Satisfactory approximate analytical solutions of potential distributions of an undegeneracy semiconductor sample having a surface inversion region and impurity densityN≳102niwere obtained by the following simple modeld2u/dx2=aN:un≳u⩾0,bN: 2un≳n⩾un,reu−un:us⩾u⩾2un, whereun= arc Sinh(N/2) = ln N,usis the surface potential anda,b, andrare adjustable parameters. Particularly, the following formulas can provide quite good values of the parameters:a= 1−(1/un),b= 1+(g/un), andr= 1+(us−2un+1−g)(eus−2un−1)−1, wheregis an adjustable parameter. For example, the error is not greater than about 2% wheng= 1 andN≳103niand it decreases with increasing impurity density. The total amount of the space charges and the amount of carriers in the inversion region (us⩾u⩾un) were accurately given. The model can be applied in a small current injection whose direction is perpendicular to the sample surface if the average quasi‐Fermi energy level of the electrons and holes can be introduced instead of the Fermi energy level at equilibrium.