Investigation of the cutoff frequency of double linear halo lightly doped drain and source CNTFET

Introduction

After discovering the carbon nanotube (CNT) by Aijima [ ¹ ], scientific researches about this structure are expanded due to its excellent electronic properties. One of the important properties of this structure is quasi-ballistic transport with very high carrier mobility [ ² , ³ ]. Using carbon nanotube, two types of field effect transistors have been discussed. The first type is Schottky barrier carbon nanotube field effect transistor (SB-CNTFET) and second type is MOSFET-like CNTFETs (MOSCNTs). The MOSCNT was more favorable because of the high on–off current ratio, but leakage current ( I _L ) of this transistor is very high because of electron band-to-band tunneling (BTBT) [ ⁴ ]. In order to deal with this problem, some solutions such as drain and source with a linearly or lightly doped, source and drain extensions and asymmetric oxide thickness, have been proposed [ ⁵ – ⁹ ]. Also, the dual material gate structure and the source and drain parameters effect on the characteristics of CNTFET are investigated [ ¹⁰ , ¹¹ ]. Moreover the p-type halo implanted deteriorates the cutoff frequency and the switching delay of CNTFET [ ¹² ].

This paper is mainly focused on the f _T of MOSCNT, linearly doped CNTFET (LD-CNTFET) and lightly doped drain and source CNTFET (LDDS-CNTFET), which are discussed in [ ⁷ ], to select a structure with the highest f _T . Moreover, we have investigated the implantation of n-type single halo in channel of LDDS-CNTFET (SH-LDDS-CNTFET) and its effects on some characteristics such as the f _T . Based on this investigation we have proposed implanting n-type double linear halo in the channel of LDDS-CNTFET which is named “DLH-LDDS-CNTFET”. These structure characteristics such as the leakage current, the on-current and the f _T have been investigated. We have used a non-equilibrium Green’s function (NEGF) method to simulate these transistors [ ⁸ , ¹³ – ¹⁷ ].

Proposed transistor and method of simulation

A cross-section schematic representation of implanting the n-type single halo in the source side of channel of LDDS-CNTFET and their geometric details is shown in Fig.  ¹ a. The channel is a (16, 0) CNT and radius 0.63 nm that is embedded in cylindrical gate insulator of HfO ₂ with thickness 2 nm and dielectric constant 16. The channel length is 15 nm, which consists of 9 nm undoped CNT and 6 nm n-type doped CNT. The concentration of this single halo is 1.4 nm ⁻¹ . Our proposed structure is shown in Fig.  ¹ b. This figure illustrates a cross-section schematic representation of the n-type double linear halo implantation in the channel of LDDS-CNTFET (DLH-LDDS-CNTFET) and their detailed geometries. The drain and source length are 30 nm, which consists of 15 nm highly doped regions and 15 nm lightly doped regions are taken to be 2 and 0.2 nm ⁻¹ , respectively. Figure  ¹ b also shows that the concentration of n-type double linear halo vary from 1.4 nm ⁻¹ to 0 in length of 6 nm.

Fig. 1

Self consistent solution of the Poisson and Schrodinger equations has been done within the NEGF formalism for simulating the device characteristics. The band structure of CNT is calculated by the tight-binding method with one orbital. The electrostatic potential of CNT required for calculating the Hamiltonian of Schrodinger is provided by solving the Poisson equation. By solving the Schrodinger equation, the density of states and the charge of the CNT are calculated. The Poisson equation is solved based on the charge and consequently the new potential is calculated. The iteration between the Poisson and the Schrodinger equations stops after reaching minimum of error [ ⁶ – ⁸ , ¹⁶ , ¹⁷ ].

Results and discussion

At first, we calculate the f _T versus V _GS for the three structures MOSCNT, LD-CNTFET and LDDS-CNTFET as discussed in [ ⁷ ], to select a structure with the highest cutoff frequency. Note that these three devices have intrinsic channel. The gate capacitance ( C _g ) and the transconductance ( g _m ) are defined by [ ¹⁸ , ¹⁹ ]. where Q _ch is the total charge of the CNT channel which can be obtained by integrating over the electron density [ n ( x )] in the channel. The I _DS is the drain-source current. We compute the cutoff frequency using [ ²⁰ ]:

Figure  ² illustrates the f _T of MOSCNT, LD-CNTFET and LDDS-CNTFET versus V _GS at drain-source voltage V _DS  = 0.4 V. In comparison with the MOSCNT and the LD-CNTFET, the LDDS-CNTFET has illustrated a larger f _T . From an analytical standpoint, the doping profile of drain and source of this device leads to increase of the g _m and decrease of the channel charge variation versus gate-source voltage ( C _g ) and as a result, increasing the f _T -characteristic. Therefore, we choose the LDDS-CNTFET for implanting the n-type impurity halo in the channel.

