New multi-axis stages: Driving dynamics in one plane for top performance

Having all of a stage’s driving dynamics in one plane can prevent problematic reaction torques on sensitive workpieces … and maximize machine performance for demanding motion applications.

By Mathys te Wierik • Lead system engineer

Jan Willem Ridderinkhof • Manager of R&D and engineering | PM B.V.

High-end mechatronic motion solutions have proliferated as various industries have come to demand more precision and throughput than ever. But the development and production of such motion stages isn’t usually a core competency of OEMs and end users … so is something typically outsourced to motion-component and system suppliers. That’s especially true for OEMs in the semiconductor, medical, optical, and analytical industries … as here, engineering is more focused on specialized production processes.

One new option for these specialized engineering OEMs and end users is next-generation motion stages with dynamics to future-proof operations.

Design objective one: High multi-axis stage throughput

Consider an example application — a semiconductor-wafer inspection process with one axis’ stroke exceeding 300 mm … but needing mechanical accuracy in X and Y better than 1 μm. Assume accelerations to 2 g and speeds to 2 m/sec in the horizontal plane. Also assume vibrations in the horizontal plane must remain below 25 nm — and that the stage runs in a cleanroom with a floor held to VC-C vibration specifications. Vibrations in the vertical direction — the direction used to move the wafer into the optics’ focal point — cannot exceed 10 nm. Quick accelerations and short settling times are crucial to get throughputs for sufficient profitability.

Having the inspection stages’ driving dynamics in one plane ensures the motors cause no detrimental reaction torques on sensitive system parts. Such dynamics require aligning the centers of mass for all moving bodies … as well as the linear bearings and motor forces’ positions. In fact, keeping all dynamics in one plane also minimizes the out-of-plane loads on the linear bearings for longer-lasting mechanical assemblies that exhibit fewer inaccuracies over time.

Designing all the dynamic components in one plane is relatively easy for a single-axis system. But beyond that, the usual approach is to stack the second axis on top of the first … for movement orthogonal to the first. Any third axis then stacks on top of the second.

The problem with such axis stacking is that the center of gravity (CoG) of the moving mass is compromised for each axis … so reaction torques occur when accelerating or decelerating. Such reaction torques create yaw, pitch, and roll errors.

In contrast, stages with a horizontal box-type frame supported by a linear bearing on each side exhibit better dynamics. Linear bearings with recirculating ball elements (when correctly mounted) are sufficiently accurate for the support of such stages, even in optical wafer-inspection equipment. In such a square frame, a second axis mounts coplanar with the first axis. Then a Zθ module (for rotations and vertical movements) integrates into the second axis. Only short-stroke vertical movements are made, so the centers of mass and actuation remain mostly in one plane. This means that the moving masses exhibit no lever-arm behavior … which in turn boosts positioning accuracy.

The new motion platform called Vega from linear-motion-system company PM B.V. takes the form of the squatter stage arrangement shown here. The stage is suitable for demanding high-precision tasks such as optical wafer inspection.

Design objective two: Multi-axis stage topology optimization

Beyond optimized macro design elements, wafer-inspection stages must also have lightweight frames with high structural stiffness. Aluminum frames are a top choice here — especially when optimized with CAE tools.

Consider one box-shaped frame optimized for good dynamics and manufacturability. Constant material thickness for cross members allows for cost-effective and accurate manufacturing. A large C-shaped profile for main cross members maximizes the overall stiffness-to-weight value and can do double duty as the linear-bearing mounting surface.

Shown here is a side view, top view, and C-shaped cross-sectional view of the Vega stage’s X-axis cross members. MATLAB-generated topology analyses shows displacement under gravitational and acceleration loading ranging from small (blue) to large (yellow).

Design objective three: Strategically mounted actuators on the multi-axis stage

Next the stage drive type and arrangement are considered. Here it’s best to look for options making optimal use of the bearing stiffness and minimizing the number of surfaces needing expensive grinding tolerances. Certain fully optimized stages based on ironless motors (with moving coils) do this with a somewhat complex construction — but one that ensures the motor, linear bearing, and encoder all mount on the lower part of its C-shaped profile.

Click to enlarge. These are three options for stage drive type and arrangement as viewed perpendicular to the stage X axis. (All incorporate the C-shaped profile described in the article’s first section on topology.) Surfaces requiring expensive grinding tolerances are in red. Left: An iron-core motor force aligns with the plane of the linear bearings and the stage’s CoG … but the motor’s attraction force loads the bearings. Middle: Dual iron-core motors’ forces align with the bearings and stage CoG … and the attraction forces cancel each other out. Right: The motor forces align with the linear bearings and CoG … and subject the assembly to no attraction force.

