Patent ID: 8296700

Claim:
A method of analyzing a semiconductor device, comprising: setting an impurity concentration with respect to a channel direction and a depth direction to node points arranged discretely in a channel region of a model transistor based on a predetermined concentration distribution rule; calculating a surface potential to each of said node points by reducing a dimension of said impurity concentration in the depth direction; correcting the surface potential based on interaction between said node points adjacent to each other to generate the corrected surface potential; calculating an electric characteristic of said model transistor by using the corrected surface potential; and storing said impurity concentration as a model parameter of said model transistor in a storage unit, when the calculated electric characteristic and an electric characteristic prepared previously are coincident with each other within a predetermined range, wherein said calculating a surface potential comprises: calculating the surface potential to each of said node points by solving a Poisson equation in the depth direction on said node point, wherein the Poisson equation is expressed by the following equation: C ox ⁡ ( V G - V F ⁢ ⁢ B - ϕ so ) = C ⁢ N sub N sub ⁢ ⁢ 0 ⁢ ( β ⁡ ( ϕ s ⁢ ⁢ 0 - V ) - 1 + exp ⁡ ( - β ⁡ ( ϕ s ⁢ ⁢ 0 - V B ) ) ) + exp ⁡ ( β ⁡ ( ϕ s ⁢ ⁢ 0 - ϕ f - 2 ⁢ Φ B ) ) where φ s0 is the surface potential, V G is a gate voltage, V FB is a flat band voltage, V B is a substrate voltage, N sub0 is an effective impurity concentration on a surface in the channel region, Φ B is an energy difference between a quasi-Fermi level and an intrinsic Fermi level, φ f is the quasi-Fermi level, ∈ ox is a dielectric constant of a gate oxide film, T ox is a film thickness of the gate oxide film, q is an elementary charge amount, ∈ si is a dielectric constant of silicon, β is a thermal voltage, k B is the Boltzmann constant, T is an absolute temperature on an operation, n i is an intrinsic carrier density, and N(x, z) expresses said impurity concentration set to each node point, wherein the following equations are met, C ox = ɛ ox T ox C = 2 ⁢ ɛ Si ⁢ q ⁢ ⁢ N sub ⁢ ⁢ 0 β Φ B = 1 β ⁢ log ⁡ ( N sub ⁢ ⁢ 0 n i ) β = q k B ⁢ T ϕ s ⁢ ⁢ 0 = q ɛ Si ⁢ ∫ 0 W dep ⁢ N ⁡ ( x , z ) ⁢ z ⁢ ⅆ z + 1 β + V B N sub = ( ∫ 0 W dep ⁢ N ⁡ ( x , z ) ⁢ ⅆ z ) 2 2 ⁢ ∫ 0 W dep ⁢ N ⁡ ( x , z ) ⁢ z ⁢ ⅆ z N sub ⁢ ⁢ 0 = N ⁡ ( x , 0 ) .