Hello,
I am simulating the effect of Ag nanoparticles (NPs) on light absorption in a Si solar cell structure using 2D FDTD in Lumerical. I am running two simulations — one reference (no NPs) and one with 12 Ag NPs of mixed diameters (100–400 nm) sitting on top of a SiO2/Si stack — and comparing the results.
My structure (bottom to top):
- Si layer: 8 µm
- SiO2 layer: 300 nm
- Ag NPs sitting on SiO2 surface (diameters: 100, 200, 300, 400 nm mixed)
- Air: 4 µm
My simulation settings:
- 2D FDTD
- Plane wave source, injection axis: y, direction: Backward (downward)
- Source position:
Air_y_max - 200e-9 (near top of Air) - Reflection monitor:
Air_y_max - 300e-9 (just below source) - Transmission monitor:
Si_y_max - 1e-6 (1 µm inside Si from top) - Boundary conditions: PML on all 4 sides
- Wavelength: 200–1000 nm
- Simulation time: 10000e-15 s
- Auto shutoff min: 1e-5
- Mesh accuracy: 2
- Material: Ag (Johnson and Christy), Si (Palik), SiO2 (Palik)
Post-processing:
`T = transmission("transmission");
R = transmission("reflection");
A = 1 - T - R;`Problem I am getting:
- Transmittance is negative (down to -0.55)
- Reflectance is negative (down to -0.9)
- Absorption (1-T-R) is greater than 1 (up to 2.5)
- T+R+A is not equal to 1 — it oscillates wildly
My questions:
- What is the correct sign convention for
transmission() function when using a Backward directed plane wave source? Should I use -transmission("transmission") or transmission("transmission")? - Is my reflection monitor placement correct — just below the source? Or should it be above the source?
- Is my transmission monitor placement correct — 1 µm inside Si from the top? Or should it be near the bottom of Si?
- Should I use Periodic boundary conditions on x instead of PML for a plane wave source?
- Is
auto shutoff min = 1e-5 sufficient for plasmonic Ag NP simulations or should it be tighter (1e-7)?
Any guidance would be very helpful. Thank you
And here is my code
clear;
####################################################
# COMBINED SCRIPT: Reference + AgNP in ONE code
# Run 1: Air + SiO2 + Si (no NPs)
# Run 2: Air + Ag NPs + SiO2 + Si
####################################################
# Layer thicknesses
Si_thickness = 8e-6;
SiO2_thickness = 300e-9;
Air_thickness = 4e-6;
# Wavelength
lambda_min = 200e-9;
lambda_max = 1000e-9;
# Mesh
mesh_accuracy = 2;
sim_time = 10000e-15;
# Cell size
cell_x = 6e-6;
# NP parameters
edge_gap = 100e-9;
# NP radii in random order (12 NPs)
np_r1 = 50e-9;
np_r2 = 100e-9;
np_r3 = 200e-9;
np_r4 = 50e-9;
np_r5 = 150e-9;
np_r6 = 100e-9;
np_r7 = 50e-9;
np_r8 = 200e-9;
np_r9 = 150e-9;
np_r10 = 100e-9;
np_r11 = 50e-9;
np_r12 = 150e-9;
# NP x positions
x1 = 0;
x2 = x1 + np_r1 + edge_gap + np_r2;
x3 = x2 + np_r2 + edge_gap + np_r3;
x4 = x3 + np_r3 + edge_gap + np_r4;
x5 = x4 + np_r4 + edge_gap + np_r5;
x6 = x5 + np_r5 + edge_gap + np_r6;
x7 = x6 + np_r6 + edge_gap + np_r7;
x8 = x7 + np_r7 + edge_gap + np_r8;
x9 = x8 + np_r8 + edge_gap + np_r9;
x10 = x9 + np_r9 + edge_gap + np_r10;
x11 = x10 + np_r10 + edge_gap + np_r11;
x12 = x11 + np_r11 + edge_gap + np_r12;
x_cen = (x1 + x12) / 2;
x1=x1-x_cen; x2=x2-x_cen; x3=x3-x_cen; x4=x4-x_cen;
