Charged Particle Beam Writing Z Map Generation

Solution Overview

Problem

The accuracy of charged particle beam writing on semiconductor substrates is compromised due to errors in surface height measurement, particularly at the peripheral regions where measurement is not possible, leading to shifts in the writing position and focal point, which cannot be adequately corrected by existing polynomial approximation methods.

Innovation Solution

A charged particle beam writing apparatus that measures the surface height of the central substrate region using a high-order polynomial for accurate interpolation and uses a low-order polynomial for extrapolation at the peripheral regions, generating a combined Z map to adjust the focal position and reduce writing errors.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Area of stationary object

If polynomial extrapolation is used to estimate surface height at peripheral portions, then the measurement coverage is extended, but the accuracy of height estimation deteriorates

Engineering Contradiction:

Improvemeasurement coverage areaVSAvoidheight estimation accuracy

Core Design Contradiction:

Area of stationary objectVSMeasurement precision

Solution Approach 1:

The patent divides the substrate surface into a measurement region (central portion) and a non-measurement region (peripheral portion). By segmenting the area, the system applies different processing methods to each region: direct measurement for the central region and controlled extrapolation for the peripheral region, thereby maintaining accuracy while extending coverage.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent applies different polynomial orders to different regions of the substrate. A first polynomial of a certain order is used for the measurement region, while a second polynomial of a higher order is used for the non-measurement region. This local differentiation optimizes the balance between coverage and accuracy for each specific area.

Inventive Principle:

Principle #3Local quality

2Measurement precision

If the order of polynomial for extrapolation is increased, then the accuracy of surface height calculation in measured regions is improved, but the error in extrapolated peripheral regions increases

Engineering Contradiction:

Improvesurface height calculation accuracyVSAvoidwriting accuracy at peripheral regions

Core Design Contradiction:

Measurement precisionVSManufacturing precision

Solution Approach 1:

The patent applies different polynomial orders to different regions of the substrate. A first polynomial of a certain order is used for the measurement region, while a second polynomial of a higher order is used for the non-measurement region. This local differentiation optimizes the balance between coverage and accuracy for each specific area.

Inventive Principle:

Principle #3Local quality

Solution Approach 2:

The patent divides the substrate surface into a measurement region (central portion) and a non-measurement region (peripheral portion). By segmenting the area, the system applies different processing methods to each region: direct measurement for the central region and controlled extrapolation for the peripheral region, thereby maintaining accuracy while extending coverage.

Inventive Principle:

Principle #1Segmentation

3Device complexity

If polynomial approximation is used to generate Z map, then the surface height estimation is simplified, but the writing position accuracy deteriorates

Engineering Contradiction:

ImproveZ map generation complexityVSAvoidwriting position accuracy

Core Design Contradiction:

Device complexityVSManufacturing precision

Solution Approach 1:

The patent divides the substrate surface into a measurement region (central portion) and a non-measurement region (peripheral portion). By segmenting the area, the system applies different processing methods to each region: direct measurement for the central region and controlled extrapolation for the peripheral region, thereby maintaining accuracy while extending coverage.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent applies different polynomial orders to different regions of the substrate. A first polynomial of a certain order is used for the measurement region, while a second polynomial of a higher order is used for the non-measurement region. This local differentiation optimizes the balance between coverage and accuracy for each specific area.

Inventive Principle:

Principle #3Local quality

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 enhances the accuracy of surface height calculation and focal position adjustment, minimizing writing position shifts and improving the overall precision of the charged particle beam writing process.

Implementation Method 1

the surface of the substrate is irradiated with light, the reflected light is detected, the height of the surface of the substrate is measured

Methodology Applied

Scientific EffectLight reflection: Reflection

Implementation Method 2

an approximate curved surface of the surface of the substrate is calculated using a cubic polynomial or the like on the basis of the measurement result

Methodology Applied

Scientific EffectPolynomial approximation:

Data Source

PatentUS11037757B2Charged particle beam writing apparatus and charged particle beam writing method

Publication Date: 2021.06.15 NUFLARE TECH INC

AI summary

A charged particle beam writing apparatus includes a writer writing a pattern on a surface of a substrate using a charged particle beam, a measurement unit measuring a height of the surface of a central portion of the substrate at a plurality of positions in the central portion, a generator performing fitting using a first polynomial on measurement values from the measurement unit, calculating, by extrapolation using the first polynomial, a first height distribution of the height of the surface of a peripheral portion of the substrate, performing fitting using a second polynomial, which is of a higher order than the first polynomial, on the measurement values, calculating a second height distribution of the height of the surface of the central portion by interpolation using the second polynomial, and generating a height distribution of the substrate by combining the first height distribution and the second height distribution, and a controller adjusting a focal position of the charged particle beam based on the height of the surface at a writing position, the height being calculated from the height distribution of the substrate.