Design objective four: Quick settling time

High throughput of delicate semiconductor wafers requires stages having predicable frequency-response functions. Reconsider our stage structure at hand having rigid base plate, linear bearings, and array of machined metal cross members.

Complicating the collection of accurate transfer-function predictions are the linear-bearing dynamics. Conventional bearing-stiffness models based on ideal Hertzian contact theory significantly overestimate the stiffness of real-world bearings in use. That’s why it’s better to combine Hertzian contact theory and component-based testing — and apply experimental modal analysis to a bearing with a rigid dummy load. Extensive testing reveals that enriched bearing models are much more realistic than conventional idealized Hertzian contact theory models.

Vibration analysis can take the form of hammer-impact testing of the bearings. That reveals their stiffness in the relevant degrees of freedom. Finite-element analysis of the Vega stage assembly (including that of bearing stiffnesses) by PM B.V. engineers yielded open-loop transfer functions. These in turn revealed that the Vega stage’s first observable eigenmode was comfortably above the target bandwidth. Then the PM B.V. engineers modeled the stage’s feedback control loops around these transfer functions to predict the stage’s settling times (including its control). This settling-time prediction along with the complete motion profile (based on a wafer inspection cycle) was then simulated to verify the machine’s maximum throughput.

Demanding requirements of residual-vibration mitigation necessitates a vibration-isolation system. High acceleration requirements in particular put high lateral forces on the stage’s granite base … so the vibration isolation system must be active. The use of a balance mass to eliminate vibrations is nonviable here because such designs are excessively bulky.

This is a schematic representation of the Vega stage on an active vibration-isolation platform. Compliant springs prevent transfer of floor vibrations to the stage. Skyhook damping and an advanced floor feedforward algorithm (green arrows) further address vibration. The stage forces on the granite (red arrow) are counteracted by feedforward control (orange arrow). As the vibration-isolation system has a strong influence on the stage settling times, PM B.V. engineers also incorporated its dynamics into their settling-time simulations.

Optimization of the stage’s vibration isolation necessitates the balancing of conflicting design requirements. Settling times benefit from a stiff setup, but a compliant vibration isolation system can minimize residual vibration … and the transmissibility of floor vibrations to the stage quickly diminish above the first eigenfrequency of the isolation system.

This new motion platform called Vega from linear-motion-system company PM B.V. is the stage featuring all the optimized design features described in this article — a rigid granite base plate, linear motors and linear bearings for each axis, and a Zθ-module in the center of the XY-axes. Wafers ride on a black circular plate on top of the Zθ-module. Interdependent design elements were concurrently optimized. Case in point: Analysis of the stage’s thermal (as well as dynamic) stability inform the locations of its optical encoders.

Design objective five: Good thermal management

Thermal management is required for all motion applications. However, in the precision applications we consider here, thermal management is most important for meeting stringent accuracy requirements. After all, any thermally induced changes in the machine dimensions can prove disastrous in wafer inspection.

The tool point’s location — at the site of interest on the wafer — must be known with an accuracy of a single micrometer, even when the system is operating at its maximum throughput cycle and the actuators are generating considerable heat.

So stages for these designs necessitate consideration of thermal effects from the initial-concept design phase — ideally with comprehensive thermal-network models for understanding of all design choices’ thermal implications. Precision semiconductor manufacture often precludes the use of liquid cooling that might leak coolant onto expensive payload or require detrimental stops during critical production steps. Precision manufacture often precludes cooling fans as well, because of how forced airflow can induce stage and payload vibrations.

In contrast, passive cooling (while limited in efficacy) can shed sufficient motor heat … especially when the finned heatsinks are large enough to prevent and thermal expansion of the stage subcomponents. Consider stages having such heat sinks that are structurally connected but thermally isolated from the rest of the system by means of thermal barriers. These see increased stiffness without any sacrifices in accuracy. FEA confirms that thermal barriers do indeed help heat shedding … though further improvements are necessary to sufficiently minimize thermally induced stage deformation.

One complementary option here is structural components of invar — a nickel-iron alloy with a low coefficient of thermal expansion. This option is costly … and the stiffness-to-weight ratio of invar is lower than that of alternative materials.

A better option is strategically placed aluminum flexures that allow the stage structure to expand freely. Then a few invar components at centers of thermal expansion keep the components’ centers position-independent of temperature variations. This makes the best use of expensive invar.

M B.V. | www.pm.nl