INTRODUCTION
In recent times, there has been an intense exploration of the Tunneling field effects transistors. This is because it has been discovered to have the potential to offer a way out of many concerns, especially the power concerns, in nanoelectronics. “Graphene nanoribbon was recently discovered and has been deemed ideal for tunneling FETs,” [1]. For graphene nanoribbons tunneling transistors, the subthreshold swing has been investigated to be a nonlinear function of temperature. The graphene nanoribbon has been declared as the best candidate for tunneling field effect transistor owing to its compatibility with planar processing, direct and narrow band gap, and low effective mass. The ribbon form of graphene, known as the GNR, has been said to have inherited ass the attractive characteristics of graphene and carbon nanotube plus the additional benefit of a tunable band-gap and the tunable semiconductor characteristics [2]. A reduction in subthreshold swing has the potential to make the Tunneling field effect transistor devices possess a reduced power supply requirement. [1]
In the experiment carried out by Mathieu Luisier and Gerhard Klimeck the functionality of tunneling transistors with a subthreshold slope which is more than 60 mV/dec at room temperature was demonstrated [6]. It is expected that graphene based tunneling transistors would offer a lower OFF current, a larger ON current, and an SS which is steeper than that of Si or groups 3-5 compound semiconductors. Tunneling field-effect transistors are usually one dimensional and have full compatibility with planar processing. Also, TFETs possesses an indistinguishable but rather light conduction, valence effective masses, and a width-tunable narrow band. [6]
One of the problems with graphene nanoribbon tunneling FETS occurs, as a result of the line edge roughness and another one is the low ON-state current of Si-based TFETs which remains a serious limitation. It is very hard to impeccably regulate the size of sub-10nm graphene nanoribbons while, at the same time, preventing line edge roughness. [6]. Also, from quantitative consecutive simulations, it was established that the leakage of the source –to-drain tunneling via the gate potential barrier gets increased as the line edge roughness gets higher. This intensely restricts the ON/OFF ratio of the SS to 25 mV/dec while those of the devices are also restricted to < 1000 even without the presence of the line edge roughness. A plot of the subthreshold swing against temperature gives a negative slope which falls below a specific drain current; this was confirmed by Youngki Yoon and Sayeef Salahuddin when they carried out a simulation for graphene nanoribbons. This simulation was done based on a non-equilibrium, self-consistent, and atomistic green function. The outcome indicated that the subthreshold swing has a nonlinear relationship with both the drain current and temperature, [5].
THE COMPARISON BETWEEN THE VARIATION OF SUB-THRESHOLD SWING WITH TEMPERATURE IN GNR MOSFET AND GNR TFET
Figure 1a (at the appendix) demonstrates the ID−VG characteristic at various temperatures for a GNR MOSFET. Figure 1b demonstrates the ID− VG characteristics of a Tunneling Field Effect Transistor; a substantial non-linearity can be in the two sub-threshold sections. In figure 1c, S was plotted as a function of T for both the TFET and the MOSFET, the outcome of this is a linear sub-threshold swing that remains unchanged no matter the value of the drain current at that point. The trend shown by the TFET is however in disparity with that displayed by the MOSFET. For the TFET, the S displayed a positive slope which denotes linear dependency to the temperature, however, as the drain current gets reduced the behavior switched to non-linear and later on becomes negative at a negligible value of drain current. This characteristic is explained better in figure 1d where S was plotted as a function of the drain current with varying temperatures. [5]
In summary, the variation of sub-threshold swing with temperature is a nonlinear function of the drain current and the slope of the S versus T plot alters it sign from positive to negative with declining drain current. [5].
THE BENEFITS OF USING GRAPHENE IN TRANSISTORS
Tunneling field effect transistors that are fabricated based on graphene nanoribbon has the potential of attaining higher currents than group three to group five and even the group four channel. One dimensional graphene nanoribbons are exceptionally suitable for high-performance tunnel transistor. Most of the benefits of the graphene-nanoribbon tunneling-field-effect-transistor are derived from the tunneling mechanism and the properties of the materials which make it possible for them to achieve low power dissipation and high speed. [4]
Also, it is also worthy of note to mention that graphene has the tendency to be used in radiofrequency applications as a result of its purely two-dimensional structure and auspicious carrier transport properties. It is almost certain that graphene might receive its first appearance in the radiofrequency applications very soon.
Some of the other benefits of using graphene in transistors are;
- The capability to operate when very low voltages are applied.
