Voltage Differencing Transconductance Amplifier based Ultra-Low Power, Universal Filters and Oscillators using 32 nm Carbon Nanotube Field Effect Transistor Technology

Carbon nanotube fi eld-eff ect transistor (CNTFET) is a strong candidate to replace existing silicon-based transistors. The ballistic transport of electrons in the CNTFET channel leads to ultra-low-power and high-frequency devices. Although a lot of digital applications of CNTTFET were presented, less work was done in analog applications of CNTFETs. This paper presents analog applications of CNTFET and its implementation of voltage diff erencing transconductance amplifi er (VDTA). The CNTFET VDTA based fi lters and oscillators were proposed. The VDTA circuits are resistorless and can be tuned electronically only by changing transconductance. The proposed CNTFET VDTA shows power consumption of 4000 times less than compared to silicon CMOS technology and a signifi cant reduction in chip area. All simulations were performed using SPICE and MATLAB simulation tools.


Introduction
Silicon-based MOSFETs have already reached their limits in scaling. CNTFET, with its ultra-long mean free path (MFP), looks to overcome the limitations of conventional silicon-based MOSFETs due to its unique electronic and mechanical properties. These properties come from their strong atom-to-atom bonds, ballistic or near ballistic transport, and quasi 1D features of the CNT channel. Besides, by changing the chirality of the CNT its material properties can be changed from semiconducting to metallic. Many attempts at building CNTFET models have been reported in the literature [1][2][3][4][5][6][7][8][9].
Two major geometries are available for CNTFET design, which are planar and gate-all-around. Sanchez et al. have compared all available architectures and their performances [1]. Dokania et al. have proposed gateall-around (GAA) or also known as wrap gate, analytical SPICE model [2]. The gate capacitance and drain current in the channel should be accurately designed to predict the precise performance of CNTFETs. Ahmed et al. proposed a model of the gate capacitance in which CNTs are arranged arbitrarily, unlike other models in which CNTs are placed at a fi xed distance [3]. The authors of [3] have reported a 3% error with numerical simulations. Ballistic or near ballistic transport models for the drain current are proposed in [4][5][6][7][8][9]. These models are SPICE compatible, which means that the model can be easily compiled and integrated with any other circuit. The model used in this paper is from the articles [8][9].
Nizamuddin et. al proposed CNTFET and CMOS-based three-stage, hybrid operational transconductance amplifi ers (OTA) [7]. Marani et al. reported improvement in DC gain by 17%, 40% less power consumption, and a decrease in output resistance by 90% in comparison to CMOS OTA [7]. Low power mixed-mode active fi lter using 12 CNT and 2 capacitors was presented by Zanjani et al. [14]. Jooq et al. designed CNTFET based ring oscillators suitable for the internet of things (IoT) applications [17]. Low power CNTFET based RF oscillator is reported in [18]. Digital applications of CNTFET, such as adders and multipliers can be found in papers [19][20][21].
Most of the CNTFET studies are limited to simulations only since commercially CNTFETs are not available. Mindy et al. have proposed a method for the production of CNTFETS in commercial silicon manufacturing facilities and reported experimental measurements of CNTFETs fabricated in two diff erent manufacturing facilities [22]. Besides, the authors have improved the speed of the fabrication process 1100 times, by decreasing the deposition of CNT on the wafer from 48 hours to 150 seconds. Rebecca et al. have reported the fi rst experimental data for CNTFET CMOS analog circuitry [23]. They have successfully fabricated 2 stages CTNFET CMOS op-amp with the channel length of 3 μm, which achieves the gain > 700. Thus, the basics of CNTFET technology is CMOS too. Even so, when we write CMOS, we refer to silicon-based CMOS in this paper.
The fi rst Voltage diff erencing transconductance amplifi er (VDTA) was introduced by D. Biolek as an active element for analog signal processing [10]. However, any author did not perform the circuit implementation and application until the authors of proposed the realization of CMOS fi lters using VDTA [11]. The miniaturizations of electronic gadgets are becoming mainstream in today's technology. It will get harder and harder to integrate passive inductors into nano level circuits. VDTAs can be used to simulate inductors in signal processing circuits.
This work is organized as follows: Section 2 and 3 present the fundamentals of CNTFETSs and VDTAs respectively. The simulations' results and discussion of CNTFET VDTA including its comparison with CMOS VDTA are presented in section 4. In section 5,the application example of VDTA is presented. The universal fi lter realization is presented in section 5.1. The simulation results of CNTFET VDTA based oscillators are presented in section 5.2. Finally, in section 6 the conclusion of this paper is presented.

