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mjd_fieldgen.c
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/* program to calculate electric fields and weighting potentials
of PPC BEGe, and inverted-coax-PC Ge detectors by relaxation
author: D.C. Radford
first written: Nov 2007
MJD modified version: Oct 2014, June 2016
- uses the same (single) config file as modified MJD siggen
- added intelligent coarse grid / refinement of grid
- added interpolation of RC and LC positions on the grid
- added optional bulletization of point contact
This modified version: Dec 2016
- added hole, inner taper length, outer taper length, taper angle
Nov 2017: added top bulletization
May-July 2019
- added dead layer / Li thickness
- added over-relaxation factor; gained factor of ~ 40 speedup, depending on size/grid
- added code to estimate full-depletion voltage in the case of bubble depletion (pinch-off)
- added -r option to allow reading of z-impurity profile from a .spe file
Nov 2019
- major rewrite and re-arragement of the code
- broke out functions grid_init, ev_calc, wp_calc, write_ev, write_wp, do_relax, interpolate
- got an additional factor of ~3 speedup
- more modular and readable
Dec 2019
- added code to properly handle pixels next to p+ and n+ contacts
- much better calculation of V and E near contacts
- todo now: execute WD=1 option
*/
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <string.h>
#include <math.h>
#include <time.h>
#include "mjd_siggen.h"
#include "detector_geometry.h"
#define MAX_ITS 50000 // default max number of iterations for relaxation
static int report_config(FILE *fp_out, char *config_file_name);
static int grid_init(MJD_Siggen_Setup *setup);
static int ev_calc(MJD_Siggen_Setup *setup, MJD_Siggen_Setup *old_setup);
static int wp_calc(MJD_Siggen_Setup *setup, MJD_Siggen_Setup *old_setup);
static int write_ev(MJD_Siggen_Setup *setup);
static int write_wp(MJD_Siggen_Setup *setup);
static int do_relax(MJD_Siggen_Setup *setup, int ev_calc);
static int ev_relax_undep(MJD_Siggen_Setup *setup);
static int wp_relax_undep(MJD_Siggen_Setup *setup);
static int interpolate(MJD_Siggen_Setup *setup, MJD_Siggen_Setup *old_setup);
/* -------------------------------------- main ------------------- */
int main(int argc, char **argv)
{
MJD_Siggen_Setup setup, setup1, setup2;
float BV; // bias voltage
int WV = 0; // 0: do not write the V and E values to ppc_ev.dat
// 1: write the V and E values to ppc_ev.dat
// 2: write the V and E values for both +r, -r (for gnuplot, NOT for siggen)
int WD = 0; // 0: do not write out depletion surface
// 1: write out depletion surface to depl_<HV>.dat
int i, j, k;
FILE *fp;
if (argc < 2 || argc%2 != 0 || read_config(argv[1], &setup)) {
printf("Usage: %s <config_file_name> [options]\n"
" Possible options:\n"
" -b bias_volts\n"
" -w {0,1} (do_not/do write the field file)\n"
" -d {0,1} (do_not/do write the depletion surface)\n"
" -p {0,1} (do_not/do write the WP file)\n"
" -r rho_spectrum_file_name\n"
" -z <rho_spectrum_offset_mm>\n", argv[0]);
return 1;
}
strncpy(setup.config_file_name, argv[1], sizeof(setup.config_file_name));
if (setup.xtal_grid < 0.001) setup.xtal_grid = 0.5;
BV = setup.xtal_HV;
WV = setup.write_field;
setup.rho_z_spe[0] = 0;
for (i=2; i<argc-1; i++) {
if (strstr(argv[i], "-b")) {
BV = setup.xtal_HV = atof(argv[++i]); // bias volts
} else if (strstr(argv[i], "-w")) {
WV = atoi(argv[++i]); // write-out options
} else if (strstr(argv[i], "-d")) {
WD = atoi(argv[++i]); // write-out options
} else if (strstr(argv[i], "-p")) {
setup.write_WP = atoi(argv[++i]); // weighting-potential options
} else if (strstr(argv[i], "-r")) {
if (!(fp = fopen(argv[++i], "r"))) { // impurity-profile-spectrum file name
printf("\nERROR: cannot open impurity profile spectrum file %s\n\n", argv[i]);
return 1;
}
if (strstr(argv[i], ".spe")) fread(setup.rho_z_spe, 36, 1, fp); // skip over .spe-format header
for (j=0; j<1024; j++) setup.rho_z_spe[j] = 0;
fread(setup.rho_z_spe, sizeof(setup.rho_z_spe), 1, fp);
fclose(fp);
} else if (strstr(argv[i], "-z")) {
