Substituting these Boltzmann relations into the local electric charge density expression, the following expression can be obtained ρ ρ e = e ( c + − − c − − ) = c 0 e ⋅ ⋅ [ e − − e ψ ψ ( x , y , z ) k B T − − e e ψ ψ ( x , y , z ) k B T ] .