Optical, Electron, and Scanning Probe Microscopy: A Technical Deep Dive
Timeline of Microscopy Development
- 17th Century: Optical microscope
- 1884: Henry Le Chatelier develops the metallographic microscope
- 1931/1933: Transmission electron microscope (TEM)
- 1942, 1950: Scanning electron microscope (SEM)
- 1981: Scanning tunneling microscope (STM)
- 1986: Atomic force microscope (AFM)
Resolution in Microscopy
Optical microscopes have a resolution in the micrometer (μm) range, while electron and scanning probe microscopes achieve nanometer (nm) resolution.
Optical Microscopy
Rays passing through the center of the lens are not diffracted. Light microscopy produces an enlarged, virtual, and inverted image.
- Probe: Visible light
- Resolution: Approximately 200 nm
- Non-destructive
Resolution is determined by the quality of the lens and is limited by aberrations (explainable by geometrical optics) and diffraction (due to the wave nature of light and the finite aperture of optical elements).
Rayleigh Criterion
The Rayleigh criterion states that for two points to be resolved, the contrast between the maximum and minimum intensity along the line connecting their centers should be at least 26% lower than the maximum.
Depth of Field
The depth of field is the axial range through which an object can be focused without any change in image sharpness.
Axial Chromatic Aberration
Axial chromatic aberration is associated with the variation of the refractive index (n) with wavelength (λ).
Bright Field Microscopy
In bright field microscopy, the light angle is incident perpendicular to the surface.
Dark Field Microscopy
Dark field microscopy uses angular illumination. Plane surfaces reflect light away from the lens, while sharp edges scatter light into the lens. Edges and dirt particles appear bright, improving contrast.
Profilometry: Measuring Surface Topography
A profilometer is an instrument that measures the profile of a surface to assess its topography or texture. This includes surface morphology (height and width of patterned lines) and surface roughness.
Components of a Profilometer
- A sample stage that holds the sample and sets the x and y coordinates.
- A detector that determines the height of the surface points (z).
Contact Profilometry
In contact systems, a stylus (probe) contacts the surface. The stylus is made of a hard material and applies a specific force (up to 15 mg). Resolution and accuracy depend on the stylus’s shape, size, and scanning speed.
Height Detection
Height detection is achieved mechanically through a feedback loop, pushing up against the probe as it scans along the surface. The feedback maintains a specific amount of torque in the arm, known as the ‘setpoint’. Changes in the Z position are used to reconstruct the surface.
Stylus and AFM Contact Profilers
Atomic force microscopy (AFM) offers more sophisticated tools for sub-nanometer resolution compared to stylus profilometers.
Contact vs. Non-Contact Profilometry
- Contact: Surface independence, better lateral resolution, angstrom (Å) vertical resolution, direct technique.
- Non-Contact: Reliability (no surface damage), higher scan speed, nanometer (nm) vertical resolution.
Surface Roughness Parameters
- Primary Profile: The raw, unfiltered profile data.
- Roughness Profile: High-frequency components of the surface profile.
- Waviness Profile: Low-frequency components of the surface profile.
The sampling length is the cut-off wavelength (λc) of the filter used to separate roughness and waviness. The evaluation length is the profile length after filtering.
Mean Line of the Profile (m)
The mean line is a perfect geometric line parallel to the profile, corresponding to the arithmetic average of the height z(x) over the sampling length.
Arithmetic Mean Deviation (Ra)
Ra is the most widely used parameter for surface roughness characterization.
Root Mean Square Deviation (Rq or σ)
Rq is generally slightly greater than Ra.
Amplitude Density Function (p(z))
The amplitude density function represents the probability distribution of surface heights. It indicates the probability that a point on the surface profile exists at a certain height. It is a tool for further mathematical evaluation of surface roughness.
Skewness of the Distribution (Sk)
Surfaces with the same Ra and Rq can have different Sk values. If peaks and valleys are distributed symmetrically in relation to the mean line, then p(z) is symmetrical in relation to m.
Kurtosis of the Distribution (K)
Kurtosis indicates how high or flat the p(z) is.
- Gaussian distribution: K = 3
- Flat peaks and valleys: K < 3
- Sharp peaks and valleys: K > 3