In principle, the equilibrium electric potential variation in problem Problem 2 and the equilibrium electric potential difference in problem Problem 1 cannot be measured? Why? How can they be measured approximately?

Problem 1:-

An n-type SI slice of a thickness L Is inhomogeneously doped with phosphorus donor whose concentration profile is given by N_DD(x) N₀ + (N_L-N₀)(x/L).

What is the formulae for the electric potential difference between the front and the tack surfaces when the sample is at thermal and electric equilibria regardless of how the mobility and diffusivity varies with position?

What is the formulae for the equilibrium electric field at a plane x from the front surface for a constant diffusivity and mobility? How is the formulae modified if diffusivity and mobility vary with impurity ion concentration?

Problem 2:-

The equilibrium electric potential variation in an n-type Si slice of thickness L Is found to be given by V₁(x)-V₀ + (V_L-V₀)(x/L). What are the equilibrium concentrations of electrons and holes as a function of x? Obtain the expressions of the drift and diffusion current densities as a function of x.