In semiconductor manufacturing, optical coating, two-dimensional materials, and the development of new optoelectronic devices, the thickness and optical constant (refractive index) of thin films n Extinction coefficient k）It is the most fundamental and critical parameter. As an optical metrology tool that uses changes in the polarization state of light to detect the properties of thin films, ellipsometry has become a core technology in the field of thin film metrology due to its advantages of sub nanometer sensitivity, non-destructive properties, and no need for vacuum environment.
This article will systematically explain the physical principles and data inversion methods of ellipsometry measurement, and compare the working mechanisms and applicable boundaries of two mainstream technology routes - multi wavelength laser ellipsometer and phase modulation ellipsometer - in order to provide a clear reference for technical personnel in related fields.
Light is a transverse wave whose electric field vector vibrates in a plane perpendicular to the propagation direction. The spatial distribution of this vibration trajectory is called polarization state. Common polarization states include linear polarization, circular polarization, and most commonly elliptical polarization. Any polarization state can be fully described by the amplitude ratio and phase difference of two orthogonal components (usually the p-component parallel to the incident plane and the s-component perpendicular to the incident plane).
When light is obliquely incident from one medium onto the interface of another medium, the reflection behavior of the p-component and s-component is different. This difference is quantitatively described by the Fresnel reflection coefficient, which depends on the complex refractive index and incident angle of the two media.
For single-layer thin film systems (environmental medium thin film substrate), light undergoes multiple reflections and interferences between the upper and lower interfaces. The total reflection coefficient is the coherent superposition of each reflected beam, which can be expressed as:
among which It is the phase thickness generated by a round trip within the film:
in the formula For film thickness,
For the complex refractive index of thin films,
For the angle of refraction. It can be seen that both film thickness and optical constant information are encoded in the reflection coefficient.
The core measurement quantity of an ellipsometer is the sum of the p-component and s-componentComplex reflection coefficient ratio, recorded as ：
This defines two directly measurableEllipsoidal parameter：
Amplitude ratio angle PSI (Psi)Characterize the difference in amplitude attenuation between the reflected p-component and s-component. The larger the PSI, the smaller the amplitude attenuation of the p component relative to the s component.
Phase difference angle Δ (Delta)Characterize the relative phase delay difference introduced by two components during the reflection process. Δ varies between 0 ° and 360 ° and is extremely sensitive to film thickness.
The ellipsometer does not directly output thickness or refractive index, but rather outputs a set of (PSI, Δ) data. These data serve as the "fingerprint" of the optical response of thin films, and physical parameters need to be extracted through modeling inversion in subsequent steps.
The sensitivity of ellipsometry measurement strongly depends on the choice of incident angle. When the incident angle approaches the Brewster angle of the substrate material, the reflectivity of the p-component sharply decreases, and the difference in reflectivity between the two components reaches its maximum. At this point, PSI and Δ are most sensitive to changes in the parameters of the thin film. Taking silicon substrate as an example, its Brewster angle is around 75 °, so for SiO2/The measurement of common systems such as Si usually sets the incident angle between 65 ° and 75 °.
The core of ellipsoidal data analysis isIndirect inversionIt is not possible to directly analyze the film thickness and optical constants from (PSI, Δ), and a layered optical model must be constructed to obtain the theoretical (PSI, Δ) through forward calculation, and then compare it with experimental data.
For single-layer films, the reflection coefficient formula in Section 1.2 can be directly used. For multilayer film systems, it is common to use a system based on Maxwell's equationsFeature matrix methodPerform recursive calculations and stack layer by layer to obtain the complex reflection coefficient of the entire film system.
The optical constants of thin films vary with wavelength, a phenomenon known as dispersion. In ellipsoidal modeling, it is necessary to select a suitable dispersion model to constrain the wavelength dependence of refractive index and extinction coefficient, in order to reduce the number of fitting parameters and ensure the physical rationality of the results.