j = atoi(argv[++i]);
if (j >= 199) {
printf("Error; rho_spectrum_offset_mm = %d is too large! max = 200\n", j);
return 1;
}
for (k=j; k <200; k++) setup.rho_z_spe[k-j] = setup.rho_z_spe[k];
} else {
printf("Possible options:\n"
" -b bias_volts\n"
" -w {0,1,2} (for WV options)\n"
" -p {0,1} (for WP options)\n"
" -r rho_spectrum_file_name\n"
" -z <rho_spectrum_offset_mm>\n");
return 1;
}
}
if (setup.verbosity >= CHATTY && setup.rho_z_spe[0] != 0) {
printf(" z(mm) rho\n");
for (j=0; j < (int) setup.xtal_length; j++)
printf(" %3d %7.3f\n", j, setup.rho_z_spe[j]);
}
if (setup.xtal_length/setup.xtal_grid * setup.xtal_radius/setup.xtal_grid > 2500*2500) {
printf("Error: Crystal size divided by grid size is too large!\n");
return 1;
}
if (WV < 0 || WV > 2) WV = 0;
/* -------------- give details of detector geometry */
if (setup.verbosity >= CHATTY) {
printf("\n\n"
" Crystal: Radius x Length: %.1f x %.1f mm\n",
setup.xtal_radius, setup.xtal_length);
if (setup.hole_length > 0) {
if (setup.inner_taper_length > 0)
printf(" Core hole: Radius x length: %.1f x %.1f mm,"
" taper %.1f x %.1f mm (%2.f degrees)\n",
setup.hole_radius, setup.hole_length,
setup.inner_taper_width, setup.inner_taper_length, setup.taper_angle);
else
printf(" Core hole: Radius x length: %.1f x %.1f mm\n",
setup.hole_radius, setup.hole_length);
}
printf("Point contact: Radius x length: %.1f x %.1f mm\n",
setup.pc_radius, setup.pc_length);
if (setup.ditch_depth > 0) {
printf(" Wrap-around: Radius x ditch x gap: %.1f x %.1f x %.1f mm\n",
setup.wrap_around_radius, setup.ditch_depth, setup.ditch_thickness);
}
printf(" Bias: %.0f V\n", BV);
}
if ((BV < 0 && setup.impurity_z0 < 0) || (BV > 0 && setup.impurity_z0 > 0)) {
printf("ERROR: Expect bias and impurity to be opposite sign!\n");
return 1;
}
if (setup.impurity_z0 > 0) {
// swap polarity for n-type material; this lets me assume all voltages are positive
BV = -BV;
setup.xtal_HV *= -1.0;
setup.impurity_z0 *= -1.0;
setup.impurity_gradient *= -1.0;
setup.impurity_quadratic *= -1.0;
setup.impurity_surface *= -1.0;
setup.impurity_radial_add *= -1.0;
}
/* use an adaptive grid; start out coarse and then refine the grid */
memcpy(&setup1, &setup, sizeof(setup));
memcpy(&setup2, &setup, sizeof(setup));
setup1.xtal_grid *= 9.0;
setup2.xtal_grid *= 3.0;
if (grid_init(&setup1) != 0 ||
grid_init(&setup2) != 0 ||
grid_init(&setup) != 0) {
printf("failed to init field calculations\n");
return 1;
}
/* -------------- calculate electric potential/field */
if (setup.write_field) {
setup1.write_field = 0; // no need to save intermediate calculations
setup2.write_field = 0;
if (setup.xtal_grid > 0.4) {
ev_calc(&setup2, NULL);
} else {
ev_calc(&setup1, NULL);
ev_calc(&setup2, &setup1);
}
ev_calc(&setup, &setup2);
}
/* -------------- calculate weighting potential */
if (setup.write_WP) {
setup1.write_WP = 0; // no need to save intermediate calculations
setup2.write_WP = 0;
if (setup.xtal_grid > 0.4) {
wp_calc(&setup2, NULL);
} else {
wp_calc(&setup1, NULL);
wp_calc(&setup2, &setup1);
}
wp_calc(&setup, &setup2);
}
/* -------------- calculate capacitance
1/2 * epsilon * integral(E^2) = 1/2 * C * V^2
so C = epsilon * integral(E^2) / V^2 V = 1 volt
*/
double esum, esum2, pi=3.14159, Epsilon=(8.85*16.0/1000.0); // permittivity of Ge in pF/mm
float E_r, E_z;
float grid = setup.xtal_grid;
int r, z, test;
int L = lrint(setup.xtal_length/grid)+1;
int R = lrint(setup.xtal_radius/grid)+1;
int LC = lrint(setup.pc_length/grid)+1;
int RC = lrint(setup.pc_radius/grid)+1;
if (setup.write_WP) {
esum = esum2 = test = 0;
for (z=1; z<L; z++) {
for (r=2; r<R; r++) {
E_r = setup.eps_dr[z][r]/16.0 * (setup.v[1][z][r] - setup.v[1][z][r+1])/(0.1*grid);
E_z = setup.eps_dz[z][r]/16.0 * (setup.v[1][z][r] - setup.v[1][z+1][r])/(0.1*grid);
esum += (E_r*E_r + E_z*E_z) * (double) (r-1);
if ((r == RC && z <= LC) || (r <= RC && z == LC) ||
(r == RC+1 && z <= LC+1) || (r <= RC+1 && z == LC+1)) { // average over two different surfaces
if (setup.point_type[z+1][r+1] == PC) test = 1;
esum2 += 0.5 * sqrt(E_r*E_r + E_z*E_z) * (double) (r-1); // 0.5 since averaging over 2 surfaces
