1.8 KiB
1.8 KiB
VSLI Homework 2 - Aidan Sharpe
Problem 1
A 90[nm] long transistor has a gate oxide thickness t_\text{ox} of 16[$\text{\r{A}}$]. What is its gate capcaitance per micrion of width?
eps_0 = 8.85E-12
k_ox = 3.9
L = 90E-9 # 90nm expressed in meters
t_ox = 16E-10 # 16A expressed in meters
C_permeter = k_ox * eps_0 * L / t_ox
C_permicron = C_permeter * 1E-6
print(C_permicron)
\boxed{C_\text{permicron} = 1.94\text{[fF/$\mu$m]}}Problem 2
Consider the nMOS transistor in a 0.6[$\mu$m] process with gate oxide thickness of 100[$\text{\r{A}}$]. The doping level is $N_A = 2 \times 10^{17}$[cm$^{-3}$] and the nominal threshold voltage is 0.7[V]. The body is tied to ground with a substrate contact. How much does the threshold change at room temperature if the source is at 4[V] instead of 0[V]?
from math import log, sqrt
V_t0 = 0.7 # The nominal threshold voltage
t_ox = 100E-8 # The gate threshold voltage in angstrom with CGS units
N_A = 2E17 # The doping level in cm^-3
k_ox = 3.9
k_si = 11.7
eps_0 = 8.85E-14 # Vacuum permittivity with CGS units
k = 1.380E-23 # Boltzmann's constant
q = 1.602E-19 # The charge of an electron
T = 300 # Room temperature in Kelvin
v_T = k*T/q
n_i = 1.45E10 # The intrinsic carrier concentration of undoped Si
eps_ox = k_ox * eps_0
eps_si = k_si * eps_0
V_b = 0
V_s0 = 0
V_s1 = 4
gamma = (t_ox / eps_ox) * sqrt(2*q*eps_si*N_A)
phi_s = 2 * v_T * log(N_A / n_i)
def V_t(V_t0, V_s, V_b, gamma, phi_s):
V_sb = V_s - V_b
return V_t0 + gamma*(sqrt(phi_s + V_sb) - sqrt(phi_s))
Delta_V_t = V_t(V_t0, V_s1, V_b, gamma, phi_s) \
- V_t(V_t0, V_s0, V_b, gamma, phi_s)
print(Delta_V_t)
\boxed{\Delta V_t = 0.955583\text{[V]}}