Thickness measurement

Basics

Basics of layer thickness measurement

The quality of protective or design coating must be constantly controlled during the coating process, in order to guarantee the functionality of the layers and thus to comply with customer requirements. The testing of samples from the ongoing production process can be performed as random sampling or as on-line measurement.  

  • Measurement theory

    By illuminating samples with white light, interference spectrums are created as a function of the geometric layer thickness and refractive index of the materials . When white light is incident on optically transparent layers, interference occurs, as the path difference between specific wavelengths is exactly a multiple of the optical layer thickness. The maximum measurable thickness is linked to the spectral resolving power, the minimum thickness to the spectral range to be covered. The measurement of even thinner layers requires that the absolute intensity value is known. A high absolute accuracy of the wavelength ensures an exact measurement result. 

    Depending on layer condition, the thickness can be calculated using two methods: 

    Peak method:
    The layer thickness is derived from the maxima and minima of the interference spectrum. This method is very accurate and fast, however, noise-sensitive. It is suitable for single layers < 5 µm.

    Fast-Fourier-Transformation (FFT) method:
    The layer thickness is calculated from the periodicity of the interference spectrum. This method is insensitive to noise and suitable for thick layers, however, requires a large computational effort and is less accurate. It is suitable for single and multi-layer systems from 1-200 µm.

    Benefits
    • Contact-free and non-destructive
    • Highly accurate results
    • Suitable for short- and long-term repeatability
    • Quick reset of coating parameters, resulting in low cost concerning quality and material consumption
    Applications
    • Optical Emission Spectroscopy
    • Reflectometry
    • Ellipsometry
    • Process Control
    • Examples: 
      • Wafer Inspection
      • Displays
      • Photoresists / Dielectric Layers
      • Plasma Monitoring

  • Generation of Interference

    Generation of Interferences

    The following is based on the theoretically simplest case of a plane-parallel layer with the refractive index n and the geometrical thickness d. Starting from the point light source P0, a ray SO is partially reflected at point A (ray S1 at angle α) and partially refracted into the layer (at angle β). At the lower boundary of the layer, the ray is reflected again at point B and refracted at point C. Finally, the ray S2 leaves the upper boundary layer parallel to S1 and exits into the air again. Further reflections in the layer refract the ray S0 infinitely and divide it into parallel rays with strongly decreasing intensity. Since all reflected and refracted rays have their origin in the S0 ray, they are coherent and can thus interfere with each other. Depending on the path difference Γ, the two main reflected rays S1 and S2 may interfere with each other.

    This path difference is calculated:

    For vertical light incidence the formula is simplified to:

    Maximum interference occurs under the condition:

    The variable i stands for the interference order and consists of a prime number (i = 0, 1, 2,...).

  • Calculation of Layer

    Calculation of Layer Thickness

    Depending on the thickness of the layer to be measured, the layer thickness can be calculated using two methods.

    Peak method

    In the peak method, the layer thickness is derived from the maxima and minima of the interference spectrum (I = atomic number). Here's an example:

    Advantage very accurate and fast
    Disadvantage noise-sensitive
    Application for single layers < 5 µm

    Fast-Fourier-Transformation (FFT)

    In the FFT method, the layer thickness is calculated from the periodicity of the interference spectrum.

    Advantage insensitive to noise suitable for thick layers
    Disadvantage large computational effort limited accuracy
    Application for single layer and multi-layer systems 1-200 µm
  • Calculation of Reflection

    Calculation of Reflection

    The intensity of the reflected subray depends on the refractive index of the elements involved. For vertical light incidence, reflectance R, when passing from one medium with the refractive index n1 into another one with the refractive index n2, totals:

    If you look at a surface made of macrolon (n = 1.59) coated with acrylic glass (n = 1.49), the reflectance for the boundary surface air (n = 1) to acrylic glass is:

    The reflectance for the boundary surface acrylic glass-to- macrolon is:


    The intensity values refer to the intensities of the primary ray (100 %). The value of the reflection intensity of the maximum is calculated by (R1 + R2) = 4 %, that of the minimum by (R1 - R2) = 3.8 %. If the reflection component of the sample's rear side of approx. 4 % cannot be suppressed, the two values increase by this amount. The shown relations only apply to closely adjacent extremes (thick layers), as the wavelength dependence of the refractive index plays no role in this case.