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Kamal Hosen, Md. Rasidul Islam, Kong Liu. Impact of Channel Length and Width for Charge Transportation of Graphene Field Effect Transistor[J]. Chinese Journal of Chemical Physics , 2020, 33(6): 757-763. doi: 10.1063/1674-0068/cjcp2004055
Citation: Kamal Hosen, Md. Rasidul Islam, Kong Liu. Impact of Channel Length and Width for Charge Transportation of Graphene Field Effect Transistor[J]. Chinese Journal of Chemical Physics , 2020, 33(6): 757-763. doi: 10.1063/1674-0068/cjcp2004055

Impact of Channel Length and Width for Charge Transportation of Graphene Field Effect Transistor

doi: 10.1063/1674-0068/cjcp2004055
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  • The effect of channel length and width on the large and small-signal parameters of the graphene field effect transistor have been explored using an analytical approach. In the case of faster saturation as well as extremely high transit frequency, the graphene field effect transistor shows outstanding performance. From the transfer curve, it is observed that there is a positive shift of Dirac point from the voltage of 0.15 V to 0.35 V because of reducing channel length from 440 nm to 20 nm and this curve depicts that graphene shows ambipolar behavior. Besides, it is found that because of widening channel the drain current increases and the maximum current is found approximately 2.4 mA and 6 mA for channel width 2 μm and 5 μm respectively. Furthermore, an approximate symmetrical capacitance-voltage ($C-V$) characteristic of the graphene field effect transistor is obtained and the capacitance reduces when the channel length decreases but the capacitance can be increased by raising the channel width. In addition, a high transconductance, that demands high-speed radio frequency (RF) applications, of 6.4 mS at channel length 20 nm and 4.45 mS at channel width 5 μm along with a high transit frequency of 3.95 THz have been found that demands high-speed radio frequency applications.
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    [6] K. Hosen, B. K. Moghal, A. S. M. J. Islam, and M. S. Islam, IEEE 21st International Conference of Computer and Information Technology, 1 (2018).
    [7] M. C. Lemme, T. J. Echtermeyer, M. Baus, and H. Kurz, IEEE Electr. Dev. Lett. 28, 282 (2007).
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    [10] S. Rodriguez, S. Vaziri, M. Ostling, A. Rusu, E. Alarcon, and M. Lemme, ECS Solid State Lett. 1, 39 (2012).
    [11] K. L. Shepard, I. Meric, and P. Kim, IEEE/ACM International Conference on Computer-Aided Design, 406 (2008).
    [12] S. Thiele, J. Schaefer, and F. Schwierz, J. Appl. Phys. 107, 094505 (2010).
    [13] D. Jimenez and O. Moldovan, IEEE Trans. Electr. Dev. 58, 4049 (2011).
    [14] F. Al-Fattah, T. Rahman, M. S. Islam, and A. G. Bhuiyan, Int. J. Nano Sci. 15, 1640001 (2016).
    [15] S. Fregonese, M. Magallo, C. Maneux, H. Happy, and T. Zimmer, IEEE Trans. Nanotechnol. 12, 539 (2013).
    [16] W. Zhu, V. Perebeinos, M. Freitag, and P. Avouris, Phys. Rev. B 80, 235402 (2009).
    [17] F. Schwierz, Nature Nanotechnol. 5, 487 (2010).
    [18] K. Kim, J. Y. Choi T. Kim, S. H. Cho, and H. J. Chung, Nature 479, 338 (2011).
    [19] S. Han, Z. Chen, and A. Bol, IEEE Electr. Dev. Lett. 32, 812 (2011).
    [20] S. Rodriguez, S. Vaziri, M. Ostling, A. Rusu, E. Alarcon, and M. A. Lemme, IEEE Trans. Electr. Dev. 64, 1199 (2014).
    [21] A. Badmaev, Y. Che, Z. Li, C. Wang, and C. Zhou, ACS Nano 6, 3371 (2012).
    [22] A. Venugopal, J. Chan, X. Li, C. W. Magnuson, W. P. Kirk, L. Colombo, R. S. Ruoff, and E. M. Vogel, J. Appl. Phys. 109, 104511 (2011).
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    [24] J. Chen, R. Solomon, T. Chan, P. K. Ko, and C. Hu, IEEE Trans. Electr. Dev. 39, 2346 (1992).
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Impact of Channel Length and Width for Charge Transportation of Graphene Field Effect Transistor