}
}
}
esum *= 2.0 * pi * 0.01 * Epsilon * pow(grid, 3.0);
// Epsilon is in pF/mm
// 0.01 converts (V/cm)^2 to (V/mm)^2, pow() converts to grid^3 to mm3
esum2 *= 2.0 * pi * 0.1 * Epsilon * pow(grid, 2.0);
// 0.1 converts (V/cm) to (V/mm), grid^2 to mm2
printf(" >> Calculated capacitance at %.0f V: %.3lf pF\n", BV, esum);
if (!test)
printf(" >> Alternative calculation of capacitance: %.3lf pF\n", esum2);
}
/* -------------- estimate depletion voltage */
double min = BV, min2 = BV, dV, dW, testv;
int vminr=0, vminz=0;
int dz[4] = {1, -1, 0, 0}, dr[4] = {0, 0, 1, -1};
if (setup.write_WP) {
if (setup.fully_depleted) {
// find minimum potential
for (z=1; z<LC+2; z++) {
for (r=1; r<RC+2; r++) {
if (setup.vsave[z][r] > 0 &&
min > setup.vsave[z][r] / (1.0 - setup.v[1][z][r])) {
min = setup.vsave[z][r] / (1.0 - setup.v[1][z][r]);
}
}
}
/* check for bubble depletion / pinch-off by seeing how much the bias
must be reduced for any pixel to be in a local potential minimum */
for (z=LC+2; z<L-2; z++) {
for (r=1; r<R-2; r++) {
if (setup.point_type[z][r] == INSIDE && setup.v[1][z][r] > 0.0001) {
testv = -1;
for (i=0; i<4; i++) {
if (r==1 && i==2) break; // do not check dr for r=1 (=0.0)
dV = setup.vsave[z+dz[i]][r+dr[i]] - setup.vsave[z][r]; // potential
dW = setup.v[1][z+dz[i]][r+dr[i]] - setup.v[1][z][r]; // WP
if (dW*grid > 0.00001 && dV < 0 && testv < -dV/dW) testv = -dV/dW;
}
if (testv >= 0 && min2 > testv) {
min2 = testv;
vminr = r; vminz = z;
}
}
}
}
if (min2 < min) {
printf("Estimated pinch-off voltage = %.0f V\n", BV - min);
printf(" min2 = %.1f at (r,z) = (%.1f, %.1f), so\n",
min2, (vminr-1)*grid, (vminz-1)*grid);
printf(" Full depletion (max pinch-off voltage) = %.0f\n", BV - min2);
min = min2;
} else {
printf("Estimated depletion voltage = %.0f V\n", BV - min);
}
}
printf("Minimum bulk field = %.2f V/cm at (r,z) = (%.1f, %.1f) mm\n\n",
setup.Emin, setup.rmin, setup.zmin);
}
#ifdef EMIN_OVERBIAS
// calculate a new minimum electric field at a specified bias above depletion (usually 500 V)
if (min > 0) {
double db = EMIN_OVERBIAS - min;
int k = 3.0/grid;
float E, ez, er, r, z;
// adjust potential
for (j = 1; j < R; j++) {
for (i = 1; i < L; i++) {
setup.vsave[i][j] -= db * setup.v[1][i][j];
}
}
setup.Emin = 99999.9;
setup.rmin = setup.zmin = 999.9;
/* calculate new field */
for (j = 1; j < R-k-1; j++) {
r = (j-1) * grid;
for (i = k+1; i < L-k-1; i++) {
z = (i-1) * grid;
if (setup.point_type[i][j] != INSIDE ||
setup.point_type[i + k][j] != INSIDE || // point is at least 3 mm from a boundary
setup.point_type[i - k][j] != INSIDE ||
setup.point_type[i][j + k] != INSIDE ||
(j > k+1 && setup.point_type[i][j - k] != INSIDE)) continue;
// calc E
er = 0;
if (j>1) er = (setup.vsave[i][j-1] - setup.vsave[i][j+1])/(0.2*grid);
ez = (setup.vsave[i-1][j] - setup.vsave[i+1][j])/(0.2*grid);
E = sqrt(er*er + ez*ez);
/* check for minimum field inside bulk of detector */
if (E > 0.1 && E < setup.Emin) {
setup.Emin = E;
setup.rmin = r;
setup.zmin = z;
}
}
}
printf("Minimum bulk field at %.0fV (%dV overbias) is %.2f V/cm at (r,z) = (%.1f, %.1f) mm\n\n",
BV-min+EMIN_OVERBIAS, EMIN_OVERBIAS, setup.Emin, setup.rmin, setup.zmin);
}
#endif
return 0;
} /* main */
/* -------------------------------------- ev_calc ------------------- */
int ev_calc(MJD_Siggen_Setup *setup, MJD_Siggen_Setup *old_setup) {
int i, j;
float grid = setup->xtal_grid;
int L = lrint(setup->xtal_length/grid)+3;
int R = lrint(setup->xtal_radius/grid)+3;
if (!old_setup) {
printf("\n\n ---- starting EV calculation --- \n");
for (i = 1; i < L; i++) {
for (j = 1; j < R; j++) {
setup->v[0][i][j] = setup->v[1][i][j] = setup->xtal_HV/2.0;
}
}
}
if (old_setup) interpolate(setup, old_setup);
setup->fully_depleted = 1;
setup->bubble_volts = 0;
/* set boundary voltages */
for (i = 1; i < L; i++) {
for (j = 1; j < R; j++) {
if (setup->point_type[i][j] == HVC)
setup->v[0][i][j] = setup->v[1][i][j] = setup->xtal_HV;
if (setup->point_type[i][j] == PC)
setup->v[0][i][j] = setup->v[1][i][j] = 0.0;
}
}
if (!old_setup || !old_setup->fully_depleted) ev_relax_undep(setup);
