# 1. [2 x 10 pts] Find the Req for the following 32 nm transistors, using Req data from the following table.

18 / 01 / 2019 Physics

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1. [2 x 10 pts] Find the Req for the following 32 nm transistors, using Req data from the following table. Assume all transistors are minimum length (L = 2 λ = 32 nm).  Table of equivalent resistance Req (W/L= 1) of NMOS and PMOS transistors in a fictitious 32 nm process (with L = Lmin) at different operating voltages. For larger devices, divide Req by W/L. VDD (V) 0.8 0.9 1.0 1.1 NMOS (kW) 5 3 2.5 2.4 PMOS (kW) 16 8 6 5   a. NMOS, W = 6 λ in series with an NMOS, W = 16 λ, Vdd = 0.9 V b. PMOS, W = 12 λ in parallel with a PMOS, W = 4 λ, Vdd = 1.1 V  2. [10 pts] All transistors in a 45 nm CMOS 4-input NOR gate are 6 λ wide and 2 λ long. Calculate the capacitance of a single input if Cox = 65 fF/nm2 and CO = 4 fF/nm.  3. [2 x 10 pts] Calculate the output (junction) capacitance for the following 32 nm CMOS gates.  For an NMOS assume: Cj = 26 fF/nm2 and Cjsw = 3 fF/nm,  and for PMOS assume: Cj = 23 fF/nm2 and Cjsw = 2.6 fF/nm.  Use LD = 5 nm. Assume minimum length transistors, and no shared diffusion between transistors. a. Inverter: PMOS W = 6 λ, NMOS W = 4 λ b. 2-input NAND: PMOS W = 6 λ, NMOS W = 8 λ  4.  [15+15 pts] A copper wire is formed into the shape shown below and has an R = 1.41667 x 10-4 W/. Since techniques to calculate the resistance of a corner are complex, approximate the resistance by calculating a reasonable lower bound and upper bound resistance between points A and B. Explain your

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