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887 lines
28 KiB
887 lines
28 KiB
/**********
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Copyright 1991 Regents of the University of California. All rights reserved.
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Author: 1987 Kartikeya Mayaram, U. C. Berkeley CAD Group
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Author: 1991 David A. Gates, U. C. Berkeley CAD Group
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**********/
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#include "ngspice/ngspice.h"
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#include "ngspice/numglobs.h"
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#include "ngspice/numenum.h"
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#include "ngspice/twomesh.h"
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#include "ngspice/twodev.h"
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#include "ngspice/bool.h"
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#include "ngspice/spmatrix.h"
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#include "twoddefs.h"
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#include "twodext.h"
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#include "ngspice/cidersupt.h"
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#include "../../maths/misc/bernoull.h"
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/*
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* Functions to setup and solve the continuity equations.
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* Both continuity equations are solved.
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* Separate functions are used for one continuity equation.
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*/
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/*
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* setup matrix pointers to Jacobian values and
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* store direct pointers with the nodes
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*/
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void
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TWOPjacBuild(TWOdevice *pDevice)
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{
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SMPmatrix *matrix = pDevice->matrix;
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TWOelem *pElem;
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TWOnode *pNode;
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TWOchannel *pCh;
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int eIndex, nIndex;
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int nextIndex; /* index of node to find next element */
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int psiEqn, pEqn; /* scratch for deref'd eqn numbers */
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int psiEqnTL = 0, pEqnTL = 0;
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int psiEqnTR = 0, pEqnTR = 0;
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int psiEqnBR = 0, pEqnBR = 0;
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int psiEqnBL = 0, pEqnBL = 0;
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int psiEqnInM = 0, psiEqnInP = 0; /* scratch for deref'd surface eqns */
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int psiEqnOxM = 0, psiEqnOxP = 0; /* M= more negative, P= more positive */
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for ( eIndex = 1; eIndex <= pDevice->numElems; eIndex++ ) {
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pElem = pDevice->elements[ eIndex ];
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/* first the self terms */
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for ( nIndex = 0; nIndex <= 3; nIndex++ ) {
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pNode = pElem->pNodes[ nIndex ];
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/* get poisson-only pointer */
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psiEqn = pNode->psiEqn;
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pNode->fPsiPsi = spGetElement( matrix, psiEqn, psiEqn );
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if ( pElem->elemType == SEMICON ) {
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/* get continuity-coupling terms */
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pEqn = pNode->pEqn;
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pNode->nEqn = 0;
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/* pointers for additional terms */
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pNode->fPsiP = spGetElement( matrix, psiEqn, pEqn );
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pNode->fPPsi = spGetElement( matrix, pEqn, psiEqn );
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pNode->fPP = spGetElement( matrix, pEqn, pEqn );
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} else {
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pEqn = 0;
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}
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/* save equation indices */
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switch ( nIndex ) {
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case 0: /* TL Node */
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psiEqnTL = psiEqn;
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pEqnTL = pEqn;
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break;
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case 1: /* TR Node */
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psiEqnTR = psiEqn;
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pEqnTR = pEqn;
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break;
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case 2: /* BR Node */
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psiEqnBR = psiEqn;
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pEqnBR = pEqn;
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break;
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case 3: /* BL Node */
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psiEqnBL = psiEqn;
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pEqnBL = pEqn;
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break;
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default:
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break;
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}
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}
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/* now terms to couple to adjacent nodes */
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pNode = pElem->pTLNode;
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pNode->fPsiPsiiP1 = spGetElement(matrix, psiEqnTL, psiEqnTR );
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pNode->fPsiPsijP1 = spGetElement(matrix, psiEqnTL, psiEqnBL );
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if ( pElem->elemType == SEMICON ) {
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/* continuity equation pointers */
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pNode->fPPsiiP1 = spGetElement( matrix, pEqnTL, psiEqnTR );
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pNode->fPPiP1 = spGetElement( matrix, pEqnTL, pEqnTR );
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pNode->fPPsijP1 = spGetElement( matrix, pEqnTL, psiEqnBL );
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pNode->fPPjP1 = spGetElement( matrix, pEqnTL, pEqnBL );
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/* Surface Mobility Model depends on diagonal node values */
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if ( MobDeriv && SurfaceMobility && pElem->channel ) {
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pNode->fPPsiiP1jP1 = spGetElement( matrix, pEqnTL, psiEqnBR );
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pNode->fPPiP1jP1 = spGetElement( matrix, pEqnTL, pEqnBR );
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}
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}
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pNode = pElem->pTRNode;
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pNode->fPsiPsiiM1 = spGetElement(matrix, psiEqnTR, psiEqnTL );
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pNode->fPsiPsijP1 = spGetElement(matrix, psiEqnTR, psiEqnBR );
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if ( pElem->elemType == SEMICON ) {
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/* continuity equation pointers */
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pNode->fPPsiiM1 = spGetElement( matrix, pEqnTR, psiEqnTL );
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pNode->fPPiM1 = spGetElement( matrix, pEqnTR, pEqnTL );
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pNode->fPPsijP1 = spGetElement( matrix, pEqnTR, psiEqnBR );
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pNode->fPPjP1 = spGetElement( matrix, pEqnTR, pEqnBR );
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/* Surface Mobility Model depends on diagonal node values */
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if ( MobDeriv && SurfaceMobility && pElem->channel ) {
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pNode->fPPsiiM1jP1 = spGetElement( matrix, pEqnTR, psiEqnBL );
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pNode->fPPiM1jP1 = spGetElement( matrix, pEqnTR, pEqnBL );
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}