else do_relax(setup, 1);
if (setup->write_field) write_ev(setup);
if (setup->fully_depleted) {
printf("Detector is fully depleted.\n");
/* save potential close to point contact, to use later when calculating depletion voltage */
for (i = 1; i < L; i++) {
for (j = 1; j < R; j++) {
setup->vsave[i][j] = fabs(setup->v[1][i][j]);
}
}
} else {
printf("Detector is not fully depleted.\n");
if (setup->bubble_volts > 0)
printf("Pinch-off bubble at %.1f V potential\n", setup->bubble_volts);
if (!old_setup) {
// write a little file that shows any undepleted voxels in the crystal
FILE *file = fopen("undepleted.txt", "w");
for (j = R-1; j > 0; j--) {
setup->undepleted[j][L-1] = '\0';
fprintf(file, "%s\n", setup->undepleted[j]+1);
}
fclose(file);
}
}
return 0;
} /* ev_calc */
/* -------------------------------------- wp_calc ------------------- */
int wp_calc(MJD_Siggen_Setup *setup, MJD_Siggen_Setup *old_setup) {
int i, j, pinched_off = 0;
float grid = setup->xtal_grid;
int L = lrint(setup->xtal_length/grid)+3;
int R = lrint(setup->xtal_radius/grid)+3;
if (!old_setup) {
printf("\n\n ---- starting WP calculation --- \n");
for (i = 1; i < L; i++) {
for (j = 1; j < R; j++) {
setup->v[0][i][j] = setup->v[1][i][j] = 0.01;
}
}
}
if (old_setup) interpolate(setup, old_setup);
/* set boundary voltages */
for (i = 1; i < L; i++) {
for (j = 1; j < R; j++) {
if (setup->point_type[i][j] == HVC)
setup->v[0][i][j] = setup->v[1][i][j] = 0.0;
else if (setup->point_type[i][j] == PC)
setup->v[0][i][j] = setup->v[1][i][j] = 1.0;
else if (setup->undepleted[j][i] == '*') {
setup->point_type[i][j] = PC;
setup->v[0][i][j] = setup->v[1][i][j] = 1.0;
} else if (setup->undepleted[j][i] == 'B') {
setup->point_type[i][j] = PINCHOFF;
pinched_off = 1;
}
}
}
if (pinched_off) wp_relax_undep(setup);
else do_relax(setup, 0);
if (setup->write_WP) write_wp(setup);
return 0;
} /* wp_calc */
/* -------------------------------------- report_config ------------------- */
int report_config(FILE *fp_out, char *config_file_name) {
char *c, line[256];
FILE *file;
fprintf(fp_out, "# Config file: %s\n", config_file_name);
if (!(file = fopen(config_file_name, "r"))) return 1;
while (fgets(line, sizeof(line), file)) {
if (strlen(line) < 3 || *line == ' ' || *line == '\t' || *line == '#') continue;
if ((c = strchr(line, '#')) || (c = strchr(line, '\n'))) *c = '\0';
fprintf(fp_out, "# %s\n", line);
}
fclose(file);
return 0;
} /* report_config */
/* -------------------------------------- write_ev ------------------- */
int write_ev(MJD_Siggen_Setup *setup) {
int i, j, new=1;
float grid = setup->xtal_grid;
//int L = setup->xtal_length/grid + 2.99;
//int R = setup->xtal_radius/grid + 2.99;
int L = lrint(setup->xtal_length/grid)+2;
int R = lrint(setup->xtal_radius/grid)+2;
float r, z, E;
FILE *file;
double ***v = setup->v;
cyl_pt **e;
setup->Emin = 99999.9;
setup->rmin = setup->zmin = 999.9;
if (setup->impurity_z0 > 0) {
// swap voltages back to negative for n-type material
for (i=1; i<L; i++) {
for (j=1; j<R; j++) {
setup->v[new][i][j] = -setup->v[new][i][j];
}
}
}
/* write potential and field to output file */
if (!(file = fopen(setup->field_name, "w"))) {
printf("ERROR: Cannot open file %s for electric field...\n", setup->field_name);
return 1;
} else {
printf("Writing electric field data to file %s\n", setup->field_name);
}
/* copy configuration parameters to output file */
report_config(file, setup->config_file_name);
fprintf(file, "#\n# HV bias in fieldgen: %.1f V\n", setup->xtal_HV);
if (setup->fully_depleted) {
fprintf(file, "# Detector is fully depleted.\n");
} else {
fprintf(file, "# Detector is not fully depleted.\n");
if (setup->bubble_volts > 0.0f)
fprintf(file, "# Pinch-off bubble at %.0f V potential\n", setup->bubble_volts);
}
if ((e = (cyl_pt **) malloc(R*sizeof(*e))) == NULL) {
printf("ERROR: Malloc failed\n");
fclose(file);
return 1;
}
for (i = 0; i < R; i++){
if ((e[i] = (cyl_pt *) calloc(L, sizeof(*e[i]))) == NULL) {
printf("ERROR: Calloc failed\n");
fclose(file);
return 1;
}
}
for (j = 1; j < R; j++) {
r = (j-1) * grid;
