IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 36, NO.9, SEPTEMBER 1989 The Nonequilibrium Inversion Layer Charge of the Thin-Film SOl MOSFET 1651 ADELMO ORTIZ-CONDE, FRANCISCO J. GARCIA SANCHEZ, PIERRE E. SCHMIDT, MEMBER, IEEE, AND AUGUSTO SA-NETO Abstract-Our previous charge-sheet model for the equilibrium in- version layer charge of the thin-film SOl MOSFET is extended to ac- count for nonequilibrium conditions, which occur under normal op- eration of the device. This is of vital importance to analytically describe its current-voltage characteristics. The extended model is valid for all inversion conditions and accounts for the charge coupling between the front and back gates. The resulting analytical expression for the in- version-layer charge produces an error of less than 5 percent with re- spect to the numerical results obtained from the one-dimensional Pois- son equation with the approximation of quasi-equilibrium. NOMENCLATURE V Gj Front-gate voltage (in volts). VGb Back-gate voltage (in volts). Front-gate (conventional) flat-band voltage (in volts ). Back-gate (conventional) flat-band voltage (in volts ). VD Drain voltage (in volts). V Potential along the channel (in volts). V Tj Front-gate threshold voltage (in volts). U Electrostatic potential (in volts). U sj Front-surface potential (in volts). Usb Back-surface potential (in volts). F Electric field normal to the surface (in volts per centimeter). F sj Front-surface electric field (in volts per centi- meter). F sb Back-surface electric field (in volts per centi- meter). F sjda Depletion electric field at the front surface (in volts per centimeter). n Electron concentration (in reciprocal cubic cen- timeters ). P Hole concentration (in reciprocal cubic centi- meters). Manuscript received May 25, 1988; revised January 21,1989, This work was supported in part by the Consejo Nacional de Investigaciones Cientf- ficas y Tecnol6gicas under Contract 22,17,230 and by the Decanatos de Investigaci6n y de Postgrado, Universidad Sim6n Bolivar. The review of this paper was arranged by Associate Editor A. F. Tasch, Jr. A, Ortiz-Conde, F. 1. Garcia Sanchez, and A. Sa-Neto are with the Departamento de Electr6nica, Universidad Sim6n Bolfvar, Apartado 89000, Caracas 1080-A, Venezuela. P. E. Schmidt is with the Department of Electrical Engineering, Florida International University, University Park, Miami, FL 33199. IEEE Log Number 8928179. no Thermal equilibrium electron density (in recip- rocal cubic centimeters). Po Thermal equilibrium hole density (in reciprocal cubic centimeters). q Magnitude of electronic charge (in coulombs). r Total charge density (in coulombs per cubic cen- timeter). Qnj Front-channel charge density per unit area (in coulombs per square centimeter). Qnja Approximate front-channel charge density per unit area (in coulombs per square centimeter). NA Semiconductor film doping density (in reciprocal cubic centimeters). n, Intrinsic carrier concentration (in reciprocal cu- bic centimeters). Coj Front-gate oxide capacitance per unit area (in Farads per square centimeter). Cob Back-gate oxide capacitance per unit area (in Farads per square centimeter). x Coordinate perpendicular to the channel (in cen- timeters ). y Coordinate along the channel (in centimeters). t b Semiconductor film thickness (in centimeters). E, Intrinsic level. E Fn Electron quasi-Fermi level. E Fp Hole quasi-Fermi level. cl>B Fermi potential [cI>B = (kT/q) In (NA/nj)]. E s Semiconductor permittivity (in Farads per cen- timeter). k Boltzmann's constant. T Absolute temperature (in degrees Kelvin). I. INTRODUCTION n ECENTLY there has been much interest in silicon- .I.'.on-insulator(SOl) MOSFET's because they allow the possibility of dielectric isolation and 3-D integration [1]. These devices have an important dissimilarity with re- spect to their bulk-silicon counterparts: the charge cou- pling between the front and back gates [2], [3]. The charge-sheet model for the bulk MOSFET, devel- oped by Brews in 1978 [4], reviewed in 1981 [5], and extended recently [6]-[8], has been successful in predict- ing the current-voltage characteristics within 5 percent of those obtained by the Pao-Sah exact model [9]. The im- portance of the charge-sheet model derives from its valid- 0018-9383/89/0900-1651$01.00 © 1989 IEEE