doi: 10.1063/1674-0068/cjcp2004055

Abstract: The effect of channel length and width on the large and small-signal parameters of the graphene field effect transistor have been explored using an analytical approach. In the case of faster saturation as well as extremely high transit frequency, the graphene field effect transistor shows outstanding performance. From the transfer curve, it is observed that there is a positive shift of Dirac point from the voltage of 0.15 V to 0.35 V because of reducing channel length from 440 nm to 20 nm and this curve depicts that graphene shows ambipolar behavior. Besides, it is found that because of widening channel the drain current increases and the maximum current is found approximately 2.4 mA and 6 mA for channel width 2 μm and 5 μm respectively. Furthermore, an approximate symmetrical capacitance-voltage ($C-V$) characteristic of the graphene field effect transistor is obtained and the capacitance reduces when the channel length decreases but the capacitance can be increased by raising the channel width. In addition, a high transconductance, that demands high-speed radio frequency (RF) applications, of 6.4 mS at channel length 20 nm and 4.45 mS at channel width 5 μm along with a high transit frequency of 3.95 THz have been found that demands high-speed radio frequency applications.

Kamal Hosen, Md. Rasidul Islam, Kong Liu. Impact of Channel Length and Width for Charge Transportation of Graphene Field Effect Transistor[J]. Chinese Journal of Chemical Physics , 2020, 33(6): 757-763. doi: 10.1063/1674-0068/cjcp2004055
Citation: Kamal Hosen, Md. Rasidul Islam, Kong Liu. Impact of Channel Length and Width for Charge Transportation of Graphene Field Effect Transistor[J]. Chinese Journal of Chemical Physics , 2020, 33(6): 757-763. doi: 10.1063/1674-0068/cjcp2004055
  • Since the dimensions approach the atomic level and physical limits come forward eventually, it is a great challenge for the reduction of dimensions in silicon-based transistors. Recently, for mitigating these limitations an enormous amount of research has focused on new materials, and graphene is one of these promising materials. Graphene is a two-dimensional material consisting of thin single-layer sheets of sp$^2$ carbon atoms tightly packed carbon atoms into a honeycomb lattice structure [1] as shown in FIG. 1 with momentous electrical and vibrational properties such as outstanding ballistic transport property [2], ultra-high carrier mobility [3] and high thermal conductivity [4]. Besides, graphene shows linear dispersion relation with zero band-gaps, and for this reason, the attainable on-off current ratios are limited but it can be used in analog radio frequency (RF) device applications [5]. Silicon has the electron mobility of roughly 1400 cm$^2$$\cdot$V$^{-1}$$\cdot$s$^{-1}$, but in the case of graphene, it is found to be around 20000 cm$^2$$\cdot$V$^{-1}$$\cdot$s$^{-1}$ at room temperature [6]. Furthermore, it shows the ambipolar conducting property which allows controlling the carrier-type and the electrostatic doping of graphene is realized with the help of outside electric field [7]. Ballistic transport property and high electron mobility of graphene make it a promising channel material replacing silicon and other semiconductors for ultra-high-speed electronics.

    Figure 1.  The single layer of the graphene sheet where red circle shape represent the position of carbon atoms.

    A comprehensive interest has risen in vehement research into practicable applications of graphene in field-effect transistors and nano-device because of its novel electronic properties [8]. Recently, it has been observed that the transit frequencies ($f_\textrm{T}$) of GFETs are higher than those of identically sized CMOS devices [9]. Besides, it has been found that the values of trans-conductance gain ($g_\textrm{m}$) are also high in GFETs [10]. Furthermore, it has been observed in GFET transistors that the drain current has a saturation region [8]. However, the research is in the rudimentary stage and most of the studies are limited to constant channel length and channel width of GFETs. Exploring GFETs for future high-speed electronics, adequate understanding about the variety of theoretical performance with channel length and width, is of enormous importance.

    In this work, the large signal and small signal virtually model of GFETs and the effect of channel length and width on their theoretical performance have been analyzed through the analytical approach. Here immensely high cutoff frequency ($f_\textrm{T}$) and an intense drain current saturating behavior of GFETs are identified at different channel lengths and widths. An asymmetrical ambipolar behavior of GFETs is found on the transfer characteristic. Besides, asymmetrical capacitance-voltage ($C-V$) behavior has been demonstrated which largely depends on quantum capacitance and oxide capacitance at low gate voltages. Furthermore, an outstanding trans-conductance ($g_\textrm{m}$) behavior is obtained at low gate voltage and observed through varying channel length and width. The effect of channel length and width on large signal and small signal properties of GFETs device is also discussed.

