René Raaijmakers
13 October 2021

Modeling of thermal behavior helps in field-troubleshooting and scaling of chips. Tooling substantially improves communication and adds speed to development.

During a technical review meeting at ASML, sometime in the 2000s, a problem is discussed with Zerodur, a type of glass that’s extremely form fitting. An employee of Zeiss comes forward with an explanation. The German points to the climate system of the warehouse where the material was stored: there was a problem in controlling the heat. “How can that be a problem?” Martin van den Brink asks. “We buy that material from you precisely because it’s temperature resistant.”

Besides showing the characteristic humor of the ASML CTO, the anecdote also demonstrates that heat influences are an increasing problem. Van den Brink, of course, knows all too well that even Zerodur is no miracle cure for unwanted shrinkage or expansion when it comes to the last nanometers. The hilarity of his response: in the meeting, the participants are discussing extreme requirements and control in chip production and then their supplier is bothering them with something as down to earth as a warehouse.

ASML optical path
The full optical light path in an EUV scanner. EUV light is absorbed by any material, whether it’s mirrors, reticles or the thin hydrogen gas in the vacuum chamber. Credit: ASML

Well, if you look at the history of the wafer stepper, heat is a prehistoric problem. In the sixties, it already affected the design of the Philips Photorepeater, a machine that produced contact printing masks and was specified to deliver an overlay performance of 0.5 micron over the full length of a 2-inch mask and wafer. The designers got a grip on it by keeping the oil that was circulating in the hydraulic stages at a constant temperature. In the early seventies, the first wafer stepper architect at Philips, Herman van Heek, also noticed deviations in the overlay when his assistants stood next to the machine for fifteen minutes. His machine warped due to body heat radiation.

Poor cooling design

At a recent Comsol webinar on modeling in semiconductor applications, Emilio Bajonero Canonico, a thermal engineer at ASML’s performance cluster for the NXE overlay project, gave a presentation about thermal modeling in EUV scanners. His talk offered lots of insights into the current challenges, specifically on reticle heating, even though many numbers in his graphs were blacked out for competition-sensitive reasons.


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The overlay team Bajonero is part of focuses on troubleshooting escalations from the field and identifying root causes of poor overlay performance. Their second main task is de-risking future implementations in hardware and software to make sure that the ASML systems can keep up with the overlay performance roadmap.

Let’s start with an early success. When Bajonero started working at ASML, his mentor told him: if you want to have a very large impact on your project, you not only need to give results, you also need to build tools. Bajonero: “He explained that by building tools, I could share the understanding of the physical phenomenon, sensitivities and what does or doesn’t matter for a thermal problem.” His tutor was right: “It indeed made my discussions easier.”

But when Bajonero first released his reticle heating model application in Comsol tooling, he didn’t immediately get the acceptance he had hoped for. But he did have the luck that a colleague wanted to do a tryout. This specialist and his team had been struggling with long-term drift. The drift was asymmetric and it had a very long time constant that seemed unrelated to reticle heating. Over the weekend, the colleague ran a very long simulation of a few hundred wafers. “In the model, my colleague set the expansion coefficient to zero,” tells Bajonero. “The result was that he identified a second heating deformation mode that came as a result of poor cooling design. It not only gave us the root cause of the deformation, but it also allowed us to find ways to overcome this deformation and correct for it.” As a result, the NXE:3600D wafer scanner, released this year, has a new correction mechanism that mitigates this problem.

Performance drop

Current chip scaling is at the nanometer level and temperature effects greatly impact the patterning precision of EUV litho machines. To prevent inaccuracies, all the elements in the projection system, like the reticle, mirrors and motors, are calibrated. But that’s only the starting point.

Since EUV light is absorbed by any material, the machine is internally kept at very low pressures. Trouble begins when the system starts exposing. EUV light is shone throughout the machine, the wafer stage and reticle stage start moving to scan and expose the wafers. Bajonero: “This means that the motors will begin dissipating heat. Initially, the position and status of my elements are calibrated for, but once the thermal drift begins and thermal deformation sets in, the performance of my machine will drop.”

If the EUV source is switched on or the machine steps from printing one kind of chip to another, it requires more or less power. “In short, my machine observes a change in production status and will drift thermally. If my machine thermally drifts, it will deform and what I will observe is a drop in positioning performance.”

Heating model

In his presentation, Bajonero focused on a crucial part: the mask and reticle stage. The stage holds the mask with a pattern that chip manufacturers want to print on every wafer. The mask relies on reflective optics. “The reflection isn’t perfect. We shine EUV light on the reticle and it reflects it into the projection optics, but the reticle will absorb a fraction of that light and it will get hot. Moreover, when we want to push the machine productivity higher and higher, we use more power in our system, which means that for future iterations of our machine, the reticle heating problem needs to be mitigated.”

Although the reticle is made of ultra-low-expansion glass, the expansion due to heating isn’t zero. Also, the thermal gradients in it can be quite steep due to its low thermal conductivity. “Which means that we need to address this by thermal conditioning. Unfortunately, we aren’t able to fully contain the thermal problem, so we need to mitigate the impact in our machine performance.”

The first step towards mitigation is understanding the physics behind the phenomenon. For this, ASML relies heavily on finite element methods. Like in the real world, the reticle in the model is clamped to the stage, using a thin elastic layer formulation that holds the reticle in place but still allows it to deform a little bit. The heating model is a combination of heat transfer, solids and mechanical deformation from thermal expansion. The thermal gradient caused by EUV absorption results in thermal strain over all the bodies.