for (i = 1; i < L; i++) {
z = (i-1) * grid;
// calc E in r-direction
if (j == 1) { // r = 0; symmetry implies E_r = 0
e[j][i].r = 0;
} else if (setup->point_type[i][j] == CONTACT_EDGE) {
e[j][i].r = ((v[new][i][j] - v[new][i][j+1])*setup->dr[1][i][j] +
(v[new][i][j-1] - v[new][i][j])*setup->dr[0][i][j]) / (0.2*grid);
} else if (setup->point_type[i][j] < INSIDE &&
setup->point_type[i][j-1] == CONTACT_EDGE) {
e[j][i].r = (v[new][i][j-1] - v[new][i][j]) * setup->dr[1][i][j-1] / ( 0.1*grid) ;
} else if (setup->point_type[i][j] < INSIDE &&
setup->point_type[i][j+1] == CONTACT_EDGE) {
e[j][i].r = (v[new][i][j] - v[new][i][j+1]) * setup->dr[0][i][j+1] / ( 0.1*grid) ;
} else if (j == R-1) {
e[j][i].r = (v[new][i][j-1] - v[new][i][j])/(0.1*grid);
} else {
e[j][i].r = (v[new][i][j-1] - v[new][i][j+1])/(0.2*grid);
}
// calc E in z-direction
if (setup->point_type[i][j] == CONTACT_EDGE) {
e[j][i].z = ((v[new][i][j] - v[new][i+1][j])*setup->dz[1][i][j] +
(v[new][i-1][j] - v[new][i][j])*setup->dz[0][i][j]) / (0.2*grid);
} else if (setup->point_type[i][j] < INSIDE &&
setup->point_type[i-1][j] == CONTACT_EDGE) {
e[j][i].z = (v[new][i-1][j] - v[new][i][j]) * setup->dz[1][i-1][j] / ( 0.1*grid) ;
} else if (setup->point_type[i][j] < INSIDE &&
setup->point_type[i+1][j] == CONTACT_EDGE) {
e[j][i].z = (v[new][i][j] - v[new][i+1][j]) * setup->dz[0][i+1][j] / ( 0.1*grid) ;
} else if (i == 1) {
e[j][i].z = (v[new][i][j] - v[new][i+1][j])/(0.1*grid);
} else if (i == L-1) {
e[j][i].z = (v[new][i-1][j] - v[new][i][j])/(0.1*grid);
} else {
e[j][i].z = (v[new][i-1][j] - v[new][i+1][j])/(0.2*grid);
}
/* temporarily store E in e[j][i].phi */
E = e[j][i].phi = sqrt(e[j][i].r*e[j][i].r + e[j][i].z*e[j][i].z);
/* check for minimum field inside bulk of detector */
int k = 3.0/grid;
if (E > 0.1 && E < setup->Emin &&
i > k+1 && j < R-k-1 && i < L-k-1 &&
setup->point_type[i][j] == INSIDE &&
setup->point_type[i + k][j] == INSIDE && // point is at least 3 mm from a boundary
setup->point_type[i - k][j] == INSIDE &&
setup->point_type[i][j + k] == INSIDE &&
(j < k+1 || setup->point_type[i][j - k] == INSIDE)) {
setup->Emin = E;
setup->rmin = r;
setup->zmin = z;
}
}
}
if (strstr(setup->field_name, "unf")) {
fprintf(file, "#\n## start of unformatted data\n");
i = R-1; j = L-1;
fwrite(&i, sizeof(int), 1, file);
fwrite(&j, sizeof(int), 1, file);
for (i = 1; i < R; i++) {
for (j = 1; j < L; j++) e[i][j].phi = 0;
if (fwrite(&e[i][1], sizeof(cyl_pt), L-1, file) != L-1) {
printf("ERROR while writing %s\n", setup->field_name);
}
}
} else {
fprintf(file, "#\n## r (mm), z (mm), V (V), E (V/cm), E_r (V/cm), E_z (V/cm)\n");
for (j = 1; j < R; j++) {
r = (j-1) * grid;
for (i = 1; i < L; i++) {
z = (i-1) * grid;
E = e[j][i].phi;
fprintf(file, "%7.2f %7.2f %7.1f %7.1f %7.1f %7.1f\n",
r, z, v[new][i][j], E, e[j][i].r, e[j][i].z);
}
fprintf(file, "\n");
}
}
fclose(file);
for (i = 0; i < R; i++) free(e[i]);
free(e);
if (!setup->write_WP)
printf("\n Minimum bulk field = %.2f V/cm at (r,z) = (%.1f, %.1f) mm\n\n",
setup->Emin, setup->rmin, setup->zmin);
if (0) { /* write point_type to output file */
file = fopen("fields/point_type.dat", "w");
for (j = 1; j < R; j++) {
for (i = 1; i < L; i++)
fprintf(file, "%7.2f %7.2f %2d\n",
(j-1)*grid, (i-1)*grid, setup->point_type[i][j]);
fprintf(file, "\n");
}
fclose(file);
}
return 0;
} /* write_ev */
/* -------------------------------------- write_wp ------------------- */
int write_wp(MJD_Siggen_Setup *setup) {
int i, j, new=1;;
float grid = setup->xtal_grid;
//int L = setup->xtal_length/grid + 2.99;
//int R = setup->xtal_radius/grid + 2.99;
int L = lrint(setup->xtal_length/grid)+2;
int R = lrint(setup->xtal_radius/grid)+2;
float r, z, w;
FILE *file;
if (!(file = fopen(setup->wp_name, "w"))) {
printf("ERROR: Cannot open file %s for weighting potential...\n", setup->wp_name);
return 1;
} else {
printf("Writing weighting potential to file %s\n\n", setup->wp_name);
}
/* copy configuration parameters to output file */
report_config(file, setup->config_file_name);
fprintf(file, "#\n# HV bias in fieldgen: %.1f V\n", setup->xtal_HV);
