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Implemented the final fitting to perform extrapolation at 10 years, when the model behavior is periodic, by using Fourier basis

This commit is contained in:
Francesco Lannutti 2015-08-02 11:13:51 +02:00
parent dda38c9df2
commit 439e229972
4 changed files with 161 additions and 28 deletions
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137
src/spicelib/devices/bsim4/b4reliability.c
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@ -8,6 +8,7 @@ Author: 2015 Francesco Lannutti - July 2015
#include "ngspice/sperror.h"
#include <gsl/gsl_fit.h>
#include <gsl/gsl_linalg.h>
static int
BSIM4reliability_internal (BSIM4instance *here, CKTcircuit *ckt, unsigned int mode)
@ -130,6 +131,9 @@ BSIM4reliability_internal (BSIM4instance *here, CKTcircuit *ckt, unsigned int mo
{
return (E_INTERN) ;
}
// Update the semiperiod counter
here->relStruct->semiPeriods++ ;
} else {
fprintf (stderr, "Reliability Analysis Error\n") ;
}
@ -149,6 +153,9 @@ BSIM4reliability_internal (BSIM4instance *here, CKTcircuit *ckt, unsigned int mo
{
return (E_INTERN) ;
}
// Update the semiperiod counter
here->relStruct->semiPeriods++ ;
} else if (here->relStruct->IsON == 0) {
// Until now, the device was OFF - Do NOTHING
delta = -1 ;
@ -173,6 +180,9 @@ BSIM4reliability_internal (BSIM4instance *here, CKTcircuit *ckt, unsigned int mo
{
return (E_INTERN) ;
}
// Update the semiperiod counter
here->relStruct->semiPeriods++ ;
} else if (here->relStruct->IsON == 0) {
// Calculate recovery
delta = ckt->CKTtime - here->relStruct->time ;
@ -187,6 +197,9 @@ BSIM4reliability_internal (BSIM4instance *here, CKTcircuit *ckt, unsigned int mo
{
return (E_INTERN) ;
}
// Update the semiperiod counter
here->relStruct->semiPeriods++ ;
} else {
fprintf (stderr, "Reliability Analysis Error\n") ;
}
@ -197,7 +210,6 @@ BSIM4reliability_internal (BSIM4instance *here, CKTcircuit *ckt, unsigned int mo
/* Calculate fitting */
double c0, c1, cov00, cov01, cov11, chisq ;
/* Count how many deltaVth we have */
unsigned int i ;
@ -222,22 +234,125 @@ BSIM4reliability_internal (BSIM4instance *here, CKTcircuit *ckt, unsigned int mo
while (current != NULL)
{
timeFit [i] = current->time ;
deltaVthFit [i] = exp (current->deltaVth) ;
printf ("Time: %-.9g\n", current->time) ;
printf ("DeltaVth: %-.9g\n", current->deltaVth) ;
printf ("DeltaVth (exp): %-.9g\n", exp (current->deltaVth)) ;
deltaVthFit [i] = current->deltaVth ;
i++ ;
current = current->next ;
}
/* Execute Fitting */
gsl_fit_linear (timeFit + 1, 1, deltaVthFit + 1, 1, i - 1, &c0, &c1, &cov00, &cov01, &cov11, &chisq) ;
// printf ("Number of Semi Periods: %u\n", here->relStruct->semiPeriods) ;
/* Perform Extrapolation */
double yFit, yFitErr ;
gsl_fit_linear_est (2e-6, c0, c1, cov00, cov01, cov11, &yFit, &yFitErr) ;
if (here->relStruct->semiPeriods > 1)
{
/* The model behavior is periodic - Use Fourier basis fitting */
/* Generate the fitting matrix */
printf ("\n\tFitting -> %-.9gs\t%-.9gmV\n\n", 31536000.0, log (yFit) * 1000) ;
double f, factor_for_2pi, *fitting_matrix, target ;
unsigned int columns, j, number_of_modes, number_of_periods, rows, size ;
number_of_periods = here->relStruct->semiPeriods / 2 ;
number_of_modes = 10 * (number_of_periods + 1) ;
// printf ("Number of Periods: %u\n", number_of_periods) ;
// printf ("Number of Modes: %u\n", number_of_modes) ;
rows = i ;
columns = 2 * number_of_modes + 1 ;
size = rows * columns ;
fitting_matrix = TMALLOC (double, size) ;
// printf ("Rows: %u\n", rows) ;
// printf ("Columns: %u\n", columns) ;
factor_for_2pi = 2 * 3.14159265359 / (timeFit [rows - 1] - timeFit [0]) ;
/* for (i = 0 ; i < rows ; i++)
{
