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)