Fig. 2

We have calculated I _DS versus V _GS characteristics of the LDDS-CNTFET, the SH-LDDS-CNTFET of Fig.  ¹ a and the proposed structure (DLH-LDDS-CNTFET) of Fig.  ¹ b at V _DS  = 0.4 V that are shown in Fig.  ³ . This figure illustrates the on-current of DLH-LDDS-CNTFET is higher than others, because the channel barrier potential of this structure is reduced by implantation of the n-type double linear halo. This figure also demonstrates that the I _L of proposed device has slightly increased when compared with the SH-LDDS-CNTFET, but it is also much less than the I _L of LDDS-CNTFET. Now we must investigate the band to band tunneling to analyze leakage current variations of these three devices.

Fig. 3

Figure  ⁴ shows the energy band structures (solid line) and color-scaled plot for the number of electrons per unit energy for three discussed transistors at V _DS  = 0.4 V and V _GS  = −0.4 V. Figure  ⁴ a illustrates a large number of tunneling electrons that causes increase the leakage current, for the LDDS-CNTFET represented in Ref. [ ⁷ ]. Figure  ⁴ b shows the n-type impurity halo implanted in channel significantly decrease the probability of electrons tunneling, because the halo causes change answers of Schrodinger equation using create the nonuniform potential. Also Fig.  ⁴ c indicates that the number of tunneling electrons in double linear halo implanted channel is a little more than the single halo structure (Fig.  ⁴ b), but much less than the intrinsic channel structure (Fig.  ⁴ a).

Fig. 4

Then, we have calculated the f _T for the LDDS-CNTFET, the SH-LDDS-CNTFET of Fig.  ¹ a and our proposed structure of Fig.  ¹ b biased under V _DS  = 0.4 V. These results are indicated in Fig.  ⁵ . Dash-dotted, dashed and solid lines represent the f _T for the LDDS-CNTFET, SH-LDDS-CNTFET, and DLH-LDDS-CNTFET, respectively. It can be seen in this figure that n-type single halo implant in the channel of LDDS-CNTFET increases the f _T at V _GS ranges of 0–0.15 V and 0.22–0.42 V. The reason of increasing the f _T increases the transconductance. This figure also demonstrates that the cutoff frequency of DLH-LDDS-CNTFET significantly increases at low V _GS range ( V _GS  = 0–0.25 V). From an analytical standpoint, using double linear halo the sensitivity of channel charge versus the V _GS variations ( C _g ) is decreased, therefore according to (3) this device cutoff frequency is increased. As well, the cutoff frequency of the proposed device in the V _GS higher than 0.42 V is more than the single halo structure. On the other hand, the cutoff frequency of DLH-LDDS-CNTFET (solid line) is more than the LDDS-CNTFET (dash-dot line) in the wide range of the V _GS from 0 to 0.47 V, In that event the cutoff frequency of single halo structure (dash line) is more than the LDDS-CNTFET in the V _GS regions of 0–0.15 V and 0.22–0.42 V. Finally, we have simulated the cutoff frequency of LDDS-CNTFET with implanting p-type single halo in the channel. Our results show that this parameter decreases strongly.

Fig. 5

Conclusion

In this paper, we have demonstrated that the cutoff frequency of LDDS-CNTFET is higher in comparison with those of both the LD-CNTFET and the MOSCNT. We have simulated these devices by non-equilibrium Green’s function method. It can be seen that in the n-type single halo structure the leakage current is significantly decreased and the f _T in the gate voltage ranges of 0–0.15 V and 0.22–0.42 V is increased. We have realized that the f _T of the proposed transistor (Fig.  ¹ b) for V _GS of 0–0.25 V is much higher than either the LDDS-CNTFET or the SH-LDDS-CNTFET. And also the f _T of the DLH-LDDS-CNTFET is higher than the SH-LDDS-CNTFET for V _GS higher than 0.42 V. Moreover, we have illustrated that the f _T of the proposed device is higher than the LDDS-CNTFET for a broad range of V _GS which means 0–0.47 V, whereas the f _T of SH-LDDS-CNTFET compared to the LDDS-CNTFET is superior only in the narrow ranges of gate-source voltage.