/* * Philips Electronics N.V. 2001. * This information is proprietary to Philips Electronics N.V. and is * protected by copyright. If you copy this material you agree to indemnify, * hold harmless and defend Philips Electronics N.V. or any of its * affiliated companies against any claims, lawsuits, including attorney's * fees that arise or result from the use of this material. This file is intended for help in implementing software, according to the documentation given in Nat.Lab. Unclassified Report NL-UR 2001/801, ``Parameter Extraction for the Bipolar Transistor Model Mextram, level 504'' J.C.J. Paasschens, W.J. Kloosterman, and R.J. Havens. see www.semiconductors.philips.com/Philips_Models In the report various routines are discussed and explained. This file contains code to support these routines in extraction software. Since the code in this file is stripped of all parts copyrighted to other companies, there is no longer any interaction with an extraction software tool coded. The code in this file is therefore not directly usable. (In some parts it is more macro code than real c-code.) For the model equations of Mextram 504, used in this code, see Nat.Lab. Unclassified Report NL-UR 2000/811, ``The Mextram Bipolar Transistor Model, level 504'' J.C.J. Paasschens and W.J. Kloosterman. see www.semiconductors.philips.com/Philips_Models */ /*------------------------------------------------*/ /* mxtpardef.h */ /* contains the various definitions of model parameters and some much used /* quantities */ double level,mult,tref,dta,exmod,exphi,exavl,is,ik,vef,ver, bf,ibf,mlf,xibi,bri,ibr,vlr,xext,wavl,vavl,sfh, re,rbc,rbv,rcc,rcv,scrcv,ihc,axi,cje,vde,pe,xcje,cbeo, cjc,vdc,pc,xp,mc,xcjc,cbco,mtau,taue,taub,tepi,taur, aqbo,ae,ab,aex,aepi,ac,dvgbf,dvgbr,vgb,vgc,vgj,dvgte, iss,iks,cjs,vds,ps,vgs,as, deg, xrec,rth,cth; double isT,ikT,vefT,verT, bfT,ibfT,briT,ibrT, reT,rbcT,rbvT,rccT,rcvT,cjeT,vdeT, cjcT,vdcT,xpT,taueT,taubT,tepiT, issT,iksT,cjsT,vdsT, degT; double cpcs, bnT_bn; double kq,Gmin,aje,vfe,ajc,bjc,vfc,ajs; double temp,tk,trk,tn,vt,vtr,inv_vDt; double aq0i, deg_vt; /* end mxtpardef.h */ /*------------------------------------------------*/ /* Giving values to the various parameter is not coded. Part of the code that does so, could contain (see Sec. 2.6.3 of aforementioned report): if (taub < 0) taub = ver * (1-xcje) * cje / ik; if (tepi < 0) tepi = taub * is * ik * rcv*rcv * exp(vdc/vtr) / (4*vtr*vtr); if (taur < 0) taur = (taub+tepi) * (1-xcjc)/xcjc; The constants are defined by Gmin = 1e-13; aje = 3.0; ajc = 2.0; ajs = 2.0; */ /*------------------------------------------------*/ /* mxtTrules.h */ /* Temperature rules */ /* tk, trk, tn, vt, vtr, inv_vDt must be set. */ reT =re *pow(tn,ae); rbvT=rbv*pow(tn,ab-aqbo); rbcT=rbc*pow(tn,aex); rccT=rcc*pow(tn,ac); rcvT=rcv*pow(tn,aepi); vdeT=-3*vt*log(tn)+vde*tn+(1-tn)*vgb; vdeT = vdeT + vt*log(1+exp((0.05-vdeT)/vt)); cjeT=cje*pow((vde/vdeT),pe); vdsT=-3*vt*log(tn)+vds*tn+(1-tn)*vgs; vdsT = vdsT + vt*log(1+exp((0.05-vdsT)/vt)); cjsT=cjs*pow((vds/vdsT),ps); vdcT =-3*vt*log(tn)+vdc*tn+(1-tn)*vgc; vdcT = vdcT + vt*log(1+exp((0.05-vdcT)/vt)); cjcT =cjc*((1-xp)*pow((vdc/vdcT),pc)+xp); xpT =xp *(cjc/cjcT); vefT=vef * pow(tn,aqbo) * cjc/cjcT; verT=ver * pow(tn,aqbo) * cje/cjeT; bfT = bf * pow(tn,ae-ab-aqbo) * exp(-dvgbf*inv_vDt); briT = bri * exp(-dvgbr*inv_vDt); isT = is * pow(tn,4.0-ab-aqbo) * exp(-vgb*inv_vDt); ikT = ik * pow(tn,1-ab); ibfT = ibf* pow(tn,6-2*mlf) * exp(-vgj*inv_vDt/mlf); ibrT = ibr* tn*tn * exp(-0.5*vgc*inv_vDt); issT = iss* pow(tn,4.0-as) * exp(-vgs*inv_vDt); if ( (issT !=0) && (is !=0) ) { iksT=iks*pow(tn,1-as)* isT/is * iss/issT; } else { iksT=iks*pow(tn,1-as); } taueT=taue*pow(tn,ab-2.0) * exp(-dvgte*inv_vDt); taubT=taub*pow(tn,aqbo+ab-1.0); tepiT =tepi* pow(tn,aepi); bnT_bn = (1+7.2E-4*(tk-300)-1.6E-6*(tk-300)*(tk-300)); bjc = (ajc-xpT)/(1-xpT); vfc = vdcT * (1-pow(bjc,-1.0/pc)); vfe = vdeT * (1-pow(aje,-1.0/pe)); degT = deg * pow(tn,aqbo); deg_vt = degT/vt; if (degT == 0) aq0i = 0.0; else aq0i = 1.0 / (exp(deg_vt)-1.0); if (axi < 0.02) axi = 0.02; /* end mxtTrules.h */ /*------------------------------------------------*/ /*------------------------------------------------*/ /* Normal functions */ MXT_show_parms { #include "mxtpardef.h" double taub0, tepi0, taur0, verI, vefI; taub0 = verT*cjeT*(1-xcje)/ikT; tepi0 = taub * is * ik * rcv*rcv * exp(vdc/vtr) / (4*vtr*vtr) * pow(tn,aepi); taur0 = (taub+tepi) * (1-xcjc)/xcjc; if (degT == 0) { verI = verT; vefI = vefT; } else { verI = verT / (deg_vt * aq0i * exp(deg_vt)); vefI = vefT / (deg_vt * aq0i); } printf("level, Temp, vt : %6.1f %6.1f %9.6f\n", level, tk-273.15,vt); printf("mult,exmod,exavl,exphi : %6.3f %6.3f %6.3f %6.3f\n", mult,exmod,exavl,exphi); printf("Tref,dta,aqbo,dvgbf/br : %6.3f %6.3f %6.3f %6.3f %6.3f\n", tref,dta,aqbo,dvgbf,dvgbr); printf("ae,ab,ac,aex,aepi,as : %6.3f %6.3f %6.3f %6.3f %6.3f %6.3f\n", ae,ab,ac,aex,aepi,as); printf("dvgte,vgj,vgb,vgc,vgs : %6.3f %6.3f %6.3f %6.3f %6.3f\n", dvgte,vgj,vgb,vgc,vgs); printf("wavl,vavl,sfh,axi : %13.3e %6.3f %6.3f %6.3f\n", wavl,vavl,sfh,axi ); printf("Rth, Cth, deg, xrec : %9.3f %9.3e %6.3f %6.3f\n", rth, cth, deg, xrec); printf("\n"); printf("Bf,Ibf,mlf : %6.2f %9.3e %6.3f\n", bfT, ibfT, mlf); printf("Br,Ibr,Vlr : %6.2f %9.3e %6.3f\n", briT, ibrT, vlr); printf("Re,Rbc,Rbv,Rcc : %9.3f %9.3f %9.3f %9.3f\n", reT, rbcT, rbvT, rccT); printf("Rcv,SCRcv,Ihc : %9.3f %9.3f %9.3e (%8.3f %8.3f)\n", rcvT, scrcv, ihc, rcvT*ihc, scrcv*ihc); printf("\n"); printf("Is ,Ik ,Iss,Iks : %9.3e %9.3e %9.3e %9.3e\n",isT, ikT,issT,iksT); printf("Ver,Vef,VerI,VefI: %9.3f %9.3f %9.3f %9.3f\n",verT,vefT,verI,vefI); printf("\n"); printf("xcje,xib1,xcjc,xext : %6.3f %6.3f %6.3f %6.3f\n", xcje,xibi,xcjc,xext); printf("Cbeo, Cbco : %9.3e %9.3e \n", cbeo, cbco); printf("Cje,Vde,pe : %9.3e %6.3f %6.3f\n", cjeT, vdeT, pe); printf("Cjc,Vdc,pc,xp,mc : %9.3e %6.3f %6.3f %6.3f %6.3f\n", cjcT, vdcT, pc, xpT, mc ); printf("Cjs,Vds,ps : %9.3e %6.3f %6.3f\n", cjsT, vdsT, ps); printf("\n"); printf("Taub,Tepi : %9.3e (%9.3e) %9.3e (%9.3e)\n", taubT,taub0,tepiT,tepi0); printf("Taur,Taue,mtau : %9.3e (%9.3e) %9.3e %9.3f\n", taur,taur0,taueT,mtau); return 0; } MXT_ft { #include "mxtpardef.h" double *qqic,*qqvbe,*qqvce; double qvbc,qic; double vb2e1, vb2c1, vb1c1, vbb2, vbb1, vbc1, vb1e1, dvb2c1_Dx, dvb1c1_dx, dvb1c1_di, dvb1c1_dz, dvbb2_dx, dvbb2_di, dvbb2_dz, dve1e_dx, dve1e_di, dve1e_dz, dvbb1_dx, dvbb1_di, dvbb1_dz, dvcc1_dx, dvcc1_di, dvcc1_dz, dvbc1_dx, dvbc1_di, dvbc1_dz, vjunc, dvjunc_di, dvjunc_dz, vec0, dvec0_di, iepi, diepi_di, diepi_dz, Dvb2e1, Din, iff, diff_dx, f1, df1,root, n0, dn0_dx, irr, dirr_di, dirr_dz, f2, df2, nb, dnb, dnb_dz, dnb_di, in, din_Dx, din_dx, din_di, din_dz, q1, dq1_dx, dq1_di, dq1_dz, qB, dqB_dx, dqB_di, dqB_dz, ib, dib_dx, Ib1, dIb1_dx, Ib2, dIb2_dx, rb, drb_dx, drb_di, drb_dz, rbvinv, drbvinv_Dx, drbvinv_dx, drbvinv_di, drbvinv_dz, vv, Dvv, vje, dvje_dx, vte, dvte_dx, dvtes_dx, dvtes_dv, vch, dvch_dz, dvch_di, vj, dvj_dv, dvj_dvch, fI, dfI_dicap, vcv, dvcv_dv, dvcv_dvch, dvcv_dicap, vjc, dvjc_dy, dvjc_dv, vtc, dvtc_di, dvtc_dz, dvtc_dv, dvtc_dvch, dvtc_dicap, icap, dicap_di, qe0, qe, dqe_dx, dqte_dx, dqtes_dx, dqtes_di, dqtes_dz, dqtes_dv, dqtc_di, dqtc_dz, qbe, qb0, dqbe_dx, dqbe_di, dqbe_dz, dqbc_dx, dqbc_di, dqbc_dz, qepi0, qepi, dqepi_di, dqepi_dz, qtex, dqtex_dx, dqtex_di, dqtex_dz, dqtex_dv, dxqtex_dv, xqtex, xdqtex_dx, xdqtex_di, xdqtex_dz, xdqtex_dv, dcbeo_dx, dcbeo_di, dcbeo_dz, dcbco_dx, dcbco_di, dcbco_dz, tau, dvce_dx, dvce_di, dvce_dz, dq_dx, dq_di,dq_dz, a, da_dx, da_di, da_dz, da_dv, da, b, db_dx, db_di, db_dz, db_dv, db, d, dd_dx, e, de_dv, de_di, tol, b1, b2; double v, dv_dv, dv_dz, dv_di, ii, dii_dz, dii_di, alfa, dalfa_di, dalfa_dz, a0, a1, da2_dz, da2_di, a2, a3, da3, a4, da4, da4_dv, da4_dvch, a5, dz_di, dx_di, denom; double alfa0; double vqs, dvqs_dz, dvqs_di, iqs, diqs_dz, diqs_di, diqs_dv, yi, dyi_dz, dyi_di, dyi_dv, xi, dxi_dz, dxi_di, g, dg_dz, dg_di, p0star, dp0star_di, dp0star_dz; double dt, hard_sat_max, vb2c1max; double dum; int itvv, it,itmax, i; int FALSE = 0; int TRUE = 1; vb2c1max = hard_sat_max * vdcT; alfa0 = 1.0/(1.0+ axi * log(1+exp(-1.0/axi))); itmax=15; tol =1E-9; /* Go through all bias points and calculate current */ for(i = 0; i < imax; i++) { qvbc=qqvbe[i]-qqvce[i]; qic =qqic[i]; dt = qqvce[i] * qic * rth; tk =temp+273.15+dt+dta; trk=tref+273.15; tn=tk/trk; vt = kq*tk; vtr= kq*trk; inv_vDt= 1/vt - 1/vtr; #include "mxtTrules.h" if (qic <= 0.0) { result = 0.0; } else { /* first estimates */ if (i==0) { vb2e1 = vt*log(qqic[0]/isT); vv = qqic[0] * rbvT/(bfT*vt); /* vv = vb1b2/vt */ } else { if (qqic[i] tol); it++) { iff = isT*exp(vb2e1/vt); diff_dx = iff/vt ; Ib1 = isT/bfT*exp(vb2e1/vt); dIb1_dx = Ib1/vt; Ib2 = ibfT*exp(vb2e1/(mlf*vt)); dIb2_dx = Ib2/(mlf*vt); ib = Ib1 + Ib2; dib_dx = dIb1_dx + dIb2_dx; a = 1.0 + (1-xibi)*rbvT/bfT; vbb2 = rbcT*ib + vt * log(1.0 + a*qic/vt); dvbb2_dx = rbcT*dib_dx; dvbb2_di = a / (1.0 + a*qic/vt); dvbb2_dz = 0.0; vb2c1 = qvbc + qic*rccT - vbb2; dvb2c1_Dx = - dvbb2_dx; a = qic*rcvT/(2*vt)+1; b = vdcT - vb2c1 + 2*vt * log(a); root = sqrt(b*b + 4*0.01*vdcT*vdcT); vqs = (b + root) / 2.0 ; dvqs_dz = -0.5 * (1.0 + b / root) ; dvqs_di = 0.5 * (1.0 + b / root) * rcvT/a; a = vqs+ihc*rcvT; iqs = vqs/scrcv * (vqs+ihc*scrcv)/ a; diqs_dv = 1.0/scrcv + (scrcv-rcvT)*rcvT*ihc*ihc/(scrcv*a*a); diqs_dz = diqs_dv * dvqs_dz; diqs_di = diqs_dv * dvqs_di; /* Calculation of yi */ ii = qic/iqs; dii_dz = ( - ii * diqs_dz)/iqs; dii_di = (1.0 - ii * diqs_di)/iqs; if (ii < 1) { a0 = exp((ii-1)/axi); a1 = axi * log(1+a0); alfa = alfa0 * (1+a1); dalfa_dz = alfa0 * a0 * dii_dz/ (1+a0); dalfa_di = alfa0 * a0 * dii_di/ (1+a0); } else { a = (1-ii)/axi; if (a > -40) a0 = exp(a); else a0 = 0.0; a1 = axi * log(1+a0); alfa = alfa0 * (ii+a1); dalfa_dz = alfa0 * dii_dz/ (1+a0); dalfa_di = alfa0 * dii_di/ (1+a0); } dv_dv = 1.0 / (ihc * scrcv); v = vqs * dv_dv; dv_dz = dvqs_dz * dv_dv; dv_di = dvqs_di * dv_dv; a2 = alfa * (1+v); da2_dz = dalfa_dz * (1+v) + alfa * dv_dv * dvqs_dz; da2_di = dalfa_di * (1+v) + alfa * dv_dv * dvqs_di; yi = (1.0 + sqrt(1.0+4.0 * v * a2))/(2 * a2); dyi_dv = 1.0 / (2 * a2 * yi - 1.0); /* dyi_da2 = - yi*yi * dyi_dv; */ dyi_dz = dyi_dv * (dv_dz - yi*yi*da2_dz); dyi_di = dyi_dv * (dv_di - yi*yi*da2_di); /* END of Calculation of yi */ xi = 