  • To analyze the electrical characteristics of GFETs with simulating circuits an electrical model of the GFET device has been developed [11-14] as shown in FIG. 2. It is made up of a monolayer of graphene which acts as channel materials onto a silicon substrate. Furthermore, source and drain are connected to this channel and an insulating layer of SiO$_2$ is used to isolate the gate from the channel. Therefore, an oxide capacitance is built up there and opens up an opportunity to control the channel charge by tuning the gate bias. For large signal and small signal analysis, the channel lengths and widths have been varied from 20 nm to 440 nm and 2 μm to 5 μm, respectively [15]. The quality of graphene used in the channel serves a crucial role in the performance of graphene-based devices, as the carrier mobility largely depends on the roughness of the layer and eventually affects the performance of GFETs. Furthermore, the device performance parameters are degraded by some other factors such as parasitic resistance and contact resistance of semiconductor to metal and all these effects were not included in our calculation. Besides, we have assumed graphene as zero band-gaps for the whole calculation in this work.

    Figure 2.  Top-gated graphene GFET model.

  • FIG. 2 represents the large signal model which consists of a thin graphene channel along with drain and source. A comprehensive analysis of the drain current with the help of the drift equation for GFET is found in Ref.[15]. According to the result in that study, the drain current can be expressed as

    Where $W$ and $L$ represent the width and length of the graphene channel respectively, $\mu$ is the mobility, $e$ is the electron charge, $Q_{\textrm{net}}$ is the net mobile charge, $V_{\textrm{SAT}}$ is the saturation velocity, and $n_{\textrm{puddle}}$ is electron-hole puddle which is induced by spatial inhomogeneity within the graphene layer, and can be expressed as [16]:

    Here the parameter $\hbar$ is the reduced Planck constant, $\Delta$ is the inhomogeneity of the electrostatic potential and $v_\textrm{f}$ is the Fermi velocity. For simplicity, Eq.(1) can be written as

    Where,

    The denominator in Eq.(3) can be expressed as

    Where $C_{\textrm{ox}}$ is the oxide capacitance, the factor $\beta$=$\displaystyle{\frac{e^3}{\pi (\hbar v _\textrm{f} )^2 }}$, $V$ is the potential variation along the channel due to $V_{\textrm{ds}}$, and the average saturation velocity $V_{\textrm{SAT, AV}}$ depends on average charge and surface phonon energy $\hbar \omega$ [15].

  • The high-frequency characteristics of the transistor can be analyzed with a small-signal representation also called the hybrid-$\pi$ model [17] as shown in FIG. 3. The small-signal parameters consist of the trans-conductance $g_\textrm{m}$, the drain conductance $g_{\textrm{ds}}$, the gate-source capacitance $C_{\textrm{gs}}$, the gate-drain capacitance $C_{\textrm{gd}}$ and the transit frequency $f_\textrm{T}$. The following equations are used for the derivation of small-signal parameters of the GFET.The trans-conductance $g_\textrm{m}$ is defined as:

    Figure 3.  The small-signal equivalent circuit of GFET. Here $C_{\textrm{gs}}$ represents the gate-source capacitance whereas $C_{\textrm{gd}}$ stands for gate-drain capacitance.

    The equation for finding the gate-capacitance $C_{\textrm{gs}}$ is [15]

    Where $Q_{\textrm{CH}}$ is the total charge and it can be expressed as [15]

    The transit frequency $f_\textrm{T}$ [18] can be written as

    The values of different parameters in above expressions [19, 20] are given in Table Ⅰ.

    Table 1.  Different parameters of GFET.