x5=x5-x_cen; x6=x6-x_cen; x7=x7-x_cen; x8=x8-x_cen;
x9=x9-x_cen; x10=x10-x_cen; x11=x11-x_cen; x12=x12-x_cen;
# Y positions
Si_y_min = 0;
Si_y_max = Si_thickness;
SiO2_y_min = Si_y_max;
SiO2_y_max = SiO2_y_min + SiO2_thickness;
Air_y_min = SiO2_y_max;
Air_y_max = SiO2_y_max + Air_thickness;
r_max = 200e-9;
margin_y = 500e-9;
sim_y_min = Si_y_min – margin_y;
sim_y_max = Air_y_max + margin_y;
sim_y_center = (sim_y_min + sim_y_max) / 2;
sim_y_span = sim_y_max – sim_y_min;
source_y = Air_y_max – 200e-9;
refl_y = Air_y_max – 300e-9;
trans_y = Si_y_max – 1e-6;
####################################################
# LOOP: sim=1 (reference), sim=2 (with NPs)
####################################################
for (sim = 1:2) {
newproject;
############################################
# STRUCTURES (common)
############################################
addrect;
set(“name”, “Si_film”);
set(“material”, “Si (Silicon) – Palik”);
set(“x”, 0);
set(“x span”, cell_x);
set(“y min”, Si_y_min);
set(“y max”, Si_y_max);
addrect;
set(“name”, “SiO2_layer”);
set(“material”, “SiO2 (Glass) – Palik”);
set(“x”, 0);
set(“x span”, cell_x);
set(“y min”, SiO2_y_min);
set(“y max”, SiO2_y_max);
############################################
# ADD NPs ONLY FOR sim=2
############################################
if (sim == 2) {
addcircle;
set(“name”, “Ag_NP_01_d100”); set(“material”, “Ag (Silver) – Johnson and Christy”);
set(“x”, x1); set(“y”, SiO2_y_max + np_r1); set(“radius”, np_r1);
addcircle;
set(“name”, “Ag_NP_02_d200”); set(“material”, “Ag (Silver) – Johnson and Christy”);
set(“x”, x2); set(“y”, SiO2_y_max + np_r2); set(“radius”, np_r2);
addcircle;
set(“name”, “Ag_NP_03_d400”); set(“material”, “Ag (Silver) – Johnson and Christy”);
set(“x”, x3); set(“y”, SiO2_y_max + np_r3); set(“radius”, np_r3);
addcircle;
set(“name”, “Ag_NP_04_d100”); set(“material”, “Ag (Silver) – Johnson and Christy”);
set(“x”, x4); set(“y”, SiO2_y_max + np_r4); set(“radius”, np_r4);
addcircle;
set(“name”, “Ag_NP_05_d300”); set(“material”, “Ag (Silver) – Johnson and Christy”);
set(“x”, x5); set(“y”, SiO2_y_max + np_r5); set(“radius”, np_r5);
addcircle;
set(“name”, “Ag_NP_06_d200”); set(“material”, “Ag (Silver) – Johnson and Christy”);
set(“x”, x6); set(“y”, SiO2_y_max + np_r6); set(“radius”, np_r6);
addcircle;
set(“name”, “Ag_NP_07_d100”); set(“material”, “Ag (Silver) – Johnson and Christy”);
set(“x”, x7); set(“y”, SiO2_y_max + np_r7); set(“radius”, np_r7);
addcircle;
set(“name”, “Ag_NP_08_d400”); set(“material”, “Ag (Silver) – Johnson and Christy”);
set(“x”, x8); set(“y”, SiO2_y_max + np_r8); set(“radius”, np_r8);
addcircle;
set(“name”, “Ag_NP_09_d300”); set(“material”, “Ag (Silver) – Johnson and Christy”);
set(“x”, x9); set(“y”, SiO2_y_max + np_r9); set(“radius”, np_r9);
addcircle;
set(“name”, “Ag_NP_10_d200”); set(“material”, “Ag (Silver) – Johnson and Christy”);
set(“x”, x10); set(“y”, SiO2_y_max + np_r10); set(“radius”, np_r10);
addcircle;
set(“name”, “Ag_NP_11_d100”); set(“material”, “Ag (Silver) – Johnson and Christy”);
set(“x”, x11); set(“y”, SiO2_y_max + np_r11); set(“radius”, np_r11);
addcircle;
