microroughness

Microroughness is the surface height variation at spatial wavelengths below ~1 µm (typically 0.01-10 µm) — characterizing the atomic-scale and near-atomic-scale surface texture that affects interface quality, gate oxide reliability, and carrier mobility in semiconductor devices.

Microroughness Measurement

• AFM: Atomic Force Microscopy — the primary tool for measuring microroughness at nanometer resolution.
• Rq (RMS): Root Mean Square roughness — $R_q = \sqrt{\frac{1}{N}\sum_i (z_i - \bar{z})^2}$ — the standard metric.
• Ra: Average roughness — $R_a = \frac{1}{N}\sum_i |z_i - \bar{z}|$ — less sensitive to outliers.
• Scan Size: Measured in 1×1 µm² or 10×10 µm² areas — roughness values depend on scan size.

Why It Matters

• Gate Oxide: Surface roughness at the Si/SiO₂ interface degrades gate oxide reliability and increases leakage.
• Carrier Mobility: Interface roughness scattering reduces carrier mobility — critical for advanced transistors.
• Bonding: Wafer bonding (for 3D integration) requires sub-nm roughness — rough surfaces don't bond.

Microroughness is the atomic-scale terrain — surface texture at the smallest scales that affects device performance, oxide quality, and wafer bonding.