if (setup->fully_depleted) {
fprintf(file, "# Detector is fully depleted.\n");
} else {
fprintf(file, "# Detector is not fully depleted.\n");
if (setup->bubble_volts > 0.0f)
fprintf(file, "# Pinch-off bubble at %.0f V potential\n", setup->bubble_volts);
}
if (strstr(setup->field_name, "unf")) {
fprintf(file, "#\n## start of unformatted data\n");
i = R-1; j = L-1;
fwrite(&i, sizeof(int), 1, file);
fwrite(&j, sizeof(int), 1, file);
for (i = 1; i < R; i++) {
for (j = 1; j < L; j++) {
w = setup->v[new][j][i];
fwrite(&w, sizeof(float), 1, file);
}
}
} else {
fprintf(file, "#\n## r (mm), z (mm), WP\n");
for (j = 1; j < R; j++) {
r = (j-1) * grid;
for (i = 1; i < L; i++) {
z = (i-1) * grid;
fprintf(file, "%7.2f %7.2f %12.6e\n", r, z, setup->v[new][i][j]);
}
fprintf(file, "\n");
}
}
fclose(file);
return 0;
} /* write_wp */
/* -------------------------------------- dist_from_contact ------------------- */
float dist_from_contact(cyl_pt pt, cyl_pt delta, MJD_Siggen_Setup *setup) {
float factor = 1, d = 0.5;
cyl_pt test;
int n;
for (n=0; n<7; n++) { // 7 steps => 1/128 precision
test.r = pt.r + factor * delta.r;
test.z = pt.z + factor * delta.z;
if (outside_detector_cyl(test, setup)) {
factor -= d;
} else {
if (n == 0) return -1.0;
factor += d;
}
d /= 2.0;
}
return factor;
} /* dist_from_contact */
/* -------------------------------------- grid_init ------------------- */
#define SQ(x) ((x)*(x))
int grid_init(MJD_Siggen_Setup *setup) {
float grid = setup->xtal_grid;
int L = lrint(setup->xtal_length/grid)+3;
int R = lrint(setup->xtal_radius/grid)+3;
int i, j;
float r, z;
/* first malloc arrays in setup */
if ((setup->impurity = malloc(L * sizeof(*setup->impurity))) == NULL ||
(setup->eps = malloc(L * sizeof(*setup->eps))) == NULL ||
(setup->eps_dr = malloc(L * sizeof(*setup->eps_dr))) == NULL ||
(setup->eps_dz = malloc(L * sizeof(*setup->eps_dz))) == NULL ||
(setup->v[0] = malloc(L * sizeof(*setup->v[0]))) == NULL ||
(setup->v[1] = malloc(L * sizeof(*setup->v[1]))) == NULL ||
(setup->dr[0] = malloc(L * sizeof(*setup->dr[0]))) == NULL ||
(setup->dr[1] = malloc(L * sizeof(*setup->dr[1]))) == NULL ||
(setup->dz[0] = malloc(L * sizeof(*setup->dz[0]))) == NULL ||
(setup->dz[1] = malloc(L * sizeof(*setup->dz[1]))) == NULL ||
(setup->undepleted = malloc(R * sizeof(*setup->undepleted))) == NULL ||
(setup->s1 = malloc(R * sizeof(*setup->s1))) == NULL ||
(setup->s2 = malloc(R * sizeof(*setup->s2))) == NULL ||
(setup->vsave = malloc(L * sizeof(*setup->vsave))) == NULL ||
(setup->point_type = malloc(L * sizeof(*setup->point_type))) == NULL) {
printf("malloc failed\n");
return -1;
}
/* start from i=1 so that i=0 can be used for reflection symmetry around r=0 or z=0 */
for (i = 1; i < L; i++) {
if ((setup->impurity[i] = malloc(R * sizeof(**setup->impurity))) == NULL ||
(setup->v[0][i] = malloc(R * sizeof(**setup->v[0]))) == NULL ||
(setup->v[1][i] = malloc(R * sizeof(**setup->v[1]))) == NULL ||
(setup->dr[0][i] = malloc(R * sizeof(**setup->dr[0]))) == NULL ||
(setup->dr[1][i] = malloc(R * sizeof(**setup->dr[1]))) == NULL ||
(setup->dz[0][i] = malloc(R * sizeof(**setup->dz[0]))) == NULL ||
(setup->dz[1][i] = malloc(R * sizeof(**setup->dz[1]))) == NULL ||
(setup->vsave[i] = malloc(R * sizeof(**setup->vsave))) == NULL ||
(setup->point_type[i] = malloc(R * sizeof(**setup->point_type))) == NULL) {
printf("malloc failed\n");
return -1;
}
}
for (i = 1; i < L; i++) {
if ((setup->eps[i] = malloc(R * sizeof(**setup->eps))) == NULL ||
(setup->eps_dr[i] = malloc(R * sizeof(**setup->eps_dr))) == NULL ||
(setup->eps_dz[i] = malloc(R * sizeof(**setup->eps_dz))) == NULL) {
printf("malloc failed\n");
return -1;
}
for (j = 0; j < R; j++)
setup->eps[i][j] = setup->eps_dz[i][j] = setup->eps_dr[i][j] = 16.0;
}
for (j = 0; j < R; j++) {
if ((setup->undepleted[j] = malloc(L * sizeof(**setup->undepleted))) == NULL) {
printf("malloc failed\n");
return -1;
}
memset(setup->undepleted[j], ' ', L);
}
/* set up reflection symmetry around r=0 or z=0 */
setup->impurity[0] = malloc(R * sizeof(**setup->impurity));
setup->v[0][0] = setup->v[0][2];