1 - yi; dxi_dz = -dyi_dz; dxi_di = -dyi_di; g = rcvT * qic * xi / (2*vt); dg_dz = rcvT * qic * dxi_dz / (2*vt); dg_di = rcvT *(qic * dxi_di + xi) / (2*vt); a = 0.25 * (g-1) * (g-1) + 2.0*g; da = 0.5 * (g-1) + 2.0; root = sqrt(a); p0star = 0.5 * (g-1) + root; dp0star_dz= 0.5 * (1.0 + da/root) * dg_dz; dp0star_di= 0.5 * (1.0 + da/root) * dg_di; a = isT*exp(vdcT/vt); irr = a * p0star * (p0star+1); dirr_dz= a * (2*p0star + 1) * dp0star_dz; dirr_di= a * (2*p0star + 1) * dp0star_di; df2 = 4/ikT; f2 = df2 * irr; root = sqrt(1+f2); nb = f2 / (1+root); dnb = df2 / (2*root); dnb_dz = dnb * dirr_dz; dnb_di = dnb * dirr_di; /* continue with other quantities */ e = exp((vb2e1-vfe)/(0.1*vdeT)); vje = vb2e1 - 0.1*vdeT*log(1+e); dvje_dx = 1/(1+e); vte = vdeT/(1-pe)*(1-pow(1-vje/vdeT,1-pe))+aje*(vb2e1-vje); dvte_dx = (pow(1-vje/vdeT,-pe) - aje) * dvje_dx + aje; vjunc = vb2c1 + vec0; dvjunc_dz = 1.0; dvjunc_di = dvec0_di; a = 1.0 / (qic + iqs); vch = vdcT * (0.1 + 2.0 * qic * a); dvch_dz = vdcT * 2.0 * ( - diqs_dz * qic) * a * a; dvch_di = vdcT * 2.0 * (iqs - diqs_di * qic) * a * a; if (vjunc <= vfc) { a2 = exp((vjunc-vfc)/vch); a3 = log(1.0+a2); vj = vjunc - vch * a3; dvj_dv = 1.0 / (1.0 + a2) ; dvj_dvch=(a2/(1.0+a2) * (vjunc-vfc)/vch - a3); } else { a2 = exp((vfc-vjunc)/vch); a3 = log(1.0+a2); vj = vfc - vch * a3; dvj_dv = a2 / (1.0 + a2) ; dvj_dvch=(a2/(1.0+a2) * (vfc-vjunc)/vch - a3); } a1 = 1 - icap/ihc; fI = pow(a1, mc); dfI_dicap = -mc * fI / (a1 * ihc); a3 = 1 - vj / vdcT; a4 = pow(a3, 1.0-pc); da4_dv = - (1.0-pc) * a4 * dvj_dv / (a3 * vdcT); da4_dvch= - (1.0-pc) * a4 * dvj_dvch / (a3 * vdcT); a5 = vdcT / (1-pc); vcv = a5 * (1- fI * a4); dvcv_dv = - a5 * fI * da4_dv ; dvcv_dvch = - a5 * fI * da4_dvch; dvcv_dicap= - a5 * dfI_dicap * a4 ; vtc = (1-xpT) * (vcv + fI * bjc * (vjunc-vj)) + xpT * vb2c1; dvtc_dz = xpT; dvtc_dv = (1-xpT) * (dvcv_dv + fI * bjc * (1-dvj_dv)); dvtc_dvch = (1-xpT) * (dvcv_dvch - fI * bjc * dvj_dvch); dvtc_dicap= (1-xpT) * (dvcv_dicap+ dfI_dicap*bjc*(vjunc-vj)); dvtc_dz = dvtc_dv * dvjunc_dz + dvtc_dvch * dvch_dz + dvtc_dz; dvtc_di = dvtc_dv * dvjunc_di + dvtc_dicap * dicap_di + dvtc_dvch * dvch_di; if (degT == 0) { q1 = 1.0+vte /verT + vtc /vefT; dq1_dx = dvte_dx/verT; dq1_dz = dvtc_dz/vefT; dq1_di = dvtc_di/vefT; } else { a = exp( deg_vt*(vte/verT+1)); b = exp(-deg_vt * vtc/vefT); q1 = aq0i * (a-b); dq1_dx = aq0i * a * deg_vt * dvte_dx/verT; dq1_dz = aq0i * b * deg_vt * dvtc_dz/vefT; dq1_di = aq0i * b * deg_vt * dvtc_di/vefT; } df1 = 4/ikT; f1 = df1*iff; root = sqrt(1+f1); n0 = f1 / (1+root); dn0_dx = df1 / (2*root) * diff_dx; qB = q1 * (1.0 + 0.5 * (n0 + nb)); dqB_dx = dq1_dx * (1.0 + 0.5 * (n0 + nb)) + q1 * 0.5 * dn0_dx; dqB_dz = dq1_dz * (1.0 + 0.5 * (n0 + nb)) + q1 * 0.5 * dnb_dz; dqB_di = dq1_di * (1.0 + 0.5 * (n0 + nb)) + q1 * 0.5 * dnb_di; in = (iff-irr)/qB; din_dx = ( diff_dx -in*dqB_dx)/qB; din_dz = (-dirr_dz -in*dqB_dz)/qB; din_di = (-dirr_di -in*dqB_di)/qB; din_Dx = din_dx + din_dz * dvb2c1_Dx; Din = qic - in; Dvb2e1 = Din/din_Dx; /* for better convergence when starting at high end*/ if (Dvb2e1 > 1.5*vt) Dvb2e1= 1.5*vt; if (Dvb2e1 <-2.0*vt) Dvb2e1=-2.0*vt; vb2e1 = vb2e1+Dvb2e1; } /* end loop determining vb2e1 */ /* post processing: all voltages are known */ if (vb2c1 > vb2c1max) result=0; else { /* voltages */ vbb1 = rbcT* ib; dvbb1_dx = rbcT*dib_dx; dvbb1_dz = 0.0; dvbb1_di = 0.0; vb1c1 = vb2c1 + vbb2 - vbb1 ; dvb1c1_dx = dvbb2_dx - dvbb1_dx; dvb1c1_dz = 1.0 + dvbb2_dz - dvbb1_dz; dvb1c1_di = dvbb2_di - dvbb1_di; vbc1 = vb2c1 + vbb2 ; dvbc1_dx = dvbb2_dx; dvbc1_dz = 1.0 + dvbb2_dz; dvbc1_di = dvbb2_di; /* vcc1 = qic * rccT */ dvcc1_dx = 0.0; dvcc1_dz = 0.0; dvcc1_di = rccT; /* ve1e = (qic + ib) * reT ; */ dve1e_dx = dib_dx*reT; dve1e_dz = 0.0; dve1e_di = reT; /* vce = vcc1 - vb2c1 + vb2e1 + ve1e ; */ dvce_dx = dvcc1_dx + 1 + dve1e_dx; dvce_dz = dvcc1_dz - 1 + dve1e_dz; dvce_di = dvcc1_di + dve1e_di; /* charges */ vb1e1 = vb1c1 - vb2c1 + vb2e1; e = exp((vb1e1-vfe)/(0.1*vdeT)); vje = vb1e1 - 0.1*vdeT*log(1+e); dvje_dx = 1/(1+e); /* vtes = vdeT/(1-pe)*(1-pow(1-vje/vdeT,1-pe))+aje*(vb2e1-vje);*/ dvtes_dv = (pow(1-vje/vdeT,-pe) - aje) * dvje_dx + aje; dqtes_dv = xcje * cjeT * dvtes_dv; dqtes_dx = dqtes_dv * ( 1.0 + dvb1c1_dx); dqtes_dz = dqtes_dv * (-1.0 + dvb1c1_dz); dqtes_di = dqtes_dv * ( dvb1c1_di); dqte_dx = (1.0-xcje)*cjeT*dvte_dx; /* qtc = xcjc*cjcT*vtc; */ dqtc_dz = xcjc*cjcT*dvtc_dz; dqtc_di = xcjc*cjcT*dvtc_di; q1 = 1.0+vte /verT + vtc /vefT; dq1_dx = dvte_dx/verT; dq1_dz = dvtc_dz/vefT; dq1_di = dvtc_di/vefT; qb0 = taubT * ikT; /* qbe = 0.5 * qb0 * q1 * n0; */ dqbe_dx = 0.5 * qb0 * (dq1_dx * n0 + q1 * dn0_dx); dqbe_dz = 0.5 * qb0 * dq1_dz * n0; dqbe_di = 0.5 * qb0 * dq1_di * n0; /* qbc = 0.5 * qb0 * q1 * nb; */ dqbc_dx = 0.5 * qb0 * dq1_dx * nb; dqbc_dz = 0.5 * qb0 * (dq1_dz * nb + q1 * dnb_dz); dqbc_di = 0.5 * qb0 * (dq1_di * nb + q1 * dnb_di); qepi0 = tepiT * 4 * vt / rcvT; /* qepi = 0.5*qepi0 * xi * (p0star + 2); */ dqepi_dz = 0.5*qepi0 * (dxi_dz * (p0star+2) + xi * dp0star_dz); dqepi_di = 0.5*qepi0 * (dxi_di * (p0star+2) + xi * dp0star_di); qe0 = taueT*ikT * pow(isT/ikT, 1/mtau ); qe = qe0*exp(vb2e1/(mtau*vt)); dqe_dx = qe/(mtau*vt); e = exp((vb1c1-vfc)/(0.1*vdcT)); vjc = vb1c1 - 0.1*vdcT*log(1+e); dvjc_dv = 1/(1+e); /* vcv = vdcT/(1-pc)*(1-pow(1-vjc/vdcT,1-pc))+bjc*(vb1c1-vjc); * qtex = (1-xcjc)*cjcT * ((1-xpT) * vcv + xpT * vb1c1); */ dvcv_dv = (pow(1-vjc/vdcT,-pc) - bjc) * dvjc_dv + bjc; dqtex_dv= (1-xcjc)*cjcT * ((1-xpT) * dvcv_dv + xpT); e = exp((vbc1-vfc)/(0.1*vdcT)); vjc = vbc1 - 0.1*vdcT*log(1+e); dvjc_dv = 1/(1+e); /* vcv = vdcT/(1-pc)*(1-pow(1-vjc/vdcT,1-pc))+bjc*(vbc1-vjc); * xqtex = (1-xcjc)*cjcT * ((1-xpT) * vcv + xpT * vbc1); */ dvcv_dv = (pow(1-vjc/vdcT,-pc) - bjc) * dvjc_dv + bjc; dxqtex_dv= (1-xcjc)*cjcT * ((1-xpT) * dvcv_dv + xpT); dqtex_dx = (1-xext)* dqtex_dv * dvb1c1_dx + xext *dxqtex_dv * dvbc1_dx ; dqtex_dz = (1-xext)* dqtex_dv * dvb1c1_dz + xext *dxqtex_dv * dvbc1_dz ; dqtex_di = (1-xext)* dqtex_dv * dvb1c1_di + xext *dxqtex_dv * dvbc1_di ; /* qbeo = cbeo * ( vbb2 + vb2e1 + ve1e ); */ dcbeo_dx = cbeo * ( dvbb2_dx + 1 + dve1e_dx); dcbeo_dz = cbeo * ( dvbb2_dz + dve1e_dz); dcbeo_di = cbeo * ( dvbb2_di + dve1e_di); /* qbco = cbco * ( vbb2 + vb2c1 + vc1c ); */ dcbco_dx = cbco * (dvbb2_dx - dvcc1_dx); dcbco_dz = cbco * (dvbb2_dz + 1.0 - dvcc1_dz); dcbco_di = cbco * (dvbb2_di - dvcc1_di); dq_dx = dqtex_dx + dqtes_dx + dqte_dx + dqbe_dx + dqbc_dx + dqe_dx + dcbeo_dx + dcbco_dx; dq_dz = dqtc_dz + dqtex_dz + dqtes_dz + dqbe_dz + dqbc_dz + dqepi_dz + dcbeo_dz + dcbco_dz; dq_di = dqtc_di + dqtex_di + dqtes_di + dqbe_di + dqbc_di + dqepi_di + dcbeo_di + dcbco_di; break; /* Now we solve the equations * dvce = dvce_dx dx + dvce_dz dz + dvce_di di = 0 * din = din_dx dx + din_dz dz + din_di di = di * This gives us dx_di and dz_di: */ denom = dvce_dx * din_dz - dvce_dz * din_dx; dx_di = (dvce_dz * (din_di-1) - dvce_di * din_dz) / denom; dz_di =-(dvce_dx * (din_di-1) - dvce_di * din_dx) / denom; tau = ( dq_di + dq_dx * dx_di + dq_dz * dz_di); result= 1 /( 2*M_PI*tau); } } } } } MXT_ic_vce { #include "mxtpardef.h" double vb2e1, vb2c1, Dvb2e1, vb1b2, dvb2c1_dx, Ib1, dIb1_dx, dIb1_di, Ib2, dIb2_dx, Ib1S, dIb1S_dx, Ib, dIb_dx, dIb_di, Ibmin, dIbmin_dx, vje, dvje_dx, vte, dvte_dx, ic1c2, Dic1c2, ic1c2prev, vqs, dvqs_dx, dvqs_di, iqs, diqs_dx, diqs_di, diqs_dv, i_i, di_i_dx, di_i_di, alfa0, alfa, dalfa_dx, dalfa_di, v, dv_dx, dv_di, yi, dyi_dv, dyi_dx, dyi_di, xi, dxi_dx, dxi_di, g, dg, dg_dx, dg_di, p0star, dp0star_dx, dp0star_di, iff, diff_dx, irr, dirr_dx, dirr_di, in, din_dx, din_di, q1, dq1_dx, dq1_di, qB, dqB_dx, dqB_di, root, f1, df1, f2, df2, nb, dnb_dx, dnb_di, n0, dn0_dx, vec0, vjunc, dvjunc_dx, dvjunc_di, icap, dicap_di, b1, b2, vch, dvch_dx, dvch_di, vj, dvj_dv, dvj_dvch, fI, dfI_dicap, vcv, dvcv_dv, dvcv_dvch, dvcv_dicap, vtc, dvtc_dv, dvtc_dvch, dvtc_dicap, dvtc_dx, dvtc_di; double ibm, g1, g2, j11, j12, j21, j22, det; double an, bn, bnT, efi, dEdx0, xd0, xd, dxd_dvb2c1, dxd_dicap, weff, dweff_dxi, wd, dwd_dvb2c1, dwd_dicap, dwd_dxi, Eav, dEav_dvb2c1, dEav_dicap, dEav_dxi, E0, dE0_dvb2c1, dE0_dicap, dE0_dxi, Em, dEm_dvb2c1, dEm_dicap, dEm_dxi, dEm_dic1c2, EW, dEW_dvb2c1, dEW_dicap, dEW_dxi, dEW_dic1c2, da1_dvb2c1, da1_dicap, da1_dxi, da1_dic1c2, droot_dvb2c1, droot_dicap, droot_dxi, droot_dic1c2, lambda, dlambda_dEm, dlambda_dEav, dlambda_dwd, dlambda_dicap, dlambda_dxi, dlambda_dic1c2,dlambda_dvb2c1, SHW, dSHW_dxi, Gem, dGem_dx, dGem_di,dGem_dvb2c1,dGem_dic1c2, dGem_dEm, dGem_dlambda, dGem_dweff, dGem_dicap, dGem_dxi; double a, da, da_dx, da_di, b, db, db_dx, db_di, d, dd, e, a0, a1, a2, da2_dx, da2_di, a3, a4, da4_dv, da4_dvch, a5; double dt, vbe, q1Q; double tol,tolvbe; double hard_sat_max, vb2c1max; double *qqic,*qqib,*qqvce,*qqvbe,*qqis; double qic,qib, qvce, qvbe; double npn=1; /* for pnp set npn to -1 */ int FALSE = 0; int TRUE = 1; int includeAVL = FALSE; int NotValid = FALSE; int ind,ir,itmax,it,ip,ii,intt,inti; alfa0 = 1.0/(1.0+ axi * log(1+exp(-1.0/axi))); vb2c1max = hard_sat_max * vdcT; if (npn==1) { an=7.03E7; bn=1.23E8; } else { an=1.58E8; bn=2.04E8; } } tol=1E-3; tolvbe=1E-6; itmax=50; /* go through all the points */ for (ir = irmax-1 ; ir > -1; ir--) { qic=qqic[ir]; qib=qqib[ir]; qvce=qqvce[ir]; dt = qvce*qic*rth; tk =temp+273.15+dt+dta; trk=tref+273.15; tn=tk/trk; vt = kq*tk; vtr= kq*trk; inv_vDt = 1.0/vt - 1.0/vtr; #include "mxtTrules.h" bnT = bn * bnT_bn; efi = (1+sfh)/(1+2*sfh); dEdx0 = 2*vavl/(wavl*wavl); xd0 = wavl * sqrt(vdcT/vavl); /* Solve vb2e1 and ic1c2 simultanously */ /* initial values */ if ( qib <= 0.0 ) /* Extra check for noisy data */ vb2e1 = qqvbe[ir]; else vb2e1= vt*log(qib*bfT/isT); if ( ) { ic1c2=qic; } /* otherwise keep the previous value as initial guess */ /* Check on validity: we demand that vb2c1 < vb2e1. Later a more * stringent test will be used */ if (qvce <= qic*rccT+(qic+qib)*reT) { NotValid=TRUE; } else { /* The loop */ for (it=0, Dvb2e1=10*tolvbe, Dic1c2=ic1c2; (it tolvbe) && (fabs(Dic1c2) > tol*fabs(ic1c2)) ; it++) { iff = isT * exp(vb2e1/vt); diff_dx = iff/vt; df1 = 4/ikT; f1 = df1*iff; root = sqrt(1+f1); n0 = f1 / (1+root); dn0_dx = df1 / (2*root) * diff_dx; e = exp((vb2e1-vfe)/(0.1*vdeT)); vje = vb2e1 - 0.1*vdeT*log(1+e); dvje_dx = 1/(1+e); vte = vdeT/(1-pe)*(1-pow(1-vje/vdeT,1-pe)) +aje*(vb2e1-vje); dvte_dx = (pow(1-vje/vdeT,-pe) - aje) * dvje_dx + aje; vb2c1 = vb2e1+qic*rccT+(qic+qib)*reT-qvce; dvb2c1_dx = 1.0; a = ic1c2*rcvT/(2*vt)+1; b = vdcT - vb2c1 + 2*vt * log(a); root = sqrt(b*b + 4*0.01*vdcT*vdcT); vqs = (b + root) / 2.0 ; dvqs_dx = -0.5 * (1.0 + b / root) * dvb2c1_dx ; dvqs_di = 0.5 * (1.0 + b / root) * rcvT/a; a = vqs+ihc*rcvT; iqs = vqs/scrcv * (vqs+ihc*scrcv)/ a; diqs_dv = 1.0/scrcv +(scrcv-rcvT)*rcvT*ihc*ihc/(scrcv*a*a); diqs_dx = diqs_dv * dvqs_dx; diqs_di = diqs_dv * dvqs_di; /* Calculation of yi */ i_i = ic1c2/iqs; di_i_dx = ( - i_i * diqs_dx)/iqs; di_i_di = (1.0 - i_i * diqs_di)/iqs; if (i_i < 1) { a0 = exp((i_i-1)/axi); a1 = axi * log(1+a0); alfa = alfa0 * (1+a1); dalfa_dx = alfa0 * a0 * di_i_dx/ (1+a0); dalfa_di = alfa0 * a0 * di_i_di/ (1+a0); } else { a = (1-i_i)/axi; if (a>-40) a0 = exp(a); else a0 = 0.0; a1 = axi * log(1+a0); alfa = alfa0 * (i_i+a1); dalfa_dx = alfa0 * di_i_dx/ (1+a0); dalfa_di = alfa0 * di_i_di/ (1+a0); } a = 1.0 / (ihc * scrcv); v = vqs * a; dv_dx = dvqs_dx * a; dv_di = dvqs_di * a; a2 = alfa * (1+v); da2_dx = dalfa_dx * (1+v) + alfa * dv_dx; da2_di = dalfa_di * (1+v) + alfa * dv_di; yi = (1.0 + sqrt(1.0+4.0 * v * a2))/(2 * a2); dyi_dv = 1.0 / (2 * a2 * yi - 1.0); /* dyi_da2 = - yi*yi * dyi_dv; */ dyi_dx = dyi_dv * (dv_dx - yi*yi*da2_dx); dyi_di = dyi_dv * (dv_di - yi*yi*da2_di); /* END of Calculation of yi */ xi = 1 - yi; dxi_dx = -dyi_dx; dxi_di = -dyi_di; g = rcvT * ic1c2 * xi / (2*vt); dg_dx = rcvT *(ic1c2 * dxi_dx ) / (2*vt); dg_di = rcvT *(ic1c2 * dxi_di + xi) / (2*vt); a = 0.25 * (g-1) * (g-1) + 2.0*g; da = 0.5 * (g-1) + 2.0; root = sqrt(a); p0star = 0.5 * (g-1) + root; dp0star_dx= 0.5 * (1.0 + da/root) * dg_dx; dp0star_di= 0.5 * (1.0 + da/root) * dg_di; a = isT*exp(vdcT/vt); irr = a * p0star * (p0star+1); dirr_dx= a * (2*p0star + 1) * dp0star_dx; dirr_di= a * (2*p0star + 1) * dp0star_di; df2 = 4/ikT; f2 = df2 * irr; root = sqrt(1+f2); nb = f2 / (1+root); dnb_dx = df2 / (2*root) * dirr_dx; dnb_di = df2 / (2*root) * dirr_di; a = ihc/(ic1c2+ihc); icap = ic1c2 * a; dicap_di = a * a; b1 = 0.5*scrcv*(ic1c2-ihc); b2 = scrcv*ihc*rcvT*ic1c2; vec0 = b1+sqrt(b1*b1+b2); vjunc = vb2c1 + vec0; dvjunc_dx = dvb2c1_dx; dvjunc_di = scrcv * (vec0+ihc*rcvT)*(vec0+ihc*rcvT)/ (vec0*vec0+2*vec0*ihc*rcvT+scrcv*rcvT*ihc*ihc); a = 1.0 / (ic1c2 + iqs); vch = vdcT * (0.1 + 2.0 * ic1c2 * a); dvch_dx = vdcT * 2.0 * ( - diqs_dx * ic1c2) * a * a; dvch_di = vdcT * 2.0 * (iqs - diqs_di * ic1c2) * a * a; if (vjunc <= vfc) { a2 = exp((vjunc-vfc)/vch); a3 = log(1.0+a2); vj = vjunc - vch * a3; dvj_dv = 1.0 / (1.0 + a2) ; dvj_dvch=(a2/(1.0+a2) * (vjunc-vfc)/vch - a3); } else { a2 = exp((vfc-vjunc)/vch); a3 = log(1.0+a2); vj = vfc - vch * a3; dvj_dv = a2 / (1.0 + a2) ; dvj_dvch=(a2/(1.0+a2) * (vfc-vjunc)/vch - a3); } a1 = 1 - icap/ihc; fI = pow(a1, mc); dfI_dicap = -mc * fI / (a1 * ihc); a3 = 1 - vj / vdcT; a4 = pow(a3, 1.0-pc); da4_dv = - (1.0-pc) * a4 * dvj_dv / (a3 * vdcT); da4_dvch= - (1.0-pc) * a4 * dvj_dvch / (a3 * vdcT); a5 = vdcT / (1-pc); vcv = a5 * (1- fI * a4); dvcv_dv = - a5 * fI * da4_dv ; dvcv_dvch = - a5 * fI * da4_dvch; dvcv_dicap= - a5 * dfI_dicap * a4 ; vtc = (1-xpT) * (vcv + fI * bjc * (vjunc-vj)) + xpT * vb2c1; dvtc_dv = (1-xpT) * (dvcv_dv + fI * bjc * (1-dvj_dv)); dvtc_dvch = (1-xpT) * (dvcv_dvch - fI * bjc * dvj_dvch); dvtc_dicap= (1-xpT) * (dvcv_dicap+ dfI_dicap*bjc*(vjunc-vj)); dvtc_dx = dvtc_dv * dvjunc_dx + dvtc_dvch * dvch_dx; dvtc_di = dvtc_dv * dvjunc_di + dvtc_dicap * dicap_di + dvtc_dvch * dvch_di; if (degT == 0) { q1 = 1+vte/verT+vtc/vefT; dq1_dx = dvte_dx/verT + dvtc_dx/vefT; dq1_di = dvtc_di/vefT; } else { a = exp( deg_vt*(vte/verT+1)); b = exp(-deg_vt * vtc/vefT); q1 = aq0i * (a-b); dq1_dx = aq0i * deg_vt * ( a * dvte_dx/verT +b * dvtc_dx/vefT); dq1_di = aq0i * deg_vt * b * dvtc_di/vefT; } qB = q1 * (1.0 + 0.5 * (n0 + nb) ); dqB_dx = dq1_dx * (1.0 + 0.5 * (n0 + nb) ) + q1*0.5*(dn0_dx + dnb_dx); dqB_di = dq1_di * (1.0 + 0.5 * (n0 + nb) ) + q1*0.5*dnb_di; in = (iff-irr)/qB; din_dx = (diff_dx -dirr_dx - in*dqB_dx)/qB; din_di = ( -dirr_di - in*dqB_di)/qB; /* now the base current */ if (xrec == 0 ) { Ib1 = (1-xibi) * iff/bfT; dIb1_dx = (1-xibi) * diff_dx/bfT; dIb1_di = 0.0; } else { b = (1+vtc/vefT); db_dx = dvtc_dx/vefT; db_di = dvtc_di/vefT; if ( b > 0 ) { a = (iff + irr); da_dx = (diff_dx + dirr_dx); da_di = ( dirr_di); Ib1 = (1-xibi)/bfT * ( (1-xrec)*iff + xrec * a * b ); dIb1_dx = (1-xibi)/bfT * ( (1-xrec)*diff_dx + xrec*(da_dx*b + a*db_dx )); dIb1_di = (1-xibi)/bfT * ( xrec*(da_di*b + a*db_di )); } else { Ib1 = 0.0; dIb1_dx = 0.0; dIb1_di = 0.0; } } Ib1S = xibi * iff / bfT; dIb1S_dx= xibi * diff_dx / bfT; Ib2 = ibfT*exp(vb2e1/(mlf*vt)); dIb2_dx = Ib2/(mlf*vt); /* for use at low currents */ Ibmin = Gmin * (vb2e1 + vb2c1); dIbmin_dx = Gmin * (1.0 + dvb2c1_dx); Ib = Ib1 + Ib2 + Ib1S + Ibmin; if (Ib<0) { /* for very small currents this is possible, i.e. in an iteration */ Ib -= Ibmin; dIbmin_dx=0.0; } dIb_dx = dIb1_dx + dIb2_dx + dIb1S_dx + dIbmin_dx; dIb_di = dIb1_di; /* now we add avalanche */ if ( includeAVL && (vb2c1 vb2c1max ) NotValid=True; switch /*actual code depends on extraction tool */ { case 0: /* ic */ if (NotValid) { result = 0.0; } else { result=npn*ic1c2; } break; case 