// // Verilog-A definition of an ideal MOSFET model. // // Version 1.0, 01-Jan-2011 // // For "Operation and Modeling of The MOS Transistor," Third Edition // by Yannis Tsividis and Colin McAndrew // Oxford University Press, 2011 // // Copyright Oxford University Press, 2011. All rights reserved. // // Software is distributed as is, without warranty or service // support. Oxford University Press and its employees are not // liable for the condition or performance of the software. // // Oxford University Press owns the copyright but shall not be liable for any // infringement of copyright or other proprietary rights brought by third // parties against the users of the software. // // Oxford University Press hereby disclaims all implied warranties. // // Oxford University Press grants the users the right to copy, modify, // and use the software in conjunction with usage of the abovementioned // book, for both personal and classroom use. // // // This an ideal surface potential based MOS transistor model. // The surface potential solution is non-iterative and is based on Appendix A of: // G. Gildenblat, H. Wang, T.-L. Chen, X. Gu, and X. Cai, "SP: An advanced surface-potential-based // compact MOSFET model," IEEE J. Solid-State Circuits, vol. 39., no. 9. pp. 1394-1406, Sep. 2004 // The basic I_DS and charge modeling equations are based on those described in: // H. Wang, T.-L. Chen, and G. Gildenblat, "Quasi-static and nonquasi-static compact MOSFET models // based on symmetric linearization of the bulk and inversion charges," IEEE Trans. Electron Devices, // vol. 50, no. 11, pp. 2262-2272, Nov. 2003 // but with a slightly different bulk charge model as described in the book. // // The model is for an intrinsic MOS transistor and does not include any parasitics // (series resistance, junction diode current and capacitance, overlap and fringing capacitance) // or flicker or shot noise. // // There is a switch in the model form at V_GB just greater than V_FB. I_DS and the inversion // charge essentially go to zero at that bias, so the model is simplified to reflect that and to avoid // numerical evaluation problems for V_GB biases below that value. The first of the above references // provides a conditioning of the surface potential equation (SPE) that ensures continuity of the // trans-capacitances if there is a switch to the simplified model form at V_GB=0. However, for // understanding the operation of the MOS transistor this level detail is not necessary and can // obscure the basic way the model works. For this reason a simple "hard" switch is used. // // Symbols used are as similar as possible to those in the book, and the underscore "_" // character indicates a subscript. Where appropriate, an additional subscript to indicate // the unit is added. All model parameters are in upper case, so the T_OX model parameter is // the t_ox symbol from the text. There are more efficient ways to write the code, the style // used is intended to emphasize clarity and readability. // `include "disciplines.vams" // // Physical constants and other generally useful numbers // `define TABS_NIST2004 273.15 // (K) (NIST2004) 0C `define QQ_NIST2004 1.60217653e-19 // (C) (NIST2004) mag. of electronic charge `define KB_NIST2004 1.3806505e-23 // (J/K) (NIST2004) Boltzmann constant `define EPS0_NIST2004 8.854187817e-14 // (F/cm) (NIST2004) Electric constant `define EPS_OX 3.45313324863e-13 // (F/cm) EPS0_NIST2004*3.90 `define EPS_SI 1.035939974589e-12 // (F/cm) EPS0_NIST2004*11.7 `define oneSixth 0.1666666666666667 `define oneThird 0.3333333333333333 `define twoThirds 0.6666666666666667 `define sqrtTwo 1.414213562373095 `define inv_sqrtTwo 0.7071067811865475 `define switchPoint 1.0e-3 // // Macro that computes the surface potential // // Outputs: // psi_s the surface potential // Inputs: // Vgb gate-bulk voltage // Vcb channel-bulk voltage // phi_t the thermal voltage // twoPhi_F twice the Fermi potential = 2*phi_t*ln(Nsub/Ni) // Vfb the flatband voltage // G gamma/sqrt(phi_t) where gamma is the body effect coefficient // blockName