Application of physics- based device models for circuit simulation Victor Spitsyn, Ilya Lisichkin Cadence Design Systems LLC, Moscow MOS-AK Meeting, September 22, 2006

A Model: equations and parameters The model derivation includes discretization mesh, Poison and continuity equations integration steps. A circuit representation is derived. Some simplifying assumptions were done. δQ k p C k p = δ(V k p – V k i ) J k p = e g k mn (V k-1 i – V k i ) * g k dn (V k-1 i – V k-1 n, V k i – V k n ) * g k vn (V k-1 n – V k n )

Pn junction circuit model Three-block equivalent circuit of a pn junction. The elements drawn in black are those which implement the minimum device functionality. The elements drawn in grey are only required for accurate high-injection and high-frequency modeling. The heavy dark lines highlight elements which reduce to short circuits in the low-injection case.

Simulation of pn junction Small-signal conductance and capacitance at 100kHz for a symmetric pn junction with 5μm long p and n regions of doping cm -3. The order parameter indicates the number of partitions on each side of the junction. Frequency response (real and imaginary part of the small-signal admittance) for the first- and second-order model, at a forward bias of 0.7V.

Npn bipolar transistor circuit model Equivalent circuit of the npn bipolar transistor. The elements drawn in black are those which implement the minimum device functionality. The elements drawn in grey are only required for accurate high-injection and high-frequency modeling. The heavy dark lines highlight elements which reduce to short circuits at low injection

Simulation of bipolar transistor Frequency dependence of the real and imaginary parts (absolute values) of the Y parameters for a 0.25 μm npn bipolar transistor at a current density of 430 μA/ μm2 (f t = 16 GHz, f max = 30 GHz)

What’s next: performance and accuracy gain measurement Using common benchmarks and typical engineering tasks to measure performance and compare accuracy wrt compact models

Summary Considered models are good to apply for small-signal analyses. For successful implementation, parameter extraction tool is needed, because optimization procedure is an essential part of the entire flow. Assessment of performance impact and accuracy gain as compared to the compact models is reasonable to complete.

References J. G. Linvill, “Lumped models of transistors and diodes”, Proc. IRE, vol. 46, pp. 1141–1152, June C. T. Sah, “The equivalent circuit model in solid-state electronics—Part I: The single energy level defect centers”, Proc. IEEE, vol. 55, pp. 654–671, May 1967 A. Pacelli, M. Mastrapasqua, and S. Luryi, “Generation of equivalent circuits from physics-based device simulation”, IEEE Trans. Computer Aided Design of Integrated Circuits, vol. 19, pp. 1241–1250, Nov