Exact linear admittance ofn+-n-n+semiconductor structures

With the self-consistent solution of the linearized Boltzmann equation in the relaxation-time approximation for a spatially inhomogeneous electron system, the admittance of $n^{+}$-n-$n^{+}$ semiconductor structures is studied as a function of the length L of the moderately doped n region. It is shown that a one-dimensional treatment of the velocity space leads to the exact, analytical solution of the problem. In addition to the conventional admittance and the geometric capacitance of the n region, the equivalent circuit of the structure also includes the contact resistance and, as a new feature, the contact capacitance. For the strongly screened cases (L≫$L_D$) the contact capacitance is approximately the permittivity ε of the n region divided by the Debye length $L_D$ and, further, becomes exactly equal to εL/6$L_D^2$ in the weak-screening regime ($L_D$≫L).