In high-end manufacturing fields such as semiconductor manufacturing, optical coating, compound semiconductors, and flexible electronics, precise control of film thickness directly determines the electrical performance, optical characteristics, and long-term reliability of devices. Taking polyimide (PI) as an example - as one of the most critical dielectric materials in flexible displays, MEMS devices, and advanced packaging, a film thickness deviation of more than 5% may lead to imbalanced stress distribution, dielectric breakdown, or significant decrease in optical transmission efficiency of the device.
In the production line environment, the practical problem faced by engineers is that in a photoresist coating batch, the uniformity of film thickness and the mean deviation between batches of the same wafer need to be quickly non-destructive tested within seconds. This is the core value of optical film thickness gauge.
This article will delve into the underlying physical principles of optical film thickness measurement and provide a complete technical guide for industry engineers from theory to selection, based on the engineering practices of the classic Filmetrics F20 and F50 devices.
The theoretical part of this article mainly refers to the systematic discussion on the measurement of film thickness by spectral reflectance method in the industry. We would like to express our gratitude.
When a beam of broad-spectrum light is vertically incident on the surface of a transparent film, the light undergoes reflection and transmission at the upper and lower interfaces of the film, forming multi beam interference. For a single-layer film system (air thin film substrate), its reflection spectrum carries all the information about the film thickness and refractive index.
Reflectivity formula (vertical incidence):
Among them, phase difference:
in the formula 、
The Fresnel reflection coefficients of the air film interface and the film substrate interface, respectively,
For the refractive index of the thin film,
For film thickness,
For wavelength.
In practical engineering measurement, the handling of half wave loss is a key prerequisite for the accuracy of film thickness calculation. Taking the typical scenario of PI film on silicon substrate as an example:
| interface | Refractive index variation | 半波损失 | Additional phase |
|---|---|---|---|
| Air (1.0) → PI (1.65) | increase | is | |
| PI (1.65) → Silicon (3.87) | increase | No | 0 |
Therefore, the total additional phase is , corresponding to the optical path difference
If this item is mishandled, the calculation of film thickness will result in systematic deviation.
The refractive index of transparent dielectric films varies with wavelength and is usually described using the Cauchy dispersion model
By Kapton ® Taking PI film as an example, the typical parameters are ，
For more accurate fitting, it can be extended to the three parameter Cauchy model or Sellmeier model.
Choosing the appropriate measurement band and resolution based on the film thickness range is a prerequisite for obtaining high-quality spectral data
| Film thickness range | Recommended wavelength range | spectral resolution | integration time |
|---|---|---|---|
| < 5 μm | 400 ~ 800 nm | 0.5 nm | 50 ms |
| 5 ~ 50 μm | 600 ~ 1000 nm | 1 nm | 100 ms |
| > 50 μm | 1000 ~ 1700 nm | 2 nm | 200 ms |
The measured spectrum must be calibrated in order to fit the theoretical model. The standard calibration process is:
Collect dark noise spectra ；
Collect reference spectra using a standard mirror with known reflectivity (such as a silicon wafer) ；
Calculate absolute reflectance:
When the root mean square roughness of the film surface When the wavelength exceeds 5%, the scattering loss effect cannot be ignored. The corrected reflectance is:
Providing a high-quality initial value is crucial before entering nonlinear least squares fitting, as it can significantly reduce the risk of falling into local optima. For the wavelengths of adjacent peaks/valleys in the interference spectrum and
：
The core objective function is:
For multilayer film systems, the recursive method (characteristic matrix method) can be used to calculate the total reflectivity:
For multilayer film systems with unknown thickness ranges or strong correlations, traditional gradient descent methods are prone to getting stuck in local optima. At this point, particle swarm optimization algorithm can be used:
Number of particles: 20~40;
Inertial weight (Linear decreasing strategy);
Learning factors .
PSO can achieve a good balance between global search and local convergence, and is a commonly used enhancement algorithm in industrial film thickness gauge software.