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}
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pNode = pElem->pBRNode;
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pNode->fPsiPsiiM1 = spGetElement(matrix, psiEqnBR, psiEqnBL );
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pNode->fPsiPsijM1 = spGetElement(matrix, psiEqnBR, psiEqnTR );
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if ( pElem->elemType == SEMICON ) {
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/* continuity equation pointers */
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pNode->fPPsiiM1 = spGetElement( matrix, pEqnBR, psiEqnBL );
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pNode->fPPiM1 = spGetElement( matrix, pEqnBR, pEqnBL );
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pNode->fPPsijM1 = spGetElement( matrix, pEqnBR, psiEqnTR );
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pNode->fPPjM1 = spGetElement( matrix, pEqnBR, pEqnTR );
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/* Surface Mobility Model depends on diagonal node values */
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if ( MobDeriv && SurfaceMobility && pElem->channel ) {
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pNode->fPPsiiM1jM1 = spGetElement( matrix, pEqnBR, psiEqnTL );
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pNode->fPPiM1jM1 = spGetElement( matrix, pEqnBR, pEqnTL );
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}
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}
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pNode = pElem->pBLNode;
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pNode->fPsiPsiiP1 = spGetElement(matrix, psiEqnBL, psiEqnBR );
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pNode->fPsiPsijM1 = spGetElement(matrix, psiEqnBL, psiEqnTL );
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if ( pElem->elemType == SEMICON ) {
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/* continuity equation pointers */
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pNode->fPPsiiP1 = spGetElement( matrix, pEqnBL, psiEqnBR );
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pNode->fPPiP1 = spGetElement( matrix, pEqnBL, pEqnBR );
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pNode->fPPsijM1 = spGetElement( matrix, pEqnBL, psiEqnTL );
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pNode->fPPjM1 = spGetElement( matrix, pEqnBL, pEqnTL );
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/* Surface Mobility Model depends on diagonal node values */
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if ( MobDeriv && SurfaceMobility && pElem->channel ) {
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pNode->fPPsiiP1jM1 = spGetElement( matrix, pEqnBL, psiEqnTR );
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pNode->fPPiP1jM1 = spGetElement( matrix, pEqnBL, pEqnTR );
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}
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}
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}
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/*
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* Add terms for surface-field of inversion-layer mobility model.
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* Elements MUST be made from silicon for this to work.
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* No empty elements are allowed.
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* Don't need these pointers if SurfaceMobility isn't set.
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*/
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if ( MobDeriv && SurfaceMobility ) {
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for ( pCh = pDevice->pChannel; pCh != NULL;
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pCh = pCh->next ) {
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pElem = pCh->pNElem;
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switch (pCh->type) {
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case 0:
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psiEqnInM = pElem->pBLNode->psiEqn;
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psiEqnInP = pElem->pBRNode->psiEqn;
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psiEqnOxM = pElem->pTLNode->psiEqn;
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psiEqnOxP = pElem->pTRNode->psiEqn;
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break;
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case 1:
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psiEqnInM = pElem->pTLNode->psiEqn;
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psiEqnInP = pElem->pBLNode->psiEqn;
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psiEqnOxM = pElem->pTRNode->psiEqn;
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psiEqnOxP = pElem->pBRNode->psiEqn;
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break;
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case 2:
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psiEqnInM = pElem->pTLNode->psiEqn;
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psiEqnInP = pElem->pTRNode->psiEqn;
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psiEqnOxM = pElem->pBLNode->psiEqn;
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psiEqnOxP = pElem->pBRNode->psiEqn;
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break;
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case 3:
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psiEqnInM = pElem->pTRNode->psiEqn;
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psiEqnInP = pElem->pBRNode->psiEqn;
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psiEqnOxM = pElem->pTLNode->psiEqn;
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psiEqnOxP = pElem->pBLNode->psiEqn;
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break;
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}
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pElem = pCh->pSeed;
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nextIndex = (pCh->type + 2)%4;
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while (pElem && pElem->channel == pCh->id) {
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for ( nIndex = 0; nIndex <= 3; nIndex++ ) {
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pNode = pElem->pNodes[ nIndex ];
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psiEqn = pNode->psiEqn;
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pEqn = pNode->pEqn;
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if ( pCh->type % 2 == 0 ) { /* Vertical Slice */
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if ( nIndex == 0 || nIndex == 3 ) { /* Left Side */
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pNode->fPPsiIn = spGetElement( matrix, pEqn, psiEqnInM );
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pNode->fPPsiInP1 = spGetElement( matrix, pEqn, psiEqnInP );
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pNode->fPPsiOx = spGetElement( matrix, pEqn, psiEqnOxM );
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pNode->fPPsiOxP1 = spGetElement( matrix, pEqn, psiEqnOxP );
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} else { /* Right Side */
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pNode->fPPsiInM1 = spGetElement( matrix, pEqn, psiEqnInM );
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pNode->fPPsiIn = spGetElement( matrix, pEqn, psiEqnInP );
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pNode->fPPsiOxM1 = spGetElement( matrix, pEqn, psiEqnOxM );
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pNode->fPPsiOx = spGetElement( matrix, pEqn, psiEqnOxP );
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}
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} else { /* Horizontal Slice */
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if ( nIndex <= 1 ) { /* Top Side */
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pNode->fPPsiIn = spGetElement( matrix, pEqn, psiEqnInM );
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pNode->fPPsiInP1 = spGetElement( matrix, pEqn, psiEqnInP );
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pNode->fPPsiOx = spGetElement( matrix, pEqn, psiEqnOxM );
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pNode->fPPsiOxP1 = spGetElement( matrix, pEqn, psiEqnOxP );
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} else { /* Bottom Side */
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pNode->fPPsiInM1 = spGetElement( matrix, pEqn, psiEqnInM );
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pNode->fPPsiIn = spGetElement( matrix, pEqn, psiEqnInP );
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pNode->fPPsiOxM1 = spGetElement( matrix, pEqn, psiEqnOxM );
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pNode->fPPsiOx = spGetElement( matrix, pEqn, psiEqnOxP );
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}
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}
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} /* endfor nIndex */
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pElem = pElem->pElems[ nextIndex ];
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} /* endwhile pElem */
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} /* endfor pCh */
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} /* endif SurfaceMobility */
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}
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/*
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* The Jacobian and Rhs are loaded by the following function.