set(“name”, “Ag_NP_12_d300”); set(“material”, “Ag (Silver) – Johnson and Christy”);
set(“x”, x12); set(“y”, SiO2_y_max + np_r12); set(“radius”, np_r12);
}
############################################
# FDTD (2D)
############################################
addfdtd;
set(“dimension”, “2D”);
set(“x”, 0);
set(“x span”, cell_x);
set(“y”, sim_y_center);
set(“y span”, sim_y_span);
set(“x min bc”, “PML”);
set(“x max bc”, “PML”);
set(“y min bc”, “PML”);
set(“y max bc”, “PML”);
set(“mesh accuracy”, mesh_accuracy);
set(“simulation time”, sim_time);
set(“auto shutoff min”, 1e-5);
############################################
# SOURCE
############################################
addplane;
set(“name”, “source”);
set(“injection axis”, “y-axis”);
set(“direction”, “Backward”);
set(“x”, 0);
set(“x span”, cell_x);
set(“y”, source_y);
set(“wavelength start”, lambda_min);
set(“wavelength stop”, lambda_max);
############################################
# MONITORS
############################################
addpower;
set(“name”, “reflection”);
set(“monitor type”, “Linear X”);
set(“override global monitor settings”, 1);
set(“use source limits”, 1);
set(“frequency points”, 100);
set(“x”, 0);
set(“x span”, cell_x);
set(“y”, refl_y);
addpower;
set(“name”, “transmission”);
set(“monitor type”, “Linear X”);
set(“override global monitor settings”, 1);
set(“use source limits”, 1);
set(“frequency points”, 100);
set(“x”, 0);
set(“x span”, cell_x);
set(“y”, trans_y);
addprofile;
set(“name”, “field_xy”);
set(“override global monitor settings”, 1);
set(“use source limits”, 1);
set(“frequency points”, 10);
set(“x”, 0);
set(“x span”, cell_x);
set(“y”, sim_y_center);
set(“y span”, sim_y_span – 100e-9);
############################################
# MESH OVERRIDE
############################################
if (sim == 2) {
addmesh;
set(“name”, “mesh_NPs”);
set(“x”, 0);
set(“x span”, cell_x);
set(“y”, SiO2_y_max + r_max);
set(“y span”, 2*r_max + 40e-9);
set(“dx”, 10e-9);
set(“dy”, 10e-9);
}
addmesh;
set(“name”, “mesh_SiO2”);
set(“x”, 0);
set(“x span”, cell_x);
set(“y”, SiO2_y_min + SiO2_thickness/2);
set(“y span”, SiO2_thickness + 40e-9);
set(“dy”, 10e-9);
############################################
# SAVE AND RUN
############################################
if (sim == 1) {
save(“Combined_Reference.fsp”);
?””;
?”=== RUNNING SIMULATION 1: REFERENCE (no NPs) ===”;
} else {
save(“Combined_WithAgNP.fsp”);
?””;
?”=== RUNNING SIMULATION 2: WITH 12 Ag NPs ===”;
}
run;
}
?””;
?”=== BOTH SIMULATIONS COMPLETE ===”;
?”Open Combined_Reference.fsp and Combined_WithAgNP.fsp to view results.”;
also result post processing code
clear;
####################################################
# POST-PROCESSING SCRIPT
# Load Reference and AgNP simulation results
# Compute T, R, A and plot comparisons
####################################################
?”=== LOADING REFERENCE SIMULATION ===”;
load(“Combined_Reference.fsp”);
run;
f = getdata(“transmission”, “f”);
lam = c / f;
T_ref = transmission(“transmission”);
R_ref = transmission(“reflection”);
A_ref = 1 – T_ref – R_ref;
?”Reference loaded. T, R, A extracted.”;
####################################################
