Applied Mathematics | Systems & Control Engineering internship: Devising a mathematical foundation for on-product overlay control

Introduction

In Business Line Applications, we create software products that run in most modern semiconductor factories in the world. Our department Development and Engineering (D&E) Process Window Control (PWC) develops, integrates, and qualifies functional modules in products used to monitor and control on-product performance under high-volume manufacturing conditions. We believe that deep understanding of on-product performance and its contributors enables the development of the technology roadmap.

Your assignment

The goal of this assignment is to develop a rigorous and comprehensive formalization of on-product overlay control. Wafer alignment and overlay control are inherently interconnected, and the control mechanisms through the stack for both alignment and overlay cannot be treated independently. This interdependency results in complex control scenarios over multiple dimensions, e.g., temporal, layer, and spatial domains, that are often difficult to interpret.

In current practice, these scenarios are typically described using elaborate illustrations, sometimes supplemented by partial mathematical expressions. However, what is lacking is a systematic and commonly accepted mathematical framework that clearly captures all relevant control aspects and their relationships. A current line of thinking tends into the direction of representations in the form of feedback and feedforward control schemes as used in "classical" control theory. Establishing such a foundation would significantly enhance understanding, communication, and consistency across different control strategies. Part of the assignment is to translate the mathematical framework to into executable code for simulation, e.g., via Matlab Simulink.

This is a master’s (thesis) internship for a minimum of 6 months, 5 (or 4) days per week (2-3 days on‑site). The start date of this internship is as of September 2026.

Your profile

• Are pursuing a master’s degree in applied mathematics or systems and control engineering, or a related field such as electrical engineering, mechanical engineering, physics, or computer science with strong mathematical modeling skills.
• Preferably have knowledge of control theory, including 'loop thinking' and discrete time filtering via transfer functions.
• Are proactive and comfortable exploring complex topics independently.
• Can work in a collaborative environment and communicate clearly.
• Have simulation skills (Python or Matlab).
• Demonstrate strong communication skills, especially when working with multiple stakeholders.
• Are able to work independently and take ownership of your work.

Other requirements you need to meet:

• You are enrolled at an educational institute for the entire duration of the internship;

• Attach your cover letter with a clear motivation why you are interested in this internship assignment in particular;

• You need to be located in the Netherlands to be perform your internship. In case you are currently living/studying outside of the Netherlands, your CV/motivation letter includes the willingness to relocate.

• If you are a non-EU citizen, studying in the Netherlands, your university is willing to sign the documents relevant for doing an internship (i.e., Nuffic agreement).

Inclusion and diversity

ASML is an Equal Opportunity Employer that values and respects the importance of a diverse and inclusive workforce. It is the policy of the company to recruit, hire, train and promote persons in all job titles without regard to race, color, religion, sex, age, national origin, veteran status, disability, sexual orientation, or gender identity. We recognize that inclusion and diversity is a driving force in the success of our company.

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