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* Inputs are the transient analysis flag and the transient
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* information structure
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*/
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void
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TWOPsysLoad(TWOdevice *pDevice, BOOLEAN tranAnalysis, TWOtranInfo *info)
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{
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TWOelem *pElem;
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TWOnode *pNode;
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TWOedge *pHEdge, *pVEdge;
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TWOedge *pTEdge, *pBEdge, *pLEdge, *pREdge;
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TWOchannel *pCh;
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int index, eIndex;
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int nextIndex; /* index of node to find next element */
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double *pRhs = pDevice->rhs;
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double dx, dy, dxdy, dyOverDx, dxOverDy;
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double ds;
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double dPsiT, dPsiB, dPsiL, dPsiR;
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double rhsP;
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double nConc, pConc;
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double perTime = 0.0;
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/* first compute the currents and derivatives */
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TWOPcommonTerms( pDevice, FALSE, tranAnalysis, info );
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/* find reciprocal timestep */
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if ( tranAnalysis ) {
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perTime = info->intCoeff[0];
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}
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/* zero the rhs vector */
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for ( index = 1 ; index <= pDevice->numEqns ; index++ ) {
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pRhs[ index ] = 0.0;
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}
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/* zero the matrix */
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spClear( pDevice->matrix );
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for ( eIndex = 1; eIndex <= pDevice->numElems; eIndex++ ) {
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pElem = pDevice->elements[ eIndex ];
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dx = 0.5 * pElem->dx;
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dy = 0.5 * pElem->dy;
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dxdy = dx * dy;
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dxOverDy = 0.5 * pElem->epsRel * pElem->dxOverDy;
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dyOverDx = 0.5 * pElem->epsRel * pElem->dyOverDx;
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pTEdge = pElem->pTopEdge;
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pBEdge = pElem->pBotEdge;
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pLEdge = pElem->pLeftEdge;
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pREdge = pElem->pRightEdge;
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dPsiT = pTEdge->dPsi;
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dPsiB = pBEdge->dPsi;
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dPsiL = pLEdge->dPsi;
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dPsiR = pREdge->dPsi;
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/* load for all i,j */
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for ( index = 0; index <= 3; index++ ) {
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pNode = pElem->pNodes[ index ];
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if ( pNode->nodeType != CONTACT ) {
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if ( index <= 1 ) {
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pHEdge = pTEdge;
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} else {
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pHEdge = pBEdge;
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}
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if ( index == 0 || index == 3 ) {