1: /* vbe */ if (NotValid) result=; } else { /* determine vbe */ q1Q = 1+vte/verT+vtc/vefT; vb1b2 = vt * log(1.0 + (1-xibi)*rbvT*qib*q1/(vt*q1Q*qB)); vbe = vb2e1 + vb1b2 + (qic+qib) * reT + qib*rbcT; result=npn*vbe; } break; } /* end switch */ } /* end for(ir = 0; ir < irmax; ir++) */ } } MXT_rev_currents { #include "mxtpardef.h" double *qqvbc, *qqvbe, *qqie; double qvbc, qvbe, qie, ie, ib, is_sub; double vb2e1, vb2c2, vb2c1, vb1c1, vbc1; double dvb2c2, dvb2c1, dvbc, dvb2c1_dy, dvb1c1_dy, dvbc1_dy ; double vbcs, dvbcs_dy; double vje, vte, vjc, dvjc_dy, vcv, dvcv_dy, vtc, dvtc_dy; double q1, dq1_dy, qB, dqB_dy; double ir, dir_dy, dir_dz, irex, in, din_dy, iepi, diepi_dy, diepi_dz; double ib3, dib3_dy, ib1, dib1_dy; double exp0, k0, dk0_dy, expw, kw, dkw_dz, ec, dec_dz, dec_dy; double iex, diex_dy, jex, djex_dy, xiex, dxiex_dy; double isub, disub_dy, jsub, djsub_dy, xisub, dxisub_dy; double arg, sqarg, vex, vbex, dvbex_dy, t1, fex, dfex_dy; double f2, df2_dy, g1, dg1_dy, nb, dnb_dy, nbex, dnbex_dy; double a, b, c, d, e, da_dz, root; double tol; int ind , irw , itmax , it , ip , intt i; int TRUE = 1; int FALSE= 0; { itmax= 100; tol = 1E-5; /* go through all the points */ for (irw = 0; irw < irwmax; irw++) { qvbe = qqvbe[irw]; qvbc = qqvbc[irw]; qie = qqie[irw]; if (irw >0) { dvb2c2 = (qvbc-qqvbc[irw-1])/dvbcs_dy; vb2c2 = vb2c2 + dvb2c2; vb2c1 = vb2c1 + dvb2c1_dy*dvb2c2; vb2e1 = qvbe + qie*reT - rbcT*(iex+isub); } else { dvb2c2 = 2*tol; vb2c2 = qqvbc[0]; vb2c1 = vb2c2; vb2e1 = qvbe; } for( it=0 ; (ittol) ; it++) { if (it>0) { vb2e1=qvbe+(in-ib1)*reT-(iex+isub+ib3+ib1)*rbcT; } e = exp((vb2e1-vfe)/(0.1*vdeT)); vje = vb2e1 - 0.1*vdeT*log(1+e); vte = vdeT/(1-pe) * (1-pow(1-vje/vdeT,1-pe)) + aje*(vb2e1-vje); ir = isT*exp(vb2c2/vt); dir_dy = ir/vt; /* Note that vjunc = vb2c2 */ e = exp((vb2c2-vfc)/(0.1*vdcT)); vjc = vb2c2 - 0.1*vdcT*log(1+e); dvjc_dy = 1/(1+e); vcv = vdcT/(1-pc)*(1-pow(1-vjc/vdcT,1-pc))+bjc*(vb2c2-vjc); dvcv_dy = (pow(1-vjc/vdcT,-pc) - bjc) * dvjc_dy + bjc; vtc = (1-xpT) * vcv + xpT * vb2c1; dvtc_dy = (1-xpT) * dvcv_dy + xpT; if (degT == 0) { q1 = 1+vte/verT+vtc/vefT; dq1_dy = dvtc_dy/vefT; } else { a = exp( deg_vt*(vte/verT+1)); b = exp(-deg_vt * vtc/vefT); q1 = aq0i * (a-b); dq1_dy = aq0i * b * deg_vt * dvtc_dy/vefT; } f2 = 4* ir /ikT; df2_dy = 4*dir_dy/ikT; root = sqrt(1+f2); nb = f2 / (1+root); dnb_dy = df2_dy / (2*root); qB = q1 * (1.0 + 0.5 * nb); dqB_dy = dq1_dy * (1.0 + 0.5 * nb) + q1 * 0.5 * dnb_dy; in = ir/qB; din_dy = (dir_dy - in*dqB_dy)/qB; /* solve Vb2c1 from: In = Iepi=-(Ec+vc1c2)/Rcv */ exp0 = exp((vb2c2-vdcT)/vt); k0 = sqrt(1+4*exp0); dk0_dy = 2*exp0/(k0*vt); for ( intt=0, dvb2c1=2*tol; (intt<5) && (fabs(dvb2c1)>0.1*tol); intt++) { expw = exp((vb2c1-vdcT)/vt); kw = sqrt(1+4*expw); dkw_dz = 2*expw/(kw*vt); ec = vt*(k0-kw-log((k0+1)/(kw+1))); dec_dz = -vt*kw/(kw+1)*dkw_dz; iepi = -(ec+vb2c2-vb2c1)/rcvT ; diepi_dz = (1-dec_dz)/rcvT; dvb2c1 = (in-iepi)/diepi_dz; /* For better convergence */ if (dvb2c1 > 1.5*vt) dvb2c1= 1.5*vt; if (dvb2c1 <-1.0*vt) dvb2c1=-1.0*vt; vb2c1 = vb2c1 + dvb2c1; } /* end for (intt<5) */ dec_dy = vt*k0/(k0+1)*dk0_dy; diepi_dy = -(dec_dy+1)/rcvT; dvb2c1_dy = (din_dy-diepi_dy)/diepi_dz; vb1c1 = vb2c1; dvb1c1_dy = dvb2c1_dy; a = exp(vb1c1/(2*vt)); e = exp(vlr/(2*vt)); ib3 = ibrT *(a*a-1)/(a+e); dib3_dy = ibrT * a*dvb1c1_dy*(a*(a+2*e)+1)/(2*vt*(a+e)*(a+e)); irex = isT*exp(vb1c1/vt); a = sqrt(1+4*irex/iksT); da_dz = 2*irex/(a*iksT*vt); isub = 2*(issT/isT)*(irex-isT)/(1+a); if (exmod>0.0) isub = (1-xext)*isub; disub_dy = isub*(1/vt - da_dz/(1+a))*dvb1c1_dy; g1 = 4*irex/ikT; dg1_dy = g1*dvb1c1_dy/vt; root = sqrt(1+g1); nbex = g1 / (1+root); dnbex_dy = dg1_dy / (2*root); iex = (1/briT)* ( 0.5*ikT*nbex - isT); diex_dy= (1/briT)* 0.5*ikT*dnbex_dy; if (exmod>0.0) { iex = (1-xext)* iex; diex_dy = (1-xext)* diex_dy; } a = isT/bfT*(1-xibi)*xrec; b = exp(vb2c2/vt); ib1 = a*b*(1+vtc/vefT); dib1_dy =a*b*(dvtc_dy/vefT + (1+vtc/vefT)/vt); vbc1 = vb1c1 + rbcT*(isub +iex +ib3 +ib1); dvbc1_dy = dvb1c1_dy + rbcT*(disub_dy+diex_dy+dib3_dy+dib1_dy); if (exmod>0.0) /* repeat the above for another voltage */ /* temporary currents are denoted by jex, instead of iex */ { irex = isT*exp(vbc1/vt); a = sqrt(1+4*irex/iksT); da_dz = 2*irex/(a*iksT*vt); jsub = xext * 2*(issT/isT)*(irex-isT)/(1+a); djsub_dy = jsub*(1/vt - da_dz/(1+a))*dvbc1_dy; g1 = 4*irex/ikT; dg1_dy = g1*dvbc1_dy/vt; root = sqrt(1+g1); nbex = g1 / (1+root); dnbex_dy = dg1_dy / (2*root); jex = (xext/briT)* ( 0.5*ikT*nbex- isT); djex_dy= (xext/briT)* 0.5*ikT*dnbex_dy; a = xext*((isT/briT)+issT)*rccT; vex = vt*(2+log(vt/a)); arg = vex-vbc1; sqarg = sqrt(arg*arg+0.0121); vbex = (-arg+sqarg)/2; dvbex_dy = (1-(arg/sqarg))*dvbc1_dy/2; t1 = a+rccT*(jex+jsub)+vbex; fex = vbex/t1; dfex_dy = (dvbex_dy- fex*(rccT*(djex_dy+djsub_dy)+dvbex_dy))/t1; xisub = fex*jsub; dxisub_dy= dfex_dy*jsub+fex*djsub_dy; xiex = fex*jex; dxiex_dy = dfex_dy*jex+fex*djex_dy; } else { xiex = 0.0; dxiex_dy = 0.0; xisub = 0.0; dxisub_dy= 0.0; } vbcs = vbc1 + rccT*( in + ib3 + iex + xiex ); dvbcs_dy = dvbc1_dy + rccT*(din_dy+dib3_dy +diex_dy+dxiex_dy); dvbc = qvbc - vbcs; dvb2c2 = dvbc/dvbcs_dy; /* Needed when starting at high vbe */ if (dvb2c2 > 0.5*vt) dvb2c2= 0.5*vt; if (dvb2c2 <-0.6*vt) dvb2c2=-0.6*vt; vb2c2 = vb2c2 + dvb2c2; } /* end for(it) (end of iteration) */ ie = in-ib1; ib = ib3 + iex + xiex + isub + xisub+ib1; is_sub=-isub-xisub; } /* end for(irw = 0; irw < irwmax; irw++) */ } } MXT_forward_ic { #include "mxtpardef.h" double *qqvcb,*qqveb,*qqic; double vbe,vbc; double e, vje, vte, vjc, vcv, vtc, q0, q1, If; double npn=1; /* for pnp set npn to -1 */ int i; int TRUE = 1; int FALSE= 0; { /* go through all the points */ for (i = 0; i < imax; i++) { vbc =-qqvcb[i]; vbe =-qqveb[i]; e = exp((vbc-vfc)/(0.1*vdcT)); vjc = vbc - 0.1*vdcT*log(1+e); vcv = vdcT/(1-pc) * (1-pow(1-vjc/vdcT,1-pc)) + bjc * (vbc-vjc); vtc = (1-xpT) * vcv + xpT * vbc; e = exp((vbe-vfe)/(0.1*vdeT)); vje = vbe - 0.1*vdeT*log(1+e); vte = vdeT/(1-pe) * (1-pow(1-vje/vdeT,1-pe)) + aje * (vbe-vje); if (degT == 0) { q0 = 1+vte/verT+vtc/vefT; } else { q0 = aq0i*(exp(deg_vt*(vte/verT+1)) - exp(-deg_vt * vtc/vefT)); } q1 = 0.5*(q0 + sqrt(q0*q0+0.01) ); If=isT*(exp(vbe/vt)-1); result=npn* If / q1; } /* end for(i = 0; i < imax; i++) */ } } MXT_forward_hfe { #include "mxtpardef.h" double *qqvcb,*qqveb,*qqic; double vbe,vbc,qic; double e, vje, vte, vjc, vcv, vtc, q0, q1, If; double Ib1, Ib2, Ibmin, Vb2e1, a, b, c; int i; int TRUE = 1; int FALSE= 0; { for (i = 0; i < imax; i++) { vbc =-qqvcb[i]; e = exp((vbc-vfc)/(0.1*vdcT)); vjc = vbc - 0.1*vdcT*log(1+e); vcv = vdcT/(1-pc) * (1-pow(1-vjc/vdcT,1-pc)) + bjc * (vbc-vjc); vtc = (1-xpT) * vcv + xpT * vbc; vbe =-qqveb[i]; qic = qqic[i]; e = exp((vbe-vfe)/(0.1*vdeT)); vje = vbe - 0.1*vdeT*log(1+e); vte = vdeT/(1-pe) * (1-pow(1-vje/vdeT,1-pe)) + aje * (vbe-vje); if (degT == 0) { q0 = 1+vte/verT+vtc/vefT; } else { q0 = aq0i*(exp(deg_vt*(vte/verT+1)) - exp(-deg_vt * vtc/vefT)); } q1 = 0.5*(q0 + sqrt(q0*q0+0.01) ); Vb2e1=vt*log(qic*q1/isT); Ib1 = isT/bfT*(exp(Vb2e1/vt)-1); Ib2 = ibfT*(exp(Vb2e1/(mlf*vt))-1); Ibmin = Gmin*vbe + Gmin*vbc; result = qic/(Ib1+Ib2 + Ibmin); } /* end for(i = 0; i < imax; i++) */ } } MXT_forward_vbe { #include "mxtpardef.h" double *qqic,*qqib,*qqveb; double ib,ic; double npn=1; /* for pnp set npn to -1 */ double a,b,c,d,g,da,db,dc,dd,dg, rbvinv, vv, dvv, Ib1,Ib2,dIb1,dIb2, Voff_Rbc,Tdut,Vb2e1,dVb2e1,Ve1e,Vbb2; int i,it; int TRUE = 1; int FALSE= 0; { Vb2e1= 0.5; vv = qqib[0] * rbvT/vt; /* vv = vb1b2/vt */ for (i = 0; i < imax; i++) { ic = qqic[i]; ib = qqib[i]; if (ib<=0) ib=1.e-20; for (it =0,dVb2e1=0.1; (it<10) && (fabs(dVb2e1) > 1.0E-6) ; it++) { Ib1 = isT/bfT*exp(Vb2e1/vt); dIb1 = Ib1/vt; Ib2 = ibfT*exp(Vb2e1/(mlf*vt)); dIb2 = Ib2/(mlf*vt); g = Ib1+ Ib2; dg = dIb1+dIb2; dVb2e1= -(log(g) - log(ib)) * g / dg; Vb2e1 = Vb2e1 + dVb2e1; } Ve1e = (ic+ib)*reT; Vbb2 = ib*rbcT + vt * log(1.0 + (1-xibi)*rbvT*ic/(vt*bfT)); result=npn*(Ve1e+Vb2e1+Vbb2+Voff_Rbc); } /* end for(i = 0; i < imax; i++) */ } } MXT_reverse_isub { #include "mxtpardef.h" double *qqvbc,*qqis; double vbc; double npn=1; /* for pnp set npn to -1 */ int i; int TRUE = 1; int FALSE= 0; { for (i = 0; i < imax; i++) { /* Calculate the substrate current in reverse-bias condition with small Vbc ( small and medium current) */ result=-npn* issT*(exp(qqvbc[i]/vt)-1); } /* end for(i = 0; i < imax; i++) */ } } MXT_hard_sat_isub { #include "mxtpardef.h" double *qqvbc,*qqic,*qqib; double vb1c1, e, isub; double npn=1; /* for pnp set npn to -1 */ int i; int TRUE = 1; int FALSE= 0; } { for (i = 0; i < imax; i++) { vb1c1 = qqvbc[i] + qqic[i] * rccT - qqib[i] * rbcT; e = exp(vb1c1/vt); isub = -2.0 * issT * (e-1) / (1+sqrt(1+4*isT*e/iksT)); result=npn*isub; } /* end for(i = 0; i < imax; i++) */ } } MXT_reverse_hfc_sub { #include "mxtpardef.h" double *qqvcb,*qqveb,*qqie,*qqis; double vbe,vbc; double e, vje, vte, vjc, vcv, vtc, q0, q1; int i; int TRUE = 1; int FALSE= 0; { for (i = 0; i < imax; i++) { vbe =-qqveb[i]; vbc =-qqvcb[i]; e = exp((vbe-vfe)/(0.1*vdeT)); vje = vbe - 0.1*vdeT*log(1+e); vte = vdeT/(1-pe) * (1-pow(1-vje/vdeT,1-pe)) + aje * (vbe-vje); e = exp((vbc-vfc)/(0.1*vdcT)); vjc = vbc - 0.1*vdcT*log(1+e); vcv = vdcT/(1-pc) * (1-pow(1-vjc/vdcT,1-pc)) + bjc * (vbc-vjc); vtc = (1-xpT) * vcv + xpT * vbc; if (degT == 0) { q0 = 1+vte/verT+vtc/vefT; } else { q0 = aq0i*(exp(deg_vt*(vte/verT+1)) - exp(-deg_vt * vtc/vefT)); } q1 = 0.5*(q0 + sqrt(q0*q0+0.01) ); if (issT == 0) { result=1.0; } else { result=isT/(q1*issT); } } /* end for(i = 0; i < imax; i++) */ } } MXT_reverse_hfc { #include "mxtpardef.h" double *qqvcb,*qqveb,*qqie; double vbe,vbc,ie; double e, vje, vte, vjc, vcv, vtc, q0, q1; double a, b, c, d, Ib3, Iex, Isub, Ibmin, Vb1c1, corr, Ib1; int i; int TRUE = 1; int FALSE= 0; { for (i = 0; i < imax; i++) { vbe =-qqveb[i]; vbc =-qqvcb[i]; ie = fabs(qqie[i]); e = exp((vbe-vfe)/(0.1*vdeT)); vje = vbe - 0.1*vdeT*log(1+e); vte = vdeT/(1-pe) * (1-pow(1-vje/vdeT,1-pe)) + aje * (vbe-vje); e = exp((vbc-vfc)/(0.1*vdcT)); vjc = vbc - 0.1*vdcT*log(1+e); vcv = vdcT/(1-pc) * (1-pow(1-vjc/vdcT,1-pc)) + bjc * (vbc-vjc); vtc = (1-xpT) * vcv + xpT * vbc; if (degT == 0) { q0 = 1+vte/verT+vtc/vefT; } else { q0 = aq0i*(exp(deg_vt*(vte/verT+1)) - exp(-deg_vt * vtc/vefT)); } q1 = 0.5*(q0 + sqrt(q0*q0+0.01) ); corr = (1-xibi)/bfT*xrec*(1+vtc/vefT); /* Vb1c1 = vt*log(ie*q1/isT); /* a = exp(Vb1c1/(2*vt)); */ a = sqrt(ie/isT/(1.0/q1-corr)); Ib3 = ibrT * (a*a-1)/(a+exp(vlr/(2*vt))); Ibmin = Gmin*vbc + Gmin*vbe; c = 2*issT*(a*a-1); d = sqrt(1+4*(isT/iksT)*a*a); Isub = c/(1+d); Iex = (isT/briT)*(a*a-1); Ib1 = corr * isT*(a*a-1); if () result=ie/(Ib3+Iex+Ibmin+Isub+Ib1); else result=ie/(Ib3+Iex+Ibmin+Ib1); } /* end for(i = 0; i < imax; i++) */ } } MXT_veaf_ic { #include "mxtpardef.h" double *qqvcb,*qqveb,*qqib; double vbe,vbc; double e, vje, vte, vjc, vcv, vtc, Ic0, q00, q0,q10,q1; int i; int TRUE = 1; int FALSE = 0; { e = exp((vbe-vfe)/(0.1*vdeT)); vje = vbe - 0.1*vdeT*log(1+e); vte = vdeT/(1-pe) * (1-pow(1-vje/vdeT,1-pe)) + aje * (vbe-vje); for (i = 0; i < imax; i++) { vbc =-qqvcb[i]; e = exp((vbc-vfc)/(0.1*vdcT)); vjc = vbc - 0.1*vdcT*log(1+e); vcv = vdcT/(1-pc) * (1-pow(1-vjc/vdcT,1-pc)) + bjc * (vbc-vjc); vtc = (1-xpT) * vcv + xpT * vbc; if (degT == 0) { q00 = 1+vte/verT; q0 = 1+vte/verT+vtc/vefT; } else { q00 = aq0i*(exp(deg_vt*(vte/verT+1)) - 1.0); q0 = aq0i*(exp(deg_vt*(vte/verT+1)) - exp(-deg_vt * vtc/vefT)); } q10 = 0.5*(q00 + sqrt(q00*q00+0.01) ); q1 = 0.5*(q0 + sqrt(q0 *q0 +0.01) ); result=Ic0* q10 / q1; } /* end for(i = 0; i < imax; i++) */ } } MXT_veaf_ib { #include "mxtpardef.h" double *qqvcb,*qqic; double vbc,ic; double dEdx0, xd0, xd, wd, Eav, Em, lambda, a, b, an, bn, bnT, Ib0, Gem; double e, vjc, vcv, vtc; int i; double npn=1; /* for pnp set npn to -1 */ int TRUE = 1; int FALSE= 0; if (npn == 1) { an=7.03E7; bn=1.23E8; } else { an=1.58E8; bn=2.04E8; } bnT = bn * bnT_bn; dEdx0 = 2*vavl/(wavl*wavl); xd0 = wavl * sqrt(vdcT/vavl); for (i = 0; i < imax; i++) { vbc = -qqvcb[i]; ic = qqic[i]; if (vbc < vdcT) { xd = xd0 * sqrt(1-vbc/vdcT); wd = xd * wavl / sqrt(xd*xd + wavl*wavl); Eav = (vdcT-vbc)/wd; Em = Eav + 0.5 * wd * dEdx0; lambda = Em * wd / (2*(Em-Eav)); a = exp(-bnT/Em); b = exp(-bnT*(1+wavl/lambda)/Em); Gem = (an/bnT) * Em * lambda * (a-b); if (xrec == 0) { result=Ib0 - ic*Gem*npn; } else { e = exp((vbc-vfc)/(0.1*vdcT)); vjc = vbc - 0.1*vdcT*log(1+e); vcv = vdcT/(1-pc) * (1-pow(1-vjc/vdcT,1-pc)) + bjc*(vbc-vjc); vtc = (1-xpT) * vcv + xpT * vbc; result=Ib0*(1+xrec*vtc/vefT) - ic*Gem*npn; } } else { result=Ib0 ; } } /* end for(i = 0; i < imax; i++) */ } } MXT_vear_ie { #include "mxtpardef.h" double *qqvcb,*qqveb,*qqic; double vbe,vbc; double e, vje, vte, vjc, vcv, vtc, Ie0, q00, q0, q10, q1; int i; int TRUE = 1; int FALSE= 0; vbc =-qqvcb[0]; e = exp((vbc-vfc)/(0.1*vdcT)); vjc = vbc - 0.1*vdcT*log(1+e); vcv = vdcT/(1-pc) * (1-pow(1-vjc/vdcT,1-pc)) + bjc * (vbc-vjc); vtc = (1-xpT) * vcv + xpT * vbc; for (i = 0; i < imax; i++) { vbe =-qqveb[i]; e = exp((vbe-vfe)/(0.1*vdeT)); vje = vbe - 0.1*vdeT*log(1+e); vte = vdeT/(1-pe) * (1-pow(1-vje/vdeT,1-pe)) + aje * (vbe-vje); if (degT == 0) { q00 = 1+vtc/vefT; q0 = 1+vtc/vefT+vte/verT; } else { q00 = aq0i*(exp(deg_vt) - exp(-deg_vt * vtc/vefT)); q0 = aq0i*(exp(deg_vt*(vte/verT+1)) - exp(-deg_vt * vtc/vefT)); } q10 = 0.5*(q00 + sqrt(q00*q00+0.01) ); q1 = 0.5*(q0 + sqrt(q0 *q0 +0.01) ); result=Ie0*q10/q1; } /* end for(i = 0; i < imax; i++) */ } } MXT_jun_cap { #include "mxtpardef.h" double *qqvjun; double vjun; double vf, vjj, e, dvjj_dv, dvtt_dv; int i; int TRUE = 1; int FALSE= 0; switch /*actual code depends on extraction tool */ { case 0:/* cbe */ for (i = 0; i < imax; i++) { vjun=qqvjun[i]; vf = vdeT * (1-pow(aje,-1.0/pe)); e = exp((vjun-vf )/(0.1*vdeT)); vjj = vjun - 0.1*vdeT*log(1+e); dvjj_dv = 1.0/(1.0+e); dvtt_dv = ( pow(1-vjj/vdeT,-pe)-aje ) * dvjj_dv + aje; result = cjeT*dvtt_dv + cbeo; } break; case 1: /* cbc */ for (i = 0; i < imax; i++) { vjun=-qqvjun[i]; bjc = (ajc-xpT)/(1-xpT); vf = vdcT * (1-pow(bjc,-1.0/pc)); e = exp((vjun-vf )/(0.1*vdcT)); vjj = vjun - 0.1*vdcT*log(1+e); dvjj_dv = 1.0/(1.0+e); dvtt_dv = ( pow(1-vjj/vdcT,-pc)-bjc ) * dvjj_dv + bjc; result = cjcT*( (1-xpT)*dvtt_dv + xpT) + cbco; } break; case 2: /* csc */ for (i = 0; i < imax; i++) { vjun=qqvjun[i]; vf = vdsT * (1-pow(ajs,-1.0/ps)); e = exp((vjun-vf )/(0.1*vdsT)); vjj = vjun - 0.1*vdsT*log(1+e); dvjj_dv = 1.0/(1.0+e); dvtt_dv = ( pow(1-vjj/vdsT,-ps)-ajs ) * dvjj_dv + ajs; result = cjsT*dvtt_dv + cpcs; } break; } /* end switch */ } MXT_cbe { #include "mxtpardef.h" double *vj; double vje, e, dvje_dvbe, dvte_dvbe; int i; int TRUE = 1; int FALSE= 0; { for(i=0;i ver *= deg/vt/(1-exp(-deg/vt)); } } else { ver = 2.5; /* set to the default value */ } } } /****************************************************************** This function calculates VEF based on the following formula: VEF = (ic * dvbc/dic @ vbc=0) The function requires ic and vbc as inputs and the model variable DEG and TREF. ******************************************************************/ MXT_vef { double *ic_data, *vcb_data, ic0, vef,deg,tref,vt; double delta_vcb, delta_ic; int i; double npn=1; /* for pnp set npn to -1 */ int TRUE = 1; int FALSE= 0; { ic0 = ic@(data point 1); delta_vcb = vcb@(data point 3) - vcb[0]@(data point 1); delta_ic = ic@(data point 3) - ic@(data point 1); if (delta_ic != 0.0) { vef = npn * ic0 * (delta_vcb/delta_ic); if (deg != 0) { vef *= deg/vt/(exp(deg/vt)-1); } } else { vef = 44.0; /* default value */ } }