The Role of Gallium in Changing the Electrical Properties and Transfer Characteristics of Indium Arsenide-Phosphorene Heterojunction Nano-TFETs

INTRODUCTION
In order to reduce power consumption in modern very large scale integration (VLSI) systems and mobile electronic appliances, the power management in the nanoelectronic circuits is regarded as one of the most important factors [1]. Tunnel field-effect transistors (TFETs) rely on quantum-mechanical tunneling unlike conventional metal–oxide–semiconductor field-effect transistors (MOSFETs) which acts on the drift-diffusion of carriers [2]. TFETs having low leakage current and a small subthreshold swing (S) has been widely studied as a promising ultra-low-power electronic device [3-5]. Material and device co-integration approach offers promising options for hybrid logic designs that combine the high energy efficiency of TFETs and the high performance of MOSFETs [6]. Tunnel Field-effect transistor (TFET) is regarded as the most promising candidate which can possibly replace the traditional MOSFET from current IC technology. It has gained much attention from the researchers because of its ability to achieve steep subthreshold slope, a greater immunity towards the short-channel effects and low standby power dissipation. Although TFET promises a lot of advantages over other contenders of MOSFET, the current transport mechanism i.e., band to band tunneling (BTBT) leads to its two major roadblocks such as low ON-state current and ambipolarity[7]. The physics of two-dimensional (2D) materials and heterostructures based on such crystals has been developing extremely fast. With new 2D materials, truly 2D physics has started to appear (e.g. absence of long-range order, 2D excitons, commensurate-incommensurate transition, etc). Novel heterostructure devices are also starting to appear - tunneling transistors, resonant tunneling diodes, light emitting diodes, etc. Composed from individual 2D crystals, such devices utilize the properties of those crystals to create functionalities that are not accessible to us in other heterostructures[8]. III–V heterostructure TFETs are promising for low-power applications [9-11]. Indium gallium arsenide (InGaAs) (alternatively gallium indium arsenide, GaInAs) is a ternary alloy (chemical compound) of indium arsenide (InAs) and gallium arsenide (GaAs) [12]. Indium and gallium are (group III) elements of the periodic table while arsenic is a (group V) element. Alloys made of these chemical groups are referred to as “III-V” compounds. InGaAs has properties intermediate between those of GaAs and InAs. InGaAs is a room-temperature semiconductor with applications in electronics and photonics. The optical and mechanical properties of InGaAs can be varied by changing the ratio of InAs and GaAs, In1-xGaxAs.
In this work, at the first step, with introducing gallium in the structure of indium arsenide, an In0.53Ga0.47As alloy is formed. In the second step, by creating a vertical hetero structure tunneling field effect transistor, its electronic properties are investigated. The effect of gallium on the structure of this nanotransistor was analyzed.

DEVICE STRUCTURE AND SIMULATION PROCEDURE
At the beginning, to construct a heterostructure nanotransistor, armchair phosphorene nanoribbon with lattice constants of 3.32A° and 4.38A° and indium arsenide with the lattice constant of 6.0583A° were used, while gallium atoms were replaced indium atoms by 47% in the structure. A one-nanometer overlap [13] is created due to the Van der Waals interaction between the two structures. In0.53Ga0.47As with p-type doping acts as source and phosphorene with n-type doping is selected as the drain in this double gate nanotransistor. The channel region is comprised of both phosphorene and indium-gallium-arsenide stacks. We created a heterostructure nanotransistor, by placing the source at the left and the drain at the right side where a doping-less channel is located in the middle. The source-channel and drain-channel regions were selected without underlap. A view of the proposed heterostructure nanotransistors are shown in Fig. 1.
Both TFETs shown in Fig. 1 are comprised of a gate electrode with 3.26nm length and 0.45nm thickness, zero underlaps between gate and source/drain regions (ULs=ULd=0) and a layer of gate dielectric with half nanometer thickness. In order to study the electrical characteristics and reveal the electronic transport phenomena, two different gate voltages of 0.1V and 0.5V are applied to the gate electrode. 
We perform the transport calculations within the framework of density functional theory (DFT) coupled with non-equilibrium Green’s function (NEGF) method integrated in the Atomistix ToolKit (ATK) 2017.2 package [14, 15]. In optimizing structures, ‘SG15’ with ‘Medium’ basis set is employed with a density mesh cutoff of 80Ha at the electron temperature of 300K. We use the generalized gradient approximation (GGA) of Perdew–Burke- Ernzerh form (PBE) [16] for the exchange correlation functional.
The Monkhorst-Pack k-points of 1×1×50 is used in the irreducible Brillouin zone (IBZ), which is dense enough for convergence.  The calculations are iterated self-consistently until the energy is converged to 10-4Ha. After forming the heterostructure and to investigate the transfer characteristics, calculation is performed with Extended-Huckel basis for phosphorus, indium, arsenic and hydrogen atoms with a mesh cutoff of 75Ha and k-point sampling of 13×1×108.
We calculate the transmission coefficient at kx point T(E.kx ) (Eq. 1), Where Gr/a and Γs/d are the retarded/advanced Green′s function and the source/drain level broadening, respectively. The transmission coefficient T(E) an average of T(E.kx ) over 57 kx -points in IBZ. The current at a given Vds and Vg is then calculated from the transmission coefficient T(E), which is regarded as the Landauer-Büttiker formula [17] (Eq. 2):

Where fs/fd  and μs/μd are the Fermi-Dirac distribution functions and electrochemical potentials of the source/drain, respectively.