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pVEdge = pLEdge;
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} else {
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pVEdge = pREdge;
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}
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/* Add surface state charges. */
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pRhs[ pNode->psiEqn ] += dx * pHEdge->qf;
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pRhs[ pNode->psiEqn ] += dy * pVEdge->qf;
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*(pNode->fPsiPsi) += dyOverDx + dxOverDy;
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if ( pElem->elemType == SEMICON ) {
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nConc = pDevice->devState0 [pNode->nodeN];
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pConc = pDevice->devState0 [pNode->nodeP];
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*(pNode->fPsiPsi) += dxdy * nConc;
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*(pNode->fPsiP) -= dxdy;
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*(pNode->fPPsi) -= dy * pHEdge->dJpDpsiP1 + dx * pVEdge->dJpDpsiP1;
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pRhs[ pNode->psiEqn ] += dxdy * (pNode->netConc + pConc - nConc);
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/* Handle generation terms */
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*(pNode->fPP) += dxdy * pNode->dUdP;
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*(pNode->fPPsi) += dxdy * pNode->dUdN * nConc;
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rhsP = dxdy * pNode->uNet;
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pRhs[ pNode->pEqn ] -= rhsP;
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/* Handle dXdT continuity terms */
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if ( tranAnalysis ) {
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*(pNode->fPP) += dxdy * perTime;
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pRhs[ pNode->pEqn ] -= dxdy * pNode->dPdT;
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}
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}
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}
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}
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/* Handle neighbor and edge dependent terms */
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pNode = pElem->pTLNode;
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if ( pNode->nodeType != CONTACT ) {
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pRhs[ pNode->psiEqn ] -= -dyOverDx * dPsiT - dxOverDy * dPsiL;
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*(pNode->fPsiPsiiP1) -= dyOverDx;
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*(pNode->fPsiPsijP1) -= dxOverDy;
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if ( pElem->elemType == SEMICON ) {
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pRhs[ pNode->pEqn ] -= dy * pTEdge->jp + dx * pLEdge->jp;
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*(pNode->fPP) += dy * pTEdge->dJpDp + dx * pLEdge->dJpDp;
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*(pNode->fPPsiiP1) += dy * pTEdge->dJpDpsiP1;
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*(pNode->fPPiP1) += dy * pTEdge->dJpDpP1;
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*(pNode->fPPsijP1) += dx * pLEdge->dJpDpsiP1;
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*(pNode->fPPjP1) += dx * pLEdge->dJpDpP1;
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}
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}
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pNode = pElem->pTRNode;
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if ( pNode->nodeType != CONTACT ) {
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pRhs[ pNode->psiEqn ] -= dyOverDx * dPsiT - dxOverDy * dPsiR;
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*(pNode->fPsiPsiiM1) -= dyOverDx;
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*(pNode->fPsiPsijP1) -= dxOverDy;
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if ( pElem->elemType == SEMICON ) {
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pRhs[ pNode->pEqn ] -= -dy * pTEdge->jp + dx * pREdge->jp;
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*(pNode->fPP) += -dy * pTEdge->dJpDpP1 + dx * pREdge->dJpDp;
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*(pNode->fPPsiiM1) += dy * pTEdge->dJpDpsiP1;
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*(pNode->fPPiM1) -= dy * pTEdge->dJpDp;