printf ("Time: %-.9g\n", timeFit [i]) ;
}
printf ("Max Time: %-.9g\n", timeFit [rows - 1]) ;
printf ("Min Time: %-.9g\n", timeFit [0]) ;
*/
for (i = 0 ; i < rows ; i++)
{
/* The first element of every row is equal to 1 */
fitting_matrix [columns * i] = 1 ;
/* The odd elements of every row are cos(x) */
for (j = 0 ; j < number_of_modes ; j++)
{
fitting_matrix [columns * i + 2 * j + 1] = cos ((j + 1) * timeFit [i] * factor_for_2pi) ;
}
/* The even elements of every row are sin(x) */
for (j = 1 ; j <= number_of_modes ; j++)
{
fitting_matrix [columns * i + 2 * j] = sin (j * timeFit [i] * factor_for_2pi) ;
}
}
gsl_matrix_view m = gsl_matrix_view_array (fitting_matrix, rows, columns) ;
gsl_vector_view b = gsl_vector_view_array (deltaVthFit, rows) ;
gsl_vector *tau = gsl_vector_alloc (MIN (rows, columns)) ;
gsl_vector *x = gsl_vector_alloc (columns) ;
gsl_vector *residual = gsl_vector_alloc (rows) ;
gsl_linalg_QR_decomp (&m.matrix, tau) ;
gsl_linalg_QR_lssolve (&m.matrix, tau, &b.vector, x, residual) ;
// printf ("fitting_matrix = \n") ;
// gsl_matrix_fprintf (stdout, &m.matrix, "%g") ;
// printf ("x = \n") ;
// gsl_vector_fprintf (stdout, x, "%g") ;
target = 315360000.0 ;
f = gsl_vector_get (x, 0) ;
/* The odd elements of every row are cos(x) */
for (j = 0 ; j < number_of_modes ; j++)
{
f += gsl_vector_get (x, 2 * j + 1) * cos ((j + 1) * target * factor_for_2pi) ;
}
/* The even elements of every row are sin(x) */
for (j = 1 ; j <= number_of_modes ; j++)
{
f += gsl_vector_get (x, 2 * j) * sin (j * target * factor_for_2pi) ;
}
printf ("\n\nExtrapolation at 10 years:\n\t\t\t\tDeltaVth: %-.9gmV\n\n\n\n", f * 1000) ;
/* Assign the extrapolated DeltaVth to the model */
here->relStruct->deltaVth = f ;
gsl_vector_free (tau) ;
gsl_vector_free (x) ;
gsl_vector_free (residual) ;
} else {
/* Execute Fitting */
double c0, c1, cov00, cov01, cov11, chisq, *deltaVthFitExp ;
unsigned int j ;
deltaVthFitExp = TMALLOC (double, i) ;
for (j = 0 ; j < i ; j++)
{
deltaVthFitExp [j] = exp (deltaVthFit [j]) ;
}
gsl_fit_linear (timeFit, 1, deltaVthFitExp, 1, i, &c0, &c1, &cov00, &cov01, &cov11, &chisq) ;
printf ("\n\n") ;
printf ("c0: %-.9g\n", c0) ;
printf ("c1: %-.9g\n", c1) ;
printf ("cov00: %-.9g\n", cov00) ;
printf ("cov01: %-.9g\n", cov01) ;
printf ("cov11: %-.9g\n", cov11) ;
printf ("chisq: %-.9g\n", chisq) ;
printf ("\n\n") ;
/* Perform Extrapolation */
double yFit, yFitErr ;
gsl_fit_linear_est (315360000.0, c0, c1, cov00, cov01, cov11, &yFit, &yFitErr) ;
printf ("\n\tFitting -> %-.9gs\t%-.9gmV\n\n", 315360000.0, log (yFit) * 1000) ;
printf ("\n\tFitting -> %-.9gs\t%-.9gmV\n\n", 315360000.0, log (c0 + c1 * 315360000.0) * 1000) ;
}
} else {
fprintf (stderr, "Reliability Analysis Error\n") ;
}

3
src/spicelib/devices/bsim4/b4set.c
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@ -2660,10 +2660,13 @@ do { if((here->ptr = SMPmakeElt(matrix,here->first,here->second))==(double *)NUL
{
here->relStruct = TMALLOC (RELMODELrelStruct, 1) ;
here->relStruct->time = 0 ;
here->relStruct->offsetTime = 0 ;
here->relStruct->deltaVth = 0 ;
here->relStruct->deltaVthMax = 0 ;
here->relStruct->t_star = 0 ;
here->relStruct->IsON = -1 ;
here->relStruct->deltaVthList = NULL ;
here->relStruct->semiPeriods = 0 ;
}
#endif

46
src/spicelib/devices/relmodel/relmodelcalcaging.c
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@ -49,7 +49,7 @@ listInsert (RELMODELrelList **list, double time, double deltaVth)
int
RELMODELcalculateAging (GENinstance *inInstance, int modType, double t_aging, unsigned int stress_or_recovery)
{
double A, Nt ;
double A, i, Nt, step ;
BSIM4instance *here ;
RELMODELmodel *relmodel ;
