/ 
Physics-Ellipsometry-VASE-1.03
/ Physics::Ellipsometry::VASE::Materials

NAME

Physics::Ellipsometry::VASE::Materials - Load and interpolate tabulated optical constants

SYNOPSIS

use PDL;
use Physics::Ellipsometry::VASE::Materials qw(load_material
                                               interpolate_material);

# Load a Woollam .mat file (auto-detects eV↔nm)
my $si = load_material('Si_jaw.mat');

printf "Material : %s\n",   $si->{name};
printf "Points   : %d\n",   $si->{npts};
printf "Range    : %.1f – %.1f nm\n", $si->{wav_min}, $si->{wav_max};

# Interpolate onto the measurement wavelength grid
my $lambda = sequence(500) * 2 + 300;        # 300–1298 nm
my ($n_si, $k_si) = interpolate_material($si, $lambda);

# Build the complex refractive index for TMM
my $N_si = $n_si + i() * $k_si;

DESCRIPTION

In spectroscopic ellipsometry the optical model usually contains at least one material whose refractive index is not described by a simple parametric formula but is instead given as a table of measured values — for example, a crystalline silicon substrate or a metal reference layer. These are called point-by-point (PBP) optical constants.

Physics::Ellipsometry::VASE::Materials loads such tabulated data from disk and provides linear interpolation to an arbitrary wavelength grid, so the constants can be used directly by Physics::Ellipsometry::VASE::TMM or any model function.

When a file stores its spectral axis in electron-volts (eV) the module converts automatically to nanometres via

λ (nm) = 1239.842 / E (eV)

and reverses the data order if necessary to ensure wavelengths are ascending.

SUPPORTED FORMATS

Woollam .mat format

The standard format produced by WVASE® and CompleteEASE. The file has a three-line header followed by data columns:

silicon
eV
469
0.6199  3.939  0.0240
0.6250  3.941  0.0242
...
Line 1 — material name (free text)
Line 2 — spectral units: nm or eV
Line 3 — number of data points
Data — three whitespace-separated columns: wavelength (or energy), n, k

Generic 3-column format

A plain text file with three whitespace-separated columns (wavelength in nm, n, k). Comment lines beginning with # and blank lines are skipped. No header is required.

# wavelength(nm)  n       k
300.0              1.540   0.000
310.0              1.538   0.000
...

FUNCTIONS

load_material

my $mat = load_material($filepath);

Reads a tabulated optical-constants file and returns a hashref with:

name — material name (from header, or filename for generic files)
wavelength — PDL piddle of wavelengths in nm (ascending order)
n — PDL piddle of refractive index values
k — PDL piddle of extinction coefficient values
npts — number of data points
wav_min — shortest wavelength (nm)
wav_max — longest wavelength (nm)

The format (Woollam vs generic) is auto-detected. If the file stores data in eV the conversion to nm is performed automatically.

my $ta = load_material('ta_pbp.mat');
my $sio2 = load_material('SiO2_Palik.dat');

interpolate_material

my ($n, $k) = interpolate_material($material, $lambda_nm);

Linearly interpolates the tabulated n and k values in $material (as returned by "load_material") onto the wavelength grid $lambda_nm.

Important: the target wavelengths should lie within the range [wav_min, wav_max] of the loaded material. Values outside this range are extrapolated linearly, which may be inaccurate.

my $lambda = sequence(500) * 2 + 300;
my ($n, $k) = interpolate_material($ta, $lambda);

# Use in a TMM calculation
my $N_sub = $n + i() * $k;

TYPICAL WORKFLOW

use Physics::Ellipsometry::VASE::Materials qw(load_material
                                               interpolate_material);
use Physics::Ellipsometry::VASE::TMM qw(psi_delta);
use Physics::Ellipsometry::VASE::Dispersion qw(cauchy_nk);

# 1. Load substrate from a .mat file
my $sub = load_material('Si_jaw.mat');

# 2. Define measurement grid
my $lambda = sequence(400) * 2.5 + 300;
my $theta  = ones($lambda) * 70;

# 3. Interpolate substrate onto measurement grid
my ($n_sub, $k_sub) = interpolate_material($sub, $lambda);
my $N_sub = $n_sub + i() * $k_sub;

# 4. Film from a parametric model
my ($n_film, $k_film) = cauchy_nk($lambda, 1.46, 0.003, 0.0);
my $N_film = $n_film + i() * $k_film;

# 5. Ambient
my $N_air = ones($lambda) + i() * zeroes($lambda);

# 6. Calculate Psi/Delta
my ($psi, $delta) = psi_delta($lambda, $theta,
    [$N_air, $N_film, $N_sub], [100.0]);

SEE ALSO

Physics::Ellipsometry::VASE, Physics::Ellipsometry::VASE::TMM, Physics::Ellipsometry::VASE::Dispersion