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*(pNode->fPPsijP1) += dx * pREdge->dJpDpsiP1;
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*(pNode->fPPjP1) += dx * pREdge->dJpDpP1;
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}
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}
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pNode = pElem->pBRNode;
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if ( pNode->nodeType != CONTACT ) {
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pRhs[ pNode->psiEqn ] -= dyOverDx * dPsiB + dxOverDy * dPsiR;
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*(pNode->fPsiPsiiM1) -= dyOverDx;
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*(pNode->fPsiPsijM1) -= dxOverDy;
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if ( pElem->elemType == SEMICON ) {
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pRhs[ pNode->pEqn ] -= -dy * pBEdge->jp - dx * pREdge->jp;
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*(pNode->fPP) += -dy * pBEdge->dJpDpP1 - dx * pREdge->dJpDpP1;
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*(pNode->fPPsiiM1) += dy * pBEdge->dJpDpsiP1;
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*(pNode->fPPiM1) -= dy * pBEdge->dJpDp;
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*(pNode->fPPsijM1) += dx * pREdge->dJpDpsiP1;
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*(pNode->fPPjM1) -= dx * pREdge->dJpDp;
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}
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}
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pNode = pElem->pBLNode;
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if ( pNode->nodeType != CONTACT ) {
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pRhs[ pNode->psiEqn ] -= -dyOverDx * dPsiB + dxOverDy * dPsiL;
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*(pNode->fPsiPsiiP1) -= dyOverDx;
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*(pNode->fPsiPsijM1) -= dxOverDy;
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if ( pElem->elemType == SEMICON ) {
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pRhs[ pNode->pEqn ] -= dy * pBEdge->jp - dx * pLEdge->jp;
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*(pNode->fPP) += dy * pBEdge->dJpDp - dx * pLEdge->dJpDpP1;
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*(pNode->fPPsiiP1) += dy * pBEdge->dJpDpsiP1;
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*(pNode->fPPiP1) += dy * pBEdge->dJpDpP1;
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*(pNode->fPPsijM1) += dx * pLEdge->dJpDpsiP1;
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*(pNode->fPPjM1) -= dx * pLEdge->dJpDp;
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}
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}
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}
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/* Calculate the Inversion-Layer Mobility Dependent Terms in Jac. */
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if ( MobDeriv && SurfaceMobility ) {
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for ( pCh = pDevice->pChannel; pCh != NULL;
|
|
pCh = pCh->next ) {
|
|
/* Find effective height of oxide element at interface. */
|
|
if ( pCh->type%2 == 0 ) { /* Vertical slice */
|
|
ds = pCh->pNElem->dy / pCh->pNElem->epsRel;
|
|
} else { /* Horizontal slice */
|
|
ds = pCh->pNElem->dx / pCh->pNElem->epsRel;
|
|
}
|
|
pElem = pCh->pSeed;
|
|
nextIndex = (pCh->type + 2)%4;
|
|
while (pElem && pElem->channel == pCh->id) {
|
|
TWOPmobDeriv( pElem, pCh->type, ds );
|
|
pElem = pElem->pElems[ nextIndex ];
|
|
}
|
|
} /* endfor pCh != NULL */
|
|
} /* endif MobDeriv and SurfaceMobility */
|
|
}
|
|
|
|
|
|
/* this function used only for direct method ac analysis
|
|
Used to load only the dc Jacobian matrix. Rhs is unaffected
|
|
*/
|
|
|
|
void
|
|
TWOPjacLoad(TWOdevice *pDevice)
|
|
{
|
|
TWOelem *pElem;
|
|
TWOnode *pNode;
|
|
TWOedge *pHEdge, *pVEdge;
|
|
TWOedge *pTEdge, *pBEdge, *pLEdge, *pREdge;
|
|
TWOchannel *pCh;
|
|
int index, eIndex;
|
|
int nextIndex; /* index of node to find next element */
|
|
double dx, dy, dxdy, dyOverDx, dxOverDy;
|
|
double ds;
|
|
double nConc;
|
|
|
|
/* first compute the currents and derivatives */
|
|
TWOPcommonTerms( pDevice, FALSE, FALSE, NULL );
|
|
|
|
/* zero the matrix */
|
|
spClear( pDevice->matrix );
|
|
|
|
for ( eIndex = 1; eIndex <= pDevice->numElems; eIndex++ ) {
|
|
pElem = pDevice->elements[ eIndex ];
|
|
dx = 0.5 * pElem->dx;
|
|
dy = 0.5 * pElem->dy;
|
|
dxdy = dx * dy;
|
