# B4: Optical spectroscopy¶

## Ellipsometry¶

Ellipsometry is an optical characterization method to describe optical properties of interfaces and thickness of films. The measurements are based on determining how the polarization state of light changes upon transmission and reflection. Interpretation is based on Fresnel equations and numerical models of the optical properties of the materials.

In the application definition we provide a minimum set of description elements allowing for a reproducible recording of ellipsometry measurements.

### Application Definitions¶

We created one application definition:

- NXellipsometry:
A general application definition for ellipsometry measurements, including complex systems up to variable angle spectroscopic ellipsometry.

### Base Classes Extended in Application Definitions¶

We use existent base classes in application definitions and add descriptors:

- NXinstrument
Added fields to add information that is important for an ellipsometry setup, such as the ellipsometer type, the light source, the type of the sample stage, or the angle(s) of incidence, as well as information on calibration, focussing probes, data correction etc.

- NXdetector
Added fields to describe spectroscopic detection with polarization (e.g. rotating analyzer).

- NXaperture
Added fields to define parameters that describe windows (e.g. windows of a UHV cryostat), such as the thickness and the orientation angle of the window, as well as reference data to calculate window effects.

- NXsample
Added fields to specify the sample and material properties, as well as the sample environment (e.g. refractive index of surrounding medium) and experimental conditions (e.g. temperature, pressure, pH value etc.).

## Dispersive Material¶

A dispersive material is a description for the optical dispersion of materials. This description may be used to store optical model data from an ellipsometric analysis (or any other technique) or to build a database of optical constants for optical properties of materials.

### Application Definition¶

- NXdispersive_material:
An application definition to describe the dispersive properties of a material. The material may be isotropic, uniaxial or biaxial. Hence, it may contain up to three dispersive functions or tables.

### Base Classes¶

There is a set of base classes for describing a dispersion.

- NXdispersion
This is an umbrella base class for a group of dispersion functions to describe the material. For a simple dispersion it may contain only on NXdispersion_function or NXdispersion_table entry. If it contains multiple entries the actual dispersion is the sum of all dispersion functions and tables. This allows for, e.g. splitting real and imaginary parts and describing them seperately or adding a dielectric background (e.g. Sellmeier model) to an oscillator model (e.g. Lorentz).

- NXdispersion_function
This dispersion is described by a function and its single and repeated parameter values. It follows a formula of the form

`eps = eps_inf + sum[A * lambda ** 2 / (lambda ** 2 - B ** 2)]`

(Sellmeier formula). See the formula grammar below for an ebnf grammar for this form.- NXdispersion_single_parameter
This denotes a parameter which is used outside the summed part of a dispersion function, e.g.

`eps_inf`

in the formula example above.- NXdispersion_repeated_parameter
This denotes arrays of repeated parameters which are used to build a sum of parameter values, e.g.

`A`

and`B`

are repeated parameters in the formula above.- NXdispersion_table
This describes a tabular dispersion where the dielectric function is an array versus wavelength or energy.

### Formula Grammar¶

Below you find a grammar to which the formula should adhere and which can be used to parse and
evaluate the dispersion function. The terms `single_param_name`

and `param_name`

should be
filled with the respective single and repeated params from the stored data.

```
?assignment: "eps" "=" kkr_expression -> eps
| "n" "=" kkr_expression -> n
?kkr_expression: expression
| "<kkr>" "+" "1j" "*" term -> kkr_term
?expression: term
| expression "+" term -> add
| expression "-" term -> sub
?term: factor
| term "*" factor -> mul
| term "/" factor -> div
?factor: power
| power "**" power -> power
?power: "(" expression ")"
| FUNC "(" expression ")" -> func
| "sum" "[" repeated_expression "]" -> sum_expr
| NAME -> single_param_name
| SIGNED_NUMBER -> number
| BUILTIN -> builtin
?repeated_expression: repeated_term
| repeated_expression "+" repeated_term -> add
| repeated_expression "-" repeated_term -> sub
?repeated_term: repeated_factor
| repeated_term "*" repeated_factor -> mul
| repeated_term "/" repeated_factor -> div
?repeated_factor: repeated_power
| repeated_power "**" repeated_power -> power
?repeated_power: "(" repeated_expression ")"
| FUNC "(" repeated_expression ")" -> func
| SIGNED_NUMBER -> number
| NAME -> param_name
| BUILTIN -> builtin
FUNC.1: "sin" | "cos" | "tan" | "sqrt" | "dawsn" | "ln" | "log" | "heaviside"
BUILTIN.1: "1j" | "pi" | "eps_0" | "hbar" | "h" | "c"
%import common.CNAME -> NAME
%import common.SIGNED_NUMBER
%import common.WS_INLINE
%ignore WS_INLINE
```