F20 is a classic desktop film thickness gauge from Filmetrics (now under KLA Instruments), suitable for research and development, small batch, and multi variety scenarios.
| core parameters | indicator |
|---|---|
| measurement range | 1 nm~50 μ m (depending on the material) |
| spectral range | 380 ~ 1050 nm |
| spot size | 200 μ m~2 mm (configurable) |
| Measuring speed | 1~5 s/point |
| repetitiveness | ≪ 1 Å (long duration) |
| Support membrane layer | Single layer to multi-layer transparent film system |
Typical application scenarios：
Monitoring of semiconductor photoresist film thickness;
Measurement of SiO ₂/Si ∝ N ₄/polycrystalline silicon dielectric layer;
Characterization of compound semiconductor epitaxial layers (GaN, SiC, InP);
OLED/display panel film thickness control;
Thickness characterization of PI film on flexible substrate.
Corresponding to the aforementioned theory: The F20 software has built-in dispersion model libraries such as Cauchy, Sellmeier, Lorentz, etc; Support automatic determination of half wave loss; Provide two fitting modes: least squares and global optimization; For rough surfaces, the scattering correction option can be enabled.
The F50 integrates an automatic XY stage and autofocus system based on the F20, achieving production line level batch measurement.
| Comparison item | F20 | F50 |
|---|---|---|
| stage | Manual displacement | Automatic XY stage |
| measurement method | Single point manual | Multi point automatic sequence measurement |
| Measurement point density | On demand manual | Programmable matrix/contour/area scanning |
| data processing | View point by point | Automatic recipe+statistical output |
| Capacity efficiency | ~10-20 tablets/hour | 100-200 wafers per hour (standard wafers) |
F50 and F20 share the same optical engine and algorithm library to ensure consistency in measurement accuracy. After enabling the autofocus function, the spot size can be adaptively adjusted to eliminate focusing errors caused by sample warping (WARP).
In engineering applications, it is necessary to establish a systematic error compensation mechanism. For specific process measurements, compensation can be established by comparing reference measurement values:
The accuracy requirement is usually set to a relative error of<3%. The verification methods include:
weighing method：
Suitable for large-area uniform film layers;
Interference microscope：
；
SEM cross-sectional methodDirectly observing the cross-section of the film layer is suitable for verifying multi-layer film systems.
Check production capacityDaily inspection ≤ 50 pieces → F20; ≥ 100 pieces → F50;
View data requirementsSingle point thickness measurement → F20; Uniformity heatmap/SPC control → F50;
Calculate ROIThe full automation of F50 can usually recoup investment within 6-12 months by saving labor and improving yield.
Wrong selection of refractive index model Systematic deviation of film thickness. Suggest performing full spectrum fitting on unknown materials to determine dispersion parameters first;
Excessive roughness → The signal-to-noise ratio decreases. It can be compensated by scattering correction or increasing integration time;
Cross correlation of multi-layer film parameters → It is recommended to fix the refractive index of the known layer or decouple it through differential measurement;
temperature effect → For heat sensitive materials (such as PI), it is necessary to record the measured temperature and introduce thermal optical coefficient correction.
The core of optical film thickness measurement lies in establishing accurate physical models, selecting appropriate fitting algorithms, and performing engineering error compensation. From F20 to F50, the device forms are different, but the technical genes are the same - all based on the principle of spectral reflectance, stable and reliable optical acquisition is achieved through hardware, and high-precision inversion calculation is completed through software.
Whether you are conducting process debugging during the R&D phase or batch monitoring on the production line, understanding the underlying physical principles and engineering details will make every measured data more valuable as a reference.
Filmetrics F20 & F50 Product Technical Specification, KLA Instruments.
Cao Zhuangqi, "Thin Film Optics and Thin Film Technology," Science Press
Macleod, H. A. Thin-Film Optical Filters, 5th ed., CRC Press.
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