Charged-Particle Lithography Thermal Expansion Correction

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Solution Overview

Problem

Charged-particle lithography apparatuses face significant challenges due to thermal expansion of the target substrate during the writing process, causing deformation and precision issues in pattern placement, as the heating from the charged particle beam leads to inhomogeneous thermal expansion and mechanical strain, affecting the quality and accuracy of the written features.

Innovation Solution

A method is developed to address thermal expansion by calculating the power of the charged particle beam, thermal diffusion, and radiative cooling at each exposure position, determining the positional changes caused by thermal expansion, and applying corrections to the exposure positions and pattern portions to compensate for these changes, using a combination of thermal and mechanical models to improve accuracy and reduce computation time.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If a charged particle beam is used for continuous heating during the writing process, then the writing speed and productivity are improved, but thermal expansion and deformation of the substrate occur, deteriorating the manufacturing precision

Engineering Contradiction:
Improvewriting speedVSAvoidpattern placement precision
Core Design Contradiction:
ProductivityVSManufacturing precision

Solution Approach 1:

The system performs preliminary calculations of thermal diffusion and radiative cooling effects before the actual writing process. By pre-computing the thermal expansion and deformation that will occur during writing, the system can advance the beam positions and pattern data in advance to compensate for the expected thermal distortion, thereby maintaining precision while enabling continuous high-speed writing

Inventive Principle:
Principle #10Preliminary action

Solution Approach 2:

The system implements a feedback mechanism where the calculated thermal effects from previous writing steps are fed back into the positioning and pattern generation for subsequent steps. This closed-loop approach continuously adjusts the beam positions and pattern data based on the accumulated thermal state of the substrate, ensuring precision is maintained throughout the continuous writing process

Inventive Principle:
Principle #23Feedback

2Manufacturing precision

If thermal diffusion and radiative cooling calculations are performed for every exposure position, then the manufacturing precision is improved, but the computation time increases

Engineering Contradiction:
Improvepositional accuracyVSAvoidcomputation time
Core Design Contradiction:
Manufacturing precisionVSLoss of time

Solution Approach 1:

The system segments the substrate surface into a discrete array of calculation positions rather than computing thermal effects at every single beam exposure position. By calculating thermal diffusion and radiative cooling only at these discrete grid points, the system significantly reduces the total number of calculations required while still achieving sufficient positional accuracy for pattern placement

Inventive Principle:
Principle #1Segmentation

Solution Approach 2:

The system performs thermal calculations at a reduced set of discrete positions rather than at all possible exposure locations. This partial action approach computes thermal effects only where necessary to determine the overall thermal state, avoiding the excessive computation that would result from calculating at every single beam position while still providing adequate precision for correction

Inventive Principle:
Principle #16Partial or excessive action

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 effectively compensates for thermal heating effects, enhancing the precision and accuracy of pattern writing by handling thermal and mechanical strains separately, reducing computation time, and improving the overall quality of the written patterns.

Implementation Method 1

the beam is used to write structures on the substrate within a beam range around the respective exposure position... calculating heating of the substrate generated by the beam during an exposure duration

Methodology Applied
Scientific EffectJoule heating: Joule Heating

Implementation Method 2

The generated heat diffuses during the exposure process and gradually dissipates by convection and thermal radiation

Methodology Applied
Scientific EffectThermal diffusion: Conduction (thermal)

Implementation Method 3

The generated heat diffuses during the exposure process and gradually dissipates by convection and thermal radiation

Methodology Applied
Scientific EffectConvection: Convection

Implementation Method 4

The generated heat diffuses during the exposure process and gradually dissipates by convection and thermal radiation

Methodology Applied
Scientific EffectThermal radiation: Thermal Radiation

Implementation Method 5

correcting thermal expansion effects... calculating, for a plurality of locations defined in a predetermined array over the surface of the substrate, the positional change of the substrate resulting from thermal expansion

Methodology Applied
Scientific EffectThermal expansion: Thermal Expansion

Data Source

PatentEP4250333A1Correction of thermal expansion in a lithographic writing method
Publication Date: 2023.09.27 IMS NANOFABTION
  • EP4250333A1 patent drawingFigure 1
  • EP4250333A1 patent drawingFigure 2
  • EP4250333A1 patent drawingFigure 3

AI summary

A pattern writing method employed in charged-particle lithography apparatuses using an improved correction for thermal distortion of the substrate is proposed. The method includes determining an exposure position where the beam impinges on the substrate and the power of the beam at the exposure position (61); calculating heating of the substrate at the exposure position, and calculating, for a plurality of locations over the surface of the substrate, and the thermal diffusion and radiative cooling (62); calculating, for the same or a reduced plurality of locations on the substrate, the positional change of the substrate (63) as a result of thermal expansion; determining a displacement distance which compensates the positional change at the exposure position, updating the structure to be written by shifting the exposure position of the beam by said displacement distance (64), and writing the updated structures (65) on the substrate by means of the beam. These steps are repeated as a function of time and/or varying exposure position of the beam substrate position. For instance, the steps may be repeated at predetermined regular time intervals or whenever the beam position arrives at one of a set of predefined positions on the substrate.