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Micromachines 2026 , 17 , 592 28 of 34 5.2.2. Scenario 2: LS-NH (Low-Speed, No Hysteresis) Algorithmic hysteresis compensation effectively eliminates the reset-to-zero over- head, although hardwar e actuation speeds rema…
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on the same die to account for environmental stability and system repeatability. By encom-
passing these variations in die location and characterization cycles, the results confirm that
the proposed algorithms can generalize effectively across the typical process and placement
variations encountered in high-volume wafer-level testing.
In terms of the interpretation of experimental rankings, results reflect the performance
of algorithms with baseline parameters on a limited but highly realistic dataset of 8 coupling
scenarios. Local BO achieved rank 1 due to its perfect 100% success rate combined with
the fastest alignment time (99.87 a.u.) among the successful methods. Fix-Grad achieved
rank 2, also with 100% success but requiring more time (154.01 a.u.). Global BO, despite
strong performance metrics (97.60% accuracy), achieved only 87.5% success rate, placing
it at rank 3. This lower success rate in the experimental phase reflects the conservative
baseline parameters used at that stage, which had not yet been optimized for the specific
characteristics of the Eclipse Dynamic system.
Following the experimental phase, an iterative improvement of the methods was
conducted to refine the algorithm. The simulation study, which evaluated all the seven
algorithms across 72 test scenarios (8 experiments
×
9 spatial offsets), employed these im-
provements. This larger statistical sample and improved parameterization led to different
performance rankings compared to the experimental results, revealing the true performance
characteristics across diverse initial conditions.
The simulation framework reliably mimics real-world constraints. The RBF inter-
polation accurately captures landscape topologies, evidenced by the strong quantitative
agreement between experimental data (e.g., Local BO experimental accuracy of 98.24%) and
simulated outcomes (98.2–98.3%), indicating minimal uncertainty from the data processing
and validating the fidelity of framework.. The difference in the success rates primarily
reflects the evolution from baseline to changes of the algorithms and parameters, and the
statistical power of the larger simulation dataset.
Given that the simulation results employ improved methods and parameters and a
statistically rigorous evaluation across 72 scenarios, they provide the most reliable basis
for production deployment recommendations. The experimental results validate the fun-
damental algorithmic approaches and confirm real-world viability, while the simulation
results guide the selection of parameters and operating regimes.
5.2. Algorithm Selection Guidelines Across Operating Scenarios
The choice of an optimal alignment algorithm for the Eclipse Dynamic system de-
pends on the operating speed capability and the effectiveness of hysteresis compensation.
Comprehensive recommendations for each of the four evaluated scenarios are provided
next, progressing from worst-case to ideal-case conditions.
5.2.1. Scenario 1: LS-H (Low-Speed with Hysteresis)
This configuration establishes the baseline worst-case scenario, defined by conser-
vative hardware actuation speeds coupled with uncompensated piezoelectric hysteresis.
Under these conditions, the mandatory reset-to-zero maneuvers impose substantial tem-
poral overhead, while the restricted slew rates further exacerbate the latency associated
with each trajectory adjustment. Based on these stringent operating parameters, Fix-Grad
emerges as the optimal choice for maximizing process yield (see Tables 3 and 5). While
the Var-Grad approach operates faster, its approximate 10% failure rate requires manual
intervention, preventing any speed advantage in a production setting. Furthermore, the
substantial temporal penalties imposed by mandatory reset-to-zero maneuvers dispropor-
tionately degrade the performance of Bayesian approaches in this slow-actuation regime,
leaving Fix-Grad as the most robust and practical solution.
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5.2.2. Scenario 2: LS-NH (Low-Speed, No Hysteresis)
Algorithmic hysteresis compensation effectively eliminates the reset-to-zero over-
head, although hardware actuation speeds remain inherently slow. This configuration
successfully isolates the specific operational benefits of software-based compensation. With
hysteresis effectively mitigated in software, alignment times improve across all methods
(Table 3). Nevertheless, Fix-Grad maintains its operational dominance. Var-Grad provides
a marginal speed advantage of roughly 2 a.u., but its lower reliability presents an unfa-
vorable speed-versus-yield trade-off. Although the removal of physical reset maneuvers
improves the relative viability of Bayesian methods compared to the LS-H scenario, their
computational overhead keeps them slower than gradient-based alternatives, solidifying
Fix-Grad as the definitively recommended strategy.