name (must be unique) for the block, to allow locally scoped variables // `define psi_calc(psi_s,Vgb,Vcb,phi_t,twoPhi_F,Vfb,G,blockName) \ begin : blockName \ real xg, xi, x23, xg23, DEL_n, Gsq, yg, z, eta, a, c, tau, y0, DEL_0, DEL_1, p, q, x, u, xn, b, xbar, Ebar, omega, x0, xsub ; \ xg = ((Vgb)-(Vfb))/(phi_t); \ xi = 1.0+(G)*`inv_sqrtTwo; \ if (abs(xg/xi)<1.0e-7) begin \ x = xg/xi; \ end else begin \ if ((Vcb)<0.0) begin \ x23 = ((twoPhi_F)+(Vcb))/(2.0*(phi_t)); \ end else begin \ x23 = (0.5*(twoPhi_F)+(Vcb))/(phi_t); \ end \ xg23 = (G)*sqrt(x23-1.0); \ DEL_n = exp(-((twoPhi_F)+(Vcb))/(phi_t)); \ Gsq = (G)*(G); \ if (xg<0.0) begin \ yg = -xg; \ z = 1.25*yg/xi; \ eta = 0.5*(z+10.0-sqrt((z-6.0)*(z-6.0)+64.0)); \ a = (yg-eta)*(yg-eta)+Gsq*(eta+1.0); \ c = 2.0*(yg-eta)-Gsq; \ tau = -eta+ln(a/Gsq); \ u = (a+c)*(a+c)/tau+0.5*c*c-a; \ y0 = eta+a*(a+c)/(u+c*(a+c)*(c*c*`oneThird-a)/u); \ DEL_0 = exp(y0); \ DEL_1 = 1.0/DEL_0; \ p = 2.0*(yg-y0)+Gsq*(DEL_0-1.0+DEL_n*(1.0-DEL_1)); \ q = (yg-y0)*(yg-y0)+Gsq*(y0-DEL_0+1.0+DEL_n*(1.0-DEL_1-y0)); \ x = -y0-2.0*q/(p+sqrt(p*p-2.0*q*(2.0-Gsq*(DEL_0+DEL_n*DEL_1)))); \ end else begin \ if (xgT_MAX) begin $strobe("ERROR (idealMos): ambient temperature is higher than allowed maximum %g",T_MAX); $finish(0); end tini_K = T_NOM+`TABS_NIST2004; del_T = tdev_C-T_NOM; rat_T = $temperature/tini_K; V_FB_T = V_FB+T_VFB*del_T; MU_T = MU*pow(rat_T,X_MU); phi_t = `KB_NIST2004*$temperature/`QQ_NIST2004; C_ox_cm2 = `EPS_OX/(T_OX*1.0e-7); twoPhi_F = 2.0*phi_t*ln(N_SUB/1.45e10); gamma = sqrt(2.0*`QQ_NIST2004*`EPS_SI*N_SUB)/C_ox_cm2; G = gamma/sqrt(phi_t); end // initializeModel // // Code independent of bias but dependent on instance parameters // begin : initializeInstance C_ox = C_ox_cm2*W*L*1.0e4; beta = MU_T*C_ox_cm2*W/L; end // initializeInstance // // DC bias dependent quantities // // Note that the model is symmetric therefore no source/drain flipping is required // begin : evaluateStatic V_GB = -TYPE*V(b_gb); V_DB = -TYPE*V(b_db); V_SB = -TYPE*V(b_sb); `psi_calc(psi_s0,V_GB,V_SB,phi_t,twoPhi_F,V_FB_T,G,psi_s0_block) `psi_calc(psi_sL,V_GB,V_DB,phi_t,twoPhi_F,V_FB_T,G,psi_sL_block) if (((V_GB-V_FB_T)/phi_t)<=`switchPoint) begin // simplified code for when the inversion charge is essentially zero mu_deg = 1.0; I_DS = 0.0; end else begin // code that includes calculations for inversion charge and current psi_sL0 = psi_sL-psi_s0; exp_mps0 = exp(-psi_s0/phi_t); phi_e0 = exp(-(twoPhi_F+V_SB)/phi_t)*(phi_t/exp_mps0-psi_s0-phi_t); exp_mpsL = exp(-psi_sL/phi_t); phi_eL = exp(-(twoPhi_F+V_DB)/phi_t)*(phi_t/exp_mpsL-psi_sL-phi_t); psi_sm = 0.5*(psi_s0+psi_sL); exp_mpsm = exp(-psi_sm/phi_t); phi_em = 0.5*(phi_e0+phi_eL)+psi_sL0*psi_sL0*(0.125*exp_mpsm/phi_t-0.25/(gamma*gamma)); phi_am = phi_t*exp_mpsm+psi_sm-phi_t; phi_im = gamma*phi_em/(sqrt(phi_am+phi_em)+sqrt(phi_am)); alpha_m = 1.0+0.5*gamma*(1.0-exp_mpsm)/sqrt(phi_am); mu_deg = 1.0/(1.0+THETA*(gamma*sqrt(phi_am)+ETA*phi_im)); I_DS = beta*mu_deg*(phi_im+alpha_m*phi_t)*psi_sL0; end I_DS = -TYPE*I_DS; I_DB = -TYPE*gmin*V_DB; I_SB = -TYPE*gmin*V_SB; end // evaluateStatic begin : evaluateDynamic if (((V_GB-V_FB_T)/phi_t)<=`switchPoint) begin // simplified code for when the inversion charge is essentially zero Q_G = C_ox*(V_GB-V_FB_T-0.5*(psi_s0+psi_sL)); Q_D = 0.0; Q_S = 0.0; end else begin // code that includes calculations for inversion charge and current H = phi_t+phi_im/alpha_m; Q_G = C_ox*(gamma*sqrt(phi_am+phi_em)+psi_sL0*psi_sL0/(12.0*H)); Q_I = -C_ox*(phi_im+alpha_m*psi_sL0*psi_sL0/(12.0*H)); Q_D = -0.5*C_ox*(phi_im-`oneSixth*alpha_m*psi_sL0*(1.0-0.5*(psi_sL0/H)*(1.0+0.1*psi_sL0/H))); Q_S = Q_I-Q_D; end Q_G = -TYPE*Q_G; Q_D = -TYPE*Q_D; Q_S = -TYPE*Q_S; end // evaluateDynamic begin : loadStatic I(b_ds) <+ I_DS; I(b_db) <+ I_DB; I(b_sb) <+ I_SB; end // loadStatic begin : loadDynamic I(b_gb) <+ ddt(Q_G); I(b_db) <+ ddt(Q_D); I(b_sb) <+ ddt(Q_S); end // loadDynamic // // Noise contributions // begin : noise S_iw = 4.0e-4*`KB_NIST2004*$temperature*MU_T*mu_deg*abs(Q_I)/(L*L); I(b_ds) <+ white_noise(S_iw); end // noise end // analog endmodule