Glossary

A comprehensive glossary of terms used throughout the COMPASS (Cross-solver Optical Modeling Platform for Advanced Sensor Simulation) documentation. Terms are organized alphabetically for quick reference.

A

Term	Definition	Related Topics
Absorption Coefficient ( $α$ )	Rate at which light intensity decreases per unit distance as it propagates through an absorbing medium. Measured in cm $^{- 1}$ . Wavelength-dependent and critical for calculating photon absorption profiles in silicon.	Beer-Lambert Law, Extinction Coefficient
Angular Spectrum	Decomposition of an electromagnetic field into a superposition of plane waves propagating at different angles. Used in propagation and diffraction calculations.	Diffraction, Fourier Order

B

Term	Definition	Related Topics
BARL (Bottom Anti-Reflection Layer)	A thin dielectric film deposited at the silicon interface to reduce optical reflection and increase light transmission into the photodiode. Thickness and refractive index are tuned for target wavelengths.	Fresnel Equations, QE
Bayer Pattern / CFA	The most common color filter array arrangement placed over image sensor pixels, using a repeating pattern of red, green, and blue filters. Standard layouts include RGGB, GRBG, BGGR, and GBRG.	CFA, Crosstalk
Beer-Lambert Law	The exponential decay law describing how light intensity decreases as it passes through an absorbing medium: $I (z) = I_{0} e^{- α z}$ . Fundamental for computing photon absorption depth profiles in silicon.	Absorption Coefficient, QE
Bloch/Floquet Theorem	States that electromagnetic fields in periodic structures are themselves periodic, up to a phase shift determined by the wave vector. Forms the theoretical basis of RCWA.	Floquet Mode, RCWA, Periodic Boundary Conditions
BSI (Back-Side Illumination)	A sensor architecture in which light enters the silicon substrate from the back side (opposite the metal wiring layers), allowing higher fill factor and improved quantum efficiency compared to FSI.	FSI, QE, Pixel Pitch
Boundary Conditions (PML, PBC, Bloch)	Mathematical conditions applied at the edges of a finite simulation domain to model an infinite or semi-infinite physical space. PML absorbs outgoing waves, PBC enforces periodicity, and Bloch conditions handle oblique-incidence periodicity.	PML, Unit Cell, CRA

C

Term	Definition	Related Topics
CFA (Color Filter Array)	An array of patterned color filters (typically RGB) placed above the photodiodes to enable color imaging. Each pixel sees only one color; full-color images are reconstructed via demosaicing.	Bayer Pattern, Crosstalk
CIS (CMOS Image Sensor)	An image sensor fabricated using complementary metal-oxide-semiconductor (CMOS) technology, integrating photodiodes and readout circuits on the same chip.	BSI, FSI, Photodiode
CRA (Chief Ray Angle)	The angle between the chief (central) ray from the imaging lens and the normal to the sensor surface. Varies across the sensor and affects pixel optical design, especially microlens offset.	Microlens, Snell's Law
Courant Condition (CFL)	The Courant-Friedrichs-Lewy stability criterion that constrains the maximum allowable time step in FDTD simulations relative to the spatial grid size: $c Δ t \leq Δ x / \sqrt{d}$ (in $d$ dimensions).	FDTD, Yee Grid
Crosstalk	Unwanted leakage of light from one pixel into an adjacent pixel, degrading spatial resolution and color accuracy. Can be optical (through the stack) or electrical (carrier diffusion).	DTI, CFA, Pixel Pitch

D

Term	Definition	Related Topics
Deep Trench Isolation (DTI)	Narrow, oxide-filled trenches etched between adjacent pixels in a CMOS image sensor to physically block optical and electrical crosstalk.	Crosstalk, BSI
Diffraction	The bending and spreading of electromagnetic waves when they encounter obstacles or apertures with dimensions comparable to the wavelength. Governs light behavior in sub-wavelength pixel structures.	Diffraction Order, Grating Equation, Huygens' Principle
Diffraction Order	An integer index ( $m$ ) labeling the discrete directions into which light is diffracted by a periodic structure, as determined by the grating equation.	Grating Equation, RCWA, Fourier Order
Dispersion	The dependence of a material's optical properties (refractive index, extinction coefficient) on wavelength. Must be accounted for in broadband simulations.	Refractive Index, Extinction Coefficient, Permittivity

