An explicit current–voltage model for undoped double-gate MOSFETs based on accurate yet analytic approximation to the carrier concentration

Taylor Expansion of Surface Potential in MOSFET: Application to Pao-Sah Integral

“…u Low and u U are defined by implicit relations to the gate voltage Vg. Following a methodology previously described in [17], u Low and u Up can easily be obtained iteratively from first order Taylor expansion by setting Vg = k • δ, in which δ is the sample step size and k an integer. For a given step size and for k varying from 0 to Vg/δ, u Low and u Up at iteration k are calculated values at previous iteration according to 10 −20 Drain…”

Carrier-based compact modeling of charge and capacitance of long channel undoped symmetric double-gate MOSFETs

“…where n i is the induced electron concentration in the silicon film with the unit cm −3 , ε si is the silicon dielectric permittity, φ Fn is the electron quasi-Fermi potential in volts, which is φ Fn = V s = 0 at the source end and φ Fn = V ds at the drain end, respectively, and x is the coordinate in centimeters along the vertical direction of the silicon film. The analytic solution of the Poisson equation for the symmetric DG MOSFETs is derived in terms of the carrier concentration from the boundary at the interface between the gate oxide and the semiconductor surface and field distribution in the silicon film following classical Boltzmann statistics [15,17]:…”

“…However, equation ( 2) is a nonlinear implicit equation and a closed-form analytic solution has not been found so far. Thus, an accurate analytic approximate solution for the carrier concentration was developed for the explicit current-voltage model development for the DG MOSFETs in [17]. This formulation, however, still seems too complex for the compact model application.…”

“…Due to the potential application of DG MOSFETs for future CMOS technology, physics-based models will be needed for the circuit benchmark test and simulation. In recent works, a one-dimensional (1D) Poisson equation was solved for the DG MOSFET in terms of the surface potential, inversion charge and electron concentration to derive analytical solutions for DG MOSFET charge and channel current coupled to the Pao-Sah current formulation [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. It is well known that a complete DG MOSFET model should not only predict the MOSFET device dc current-voltage characteristics, but also include the calculation and prediction of terminal charges and the various capacitance coefficients for circuit simulation of the MOSFETs.…”

“…In previous results [12][13][14][15][16][17], a channel current-voltage model, which is written in terms of the carrier concentration at the source and drain ends, was derived from the fundamental device physics of the DG MOSFETs.…”