?”=== LOADING AgNP SIMULATION ===”;
load(“Combined_WithAgNP.fsp”);
run;
T_np = transmission(“transmission”);
R_np = transmission(“reflection”);
A_np = 1 – T_np – R_np;
?”AgNP loaded. T, R, A extracted.”;
####################################################
# COMPARISON PLOTS
####################################################
?””;
?”=== GENERATING COMPARISON PLOTS ===”;
# — Transmittance Comparison —
plot(lam*1e9, T_ref, T_np, “Wavelength (nm)”, “Transmittance”, “Transmittance Comparison”);
legend(“Reference (no NPs)”, “With Ag NPs”);
exportfigure(“Compare_Transmittance.png”, 800, 600);
# — Reflectance Comparison —
plot(lam*1e9, R_ref, R_np, “Wavelength (nm)”, “Reflectance”, “Reflectance Comparison”);
legend(“Reference (no NPs)”, “With Ag NPs”);
exportfigure(“Compare_Reflectance.png”, 800, 600);
# — Absorption Comparison —
plot(lam*1e9, A_ref, A_np, “Wavelength (nm)”, “Absorption (1-T-R)”, “Absorption Comparison”);
legend(“Reference (no NPs)”, “With Ag NPs”);
exportfigure(“Compare_Absorption.png”, 800, 600);
# — T+R+A = 1 Check (should be flat line at 1) —
plot(lam*1e9, T_ref+R_ref+A_ref, T_np+R_np+A_np, “Wavelength (nm)”, “T+R+A”, “Energy Conservation Check”);
legend(“Reference”, “With Ag NPs”);
exportfigure(“EnergyConservation_Check.png”, 800, 600);
# — Transmittance Enhancement (T_NP / T_ref) —
T_Enhancement = T_np / T_ref;
plot(lam*1e9, T_Enhancement, “Wavelength (nm)”, “T_NP / T_ref”, “Transmittance Enhancement”);
exportfigure(“Transmittance_Enhancement.png”, 800, 600);
# — Absorption Enhancement (A_NP / A_ref) —
A_Enhancement = A_np / A_ref;
plot(lam*1e9, A_Enhancement, “Wavelength (nm)”, “A_NP / A_ref”, “Absorption Enhancement”);
exportfigure(“Absorption_Enhancement.png”, 800, 600);
# — Absorption Difference (Delta A) —
Delta_A = A_np – A_ref;
plot(lam*1e9, Delta_A, “Wavelength (nm)”, “Delta A = A_NP – A_ref”, “Absorption Increase due to Ag NPs”);
exportfigure(“Absorption_Difference.png”, 800, 600);
# — Complete Comparison (T, R, A together) —
plot(lam*1e9, T_ref, T_np, R_ref, R_np, A_ref, A_np, “Wavelength (nm)”, “Value”, “Complete T R A Comparison”);
legend(“T (ref)”, “T (NP)”, “R (ref)”, “R (NP)”, “A (ref)”, “A (NP)”);
exportfigure(“Complete_Comparison.png”, 800, 600);
####################################################
# RESULTS SUMMARY
####################################################
?””;
?”=== RESULTS SUMMARY ===”;
?””;
?”— Transmittance —“;
?”Avg T (ref) : ” + num2str(mean(T_ref));
?”Avg T (NP) : ” + num2str(mean(T_np));
?”Avg T Enhancement : ” + num2str(mean(T_Enhancement));
?”Max T Enhancement : ” + num2str(max(T_Enhancement));
?”Min T Enhancement : ” + num2str(min(T_Enhancement));
?””;
?”— Reflectance —“;
?”Avg R (ref) : ” + num2str(mean(R_ref));
?”Avg R (NP) : ” + num2str(mean(R_np));
?””;
?”— Absorption (1-T-R) —“;
?”Avg A (ref) : ” + num2str(mean(A_ref));
?”Avg A (NP) : ” + num2str(mean(A_np));
?”Avg A Enhancement : ” + num2str(mean(A_Enhancement));
?”Max A Enhancement : ” + num2str(max(A_Enhancement));
?”Avg Delta A : ” + num2str(mean(Delta_A));
?”Max Delta A : ” + num2str(max(Delta_A));
?””;
?”=== ALL DONE! 8 plots saved ===”;
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