|
dxOverDy = 0.5 * pElem->epsRel * pElem->dxOverDy;
|
|
dyOverDx = 0.5 * pElem->epsRel * pElem->dyOverDx;
|
|
|
|
pTEdge = pElem->pTopEdge;
|
|
pBEdge = pElem->pBotEdge;
|
|
pLEdge = pElem->pLeftEdge;
|
|
pREdge = pElem->pRightEdge;
|
|
|
|
/* load for all i,j */
|
|
for ( index = 0; index <= 3; index++ ) {
|
|
pNode = pElem->pNodes[ index ];
|
|
if ( pNode->nodeType != CONTACT ) {
|
|
*(pNode->fPsiPsi) += dyOverDx + dxOverDy;
|
|
if ( pElem->elemType == SEMICON ) {
|
|
if ( index <= 1 ) {
|
|
pHEdge = pTEdge;
|
|
} else {
|
|
pHEdge = pBEdge;
|
|
}
|
|
if ( index == 0 || index == 3 ) {
|
|
pVEdge = pLEdge;
|
|
} else {
|
|
pVEdge = pREdge;
|
|
}
|
|
nConc = pDevice->devState0 [pNode->nodeN];
|
|
*(pNode->fPsiPsi) += dxdy * nConc;
|
|
*(pNode->fPsiP) -= dxdy;
|
|
*(pNode->fPPsi) -= dy * pHEdge->dJpDpsiP1 + dx * pVEdge->dJpDpsiP1;
|
|
|
|
/* Handle generation terms */
|
|
*(pNode->fPP) += dxdy * pNode->dUdP;
|
|
*(pNode->fPPsi) += dxdy * pNode->dUdN * nConc;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Handle neighbor and edge dependent terms */
|
|
pNode = pElem->pTLNode;
|
|
if ( pNode->nodeType != CONTACT ) {
|
|
*(pNode->fPsiPsiiP1) -= dyOverDx;
|
|
*(pNode->fPsiPsijP1) -= dxOverDy;
|
|
if ( pElem->elemType == SEMICON ) {
|
|
*(pNode->fPP) += dy * pTEdge->dJpDp + dx * pLEdge->dJpDp;
|
|
*(pNode->fPPsiiP1) += dy * pTEdge->dJpDpsiP1;
|
|
*(pNode->fPPiP1) += dy * pTEdge->dJpDpP1;
|
|
*(pNode->fPPsijP1) += dx * pLEdge->dJpDpsiP1;
|
|
*(pNode->fPPjP1) += dx * pLEdge->dJpDpP1;
|
|
}
|
|
}
|
|
pNode = pElem->pTRNode;
|
|
if ( pNode->nodeType != CONTACT ) {
|
|
*(pNode->fPsiPsiiM1) -= dyOverDx;
|
|
*(pNode->fPsiPsijP1) -= dxOverDy;
|
|
if ( pElem->elemType == SEMICON ) {
|
|
*(pNode->fPP) += -dy * pTEdge->dJpDpP1 + dx * pREdge->dJpDp;
|
|
*(pNode->fPPsiiM1) += dy * pTEdge->dJpDpsiP1;
|
|
*(pNode->fPPiM1) -= dy * pTEdge->dJpDp;
|
|
*(pNode->fPPsijP1) += dx * pREdge->dJpDpsiP1;
|
|
*(pNode->fPPjP1) += dx * pREdge->dJpDpP1;
|
|
}
|
|
}
|
|
pNode = pElem->pBRNode;
|
|
if ( pNode->nodeType != CONTACT ) {
|
|
*(pNode->fPsiPsiiM1) -= dyOverDx;
|
|
*(pNode->fPsiPsijM1) -= dxOverDy;
|
|
if ( pElem->elemType == SEMICON ) {
|
|
*(pNode->fPP) += -dy * pBEdge->dJpDpP1 - dx * pREdge->dJpDpP1;
|
|
*(pNode->fPPsiiM1) += dy * pBEdge->dJpDpsiP1;
|
|
*(pNode->fPPiM1) -= dy * pBEdge->dJpDp;
|
|
*(pNode->fPPsijM1) += dx * pREdge->dJpDpsiP1;
|
|
*(pNode->fPPjM1) -= dx * pREdge->dJpDp;
|
|
}
|
|
}
|
|
pNode = pElem->pBLNode;
|
|
if ( pNode->nodeType != CONTACT ) {
|
|
*(pNode->fPsiPsiiP1) -= dyOverDx;
|
|
*(pNode->fPsiPsijM1) -= dxOverDy;
|
|
if ( pElem->elemType == SEMICON ) {
|
|
*(pNode->fPP) += dy * pBEdge->dJpDp - dx * pLEdge->dJpDpP1;
|
|
*(pNode->fPPsiiP1) += dy * pBEdge->dJpDpsiP1;
|
|
*(pNode->fPPiP1) += dy * pBEdge->dJpDpP1;
|
|
*(pNode->fPPsijM1) += dx * pLEdge->dJpDpsiP1;
|
|
*(pNode->fPPjM1) -= dx * pLEdge->dJpDp;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Calculate the Inversion-Layer Mobility Dependent Terms in Jac. */
|
|
if ( MobDeriv && SurfaceMobility ) {
|
|
for ( pCh = pDevice->pChannel; pCh != NULL;
|
|
pCh = pCh->next ) {
|
|
/* Find effective height of oxide element at interface. */
|
|
if ( pCh->type%2 == 0 ) { /* Vertical slice */
|
|
ds = pCh->pNElem->dy / pCh->pNElem->epsRel;
|
|
} else { /* Horizontal slice */
|
|
ds = pCh->pNElem->dx / pCh->pNElem->epsRel;
|
|
}
|
|
pElem = pCh->pSeed;
|
|
nextIndex = (pCh->type + 2)%4;
|
|
while (pElem && pElem->channel == pCh->id) {
|
|
TWOPmobDeriv( pElem, pCh->type, ds );
|
|
pElem = pElem->pElems[ nextIndex ];
|
|
}
|
|
} /* endfor pCh != NULL */
|
|
} /* endif MobDeriv and SurfaceMobility */
|
|
}
|
|
|
|
/* load only the Rhs vector */
|
|
void
|
|
TWOPrhsLoad(TWOdevice *pDevice, BOOLEAN tranAnalysis, TWOtranInfo *info)
|
|
{
|
|
TWOelem *pElem;
|
|
TWOnode *pNode;
|
|
TWOedge *pHEdge, *pVEdge;
|
|
TWOedge *pTEdge, *pBEdge, *pLEdge, *pREdge;
|
|
int index, eIndex;
|
|
double *pRhs = pDevice->rhs;
|
|
double dx, dy, dxdy, dyOverDx, dxOverDy;
|
|
double dPsiT, dPsiB, dPsiL, dPsiR;
|
|
double rhsP;
|
|
double nConc, pConc;
|
|
double perTime;
|
|
|
|
/* first compute the currents */
|
|
TWOPcommonTerms( pDevice, TRUE, tranAnalysis, info );
|
|
|
|
/* find reciprocal timestep */
|
|
if ( tranAnalysis ) {
|
|
perTime = info->intCoeff[0];
|
|
}
|
|
|
|
/* zero the rhs vector */
|
|
for ( index = 1 ; index <= pDevice->numEqns ; index++ ) {
|
|
pRhs[ index ] = 0.0;
|
|
}
|
|
|
|
for ( eIndex = 1; eIndex <= pDevice->numElems; eIndex++ ) {
|
|
pElem = pDevice->elements[ eIndex ];
|
|
|
|
dx = 0.5 * pElem->dx;
|
|
dy = 0.5 * pElem->dy;
|
|
dxdy = dx * dy;
|
|