Bajonero: “All the physics going into the simulation, like the thermal strain curves of the materials, the stiffness of the clamp, the effectivity of the cooling system and the heat transfer through the low-pressure environment, ends up as parameters that control either the thermal or the mechanical formulation.” And as usual with finite element modeling, the parameters of the model are tuned according to measurements and experiments. “So the learning curve follows an iteration loop,” explains Bajonero. “We ask ourselves questions like: from experimental data, can we reproduce the behavior that we see in our modeling? And can we investigate a solution space in our modeling and make sure that it will reproduce in our machine.”

Unfortunately, the simulation loop doesn’t always go well. “Then we’re forced to ask ourselves questions like: why can’t we see this in our model? Are we really extracting pure heating deformation data from our system?”

ASML Comsol slide 10
The reticle heating model. Credit: ASML

Comsol application

One of the limitations that the NXE overlay project experienced working the feedback loop was the long cycle time for the learning. “Our company is quite large and there’s an inherent separation between analysts, our architecture team and the overlay team. This made the iterations on the model a bit too slow and the learning a bit slow as well for our liking.”

To expedite this process, the model was transferred to a Comsol standalone application that simulates reticle heating expansion as a function of a multitude of input variables. “With it, we can simulate how reticle heating will cause overlay errors and how they depend on parameters such as reticle-absorbed power and environmental conditioning of the reticle like the cooling characteristics of the water flow, the temperature of the water flow and so on.”

The thermal experts at ASML intentionally keep the more advanced finite element features such as meshing hidden for their colleagues. Bajonero explains why: “Our end users aren’t FEM experts. We basically and mainly want them to learn from the use cases they run. We want them to be our colleagues and we want them to generate data based on the use cases they consider themselves important.” The thermal experts did make it possible for users to not only vary the input but also isolate modules and generate images “so that they can present the information they find best.”

ASML Comsol slide 12
The transient mode in the model allows the user to simulate heating cycles and obtain information on how the pattern heats up during a wafer or across several wafers. On the right, different wafer exposure durations are simulated. This simulation helps to find root causes for poor performance because also in real life, the machine doesn’t always take the same time for each wafer and there can be periods that vary across a set of different wafers. Credit: ASML
ASML Comsol slide 13
Export of deformation data is one of the most important features of the application mode. Users can choose to export reticle deformation as a function of time and simulate the effects of an exposure sequence. It makes it possible for the overlay analysis team to simulate the effects of machine calibrations. The graph shows the exposure cycles. During cooling, the machine performs calibrations and these are simulated. The overlay content that those calibrations will take away from the deformation of the field is visualized and the actual reticle heating problem can be estimated. Once the system saturates, a certain amount of deformation can be corrected for by a control loop. Credit: ASML

New solutions

Bajonero also gave some interesting insights into the material problems of glass and the underlying physics if you enter the nanodomain. Even with an ultra-low expansion material, the expansion coefficient isn’t zero. Worse: it varies with temperature. It’s also glass, not a crystal. Glass is amorphous, which makes it inherently inhomogeneous.

“The very low thermal expansion comes at the cost of having a nonlinear thermal strain curve,” clarifies Bajonero. “This means that when my reticle is hot, one degree delta will generate more expansion than if my reticle is at ambient temperature.” This is modulated by the zero-crossing temperature, which determines the temperature of the minimum in the reticle deformation, and the zero-crossing slope, which determines the rate of growth of deformation as a function of temperature. Bajonero: “The reticle heating is very sensitive to these two parameters and the bad news is that we saw that these parameters vary across the body of a reticle. Moreover, our correction techniques are heavily affected by the spatial distribution of the deformation. This means that we’re less able to correct high-frequency deformations.”

The thermal expert team made it possible for users to import two-dimensional maps of zero-crossing temperature offsets. “With the import of this map, the application will project the zero-crossing temperature offset into the reticle and we’ll make sure that every point in the reticle will move or will deform with a different thermal strain curve.”

ASML Comsol slide 16
The left side of the reticle has a lower zero-crossing temperature (dotted line) and the right side has no zero-crossing temperature offset (orange line). The simulated deformation shows that the right side observes a lower deformation than the left side (at steady-state conditions). Credit: ASML

This kind of capability allows the ASML engineers to import the material characteristics maps provided by the glass supplier. “We can also estimate what kind of impact such variations can have on our alignment techniques that will transfer into conformant performance. Not only this; we also allow our engineers to give tools to a supplier to explore their design space, and see if they can help us by providing a material that will meet our specifications.”

The models also allow for exploring specific situations at the customer. “Customers may want to print more fields per wafer at the cost of making them smaller. For us, it means that the deformation mode of the whole reticle will differ from usual use cases. This means that the correction capability of our usual correction mechanisms will also have to change. We’re able to simulate the effect of these smaller field sizes. It lets us explore the weak points of our correction schemes and find new solutions. Most importantly, it lets us do it quickly to investigate which conditions or which solutions require further investigation.”

It was an investment in time to build an application in Comsol tooling, but Bajonero says that has been compensated by the improved results and by the shared simulation information. The thermal experts at ASML are now getting challenged more often. “As our team better understands the physics behind their problem, the level of the questions that come back to you get a bit higher,” says Bajonero. “This makes my job a little bit more difficult but a lot more exciting.”