setup->v[1][0] = setup->v[1][2];
setup->eps[0] = setup->eps[1];
setup->eps_dr[0] = setup->eps_dr[1];
setup->eps_dz[0] = setup->eps_dz[1];
setup->point_type[0] = setup->point_type[1];
/* ------------------------------------------------------------ */
/* weighting values for the relaxation alg. as a function of r
in the following we divide areas and volumes by pi
r_bin rmax A_top A_outside A_inside volume total_surf out/top tot/vol
0 1/2 1/4 1 0 1/4 1.5 4 6 << special case
1 3/2 2 3 1 2 8 3/2 4
2 5/2 4 5 3 4 16 5/4 4
3 7/2 6 7 5 6 24 7/6 4
r r+0.5 2r 2r+1 2r-1 2r 8r (2r+1)/2r 4
= 1+0.5/r
*/
setup->s1[1] = 4.0;
setup->s2[1] = 0.0;
for (i=2; i<R; i++) {
setup->s1[i] = 1.0 + 0.5 / (double) (i-1); // for r+1
setup->s2[i] = 1.0 - 0.5 / (double) (i-1); // for r-1
}
setup->s2[1] = setup->s1[1]; // special case for reflection symm at r=0
for (i = 1; i < L; i++) {
for (j = 0; j < R; j++) {
setup->dr[0][i][j] = setup->s2[j]; // for r-1
setup->dr[1][i][j] = setup->s1[j]; // for r+1
setup->dz[0][i][j] = 1; // for z-1
setup->dz[1][i][j] = 1; // for z+1
}
}
/* set up pixel point types for boundary conditions etc */
float d, g = 0.05 * grid, lith = setup->Li_thickness;
cyl_pt pt, pt1, pt2, pt3, pt4;
setup->rmax = setup->xtal_radius - lith;
setup->zmax = setup->xtal_length - lith;
setup->hole_radius += lith;
setup->hole_bullet_radius += lith;
setup->bottom_taper_length += 0.71*lith; // add top tapers?
for (i = 1; i < L; i++) {
pt.z = pt3.z = pt4.z = (i-1) * grid;
pt1.z = pt.z + g;
pt2.z = pt.z - g;
for (j = 1; j < R; j++) {
pt.r = pt1.r = pt2.r = (j-1) * grid;
pt3.r = pt.r + g;
pt4.r = pt.r - g;
setup->point_type[i][j] = INSIDE;
/* see if pixel is ouside (or very nearly outside) the detector bulk */
if (i == 1 || (pt.r >= setup->wrap_around_radius && pt.z - g < lith) ||
outside_detector_cyl(pt1, setup) || outside_detector_cyl(pt2, setup) ||
outside_detector_cyl(pt3, setup) || outside_detector_cyl(pt4, setup)) {
/* check for inside ditch
boundary condition at Ge-vacuum interface:
epsilon0 * E_vac = espilon_Ge * E_Ge */
if (setup->ditch_depth > 0 && pt.z < setup->ditch_depth + grid &&
pt.r <= setup->wrap_around_radius &&
pt.r >= setup->wrap_around_radius - setup->ditch_thickness) {
setup->point_type[i][j] = DITCH;
setup->eps[i][j] = setup->eps_dz[i][j] = setup->eps_dr[i][j] = 1.0;
/* check for inside (point) contact */
} else if (pt.z < setup->pc_length + g && pt.r < setup->pc_radius+g) {
setup->point_type[i][j] = PC;
/* check for passivated area */
} else if (i == 1 && pt.r < setup->wrap_around_radius && // BEGE/ICPC
pt.r < setup->rmax - setup->bottom_taper_length) { // PPC
setup->point_type[i][j] = PASSIVE;
/* only remaining surface is HV contact */
} else {
setup->point_type[i][j] = HVC;
}
}
}
}
/* find the pixels next to the contact surfaces */
cyl_pt dp1, dp2, dp3, dp4;
dp1.z = dp3.r = grid;
dp2.z = dp4.r = -grid;
dp1.r = dp2.r = dp3.z = dp4.z = 0;
for (i = 2; i < L-1; i++) {
pt.z = (i-1) * grid;
for (j = 1; j < R; j++) {
pt.r = (j-1) * grid;
if (setup->point_type[i][j] == INSIDE &&
(setup->point_type[i+1][j] < INSIDE || setup->point_type[i-1][j] < INSIDE ||
setup->point_type[i][j+1] < INSIDE || (j > 1 && setup->point_type[i][j-1] < INSIDE))) {
setup->point_type[i][j] = CONTACT_EDGE;
/* find distance to contact surface */
if (setup->point_type[i+1][j] < INSIDE && (d = dist_from_contact(pt, dp1, setup)) > 0)
setup->dz[1][i][j] = 1.0/d;
if (setup->point_type[i-1][j] < INSIDE && (d = dist_from_contact(pt, dp2, setup)) > 0)
setup->dz[0][i][j] = 1.0/d;
else if (setup->point_type[i-1][j] < INSIDE &&
pt.r >= setup->wrap_around_radius && pt.z - grid < lith)
setup->dz[0][i][j] = grid/(pt.z - lith);
if (setup->point_type[i][j+1] < INSIDE && (d = dist_from_contact(pt, dp3, setup)) > 0)
setup->dr[1][i][j] = setup->s1[j] * 1.0/d;
if (j > 1 && setup->point_type[i][j-1] < INSIDE &&
(d = dist_from_contact(pt, dp4, setup)) > 0)
setup->dr[0][i][j] = setup->s2[j] * 1.0/d;
}
}
}
setup->hole_radius -= lith;
setup->hole_bullet_radius -= lith;
setup->bottom_taper_length -= 0.71*lith;
/* for pixels adjacent to the ditch, set point_type to DITCH_EDGE
