are anticipated to break the SS limitations while serving as the injection source.

4.Conclusion

The TcX2and ReX2cold metals were proposed as the injection sources in p-type CS-FETs to achieve sub-thermal switches.First-principles calculations revealed the cold metal characteristics of TcX2and ReX2with a sub-gap below the Fermi level, which can effectively suppress or cut off the thermal tails of holes.Comprehensive transport simulations demonstrated that the steep SS (29-38 mV/dec) and highIon/Ioff((2.3-5.6)×107) were achieved in WSe2CS-pFETs with TcX2and ReX2injection sources, significantly super to those of WSe2MOSFET(64 mV/dec and 4.1×106).Depending on their DOS features,the super-exponential decay of hole tails and direct cutting-off occurred for TcS2(ReS2)and TcSe2(ReSe2)injection sources,respectively.Moreover,by varying the thickness of cold metal from 1L to 4L,the steep switching properties could be obtained in ReS2-WSe2FETs.

Acknowledgments

Project was supported by the National Natural Science Foundation of China (Grant Nos.62034006, 92264201, and 62104134) and the Natural Science Foundation of Shandong Province of China (Grant Nos.ZR2023QF076 and ZR2023QF054).