- Great sensitivity
- It can operate at room temperature
- It has a size of one atom by ten atoms wide
- It has the ability to operate on flexible and transparent substrates.
THINGS THAT CAN BE ACHIEVED IN SUB-THRESHOLD OF THE TRANSISTOR WHEN GRAPHENE NANORIBBONS TUNNELING TRANSISTORS ARE USED
The graphene nanoribbon tunneling FETs, employs positively doped graphene nanoribbon as the source and negatively doped GNR as the drain. The geometry of the TFET is demonstrated in the schematic cross-sections, shown in figure 8 in the appendix, displaying how a lateral p-n junction is made by placing the gate on either the p or the n side of the junction resulting in n-channel transistor or a p-channel transistor. The selected gate work function is such as to fully lessen the channel in the OFF state. Figure 9, in the appendix, illustrates the energy band gap for a graphene nanoribbon p-TFET with a supply voltage of 0.1V and at (a) OFF state and (b) ON State. It is displayed that a 5-nm ribbon width TFET can switch from on to off with only 0.1-V gate swing. The transistor reaches 26 pA /μm OFF-state current and 800 μ A /μm ON-state current, with an operational subthreshold swing of 0.19 mV/dec. The high performance of GNR TFETs is as a result of their narrow bandgaps and their on dimensional nature. [4].
The graphene nanoribbon tunneling FETs achieves steep sub-threshold slopes, [7]. The use of graphene nanoribbons brings about a rather high ON/OFF ratios with subthreshold slopes less than 60 mV/decade. It has been postulated that a minimum subthreshold swing of 0.19 mV/dec can potentially be attained in GNR TFETs.
As illustrated in figures 7 (in the appendix), it is expected that graphene based tunneling transistors would offer a lower OFF current, a larger ON current, and an SS which is steeper than Si or groups 3-5 compound semiconductors. Tunneling field-effect transistors are usually one dimensional and have full compatibility with planar processing. Also, TFETs possesses an identical but rather light conduction, valence effective masses, and a width-tunable narrow band. [6]. The drawback of the low ON/OFF ratios can be significantly overcome by making use of Ballistic tunneling transistors; this would make the tunneling devices to have a highly insulated OFF state having no dissipation. This allows both individual transistors and integrated circuits at room temperature. [6][8].
Figure 7a displays the band edges of a graphene nanoribbon tunneling transistor without line edge roughness in its OFF state which is when the values of Vgs and Vds equals 0.1 V. Here, it can be seen that the total potential drop from source to drain correlates to the in-built potential and the applied Vds. Subplots (b) and (c) show the density -of-states o Figure 7b and 7c illustrates the subplots showing the transistor’s density of state in its OFF state, 7b illustrates when LER is absent while 7c illustrates the subplot when 7c is present.
HOW NEGF IS MODELED ACCORDING TO GRAPHENE NANORIBBONS TUNNELING TRANSISTORS
The model of the electronic transport is made in such a way that the non-equilibrium Green’s function NEGF is employed in solving the open boundary Schrödinger equation, this account automatically for both the hole and electron currents. The Green function, G, of a device at an energy E is derived from
G= [EI – H - ∑1 - ∑2]-1
Where: I represent identity matrix, H stands for the Hamiltonian of the device.
The Contact broadening is given by
Where ∑1,2 is the self-energy matrices that has been calculated with the assumption of semi-infinite leads. [5].
The gate oxide thickness of the double gate geometry of the nominal device is 1.6nm while the length of the channel and the channel length is 15 nm. The assumed power supply voltage is assumed to be 0.4 V and gate metal work difference is also assumed in order to make it possible for the assumed minimum leakage current to be zero. The three dimensional Poisson equation is used to solve the NEGF transport equation until self-consistency is attained. Two varying types of structures are explored to make comparison; these structures can be found as figure 2a and 2b in the appendix. Figure 2a illustrates an energy band gap of a graphene nanoribbon MOSFET which when positively doped would become a tunneling FET, i.e. Figure 2b. The ballistic current in this newly made tunneling device, according to Yoon & Salahuddin, is written as
Where the probability of transmission at gate voltage VG and energy E is represented by T(E, VG), [5].