RESULTS AND DISCUSSIONS
Fig. 2 illustrates the transfer characteristics of proposed heterogeneous TFET at low and high drain bias corresponding to Vds = 0.1V, Vds= 0.5V, respectively. From Fig. 2(a) it can be seen that by changing the gate voltage in the range of -3 to 6 volts, the ambipolar phenomenon is occurred and the Dirac point is located at the zero gate voltage. The maximum current occurs at Vg=6 V, with the quantity of 256 μA/μm. At the zero gate voltage the lowest current intensity happens.
In the transfer characteristics shown in Fig. 2(b), which belongs to high-drain bias of 0.5V (high performance), the gate voltage range varies from zero to 1 volt. Although the current intensity is less than the low drain bias mode, there is still the evidence of a Dirac point as well as ambipolar conduction in this case. The maximum current in this case is 85μA/μm and occurs at Vg=1V.
The value of the subthreshold slope is measured as 20mV/decade at high performance and 17mV/decade at low performance mode. It is improved in comparison with other similar works, either heterojunction TFET made with WSe2/SnSe2 [18] or homojunction TFET utilized SnSe [19]. Also the works done on other materials [20-23] and research on InGaAs/InAs/InGaAs[24] have been conducted in recent years.
In order to further analyze the conduction mechanism, the corresponding PLDOS (Partial Local Density of States) and transmission spectra were calculated. In Fig. 3(a, b) transmission spectrum for high and low performance is plotted. In Fig. (3a), we draw the value of the transmission coefficient for the ON and OFF states of the proposed nano-TFET. Higher peaks for the transmission intensity in the on- state are observed. Peaks of varying intensity in half of the bias window can be seen which is clearly consistent with PLDOS spectrum shown in Fig. 3(c, e). It seems that the voltage applied to the side gates did not apply such a strong electric field that the whole bias window can be located outside the energy gap [25]. Fig. (3b) shows transmission coefficient for Vds=0.1V. In this case, we see peaks in the bias window. The intensity of the peaks is significant in the on-state compared to the off state.
 NDR (negative differential resistance) is a nonlinear carrier transport phenomenon whereby the electric current decreases with increasing of the bias voltage [26]. The NDR effect can also be understood by comparing the transmission spectra when the current reaches a peak and valley [27]. The effect of negative differential resistance for indium-gallium-arsenide sample is investigated in high and low performance in the bias voltage range of 0-1.4 V and 0-2 V, respectively.
As shown in Fig. 4, we see multiple peak and valley points in the output characteristics. It is worth noting that in the absence of gallium in the structure, NDR phenomenon in low performance is not observed. However, with the presence of gallium in the InGaAs/P heterojunction nano-TFET, multiple NDR effects is manifested in both low and high performance conditions. At Vgs = 0.5V, three peaks can be seen at 82.8, 125 and 485.5µA/µm. Measured peak to valley ratio current (Ip/Iv) is 138 and 10, respectively. For low performance mode (Vgs = 0.1V), the presence of two peaks can be seen in 337 and 2014µA/µm. Measured Ip/Iv in this case is either 16 or 10.
The transmission eigenstate is a complex 3-D wave function and is illustrated by an isosurface with isovalue given by the magnitude of the eigenstate. The color maps represent the phase of the eigenstate [28]. For a visual understanding of the electronic transmission mechanism, the transmission eigenstates in the on-state and off-state are given in Fig. 5. The wave functions were replaced on the source side. When the transistor becomes on, they extend to the center and drain side. The difference between on/off states is clearly consistent with current diagrams and transmission spectra.
When the system is divided into two parts A and B, the transmission pathway of the electrons through the A and B boundaries is the sum of total transmission coefficients [29,30]. The transmission pathway can split the transmission coefficients into the contribution of local bond Tij and it can be both positive and negative.

Positive Tij indicates the electrons forward scattered along the bond and it is visualized as the arrow from i to j. On the contrary, negative Tij indicates the electrons back-scattered along the bond and it is visualized as the arrow from j to i. Therefore, the arrows of the transmission pathway indicate the direction of the electrons transmission [30]. The transmission pathway is shown in Fig. 6. The arrows indicate the possible electron transfer path. Figs. 6(a-c) show the off-state while Figs. 6(b-d) show the on-state in nano-TFET under study. The volume of the arrows is significant in the on-state at the overlap area and on the drain side.

CONCLUSION
An In0.53Ga0.47As /Phosphorene heterojunction TFTE as nano-device has been proposed and studied. Numerous device analysis were performed at high and low performance. It was revealed that this transistor can be further studied due to its NDR multiplicity as a very fast switching device at high and low voltages. Calculation of the subthreshold slope at high and low performance of 20 and 17.2 mV/decade was obtained, which has been improved due to the presence of gallium in the structure.
For a visual understanding of the electronic transmission mechanism, we used transmission eigenstate and transmission pathway. With the presence of gallium, we have witnessed the NDR phenomenon with current values of 82.8, 125 and 485.5µA/µm with gate voltage of 0.5V while the current values equal to 337 and 2014 µA/µm were observed with the gate voltage of 0.1V.

ACKNOWLEDGEMENTS
This research was supported by University of Kashan under supervision of Dr. Daryoosh Dideban. Authors are thankful to the support received for this work from Micoelectronics Lab (meLab) at the University of Glasgow, United Kingdom.

CONFLICT OF INTEREST
The authors declare that there is no conflict of interests regarding the publication of this manuscript.