Design and Characterization of the Next Generation Nanowire Amplifiers

Vertical nanowire surrounding gate field effect transistors (SGFETs) provide full gate control over the channel to eliminate shortchannel effects. This paper presents design and characterization of a differential pair amplifier using NMOS and PMOS SGFETs with a 10 nm channel length and a 2 nm channel radius. The amplifier dissipates 5 μW power and provides 5 THz bandwidth with a voltage gain of 16, a linear output voltage swing of 0.5 V, and a distortion better than 3% from a 1.8 V power supply and a 20 aF capacitive load. The 2ndand 3rd-order harmonic distortions of the amplifier are −40 dBm and −52 dBm, respectively, and the 3rd-order intermodulation is −24 dBm for a two-tone input signal with 10 mV amplitude and 10 GHz frequency spacing. All these parameters indicate that vertical nanowire surrounding gate transistors are promising candidates for the next generation high-speed analog and VLSI technologies.


INTRODUCTION
The speed of silicon integrated circuits is reaching beyond 100 GHz to enable wireless communications with wideband channels [1]. Even though the current VLSI technology has approached to its scaling limits necessitating a replacement technology, silicon-based devices are still favored to realize large-scale circuits and systems because of their low cost.
Downscaling of the bulk metal oxide semiconductor field effect transistors (MOSFETs) to nanometer dimensions has increased the leakage current and short-channel effects. Therefore, alternative silicon compatible transistor devices such as silicon on insulator (SOI) MOSFETs, FinFETs, and nanotube FETs have been investigated for improved performance [2].
Vertical surrounding gate field effect transistors (SGFETs) have full gate control around channel and have minimized short-channel effects [3]. The elimination of bulk in these transistors reduces latchup and substrate noise. The layout views of a vertical nanowire SGFET and a planar bulk MOSFET are shown in Figure 1 for comparison. Both transistors have identical channel widths of 13 nm and channel lengths of 10 nm and are designed with similar layout design rules. The area of the vertical transistor is (40 nm × 40 nm) 1600 nm 2 , and the area of the planar transistor is also 1600 nm 2 (76 nm × 21 nm) with body contact.

HIGH-FREQUENCY MODELING
The three-dimensional view and the corresponding parasitic components of the vertical nanowire SGFET are shown in Figure 2. Only, the dominant parasitics are considered to simplify the circuit model.
The intrinsic transistor M is modeled using a BSIM-SOI compatible model to ensure that all the input and output transfer characteristics of the circuit and device simulators match each other. The parasitic capacitance between the source contacts and the metal gate is denoted as C gs2 in the figure. The parasitic capacitance, C gs1 , between the metal gate and the concentric source makes contact, and the junction well is the largest dominant capacitor of the SGFET device. The gate and drain capacitors (C gd1 and C gd2 ) and the drain and source capacitors (C ds1 and C ds2 ) can be lumped into C gd and C ds , respectively. Compared to planar bulk transistors, C gd is very small and there is no junction to bulk capacitance, therefore, C ds is quite linear. The well resistance, R s , can be quite large and is the major drawback of the vertical SGFETs compared with planar transistors. The magnitude of this Figure 5: Schematic of a differential pair amplifier.
For simplified hand calculations and finding the AC parameters of the amplifiers, designed using SGFETs, the linearized small-signal model shown in Figure 4 can be used. Using this model at low frequencies, the DC voltage gain and output resistance of various amplifier stages can be calculated. The model shown in Figure 4 is valid for transistors biased in the active operating region, and transistor models S. Hamedi-Hagh and A. Bindal Figure 6: The low-frequency small signal model of the differential pair amplifier.  in triode or cutoff regions can be easily constructed from this model by minor modifications.

DIFFERENTIAL-PAIR AMPLIFIER
The full gate control and the low leakage current of SGFETs make them suitable for many digital applications [4].
Operational amplifiers are one of the most important building blocks of analog integrated circuits, and differentialpair amplifiers are the input building blocks of any opamp, as shown in Figure 5. Therefore, the performance of a differential-pair amplifier, designed using SGFETs, needs to be measured before designing an opamp and will be investigated in this work. We design the input transistors of the differential pair amplifier using PMOS transistors to enable realizing the Miller stage using NMOS transistors and achieving higher gains.
The low-frequency small signal model of the differential pair amplifier designed using SGFETs is shown in Figure 6.
The layout of the differential pair amplifier realized using 3 metallization layers is presented in Figure 7. All interconnect parasitics are extracted and added to the amplifier netlist for postlayout simulations.
The resistor R 3 is given by The voltage gain of the differential pair amplifier is given by where U 1 denotes g m2 r ds2 [r ds1 (g m1 + G s1 ) + G s1 (R s3 + r ds3 /(1 + g m3 r ds3 ))] and U 2 denotes g m1 r ds1 G s1 G s4 r ds4 (R s3 + r ds3 /(1 + g m3 r ds3 )). For G s g m g ds , the voltage gain is approximately given by For G s g m g ds , the output resistance is approximately given by The main transistors of the input differential pair amplifier are realized by parallel combination of two p-type SGFETs to ensure a large transconductance. The width of the metal interconnects is selected to be 14 nm to reduce their resistivity, and four parallel vias are used to connect metal-2 and metal-3 layers to minimize the signal loss. Each via with 4 nm × 4 nm dimension and 36 nm height has a resistance of 400 Ω. Overlap capacitance between metal-1 and metal-2 routing interconnects is 0.2 aF for 14 nm × 14 nm dimension and 36 nm height. The layout area of the differential pair amplifier is x = 136 nm and y = 190 nm.

POSTLAYOUT CHARACTERISTICS
The transient and frequency responses of the SGFET differential pair amplifier are shown in Figure 8. The amplifier provides a gain of 16 with the first pole located at 100 GHz and the second pole located at 100 THz. To attain high accuracy in the transfer functions of various analog circuits such as switch capacitor filters and amplifiers, it might be necessary to cascade multiple stages in nested Miller architectures and achieve a voltage gain higher than 1000. The spectrum of the output waveform of the amplifier is given in Figure 9. It has very good linearity characteristics, and the total harmonic distortions of the amplifier are only 3% for ±233 mV output swing. Such a high linearity is due to the source resistance, R s , acting as the degeneration resistance and minimizing the harmonic distortions of input differential pair transistors.
The postlayout characteristics of the opamp are listed in Table 1. The good performance of the SGFET amplifier indicates that these transistors are good choices for future integration of high-speed and low-power analog and mixed signal circuits.

CONCLUSIONS
The design and characteristics of a differential pair amplifier designed using nanowire SGFETs and having channel length of 10 nm and channel radius of 2 nm were presented. The amplifier dissipates 5 μW power and provides 5 THz bandwidth with a voltage gain of 16 and a distortion better than 3%. All these parameters indicate that vertical nanowire SGFETs are promising candidates for realizing next generation high-speed analog integrated circuits.