and for z=0, set flag for passivated surface */
for (i = 1; i < L; i++) {
for (j = 1; j < R; j++) {
setup->eps_dr[i][j-1] = (setup->eps[i][j-1] + setup->eps[i][j]) / 2.0f;
setup->eps_dz[i-1][j] = (setup->eps[i-1][j] + setup->eps[i][j]) / 2.0f;
if (setup->point_type[i][j] == INSIDE &&
(setup->point_type[i-1][j] == DITCH ||
setup->point_type[i][j-1] == DITCH ||
setup->point_type[i][j+1] == DITCH)) setup->point_type[i][j] = DITCH_EDGE;
}
setup->eps_dr[i][0] = setup->eps_dr[i][1];
}
/* set up impurity array */
double *imp_z, imp_ra = 0, imp_rm = 1;
double e_over_E = 11.310; // e/epsilon; for 1 mm2, charge units 1e10 e/cm3, espilon = 16*epsilon0
/* malloc local array */
if ((imp_z = malloc(L * sizeof(*imp_z))) == NULL) {
printf("malloc failed\n");
return -1;
}
if (setup->rho_z_spe[0] == 0) {
for (i = 1; i < L; i++) {
z = (i-1) * grid;
imp_z[i] = e_over_E * grid*grid / 4.0 *
(setup->impurity_z0 +
setup->impurity_gradient * z * 0.1 +
setup->impurity_quadratic *
(1.0 - SQ(z - setup->xtal_length/2.0) / SQ(setup->xtal_length/2.0)));
}
} else if (setup->rho_z_spe[(int) setup->xtal_length] == 0) {
printf("Error: Impurity profile spectrum is too short? rho[xtal_len = %d] = 0\n", (int) setup->xtal_length);
return -1;
} else {
for (i = 1; i < L; i++)
imp_z[i] = e_over_E * grid*grid / 4.0 * setup->rho_z_spe[(int) ((i-1) * grid)];
}
for (j = 1; j < R; j++) {
r = (j-1) * grid;
if (setup->impurity_rpower > 0.1) {
imp_ra = setup->impurity_radial_add * e_over_E * grid*grid / 4.0 *
pow((double) r / setup->xtal_radius, setup->impurity_rpower);
imp_rm = 1.0 + (setup->impurity_radial_mult - 1.0f) *
pow((double) r / setup->xtal_radius, setup->impurity_rpower);
}
for (i = 1; i < L; i++) setup->impurity[i][j] = imp_z[i] * imp_rm + imp_ra;
if (setup->point_type[1][j] == PASSIVE) {
setup->impurity[1][j] += setup->impurity_surface * e_over_E * grid/4.0;
}
/* reduce charge volume for CONTACT_EDGE pixels */
for (i = 1; i < L; i++) {
if (setup->point_type[i][j] == CONTACT_EDGE) {
setup->impurity[i][j] /=
SQ(setup->dz[1][i][j]*setup->dz[0][i][j] * setup->dr[1][i][j]*setup->dr[0][i][j]);
}
}
}
/* free local and no-longer-needed arrays */
free(imp_z);
for (i = 1; i < L; i++) free(setup->eps[i]);
free(setup->eps);
return 0;
} /* grid_init */
#undef SQ
/* -------------------------------------- do_relax ------------------- */
int do_relax(MJD_Siggen_Setup *setup, int ev_calc) {
int old = 1, new = 0, iter, r, z;
float grid = setup->xtal_grid;
int L = lrint(setup->xtal_length/grid)+2;
int R = lrint(setup->xtal_radius/grid)+2;
double eps_sum, v_sum, dif, sum_dif=0, max_dif;
double ***v = setup->v, **eps_dr = setup->eps_dr, **eps_dz = setup->eps_dz;
double ***dr = setup->dr, ***dz = setup->dz;
double *s1 = setup->s1, *s2 = setup->s2;
double e_over_E = 11.310; // e/epsilon; for 1 mm2, charge units 1e10 e/cm3, espilon = 16*epsilon0
if (ev_calc) {
// for field calculation, save impurity value along passivated surface
for (r = 1; r < R; r++)
setup->impurity[0][r] = setup->impurity[1][r];
} else {
// for WP calculation, clear all impurity values
for (z = 0; z < L; z++) {
for (r = 1; r < R; r++) {
setup->impurity[z][r] = 0;
}
}
}
for (iter = 0; iter < setup->max_iterations; iter++) {
/* the following definition of the factor for over-relaxation improves convergence
time by a factor ~ 70-120 for a 2kg ICPC detector, grid = 0.1 mm
OR_fact increases with increasing volxel count (L*R)
and with increasing iteration number
0.997 is maximum asymptote for very large pixel count and iteration number */
double OR_fact;
if (ev_calc) OR_fact = (1.991 - 1500.0/(L*R));
else OR_fact = (1.992 - 1500.0/(L*R));
if (OR_fact < 1.4) OR_fact = 1.4;
// if (iter == 0) printf("OR_fact = %f\n", OR_fact);
if (iter < 1) OR_fact = 1.0;
old = new;
new = 1 - new;
sum_dif = 0;
max_dif = 0;
if (setup->vacuum_gap > 0) { // modify impurity value along passivated surface
for (r = 1; r < R; r++) // due to surface charge induced by capacitance
setup->impurity[1][r] = setup->impurity[0][r] -
v[old][1][r] * 5.52e-4 * e_over_E * grid / setup->vacuum_gap;
}