Miller Indices

Miller indices is the integer notation system used to describe crystal planes and directions in crystalline materials such as silicon - they provide the geometric language for orientation-dependent processing.

What Is Miller indices?

• Definition: Plane notation using reciprocal intercepts expressed as h, k, l indices.
• Semiconductor Relevance: Common wafer planes include 100, 110, and 111 with distinct properties.
• Direction Mapping: Indices define both surface orientation and key in-plane crystallographic axes.
• Engineering Role: Used in etch, growth, stress, and mechanical-anisotropy analysis.

Why Miller indices Matters

• Process Prediction: Etch rates and facet formation depend on crystal plane identity.
• Design Accuracy: MEMS geometries rely on correct plane-direction assumptions.
• Material Communication: Miller notation standardizes orientation discussion across teams.
• Quality Control: Orientation verification uses index-based specifications.
• Education and Training: Foundational for interpreting crystallography-driven process behavior.

How It Is Used in Practice

• Spec Usage: Define wafer and mask alignment requirements with explicit Miller notation.
• Simulation Inputs: Use indices in process models for anisotropic etch and stress behavior.
• Metrology Correlation: Relate observed facet angles back to expected crystal planes.

Miller indices is the standard crystallographic coordinate system in semiconductor manufacturing - correct Miller-index use is essential for orientation-sensitive process control.