E

Term	Definition	Related Topics
Eigenvalue Problem	The core mathematical problem solved within each layer during RCWA computation. The eigenvalues and eigenvectors of the coupling matrix determine the propagating and evanescent modes in each layer.	RCWA, Fourier Order
Electromagnetic Wave	A self-propagating wave of coupled, oscillating electric (E) and magnetic (H) fields, governed by Maxwell's equations. Light is an electromagnetic wave in the optical frequency range.	Maxwell's Equations, Poynting Vector
Extinction Coefficient ( $k$ )	The imaginary part of the complex refractive index ( $\tilde{n} = n + i k$ ). Quantifies how strongly a material absorbs light at a given wavelength.	Refractive Index, Absorption Coefficient, Permittivity

F

Term	Definition	Related Topics
FDTD (Finite-Difference Time-Domain)	A numerical method that solves Maxwell's equations directly in the time domain on a discrete (Yee) grid. Naturally handles broadband and nonlinear problems. One of the two primary solvers in COMPASS.	Yee Grid, Courant Condition, PML
Floquet Mode	A characteristic field pattern in a periodic structure whose spatial profile repeats with a phase factor determined by the Bloch wave vector. Each diffraction order corresponds to a Floquet mode.	Bloch/Floquet Theorem, Diffraction Order
Fourier Order ( $N$ )	The number of Fourier harmonics retained in the RCWA plane-wave expansion. Higher $N$ increases accuracy but also computational cost (matrix size scales as $(2 N + 1)^{2}$ in 2D).	RCWA, Eigenvalue Problem, Gibbs Phenomenon
Fresnel Equations	Analytical expressions for the reflection and transmission coefficients of light at a planar interface between two media, as functions of incidence angle and polarization.	Snell's Law, TE/TM Polarization, S-Matrix
FSI (Front-Side Illumination)	The traditional sensor architecture in which light enters from the same side as the metal interconnect layers. Metal wiring partially blocks incoming light, limiting fill factor.	BSI, QE

Interactive Fresnel Calculator

Explore how reflection and transmission depend on refractive indices and incidence angle.

n₁ (incident medium)Air=1.0, Glass=1.5, Water=1.33

n₂ (transmitted medium)SiO₂=1.46, Si₃N₄=2.0, Si=3.5

Angle of incidence: 0.0°

R_s (TE)

4.00%

R_p (TM)

4.00%

R_avg (unpolarized)

4.00%

Brewster Angle

56.31°

G

Term	Definition	Related Topics
Gibbs Phenomenon	Oscillatory ringing artifacts that appear near sharp discontinuities in a truncated Fourier series representation. In RCWA, it can degrade convergence when representing abrupt material boundaries.	Fourier Order, Li's Factorization Rules, RCWA
Grating Equation	The fundamental relation $n_{t} \sin θ_{m} = n_{i} \sin θ_{i} + m λ / Λ$ linking the diffraction angles ( $θ_{m}$ ) to the grating period ( $Λ$ ), wavelength ( $λ$ ), and diffraction order ( $m$ ).	Diffraction Order, Diffraction, Snell's Law

H

Term	Definition	Related Topics
Huygens' Principle	The concept that every point on a wavefront acts as a source of secondary spherical wavelets, and the new wavefront is the envelope of these wavelets. Provides intuitive understanding of diffraction and propagation.	Diffraction, Angular Spectrum

L

Term	Definition	Related Topics
Li's Factorization Rules	Correct rules for computing Fourier coefficients of products of discontinuous functions, essential for achieving proper convergence in RCWA (especially for TM polarization). Introduced by Lifeng Li in 1996.	RCWA, Fourier Order, Gibbs Phenomenon

M

Term	Definition	Related Topics
Maxwell's Equations	The four fundamental partial differential equations governing all classical electromagnetic phenomena. Both RCWA and FDTD are numerical methods for solving these equations.	Electromagnetic Wave, RCWA, FDTD
Microlens	A small curved lens fabricated on top of each pixel to collect and focus incoming light onto the photodiode, improving quantum efficiency. Shape is often modeled as a superellipse.	Superellipse, CRA, QE