The Non-Equilibrium Green’s Function (NEGF) is then used to perform a quantum mechanical simulation of graphene nano-ribbons. The aim of this formalism is to study the sub-threshold slope and the ratio of the OFF to ON current. The derived result is put together with the Landauer transport models which enable an adequate comprehension of the structure of the device and make suggestions of the careful design methodology needed to make the trade-off balance. The application of Landauer formula alongside the ballistic transport reveals the drain current as a function of device parameters.
According to the research work carried out by Chin et al. to observe the current-voltage characteristics of ballistic graphene nanoribbon tunneling field effect transistors of varying size having different channel length and temperatures. The same self-consistent non-equilibrium Green’s function was used also but with quasi two dimensional Poisson with the materials details of the graphene nanoribbon modeled by the uncoupled mode space dirac equation, [8]. Figures 3, 4 and 5, shown in the appendix, show the plots and the graphical illustrations that were gotten during the course of this study. For these figures, (a) illustrates the relationship between drain current and gate-to-drain voltage while figure (b) illustrates the effect of the independent variable on subthreshold swing IOFF and ION.
Figure 3 shows that there is less leakage i.e. the IOFF decreases as the device length increases, which means that, the ratio of ION to IOFF also increases while the subthreshold swing decreases. The significant decrease in the subthreshold swing and the significant increase in the ratio of ION to IOFF are up to an approximate length of 40nm. It is therefore obvious that if the length is specifically increased to 160nm, the best threshold swing of 6mV/decade and ION to IOFF ratio of above 50,000 will be achieved.
Figure 4 shows that there is an increase in the channel width as the band-gap decreases resulting into a significant increase in IOFF and a minute increase in ION which also means that the subthreshold swing will increase. It can be seen from this illustrations that for a width less than or equal to 1.25nm; ION will be too noisy, widths between 2.5nm and 1.25nm are not feasible, and if ION is too small it won’t drive another transistor. If the width exceeds 3.75nm then the ratio of ION to IOFF would be correlated exponentially with the width, the SS will thus be similarly affected.
Figure 5 shows how the ratio of ION to IOFF initially increases and later decreases as a result of the passing of the conduction band of the channel between doping of 0.32 eV and 0.28 eV and the valence band of the drain. The value of the SS does not change until 0.28 eV and once that is exceeded it degrades. Figure 6 illustrates the increment in the drain bias as ION and IOFF also increases. A trade-off is however made here as IOFF increase faster which means there will be an increase in leakage currents. Hence as the drain voltage increases the ION to IOFF actually decreases. Here, the SS fluctuates. To maintain a high ION a 0.05V minimum drain bias is needed. [10]
It was discovered that the graphene nanoribbon tunneling field effect transistors from the 3p+1 family have better ION/ IOFF characteristics than those from that are made from 3p family as a result of the smaller effective masses of the 3p+1 family. It was found out that ION is boosted by a higher doping concentration at the source; however, this degrades the subthreshold swing (SS). The graphene nanoribbon tunneling FETs gave very promising characteristics in terms of power delay product and intrinsic delay. Also, it was discovered that the tradeoff between the SS and the ION are controlled by the source concentration Ns. Whenever Ns is increased, ION automatically gets higher, and the SS too also get higher. [8].
CONCLUSION
The subtheshold swing of a nanoribbon TFET has been presented as being a non-linear function of temperature which is quite in contrast with the general FET convention, the swing versus temperature has also been shown to give a negative slope below a specific drain current. It has been stated that a TFET ribbon width of about 5 nanometer can switch from OFF to ON with just a gate swing of 0.1V, that, the TFET attains 26 pA/ µm OFF state and 800µA/µm ON-state current, and also that, the GNR TFET’s high performance is as a result of their one dimensional nature and their narrow bandgaps. The ON/OFF ratio of the GNR TFETs is strongly limited to less than 1000 and the Subthreshold Swing to 25 mV/dec as a result of the source-to-drain tunneling leakage and also due to LER. It has been fully stated that as a result of the effective masses, the GNR TFET from the 3p+1 family, in general, possess a better ION/IOFF characteristics than the 3p family, and also that, the ION is enhanced by a higher doping concentration at the source but this degrades the SS. Relative to a MOSFET, the steep SS and the high ION to IOFF over many decades exhibited by GNR TFET makes it superior for ultra-low power applications.
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Appendix
Figure 1
Figure 2
Figure 3: Varying Channel length
Figure 4: Varying Channel Width
Figure 5: Varying Contact Doping
Figure 6: Varying Drain Bias
Figure 7
Figure 8
Figure 9