  • It is experimentally reported that there is a strong impact of short-channel lengths on the GFET drain current [19, 20]. The effect of channel length can be explained analytically by Eq.(6) where it is seen that for very short lengths and high $V_{\textrm{ds}}$ the drain current becomes independent of the channel length. Here, we have demonstrated the transfer characteristic of the GFET at the different channel length and channel width respectively by using Eq.(1). FIG. 4 represents $I_{\textrm{ds}}$ vs. $V_{\textrm{gs}}$ plots of GFET at the different drain to source voltages and at different channel length and width respectively. Graphene shows a linear band structure, and at Dirac point top of the valence band and bottom of the conduction band touch each other. From FIG. 4(a), it is found that there are three basing regions; firstly, with positive gate voltage, the conduction current flows only for electrons. The Dirac point moves downward owing to the reduction of the gate to source voltage, consequently, the drain current also reduces to downward. Secondly, at certain gate voltage, the conduction band and the valence band meet together and at this point drain current reaches its minimum value rather than zero because of the electron-hole puddle. Finally, in the negative gate voltage region, the Fermi level shifts downward through the valence band and the conduction current starts increasing again. At this time the hole is responsible for conduction current only. Here, we have also demonstrated the effect of channel length and width in the transfer characteristic of GFET. From FIG. 4(b) it is found that charges become neutralized approximately at gate voltage $V_{\textrm{gs}}$=0.15 V for 440 nm and at $V_{\textrm{gs}}$=0.35 V for 20 nm channel length which indicates that there is a positive shift on Dirac point because of scaling down the channel length. Besides, Han et al. reported that the value of $I_{\textrm{on}}$/$I_{\textrm{off}}$ ratio decreases due to the shrinking of the channel length [19]. Furthermore, the drain current have been reported 1.3 mA for 170 nm device at $V_{\textrm{gs}}$=-1.1 V [26] and at the same gate voltage from FIG. 4(b) it is shown that the drain current is 1.8 mA for 230 nm device. It is observed that channel width does not change the Dirac point but conduction current $I_{\textrm{ds}}$ increases to 0.85 mA from 0.35 mA at the Dirac point with the increase of channel width from 2 μm to 5 μm as shown in FIG. 4(c). Furthermore, it is an explicit observation from FIG. 4 that graphene shows ambipolar behavior and GFET can be used as either n-channel or a p-channel transistor.

    Figure 4.  The transfer characteristics curve with changing (a) $V_{\textrm{ds}}$, (b) channel length, (c) channel width.

    FIG. 5 depicts the relation between $I_{\textrm{ds}}$ and $V_{\textrm{ds}}$ of GFET at different bias voltages with various channel length and width respectively. From FIG. 5(a) it is observed that for relatively long channel length GFETs show an approximate linear current characteristic with zero gate voltage. FIG. 5(b) indicates an increase in the drain current with the shrinking of the channel length. In FIG. 5(b), it is found that at $V_{\textrm{ds}}$=0.2 V drain current $I_{\textrm{ds}}$ has its maximum value of 3.1 mA for channel length 20 nm whereas, in the case of 440 nm it is approximately 1.8 mA with the same gate bias voltage of 2 V. Because shrinking channel length causes a reduction of scattering of the electrons. It is also noticed that at channel length 20 nm. $I_{\textrm{ds}}$ reaches the saturation region more quickly than other channel lengths, because short channel length offers high saturation velocity, as a result electrons need small transit time to reach from source to drain. The most significance of the saturation region is that it is easy to make the use of GFETs in analog RF device applications. From FIG. 5(c), it is found that the maximum drain current is obtained at $V_{\textrm{ds}}$=0.85 V and this current increases to 6 mA from 2.4 mA when the channel width varies from 2 μm to 5 μm with the same gate bias voltage of 2 V.

    Figure 5.  The $I-V$ characteristics of GFET with varying (a) $V_{\textrm{gs}}$, (b) channel length, (c) channel width.

  • The small-signal and RF characteristic of GFETs can be explained by the equivalent circuit called hybrid-$\pi$ model as shown in FIG. 3. The small-signal parameters for the GFETs consist of the transconductance $g_\textrm{m}$, the gate-source capacitance $C_{\textrm{gs}}$ and the transit frequency $f_\textrm{T}$ and the derivation of these parameters are presented in the following sections.