For transparent films such as SiO2、 Al2O3Photoresist, commonly used Cauchy dispersion model：
For thin films with light absorption (such as metal thin films and semiconductor materials), a oscillator model containing extinction coefficient needs to be used, for example Lorentz oscillator modelOr specifically developed for amorphous semiconductors Tauc Lorentz modelWait.
After the modeling is completed, the unknown parameters in the model (such as film thickness, dispersion coefficient, etc.) are adjusted to make the theoretical calculation (mod, Δmod）Compared to experimental measurementsexp, Δexp）Minimize the differences between them. The most commonly used objective function is mean square error:
among which N Is the total number of data points,M It is the number of fitting parameters. The smaller the MSE, the more consistent the model is with the experimental data. For complex membrane systems with strong parameter coupling and multiple local optima, the introduction ofParticle Swarm OptimizationWait for the global search strategy, first locate the global optimal region, and then switch to gradient algorithms such as Levenberg Marquardt for fine convergence.
According to the different types of light sources and polarization modulation methods, ellipsometers have developed various technical routes in practical engineering. The following describes two representative architectures.
working principle. The multi wavelength laser ellipsometer uses multiple discrete wavelength lasers as light sources, with typical wavelengths such as 405 nm, 532 nm, 633 nm, 785 nm, etc. Its optical layout usually adopts classicRotating polarization deviceStructure: Under a fixed incident angle, the polarizer or analyzer rotates in a certain pattern, and the detector records the reflected light intensity under different polarization configurations. By analyzing the curve of light intensity changing with polarizer angle, the corresponding values of (PSI, Δ) at the wavelength can be inverted.
Technical features. Laser light sources have the characteristics of good monochromaticity, high light intensity, and excellent directionality, so the spot can be focused to the micrometer level, suitable for measuring small areas. Also, because the optical path does not contain fast resonant components, the system has good stability and low maintenance costs. The limitation lies in the limited number of wavelengths (usually 2 to 4), which cannot provide continuous dispersion information. For strongly dispersive materials or scenarios that require comprehensive solution of optical constants, the information content is slightly insufficient.
Applicable scenarios. Silicon based SiO2 Or Si3N4 Monitoring of gate dielectric thickness, online rapid sampling of compound semiconductor epitaxial layers (GaAs, InP), single point micro area measurement of transparent thin films, etc.
working principle. The phase modulation ellipsometer uses a broadband light source (such as xenon lamp, halogen lamp) and inserts aphotoelastic modulator The modulator applies periodic modulation to the phase delay of transmitted light under high-frequency (usually 50 kHz) resonant driving. The light signal reflected by the sample is synchronously demodulated by the spectrometer, and the full band (PSI, Δ) spectrum can be obtained within milliseconds to seconds, covering the wavelength range from ultraviolet to near-infrared (such as 190 nm to 1700 nm).
Technical features. One measurement can obtain ellipsoidal parameters of hundreds to thousands of wavelength points, with extremely high information flux. Continuous spectral data allows for joint fitting using complex dispersion models (such as Tauc Lorentz, Cody Lorentz, etc.), which can accurately solve both film thickness and full band optical constant dispersion curves simultaneously. The system architecture includes high-frequency modulation and lock-in amplification, and the overall complexity is higher than that of a rotating polarization device ellipsometer.
Applicable scenarios. Characterization of multilayer film systems for optical coatings (anti reflection films, high reflectivity films, filters), parameter analysis of ITO and polyimide films in flat panel displays, development of multilayer film processes for photoresist and anti reflection layers, determination of epitaxial layer thickness and alloy composition for wide bandgap semiconductors (GaN, SiC), etc.
