Spectral analyzer

1spectroscopic ellipsometerApplicable to material range:

Semiconductors, dielectrics, polymers, organic compounds, metals, multilayer materials, etc

IIspectroscopic ellipsometerTechnical Specifications:

IIIspectroscopic ellipsometerRelated fields and industries:

Semiconductor, communication, data storage, optical coating, flat panel display, scientific research, biology, medicine

4spectroscopic ellipsometerDetection scope:

1. In earlier years, the working wavelength of ellipsometers was a single wavelength or a few independent wavelengths, typically using a monochromatic light source generated by filtering strong spectral light such as lasers or arcs. Most ellipsometers nowadays operate at multiple wavelengths over a wide range of wavelengths (typically several hundred wavelengths, close to continuous). Compared with single wavelength ellipsometers, multi wavelength spectroscopic ellipsometers have the following advantages: they can enhance multi-layer detection capabilities and test the refractive index of substances to different wavelengths of light waves.

2. The spectral range of the spectroscopic ellipsometer is selectable from 142nm in deep ultraviolet to 33 µ m in infrared. The selection of spectral range depends on factors such as the properties of the tested material, film thickness, and the spectral range of interest. For example, doping concentration has a significant impact on the infrared optical properties of materials, so an ellipsometer capable of measuring the infrared band is needed; The thickness measurement of a thin film requires light energy to penetrate the film, reach the substrate, and then be detected by a detector. Therefore, it is necessary to select a transparent or partially transparent spectral range of the material to be tested; Choosing longer wavelengths is more advantageous for measuring thick films.

5Working principle of spectroscopic ellipsometer：

1. The basic optical and physical structure of an ellipsometer is provided. Given the polarization state of the incident light, polarized light is reflected on the surface of the sample, and the polarization state (amplitude and phase) of the reflected light is measured to calculate or fit the properties of the material.

2. The electric field of the incident beam (linearly polarized light) can be decomposed into vector elements in two perpendicular planes. The P plane contains incident and outgoing light, while the s plane is perpendicular to this plane. Similarly, reflected or transmitted light is a typical elliptically polarized light, hence the instrument is called an ellipsometer. A detailed description of polarized light can be found in other literature. In physics, the change in polarization state can be represented by the complex number ρ:

3. Among them, ψ and ∆ respectively describe amplitude and phase. The Fresnel reflection coefficients on the P plane and s plane are represented by complex functions rp and rs, respectively. The mathematical expressions for rp and rs can be derived using Maxwell's equations for electromagnetic radiation at different material boundaries.

4Where ϕ 0 is the incident angle and ϕ 1 is the refractive angle. The incident angle is the angle between the incident beam and the normal of the surface to be studied. The incidence angle range of an ellipsometer is usually 45 ° to 90 °. This can provide * sensitivity when detecting material properties. The refractive index of each layer of medium can be represented by the following complex function

5Usually n is called refractive index, and k is called extinction coefficient. These two coefficients are used to describe how incident light interacts with the material. They are called optical constants. In fact, although this value varies with parameters such as wavelength and temperature. When the surrounding medium of the contemporary sample is air or vacuum, the value of N0 is usually taken as 1.000.

6. Typically, ellipsometers are used to measure the value of ρ as a function of wavelength and incident angle (often expressed in terms of ψ and ∆ or related quantities). After a measurement is completed, the data obtained is used to analyze the optical constants, film thickness, and other parameter values of interest. As shown in the figure below, the analysis process involves many steps.

7A model can be used to describe the measured sample, which includes multiple planes of each material, including the substrate. Within the measured spectral range, describe each layer using thickness and optical constants (n and k), and make initial assumptions for unknown parameters. The simplest model is a uniform bulk solid with no roughness or oxidation on the surface. In this case, the complex function of refractive index is directly represented.However, in practical applications, most materials have rough or oxidized surfaces, so the above function often cannot be applied.

8. Next, use the model to generate Gen. Data, generate Psi and Detla data based on the parameters determined by the model, and compare them with the measured data. Continuously adjust the parameters in the model to make the generated data as accurate as possible compared to the measured data. Even if there is only one thin film on a large substrate, the algebraic equation description of this model is theoretically very complex. Therefore, it is usually not possible to provide a mathematical description for optical constants, thickness, etc. similar to the equation above. Such problems are commonly referred to as inversion problems.

9. The most common method for solving ellipsometer inversion problems is to apply the Levenberg Marquardt algorithm in attenuation analysis. Compare the experimental data with the data generated by the model using a comparative equation. Usually, the mean square error is defined as:

10In some cases, the smallest MSE may result in non physical or non * outcomes. However, by adding restrictions or judgments that comply with physical laws, good results can still be obtained. Attenuation analysis has been successfully applied in ellipsometer analysis, and the results are reliable, in accordance with physical laws, and accurate and reliable.

6、 Spectral analyzer structure construction:

1. Different hardware configurations are used in the measurement of spectroscopic ellipsometry, but each configuration must be able to generate a beam with a known polarization state. Measure the polarization state of light reflected from the tested sample. This requires the instrument to be able to quantify the change in polarization state ρ.

2Some instruments measure ρ by rotating a polarizer (called a polarizer) that determines the initial polarization state. Utilize a polarizer at a second fixed position (called a polarizer) to measure the polarization state of the output beam. Other instruments use fixed polarizers and detectors, and modulate the polarization state of the output beam in the middle part, such as using acousto-optic crystals, to ultimately obtain the polarization state of the output beam. The final results of these different configurations are measured as complex functions of wavelength and incident angle, denoted as ρ.

3. When selecting a suitable ellipsometer, spectral range and measurement speed are also important factors that need to be considered. The optional spectral range ranges from 142nm in deep ultraviolet to 33 µ m in infrared. The choice of spectral range is usually determined by the application. Different spectral ranges can provide different information about materials, and suitable instruments must match the spectral range to be measured.

4. The measurement speed is usually determined by the selected spectrometer (used to separate wavelengths). A monochromator is used to select a single, narrowband wavelength. By moving the optical equipment inside the monochromator (usually controlled by a computer), the monochromator can select the wavelength of interest. This method is more accurate in wavelength, but slower in speed because only one wavelength can be tested at a time. If the monochromator is placed in front of the sample, one advantage is that it significantly reduces the amount of incident light reaching the sample (avoiding changes in the photosensitive material). Another measurement method is to simultaneously measure the entire spectral range, unfold the wavelengths of the composite beam, and use a detector array to detect different wavelength signals. When rapid measurement is required, this method is usually used. Fourier transform spectrometer can also measure the entire spectrum simultaneously, but usually only requires one detector instead of an array, which is applied in the infrared spectral range.