dxOverDy = 0.5 * pElem->epsRel * pElem->dxOverDy;
|
|
dyOverDx = 0.5 * pElem->epsRel * pElem->dyOverDx;
|
|
|
|
pTEdge = pElem->pTopEdge;
|
|
pBEdge = pElem->pBotEdge;
|
|
pLEdge = pElem->pLeftEdge;
|
|
pREdge = pElem->pRightEdge;
|
|
dPsiT = pTEdge->dPsi;
|
|
dPsiB = pBEdge->dPsi;
|
|
dPsiL = pLEdge->dPsi;
|
|
dPsiR = pREdge->dPsi;
|
|
|
|
/* load for all i,j */
|
|
for ( index = 0; index <= 3; index++ ) {
|
|
pNode = pElem->pNodes[ index ];
|
|
if ( pNode->nodeType != CONTACT ) {
|
|
if ( index <= 1 ) {
|
|
pHEdge = pTEdge;
|
|
} else {
|
|
pHEdge = pBEdge;
|
|
}
|
|
if ( index == 0 || index == 3 ) {
|
|
pVEdge = pLEdge;
|
|
} else {
|
|
pVEdge = pREdge;
|
|
}
|
|
/* Add surface state charges. */
|
|
pRhs[ pNode->psiEqn ] += dx * pHEdge->qf;
|
|
pRhs[ pNode->psiEqn ] += dy * pVEdge->qf;
|
|
if ( pElem->elemType == SEMICON ) {
|
|
nConc = pDevice->devState0 [pNode->nodeN];
|
|
pConc = pDevice->devState0 [pNode->nodeP];
|
|
pRhs[ pNode->psiEqn ] += dxdy * (pNode->netConc + pConc - nConc);
|
|
|
|
/* Handle generation terms */
|
|
rhsP = dxdy * pNode->uNet;
|
|
pRhs[ pNode->pEqn ] -= rhsP;
|
|
|
|
/* Handle dXdT continuity terms */
|
|
if ( tranAnalysis ) {
|
|
pRhs[ pNode->pEqn ] -= dxdy * pNode->dPdT;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Handle neighbor and edge dependent terms */
|
|
pNode = pElem->pTLNode;
|
|
if ( pNode->nodeType != CONTACT ) {
|
|
pRhs[ pNode->psiEqn ] -= -dyOverDx * dPsiT - dxOverDy * dPsiL;
|
|
if ( pElem->elemType == SEMICON ) {
|
|
pRhs[ pNode->pEqn ] -= dy * pTEdge->jp + dx * pLEdge->jp;
|
|
}
|
|
}
|
|
pNode = pElem->pTRNode;
|
|
if ( pNode->nodeType != CONTACT ) {
|
|
pRhs[ pNode->psiEqn ] -= dyOverDx * dPsiT - dxOverDy * dPsiR;
|
|
if ( pElem->elemType == SEMICON ) {
|
|
pRhs[ pNode->pEqn ] -= -dy * pTEdge->jp + dx * pREdge->jp;
|
|
}
|
|
}
|
|
pNode = pElem->pBRNode;
|
|
if ( pNode->nodeType != CONTACT ) {
|
|
pRhs[ pNode->psiEqn ] -= dyOverDx * dPsiB + dxOverDy * dPsiR;
|
|
if ( pElem->elemType == SEMICON ) {
|
|
pRhs[ pNode->pEqn ] -= -dy * pBEdge->jp - dx * pREdge->jp;
|
|
}
|
|
}
|
|
pNode = pElem->pBLNode;
|
|
if ( pNode->nodeType != CONTACT ) {
|
|
pRhs[ pNode->psiEqn ] -= -dyOverDx * dPsiB + dxOverDy * dPsiL;
|
|
if ( pElem->elemType == SEMICON ) {
|
|
pRhs[ pNode->pEqn ] -= dy * pBEdge->jp - dx * pLEdge->jp;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/*
|
|
* computation of current densities, recombination rates,
|
|
* mobilities and their derivatives
|
|
*/
|
|
void
|
|
TWOPcommonTerms(TWOdevice *pDevice, BOOLEAN currentOnly,
|
|
BOOLEAN tranAnalysis, TWOtranInfo *info)
|
|
{
|
|
TWOelem *pElem;
|
|
TWOedge *pEdge;
|
|
TWOnode *pNode;
|
|
int index, eIndex;
|
|
int nextIndex; /* index of node to find next element */
|
|
double psi1, psi2, refPsi, pC, pP1;
|
|
double dPsiP;
|
|
double bPsiP, dbPsiP, bMPsiP, dbMPsiP;
|
|
double muP, dMuP, rDx, rDy;
|
|
double psi, nConc = 0.0, pConc = 0.0;
|
|
double cnAug, cpAug;
|
|
double eSurf = 0.0; /* For channel mobilities */
|
|
double qInt = 0.0;
|
|
TWOchannel *pCh;
|
|
|
|
/* evaluate all node (including recombination) and edge quantities */
|
|
for ( eIndex = 1; eIndex <= pDevice->numElems; eIndex++ ) {
|
|
pElem = pDevice->elements[ eIndex ];
|
|
refPsi = pElem->matlInfo->refPsi;
|
|
cnAug = pElem->matlInfo->cAug[ELEC];
|
|
cpAug = pElem->matlInfo->cAug[HOLE];
|
|
for ( index = 0; index <= 3; index++ ) {
|
|
if ( pElem->evalNodes[ index ] ) {
|
|
pNode = pElem->pNodes[ index ];
|
|
if ( pNode->nodeType != CONTACT ) {
|
|
psi = pDevice->dcSolution[ pNode->psiEqn ];
|
|
if ( pElem->elemType == SEMICON ) {
|
|
nConc = pNode->nie * exp( psi - refPsi );
|
|
pConc = pDevice->dcSolution[ pNode->pEqn ];
|
|
if ( Srh ) {
|
|
recomb(nConc, pConc,
|
|
pNode->tn, pNode->tp, cnAug, cpAug, pNode->nie,
|
|
&pNode->uNet, &pNode->dUdN, &pNode->dUdP);
|
|
} else {
|
|
pNode->uNet = 0.0;
|
|
pNode->dUdN = 0.0;
|
|
pNode->dUdP = 0.0;
|
|
}
|
|
}
|
|
} else {
|
|
/* a contact node */
|
|
psi = pNode->psi;
|
|
if ( pElem->elemType == SEMICON ) {
|
|
nConc = pNode->nConc;
|
|
pConc = pNode->pConc;
|
|
}
|
|
}
|
|
|
|
/* store info in the state tables */
|
|
pDevice->devState0 [pNode->nodePsi] = psi;
|
|
if ( pElem->elemType == SEMICON ) {
|
|
pDevice->devState0 [pNode->nodeN] = nConc;
|
|
pDevice->devState0 [pNode->nodeP] = pConc;
|
|
if ( tranAnalysis && pNode->nodeType != CONTACT ) {
|
|
pNode->dNdT = integrate( pDevice->devStates, info, pNode->nodeN );
|
|
pNode->dPdT = integrate( pDevice->devStates, info, pNode->nodeP );
|
|
}
|
|
}
|
|
}
|
|
}
|
|
for ( index = 0; index <= 3; index++ ) {
|
|
if ( pElem->evalEdges[ index ] ) {
|
|
pEdge = pElem->pEdges[ index ];