P

Term	Definition	Related Topics
Permittivity ( $ε$ )	A material property relating the electric field E to the electric displacement field D. Related to the complex refractive index by $ε = (n + i k)^{2}$ .	Refractive Index, Extinction Coefficient, Dispersion
Photodiode (PD)	The light-sensitive semiconductor region within each pixel that absorbs photons and generates electron-hole pairs (photocurrent). The fundamental detection element of a CMOS image sensor.	QE, BSI, Beer-Lambert Law
Pixel Pitch	The center-to-center distance between adjacent pixels, typically measured in micrometers. Determines spatial resolution and sets the periodic unit cell size in simulations.	Unit Cell, Microlens, Crosstalk
Planarization Layer	A dielectric layer deposited and polished to create a flat surface above the color filter array, providing a uniform substrate for microlens fabrication.	Microlens, CFA
PML (Perfectly Matched Layer)	An artificial absorbing boundary layer surrounding the simulation domain, designed to absorb outgoing electromagnetic waves with minimal reflection. Used in both FDTD and RCWA.	Boundary Conditions, FDTD
Poynting Vector	The vector $S = E \times H$ representing the directional energy flux (power per unit area) of an electromagnetic wave. Used to compute power flow and absorption in sensor structures.	Electromagnetic Wave, Maxwell's Equations, QE

Q

Term	Definition	Related Topics
QE (Quantum Efficiency)	The ratio of the number of charge carriers (electrons) collected by a photodiode to the number of incident photons. The primary figure of merit for image sensor pixel optical performance.	Photodiode, BSI, Absorption Coefficient

R

Term	Definition	Related Topics
RCWA (Rigorous Coupled-Wave Analysis)	A frequency-domain numerical method that solves Maxwell's equations in Fourier space for layered periodic structures. Decomposes fields into plane-wave harmonics and solves an eigenvalue problem in each layer. One of the two primary solvers in COMPASS.	Fourier Order, Eigenvalue Problem, S-Matrix
Refractive Index ( $n$ )	The ratio of the speed of light in vacuum to its phase velocity in a medium. The real part of the complex refractive index $\tilde{n} = n + i k$ .	Extinction Coefficient, Permittivity, Snell's Law

S

Term	Definition	Related Topics
S-Matrix (Scattering Matrix)	A numerically stable algorithm for cascading the transfer matrices of multiple layers, avoiding the exponential overflow problems of the direct transfer-matrix method. Essential for deep multilayer stacks.	RCWA, Fresnel Equations
Snell's Law	The relation $n_{1} \sin θ_{1} = n_{2} \sin θ_{2}$ governing the refraction angle of light crossing an interface between two media with different refractive indices.	Fresnel Equations, Refractive Index, Total Internal Reflection
Staircase Approximation	The technique of discretizing curved or sloped surfaces (e.g., microlenses) into a stack of flat, laterally uniform layers for RCWA computation. Accuracy improves with finer slicing.	RCWA, Superellipse, Microlens
Superellipse	A generalized ellipse described by $\| x / a \|^{p} + \| y / b \|^{p} = 1$ , used to parameterize microlens cross-sectional profiles. The exponent $p$ controls the shape from diamond ( $p < 2$ ) to rounded square ( $p > 2$ ).	Microlens, Staircase Approximation

T

Term	Definition	Related Topics
TE/TM Polarization	Two fundamental polarization states for light incident on a layered structure. TE (transverse electric) has the electric field parallel to the interface; TM (transverse magnetic) has the magnetic field parallel to the interface.	Fresnel Equations, Maxwell's Equations
Total Internal Reflection (TIR)	The complete reflection of light at an interface when the angle of incidence exceeds the critical angle $θ_{c} = \arcsin (n_{2} / n_{1})$ and $n_{1} > n_{2}$ . Relevant for light trapping in high-index silicon.	Snell's Law, Refractive Index

U

Term	Definition	Related Topics
Unit Cell	The smallest repeating unit of a periodic structure. In image sensor simulation, typically corresponds to one or a small group of pixels. Defines the simulation domain for RCWA.	Pixel Pitch, Bayer Pattern, Bloch/Floquet Theorem

Y

Term	Definition	Related Topics
Yee Grid/Cell	The staggered spatial grid introduced by Kane Yee (1966) in which E and H field components are offset by half a grid cell in both space and time. The standard discretization scheme for FDTD.	FDTD, Courant Condition

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