@ -71,32 +71,44 @@ RELMODELcalculateAging (GENinstance *inInstance, int modType, double t_aging, un
Nt = pow ((sqrt (relmodel->RELMODELnts)), 3) * 1e-21 ;
A = (CHARGE / (4 * CONSTepsZero * 1e-9 * relmodel->RELMODELeps_hk)) * pow ((relmodel->RELMODELh_cut / (2 * sqrt (2 * relmodel->RELMODELm_star * relmodel->RELMODELw)) * 1e9), 2) ;
if (stress_or_recovery)
// printf ("\n\nStart Aging...\n") ;
// printf ("\tEnd step: %-.9g\n\n", here->relStruct->t_star + t_aging) ;
step = 1e-12 ;
for (i = 0 ; i < t_aging ; i += step)
{
if (relmodel->RELMODELh_cut / (2 * sqrt (2 * relmodel->RELMODELm_star * relmodel->RELMODELw)) * log (1 + pow (((t_aging + here->relStruct->t_star) / relmodel->RELMODELtau_0), relmodel->RELMODELbeta)) * 1e9 <= 2)
if (stress_or_recovery)
{
here->relStruct->deltaVth = Nt * A * pow (log (1 + pow (((t_aging + here->relStruct->t_star) / relmodel->RELMODELtau_0), relmodel->RELMODELbeta)), 2) ;
if (relmodel->RELMODELh_cut / (2 * sqrt (2 * relmodel->RELMODELm_star * relmodel->RELMODELw)) * log (1 + pow (((i + here->relStruct->t_star) / relmodel->RELMODELtau_0), relmodel->RELMODELbeta)) * 1e9 <= 2)
{
here->relStruct->deltaVth = Nt * A * pow (log (1 + pow (((i + here->relStruct->t_star) / relmodel->RELMODELtau_0), relmodel->RELMODELbeta)), 2) ;
} else {
here->relStruct->deltaVth = pow ((CHARGE / (4 * CONSTepsZero * 1e-9 * relmodel->RELMODELeps_hk)) * Nt * here->BSIM4modPtr->BSIM4toxe * 1e9, 2) ;
}
here->relStruct->deltaVthMax = here->relStruct->deltaVth ;
} else {
here->relStruct->deltaVth = pow ((CHARGE / (4 * CONSTepsZero * 1e-9 * relmodel->RELMODELeps_hk)) * Nt * here->BSIM4modPtr->BSIM4toxe * 1e9, 2) ;
// printf ("\n\nDeltaVth Prior Recovery: %-.9gmV\n\n", here->relStruct->deltaVth * 1000) ;
here->relStruct->deltaVth = here->relStruct->deltaVthMax * log (1 + (1.718 / (1 + pow ((i / relmodel->RELMODELtau_e), relmodel->RELMODELbeta1)))) ;
}
} else {
here->relStruct->deltaVth = here->relStruct->deltaVth * log (1 + (1.718 / (1 + pow ((t_aging / relmodel->RELMODELtau_e), relmodel->RELMODELbeta1)))) ;
}
/* Insert 'here->relStruct->deltaVth' into the list for the later fitting */
listInsert (&(here->relStruct->deltaVthList), here->relStruct->time, here->relStruct->deltaVth) ;
// RELMODELrelList *temp ;
// temp = TMALLOC (RELMODELrelList, 1) ;
// temp->time = here->relStruct->time ;
// temp->deltaVth = here->relStruct->deltaVth ;
// temp->next = here->relStruct->deltaVthList ;
// here->relStruct->deltaVthList = temp ;
// printf ("QUI\n\n") ;
/* Insert 'here->relStruct->deltaVth' into the list for the later fitting */
listInsert (&(here->relStruct->deltaVthList), here->relStruct->offsetTime + i, here->relStruct->deltaVth) ;
// printf ("\nStep: %-.9g\tDeltaVth: %-.9gmV\n\n", i, here->relStruct->deltaVth * 1000) ;
// RELMODELrelList *temp ;
// temp = TMALLOC (RELMODELrelList, 1) ;
// temp->time = i + here->relStruct->t_star ;
// temp->deltaVth = here->relStruct->deltaVth ;
// temp->next = here->relStruct->deltaVthList ;
// here->relStruct->deltaVthList = temp ;
// printf ("QUI\n\n") ;
}
// printf ("Stop Aging...\n\n") ;
if (!stress_or_recovery)
{
here->relStruct->t_star = pow ((exp (sqrt (here->relStruct->deltaVth / (Nt * A))) - 1), (1 / relmodel->RELMODELbeta)) * relmodel->RELMODELtau_0 ;
}
here->relStruct->offsetTime += i ;
return 0 ;
}

3
src/spicelib/devices/relmodel/relmodeldefs.h
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@ -19,10 +19,13 @@ typedef struct sRELMODELrelList {
typedef struct sRELMODELrelStruct {
double time ;
double offsetTime ;
double deltaVth ;
double deltaVthMax ;
double t_star ;
int IsON ;
RELMODELrelList *deltaVthList ;
unsigned int semiPeriods ;
} RELMODELrelStruct ;
typedef struct sRELMODELmodel