The following table provides a systematic comparison of these two ellipsometry measurement techniques from multiple dimensions, in order for technicians to make reasonable choices based on actual needs.
| comparative dimension | Multi wavelength laser ellipsometer | Phase modulated ellipsometer |
|---|---|---|
| light source | 2-4 discrete laser wavelengths | Wide spectrum light source, covering continuous spectrum |
| data volume | Several wavelength points (∝, Δ) | Spectrum of hundreds to thousands of wavelength points (PSI, Δ) |
| Measuring speed | Each wavelength is collected sequentially, in seconds | Full spectrum synchronous acquisition, ranging from milliseconds to seconds |
| Film thickness range | About 1 nm to several μ m | From sub nanometer to tens of μ m |
| Ability to characterize optical constants | Limited, suitable for materials with known dispersion trends | Complete solution of n-k dispersion curve, supporting complex oscillator models |
| Multilayer film capability | Suitable for 1-2 layer simple membrane systems | Capable of handling complex membrane systems with more than 5 layers |
| System complexity | Simple optical path and low maintenance cost | Containing high-frequency modulation and synchronous demodulation, the system is relatively complex |
| Typical positioning | Online monitoring, single film quality control | Laboratory research and development characterization, precision analysis of complex membrane systems |
In summary,Multi wavelength laser ellipsometerKnown for its simple structure, micro spot size, and long-term stability, it is suitable for online monitoring of cured processes and rapid inspection of single film layers;Phase modulated ellipsometerWith wideband continuous spectroscopy and high information flux as the core competitiveness, it is suitable for R&D characterization scenarios where material optical constants are unknown and membrane structures are complex. The two complement each other in terms of measurement ability, and can be flexibly selected according to the complexity of the membrane system and data depth requirements in practical work.
In the practical application of ellipsometry, the following sources of error deserve special attention:
Incident angle calibration deviation. The incident angle is a key input parameter for forward modeling, and calibration errors can directly lead to systematic shifts in (PSI, Δ). It is recommended to use standard SiO with known thickness after each startup or change of measurement configuration2/Si sample is calibrated for incident angle.
Improper selection of dispersion model. The model is a prerequisite for inversion, and improper selection can lead to large fitting residuals or loss of physical meaning in the results. For materials with unknown optical constants, model free methods such as B-Spline can be used to explore dispersion trends, and then a suitable oscillator model can be selected for parametric fitting.
The influence of surface roughness. When there is nanoscale roughness on the surface of the film, the interface is no longer an ideal abrupt refractive index interface. An effective medium approximation layer can be introduced into the model to incorporate roughness into the forward calculation framework.
Backside reflection interference. For transparent substrates such as glass and sapphire, reflected light from the back of the substrate can mix into the signal path, disrupting the measurement of ellipsoidal parameters. This effect can be suppressed by roughening the back of the substrate, using a wedge-shaped substrate, or pasting absorbing materials on the back.
The core idea of ellipsometry measurement technology is concise yet profound: by using the polarization state as a high-sensitivity probe, it captures the amplitude attenuation and phase delay differences of the p-component and s-component after the interaction between light and thin film, thereby reflecting the thickness and optical constants of the thin film. The multi wavelength laser ellipsometer serves online monitoring scenarios with stable discrete wavelength measurements, while the phase modulation ellipsometer responds to the characterization requirements of complex membrane systems with high information flux of continuous wide spectrum. The two are simple and complex, forming a complementary and coexisting technological landscape in current thin film optical metrology.
Understanding the physical essence of polarization measurement, the logic of forward modeling, and the applicable boundaries of different technical routes is the foundation for correctly using ellipsometry data and making reasonable process decisions. Only by combining physical intuition, mathematical tools, and engineering experience can the ability of this precision metrology technology be fully utilized.
Fujiwara, H. Spectroscopic Ellipsometry: Principles and Applications. John Wiley & Sons, 2007.
Azzam, R. M. A. & Bashara, N. M. Ellipsometry and Polarized Light. North-Holland, 1977.
Tompkins, H. G. & Irene, E. A. (Eds.). Handbook of Ellipsometry. William Andrew, 2005.
Cao Zhuangqi Thin Film Optics and Thin Film TechnologyScience Press
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