Substrate Overlay Inspection Using Polynomial Fit Asymmetry

Solution Overview

Problem

Existing overlay measurement systems in lithographic processes require multiple targets per field, consuming time and resources, and assume a linear relationship between overlay and asymmetry, which is inaccurate for larger errors and small errors not close to zero.

Innovation Solution

A method and apparatus that use a radiation source to direct radiation onto targets with predetermined offsets, detecting reflected radiation to determine asymmetry and overlay values, and applying a polynomial fit to establish the relationship between asymmetry and overlay without assuming linearity, reducing the number of targets needed.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If multiple overlay targets are used per field to measure overlay errors, then measurement accuracy is improved, but the number of targets and measurement time increase

Engineering Contradiction:

Improveoverlay measurement accuracyVSAvoidmeasurement time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The invention changes the mathematical model from linear to polynomial (second-order or higher) to accurately describe the non-linear relationship between asymmetry and overlay. This allows single-target measurements to achieve the same accuracy that previously required multiple targets, reducing measurement time while maintaining precision.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The invention uses a single target per field instead of multiple targets, applying partial action (one target) to achieve sufficient measurement accuracy through the polynomial model, thereby reducing the number of measurements needed while maintaining adequate overlay error detection capability.

Inventive Principle:

Principle #16Partial or excessive action

2Device complexity

If a linear relationship is assumed between overlay and asymmetry, then measurement process is simplified, but measurement accuracy deteriorates for larger or small overlay errors

Engineering Contradiction:

Improvemeasurement model complexityVSAvoidoverlay measurement accuracy

Core Design Contradiction:

Device complexityVSMeasurement precision

Solution Approach 1:

The invention changes the mathematical model from linear to polynomial (second-order or higher) to accurately describe the non-linear relationship between asymmetry and overlay. This allows single-target measurements to achieve the same accuracy that previously required multiple targets, reducing measurement time while maintaining precision.

Inventive Principle:

Principle #35Parameter changes

3Productivity

If fewer overlay targets are used on the substrate, then resource usage is optimized, but measurement reliability may be compromised

Engineering Contradiction:

Improvesubstrate processing efficiencyVSAvoidoverlay measurement reliability

Core Design Contradiction:

ProductivityVSReliability

Solution Approach 1:

The invention changes the mathematical model from linear to polynomial (second-order or higher) to accurately describe the non-linear relationship between asymmetry and overlay. This allows single-target measurements to achieve the same accuracy that previously required multiple targets, reducing measurement time while maintaining precision.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The invention uses the polynomial fit model to establish a reliable relationship between asymmetry and overlay measurements across multiple fields. This feedback model allows accurate overlay determination from single-target measurements, maintaining measurement reliability while reducing the number of targets needed.

Inventive Principle:

Principle #23Feedback

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

This approach allows for accurate measurement of overlay and asymmetry with fewer targets, optimizing resource use and improving measurement efficiency by accounting for non-linear relationships across the substrate.

Implementation Method 1

a detector to detect the radiation reflected from the first one of the targets

Methodology Applied

Scientific EffectReflection: Reflection

Data Source

PatentUS8665417B2Apparatus and method for inspecting a substrate

Publication Date: 2014.03.04 ASML NETHERLANDS BV

AI summary

An apparatus measures properties, such as overlay error, of a substrate divided into a plurality of fields. The apparatus includes a radiation source configured to direct radiation onto a first target of each field of the substrate. Each first target (T4G) has at least a first grating and a second grating having respective predetermined offsets, the predetermined offset (+d) of the first grating being in a direction opposite the predetermined offset (−d) of the second grating. A detector is configured to detect the radiation reflected from each first target and to obtain an asymmetry value for each first target from the detected radiation. Further, a module is configured to determine an overlay value for each first target based on at least the obtained asymmetry value and the predetermined offsets and determine a polynomial fit across a plurality of first targets of a corresponding plurality of fields of the substrate for a relationship between the obtained asymmetry value and determined overlay value of each first target.