Nanotechnology & MEMS Metrology

AFM Cantilever & Micro-Probe Photolithography Calculator

Euler-Bernoulli beam micromechanics, spring constant calibration, and wet anisotropic KOH mask offset calculator for atomic force microscopy.

Process Parameters & Inputs

Cantilever Material & Geometry:

Cantilever Length ($L$ in $\mu\text{m}$):

Nominal length of the micromachined cantilever beam.

Beam Width ($w$ in $\mu\text{m}$):

Width of the photolithographic cantilever pattern.

Silicon Layer Thickness ($t$ in $\mu\text{m}$):

Epitaxial / SOI device layer thickness.

Integrated Pyramidal Tip Height ($h_{\text{tip}}$ in $\mu\text{m}$):

KOH wet anisotropic etched probe tip height.

Calculated Engineering Metrics

Spring Constant ($k$)

2.84N/m

Fundamental Resonance ($f_0$)

75.4kHz

Thermal Noise Amplitude ($z_{\text{th}}$)

0.038nm

KOH Undercut Mask Offset

9.89µm

Toolpath & Geometry Simulation

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Engineering Methodology & Technical Notes

AFM Cantilever Micromechanics & Euler-Bernoulli Theory: Atomic Force Microscopy cantilevers are micro-fabricated silicon or silicon nitride beams designed to detect sub-angstrom surface topography forces. The spring constant for a rectangular beam is governed by $k = \frac{E w t^3}{4 L^3}$, where young's modulus $E$ is $169\text{ GPa}$ along the $\langle 110 \rangle$ silicon plane. Resonant frequency in vacuum is $f_0 = \frac{1.03}{2\pi} \frac{t}{L^2} \sqrt{\frac{E}{\rho}}$.

Anisotropic Wet Etching & Mask Vector Compensation: Fabricating ultra-sharp tetrahedral/pyramidal tips requires KOH wet etching of $\{100\}$ silicon wafers. The etching self-terminates on $\{111\}$ crystal planes at an exact angle of $54.74^\circ$. Photolithography mask DXF vectors require corner compensation octagons to prevent convex corner blooming during under-etching.