Carbon nanotube field-effect transistors fundamentals
Carbon nanotubes can be classifi ed as single-walled and multi-walled. CNTFETs presented in this paper are made from single-walled CNTS as shown in Fig. 1. The chirality of CNT is the key parameter that determines whether a material is metal or semiconducting. There are two parameters of chirality, n and m (in some books or papers also referred to as n1 and n2). The values of these chirality parameters vary according to the rolling up method of CNT. The CNT is metallic if the diff erence of n and m is a multiple of 3. Otherwise, if the diff erence of n and m is not a multiple of 3 then the CNT is semiconducting [12][13]. The CNTFET presented in this paper is designed with semiconducting CNT. The bandgap is another key parameter which can be calculated from [12]: Where, tight binging energy t is 3.0eV (also referred to as C-C bonding energy) and C-C bonding distance a cc of the nearest neighbor is 1.42A o . Whereas, equations for CNT diameter CNTFET threshold are given as [13]- [14]: Here, a (C-C unit vector length) is 0.246 nm. From equations, it is obvious that both bandgap and threshold voltages are dependent on the diameter of CNT. The width of CNTFET can be calculated from the parameters like the number of tubes, the distance between tubes, and the diameter of CNT.
( ) Numerical simulations of equations (1) and (3) were performed via MATLAB tool and the results are shown in Fig. 2 and Fig. 3. The exponential proportional dependency of CNT diameter for both bandgap and threshold voltage was observed. Both, threshold and band gap values increase as the CNT diameter value decreases.
The CNTFET model used in this research is shown in Fig. 4

VDTA
The proposed VDTA's circuit symbol and its circuit architecture at CNTFET level are shown in Fig. 5 and Fig. 6 respectively. The VDTA is an active element with high impedance input terminals V P , V N , and high impedance output terminals Z, X+, and X-. The relationship between I/O terminals of an ideal VDTA can be expressed as follow [11]:  Where g m1 is the transconductance of the fi rst stage and g m2 is the transconductance of the second stage. The voltage diff erence at the input terminals P and N transforms into output currents at terminal Z by g m1 . Then the voltage at the terminal Z is converted to output currents by g m2 at the output terminals x+ and x- [15]. VDTA can be tuned electronically by adjusting the values of g m of the fi rst stage or second stage.

Simulations, results, and Discussions
All simulations were performed using HSPICE software. The parameters of CNT transistors used to get DC and AC characteristics of CNTFET VDTA are shown in Table 2. Supply voltages are fi xed to V DD = -V SS = 0.3V and biasing currents are -considered as I B1 = I B2 = I B3 = 1μA. DC varying between -0.3V and 0.3V was applied fi rst to the P and N terminals to measure the output current and to the Z terminal. Then DC changing between -0.3V and 0.3V was applied Z terminal of VDTA to measure output currents at terminals +X and -X. The results of DC transfer characteristics for ideal current sources are shown in Fig. 7 and Fig. 8 in two steps. As expected, the output current increases as the CNT diameter increases. Because the I on of CNTFET increases as diameter increases due to an increase in carrier mobility and velocity [25]. For instance, in Fig. 7, the output current of CNTFET VDTA for 0.1V with CNT (7,0) is around 0,85μA, CNT (13,0) is around 0,89μA, CNT (19,0) and CNT (34,0) is 0,90 μA.  The AC response of CNTFET VDTA for diff erent CNT parameters is shown in Fig. 9 and Fig. 10. The same supply voltage and bias currents as in the previous section were used. Similar to DC simulations, two-step simulation and measurement was done to get the AC response of VDTA. In the fi rst step, the input AC voltage of 1V was applied at one of the input terminals P or N, and the gain at the output terminal Z was measured. In the second step, both input terminals were grounded and the input AC voltage of 1V was applied to the Z terminal. The output gain was measured from the X+ terminal. Both steps of DC/AC simulations show the same results which prove that CNTFET VDTA is operating properly. As we can see from graphs in DC simulations ( Fig. 7-8) there is no much diff erence between CNT (7,0), (13,0), (19,0), and (34,0). However, the V th of (7,0) is much higher compared to (34,0).In AC simulations of VDTA ( Fig. 9-10), we can observe a signifi cant increase in gain with the change of CNT chirality from (7,0) to (19,0). Between (19,0) and (34,0) there is no much diff erence in gain but the diameter changes from 1.5 nm to 2.6 nm which will drastically increase the transistor dimension as well. Hence, we have selected CNT

