Full RLGC model extraction of Through Silicon Via (TSV) with charge distribution effects

Abstract

The analytical model based on Poisson–Boltzmann equation in a cylindrical coordinate system is developed for simulating the electrical parameters of the three-dimensional Through Silicon Via (TSV) interconnection. Considering the effects of bias voltage, the accurate charge distribution and the high-frequency capacitance in the depletion layer of the semiconductor is obtained. Moreover, the resistance and inductance parameters of TSV are extracted by using the partial element equivalent circuit method. Finally, the full resistance–inductance–capacitance–conductance electrical model of TSV interconnection is presented first time with the semiconductor behaviour, and the transmission characteristics of signal-ground TSV structure are studied.

Keywords:

• charge distribution
• depletion capacitance
• Poisson–Boltzmann equation
• Through Silicon Via

Funding

This work was supported in part by the National Science Foundation of China [grant number 61274110], [grant number 61205054], [grant number 61371031]; in part by Zhejiang Provincial Natural Science Foundation of China [grant number Z1110330], [grant number LQ12F05006]; and in part by the Fundamental Research Funds for the Central Universities 12MS125, China.