  • Here, the transconductance of GFETs is calculated by using the Eq.(10). FIG. 6 shows the transconductance for different gate-source voltage $V_{\textrm{gs}}$, different channel length, and channel width respectively. From FIG. 6(a) it is shown that because of the saturation velocity, the value of transconductance $g_\textrm{m}$ is drastically reduced with the increase of gate-source voltage $V_{\textrm{gs}}$ from zero to both directions. It is also found that there is a positive shift of the peak point of $g_\textrm{m}$ for the same channel length and width and the value of $g_\textrm{m}$ increases with the increase of drain-source voltage $V_{\textrm{ds}}$. The maximum transconductance $g_\textrm{m}$=1.8 mS is found at approximately $V_{\textrm{gs}}$=0.11 V for 440 nm channel length and 2 μm channel width when $V_{\textrm{ds}}$ remains constant at 0.2 V. Besides, it is previously reported that, a peak scaled transconductance $g_\textrm{m}$/$W$ up to 0.5 mS/μm was achieved for the 170 nm top-gate graphene field effect transistor [21]. FIG. 6(b) shows the variation of $g_\textrm{m}$ with different channel length varying from 20 nm to 440 nm. From this figure, it is observed that transconductance gradually increases with the decrease of channel length. At the lower gate-source voltage $V_{\textrm{gs}}$, the transconductance is high and increasing rate becoming more prominent at shorter channel length. The maximum transconductance $g_\textrm{m}$=6.4 mS is found at $V_{\textrm{gs}}$=0.1 V for the channel length 20 nm with $V_{\textrm{ds}}$=0.2 V. FIG. 6(c) shows the variation of transconductance with channel width varying from 2 μm to 5 μm for channel length 440 nm. From these figures, it is observed that transconductance increases with the increase of channel width and it is also noticed that transconductance rising rate is higher when lower gate-source voltage $V_{\textrm{ds}}$ is applied. We have found that at gate voltage $V_{\textrm{gs}}$=0.1 V the value of transconductance is 1.8 mS for channel width 2 μm and it reaches the value of 4.45 mS for channel width 5 μm. The transconductance $g_\textrm{m}$ plays an important role in device performance providing an idea about the power consumption of the device because $g_\textrm{m}$/$I_\textrm{d}$ is a measure of power consumption efficiency. So, from FIG. 6 it can be concluded that power consumption by the device is less when the shorter and wider channel is considered and it is also observed that best transconductance performance is achieved at the lower gate bias.

    Figure 6.  The transconductance curve with different (a) $V_{\textrm{ds}}$, (b) channel length at drain-source voltage of $V_{\textrm{ds}}$=0.2 V, (c) channel width at $V_{\textrm{ds}}$=0.2 V.

  • The gate-source capacitance behaviors are of huge importance to analyze semiconductor materials and devices for the assessment of their singular parameters. Besides, using contamination effects and interface trap density, the $C-V$ characteristics can be used to find out oxide thickness, oxide charges, mobile ions [23], threshold voltage [24]. Here the total gate-source capacitance $C_{\textrm{gs}}$ is calculated by using Eq.(11) as a function of gate voltage $V_{\textrm{gs}}$ which is mainly formed by oxide capacitance $C_{\textrm{ox}}$ and quantum capacitance $C_\textrm{p}$. The distributed charges throughout the channel have a huge effect on the quantum capacitance $C_\textrm{p}$ and it depends on both $V_{\textrm{gs}}$ and $V_{\textrm{ds}}$. Here FIG. 7 shows the variations of gate-source capacitance $C_{\textrm{gs}}$ as a function of gate-source voltage $V_{\textrm{gs}}$ for different drain-source voltage $V_{\textrm{ds}}$, the channel length $L$, and channel width $W$ respectively. From FIG. 7(a) it is observed that at large negative bias voltage gate capacitance is high because in this case the Fermi level shift to the valence band and a large number of positive charge accumulates in the graphene channel. For the increase of gate voltage, the Fermi level starts to move upward and the hole density decreases at the channel which results in a reduction in the gate capacitance $C_{\textrm{gs}}$. it is found that the value of minimum capacitance is approximately 2.65 femtofarad (fF) at bias voltage 0.15 V, which is shown in FIG. 7(a). When the bias voltage increases from zero to positive, Fermi level goes to the conduction band resulting in an accumulation of a large number of negative charge in the graphene channel. This abundant supply of the negative charge contributes a large capacitance to the gate capacitance, as a result, it increases gradually. Here we have found the maximum gate-source capacitance is approximately 3.38 fF at bais voltage 3.0 V. From FIG. 7(b) it is observed that gate bias voltage has a negligible effect on gate-source capacitance for short channel length but these effects gradually increased with the rise of channel length at a constant width. Furthermore, gate capacitance increases with the increase of channel length because large channel accumulates a large number of charge and these charges provide a huge capacitance. FIG. 7(c) depicts the $C-V$ characteristic of GFET for different channel widths. In FIG. 7, it is noticed that near the zero bias voltage GFET shows a symmetrical $C-V$ characteristic. And it is also observed that the gate capacitance $C_{\textrm{gs}}$ grows up with the raise of channel width at constant length because for a wider channel a copious number of charges are accumulated throughout the channel resulting in the total capacitance equal to oxide capacitance.