Application example
VDTA has a wide range of applications in the analog signal processing fi eld. One of them is a spectrum analyzer shown in Fig. 11. This spectrum analyzer uses low pass fi lters, bandpass fi lters, local oscillators, and mixers to get the fi nal intermediate frequency (IF). Step 1 V in = V P and V N vs I z . Step 2 V in = V z vs I x+ and I x-.
As an application example, this paper presents four fi lters and three local oscillators used in the spectrum analyzer.

Filters
VDTA can be categorized as voltage mode and current mode. This paper presents voltage mode CNTFET VDTA. The realization of CNTFET voltage mode VDTA derived from ref [11] is shown in Fig. 6. Further, the universal fi lter topology of CNTFET VDTA is proposed as shown in Fig. 12 And the expressions for Quality factor and natural frequency are given below: The fi lter blocks from Fig. 11 have been realized using proposed CNTFET VDTA from Fig.12 and the results are plotted in Fig. 13. The parameters of CNT transistors used for fi lter applications are shown in Table 2. The values of capacitors used for the fi lter application of CNTFET VDTA are shown in Table 4. The same supply voltage and bias currents as in the previous section were used. CNT (19,0) was selected for further applications of VDTA. There is no much diff erence between (7,0) and (19,0) CNT when the biasing current is set to 1μA. As biasing current increases, the center frequency of fi lters also increases due to an increase in transconductance.

Oscillator
The oscillator is a DC to AC converter, which converts DC input signals to AC output signals such as sinusoidal waves. Local oscillators are used to change the frequency of the signal as in a spectrum analyzer from Fig. 11 and along with mixers, they improve the performance of receivers in electronic circuits. The circuit symbol of the CNTFET VDTA oscillator is shown in Fig. 14. The oscillator blocks from Fig. 11 have been realized using the proposed oscillator structure.
Where g m3 = g m4 is the condition for oscillation and ωo is oscillation frequency. The parameters of CNT transistors used for oscillators applications are shown in Table 5. Supply voltages are fi xed to V DD = -V SS = 0.3V and biasing currents are considered as I B1 = I B2 = I B3 = 1μA. The simulation results are plotted through Fig. 15- Fig. 17.

Conclusion
Ultra-low-power CNTFET based VDTA fi lters and oscillators were presented. As shown in Table 3.
CNTFET 32 nm based VDTAs consume the power of 4000 times less than CMOS 32nm based VDTAs. Also, n-type CNTFETS occupy approximately 989 times less than space in the chip area (only considering eff ective channel WxL) compared to n-type MOSFET transistors while p-type CNTFETS occupy approximately 848 times less space(only considering eff ective channel WxL) compared to p-type 0.18μm technology node MOSFETS used in typical VDTAs. Higher biasing current or capacitors may be adjusted to change the center frequency of CNTFET fi lters. CNTFET VDTA based fi lters and fi rst-ever CNTFET VDTA based oscillators for spectrum analyzer are presented as an application example.

Conflict of interest
The authors declare that they have no known competing fi nancial interests or personal relationships that could have appeared to infl uence the work reported in this paper.