|
|
pNode = pElem->pNodes[ index ];
|
|
if ( pNode->nodeType != CONTACT ) {
|
|
psi1 = pDevice->dcSolution[pNode->psiEqn];
|
|
} else {
|
|
psi1 = pNode->psi;
|
|
}
|
|
pNode = pElem->pNodes[ (index + 1) % 4 ];
|
|
if ( pNode->nodeType != CONTACT ) {
|
|
psi2 = pDevice->dcSolution[pNode->psiEqn];
|
|
} else {
|
|
psi2 = pNode->psi;
|
|
}
|
|
if ( index <= 1 ) {
|
|
pEdge->dPsi = psi2 - psi1;
|
|
} else {
|
|
pEdge->dPsi = psi1 - psi2;
|
|
}
|
|
pDevice->devState0 [pEdge->edgeDpsi] = pEdge->dPsi;
|
|
|
|
if ( pElem->elemType == SEMICON ) {
|
|
/* Calculate weighted driving forces - wdfn & wdfp for the edge */
|
|
dPsiP = pEdge->dPsi - pEdge->dVBand;
|
|
bernoulli( dPsiP, &bPsiP, &dbPsiP,
|
|
&bMPsiP, &dbMPsiP, !currentOnly);
|
|
if ( index <= 1 ) {
|
|
pC = *(pDevice->devState0 + pElem->pNodes[ index ]->nodeP);
|
|
pP1 = *(pDevice->devState0 + pElem->pNodes[ index+1 ]->nodeP);
|
|
} else {
|
|
pC = *(pDevice->devState0 + pElem->pNodes[(index+1)%4]->nodeP);
|
|
pP1 = *(pDevice->devState0 + pElem->pNodes[ index ]->nodeP);
|
|
}
|
|
pEdge->wdfp = bPsiP * pC - bMPsiP * pP1;
|
|
pEdge->jp = 0.0;
|
|
if ( !currentOnly ) {
|
|
pEdge->dWpDpsiP1 = dbPsiP * pC - dbMPsiP * pP1;
|
|
pEdge->dWpDp = bPsiP;
|
|
pEdge->dWpDpP1 = - bMPsiP;
|
|
pEdge->dJpDpsiP1 = 0.0;
|
|
pEdge->dJpDp = 0.0;
|
|
pEdge->dJpDpP1 = 0.0;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* DAG: calculate mobilities for channel elems */
|
|
if ( SurfaceMobility ) {
|
|
for ( pCh = pDevice->pChannel;
|
|
pCh != NULL; pCh = pCh->next ) {
|
|
pElem = pCh->pNElem;
|
|
switch (pCh->type) {
|
|
case 0:
|
|
eSurf = - 0.5 * (pElem->pLeftEdge->dPsi + pElem->pRightEdge->dPsi )
|
|
* pElem->epsRel / pElem->dy;
|
|
qInt = 0.5 * pElem->pBotEdge->qf;
|
|
break;
|
|
case 1:
|
|
eSurf = - 0.5 * (pElem->pTopEdge->dPsi + pElem->pBotEdge->dPsi )
|
|
* pElem->epsRel / pElem->dx;
|
|
qInt = 0.5 * pElem->pLeftEdge->qf;
|
|
break;
|
|
case 2:
|
|
eSurf = - 0.5 * (pElem->pLeftEdge->dPsi + pElem->pRightEdge->dPsi )
|
|
* pElem->epsRel / pElem->dy;
|
|
qInt = 0.5 * pElem->pTopEdge->qf;
|
|
break;
|
|
case 3:
|
|
eSurf = - 0.5 * (pElem->pTopEdge->dPsi + pElem->pBotEdge->dPsi )
|
|
* pElem->epsRel / pElem->dx;
|
|
qInt = 0.5 * pElem->pRightEdge->qf;
|
|
break;
|
|
}
|
|
eSurf += qInt;
|
|
pElem = pCh->pSeed;
|
|
nextIndex = (pCh->type + 2)%4;
|
|
while (pElem && pElem->channel == pCh->id) {
|
|
TWOPmobility( pElem, eSurf );
|
|
pElem = pElem->pElems[ nextIndex ];
|
|
}
|
|
} /* endfor pCH != NULL */
|
|
} /* endif SurfaceMobility */
|
|
|
|
/* calculate the current densities assuming mobility value depend on Ex,Ey*/
|
|
for ( eIndex = 1; eIndex <= pDevice->numElems; eIndex++ ) {
|
|
pElem = pDevice->elements[ eIndex ];
|
|
|
|
rDx = 1.0 / pElem->dx;
|
|
rDy = 1.0 / pElem->dy;
|
|
for ( index = 0; index <= 3; index++ ) {
|
|
pEdge = pElem->pEdges[ index ];
|
|
/* calculate conductive currents */
|
|
if ( pElem->elemType == SEMICON ) {
|
|
/* get mobility for this edge */
|
|
if ( !pElem->channel ) {
|
|
/* Calculate mobility for non-channel elements */
|
|
muP = pElem->mup0;
|
|
dMuP = 0.0;
|
|
dPsiP = pEdge->dPsi - pEdge->dVBand;
|
|
if ( index%2 == 0 ) {
|
|
MOBfieldDep( pElem->matlInfo, HOLE, - dPsiP * rDx, &muP, &dMuP );
|
|
} else {
|
|
MOBfieldDep( pElem->matlInfo, HOLE, - dPsiP * rDy, &muP, &dMuP );
|
|
}
|
|
} else {
|
|
/* Retrieve previously calculated value. */
|
|
muP = pElem->mup;
|
|
dMuP = 0.0;
|
|
}
|
|
switch ( index ) {
|
|
case 0:
|
|
muP *= pEdge->kPos * rDx;
|
|
dMuP *= pEdge->kPos * rDx * rDx;
|
|
break;
|
|
case 1:
|
|
muP *= pEdge->kNeg * rDy;
|
|
dMuP *= pEdge->kNeg * rDy * rDy;
|
|
break;
|
|
case 2:
|
|
muP *= pEdge->kNeg * rDx;
|
|
dMuP *= pEdge->kNeg * rDx * rDx;
|
|
break;
|
|
case 3:
|
|
muP *= pEdge->kPos * rDy;
|
|
dMuP *= pEdge->kPos * rDy * rDy;
|
|
break;
|
|
}
|
|
/* Now that the mobility for this edge is known, do current */
|
|
pEdge->jp += muP * pEdge->wdfp;
|
|
if ( !currentOnly ) {
|
|
pEdge->dJpDpsiP1 += muP * pEdge->dWpDpsiP1;
|
|
pEdge->dJpDp += muP * pEdge->dWpDp;
|
|
pEdge->dJpDpP1 += muP * pEdge->dWpDpP1;
|
|
if ( MobDeriv && (!pElem->channel) ) {
|
|
pEdge->dJpDpsiP1 -= dMuP * pEdge->wdfp;
|
|
}
|
|
}
|
|
}
|
|
/* calculate displacement current only once */
|
|
if ( pElem->evalEdges[ index ] ) {
|
|
if ( tranAnalysis ) {
|
|
if ( index == 0 || index == 2 ) {
|
|
/* horizontal edges */
|
|
pEdge->jd = -integrate(pDevice->devStates, info,
|
|
pEdge->edgeDpsi) * rDx;
|
|
} else {
|
|
/* vertical edges */
|
|
pEdge->jd = -integrate(pDevice->devStates, info,
|
|
pEdge->edgeDpsi) * rDy;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|