    Figure 7.  The gate-capacitance curve with different (a) $V_{\textrm{ds}}$, (b) channel length, (c) channel width.

  • The transit frequency is referred as the frequency at which its current gain becomes unity and it also determines the speed of the device and bandwidth capabilities. As a result, it has become an indispensable parameter to analyze the device performance in RF application. Here, the variations of transit frequency with channel length and width have been investigated by Eq.(14). FIG. 8(a) depicts the dependence of transit frequency $f_\textrm{T}$ on the gate-source voltage $V_{\textrm{gs}}$. From this figure, it is found that there is an increase in the transit frequency when the bias voltage is reduced. Besides, from FIG. 8(a), the cutoff frequency $f_\textrm{T}$ is found 28 GHz for 440 nm device at $V_{\textrm{gs}}$=0.8 V and experimentally it is shown that for 110 nm device the value of $f_\textrm{T}$ is 23 GHz [26]. FIG. 8(b) depicts the variation of transit frequency as a function of channel length for different gate-source voltage. In FIG. 8(b) it is found that transit frequency rises with the decrease of channel length which satisfies the previous result. It is also observed that at the shorter channel, gate voltage has a tremendous impact on transit frequency but with the increase of channel length this effect is reduced and in the case of the longer channels it is almost negligible. The simulation result represents that at 440 nm, 200 nm, 80 nm, and 20 nm channel length the transit frequency is approximately 75 GHz, 240 GHz, 725 GHz, and 3.95 THz respectively. The effect of channel width in transit frequency is negligible but in case of the same channel length and channel width, the maximum transit frequency is found for lower gate voltage as shown in FIG. 8(c). Here, a momentous transit frequency behavior is achieved for the low bias voltage and short channel length which has drawn huge interest for analog circuit design as GFETs are suitable for RF applications beyond the cut-off frequency $f_\textrm{T}$ of 120 GHz [9].

    Figure 8.  The transit frequency curve with different (a) $V_{\textrm{ds}}$, (b) channel length, (c) channel width.

  • In summary, a theoretical approach has been used to examine the large and small-signal performance of GETs here. From the simulation results, it is observed that GFET shows outstanding small-signal performances and splendid transfer characteristics. The maximum drain current is found approximately 1.8 mA for channel length 440 nm which increases to 3.1 mA at the channel length 20 nm at $V_{\textrm{ds}}$=0.2 V. It is also found that there is a positive shift of Dirac point from the voltage of 0.15 V to 0.35 V for decreasing channel length from 440 nm to 20 nm. The transfer curve also depicts that graphene shows ambipolar behavior, as a result, GFET can be used as either n-channel or a p-channel transistor. Besides, it is noticed that because of widening channel the peak value of $I_{\textrm{ds}}$ increases and this value is found approximately 2.4 mA and 6 mA for channel width 2 μm and 5 μm respectively. An approximate symmetrical $C-V$ characteristics of GFET are found with the lowest and the highest capacitive value of 2.65 fF and 3.38 fF at 0.15 V and 3.0 V bias voltages respectively. It is also observed that there is a reduction of capacitance when the channel length decreases but the capacitance rises when the channel width increases. Besides, for shorter and wider channel an excellent transconductance performance is found at lower bias voltage. Moreover, it is found that at $V_\textrm{g}$=0.1 V, the value of transconductance rises to 6400 μS from 1800 μS for the variation of channel length from 440 nm to 20 nm. Furthermore, the dependency of transit frequency on channel length and width has been observed in this simulation. We have found that the transit frequency dramatical increased before the 50 nm channel length. It is also observed that the maximum transit frequency is found of 3.95 THz for 20 nm where it is 75 GHz for 440 nm and there is no significant effect of channel width on transit frequency. At last, these simulated results would provide impressive information about the effect of channel length and width on the large and small-signal parameters of the GFETs and hence the performance of the graphene-based nanoelectronic devices.

  • This work was mostly supported by the National Key Research and Development Program of China (No.2018YFE0204000), the National Natural Science Foundation of China (No.61674141, No.51972300, No.61504134 and No.21975245), The Strategic Priority Research Program of Chinese Academy of Sciences (No.XDB43000000). The World Academy of Sciences (TWAS), and the Key Research Program of Frontier Science, Chinese Academy of Sciences (No.QYZDBSSW-SLH006). Kong Liu appreciates the support from Youth Innovation Promotion Association, Chinese Academy of Sciences (No.2020114).

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