5.2.3. Scenario 3: HS-H (High-Speed with Hysteresis)
Representing typical production conditions, this scenario pairs rapid hardware kine-
matics with uncompensated hysteresis. Evaluating algorithmic efficacy under these con-
straints is vital for industrial systems where implementing feedforward compensation
remains impractical. In this realistic high-volume configuration, Fix-Grad is strongly rec-
ommended when alignment reliability is paramount, maintaining peak success rates while
remaining highly competitive in execution speed. Var-Grad should be restricted to prelimi-
nary screening applications where occasional failures are an acceptable trade-off for rapid
alignment. Notably, this scenario highlights a critical limitation of the Global BO approach:
without cross-scan initialization, pure probabilistic exploration struggles to resolve the
hysteresis-distorted landscape efficiently, resulting in both the lowest reliability and longest
execution time among the optimization methods.
5.2.4. Scenario 4: HS-NH (High-Speed No Hysteresis)
This ideal regime couples rapid hardware kinematics with effective feedforward hys-
teresis compensation [
14
,
16
]. Representing the gold standard for production deployment,
this configuration highlights the ultimate capabilities of the algorithms. Fix-Grad is defini-
tively recommended, delivering an optimal balance of high reliability and rapid alignment
to effectively mitigate throughput bottlenecks [
3
]. While Var-Grad achieves the absolute
fastest alignment time (approaching 1 a.u.), its persistent 9.7% failure rate remains a lim-
iting factor for strict production environments. Conversely, despite requiring the fewest
physical measurement steps, the substantial computational overhead of GP fitting severely
inflates the temporal cost of the Global BO method, rendering it unsuitable for high-volume
environments demanding both absolute reliability and sub-second speed.
5.3. Cross-Scenario Performance Analysis
A cross-scenario comparison reveals several critical insights. First, the Fix-Grad
algorithm demonstrates exceptional robustness, consistently achieving 95.8% reliability
across all speeds and hysteresis conditions. Conversely, Global BO is most sensitive to
uncompensated hysteresis: in the LS regime, reliability drops from 93.1% to 88.9% (
−
4.2%),
and in the HS regime, from 90.3% to 88.9% (
−
1.4%), while its alignment time inflates by
92%, rendering it problematic without active feedforward compensation.
Hardware kinematics and hysteresis mitigation drastically impact throughput. Transition-
ing from low-speed to high-speed regimes accelerates Fix-Grad alignment by 14.6
×
(from 20.95
to 1.44 a.u. without hysteresis) and 21.9
×
(from 72.47 to 3.32 a.u. with hysteresis). Managing
hysteresis via the mandatory reset-to-zero strategy roughly doubles execution time across
all algorithms (detailed in Table 3). Importantly, despite this severe temporal penalty, final
positioning accuracy consistently exceeds 98%, validating the open-loop control architecture.
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Finally, the data exposes a critical divergence between sample efficiency and true
temporal efficiency. Although Global BO consistently requires the fewest physical mea-
surements (24 steps), its substantial computational overhead for Gaussian Process updates
results in a longer total execution time (2.24 a.u.) than Fix-Grad (1.44 a.u. across 34 steps).
Consequently, sample efficiency alone is a misleading metric for evaluating high-volume
production throughput.
5.4. Impact of Operating Speed
High-speed operation is essential for achieving production-viable throughput, as it
drastically reduces per-die optical alignment time. Using the Fix-Grad algorithm as a
benchmark, execution time decreases from 72.47 a.u. in the worst-case low-speed hysteretic
regime (LS-H) to 20.95 a.u. in the low-speed non-hysteretic regime (LS-NH), 3.32 a.u. in
the high-speed hysteretic regime (HS-H), and ultimately 1.44 a.u. in the ideal high-speed
non-hysteretic regime (HS-NH). Transitioning from low-speed to high-speed operation
therefore yields a 14.6-fold acceleration in the absence of hysteresis and an even larger
21.9-fold speedup when hysteresis is present.
The practical significance of this acceleration becomes clear at the wafer scale. For a
standard 300 mm wafer containing 200 PIC dies, the total optical alignment burden rises to
approximately 14,500 a.u. in the LS-H regime, which is clearly impractical for manufactur-
ing. Under realistic high-speed operation with hysteresis (HS-H), this total is reduced to
approximately 664 a.u., already representing a major improvement in throughput. In the
ideal HS-NH regime, the total falls further to approximately 288 a.u. per wafer.
To relate these normalized values to real production conditions, we note that the ideal
Fix-Grad alignment time of 1.44 a.u. is consistent with the sub-second per-die optical cou-
pling times reported in state-of-the-art automated photonic test systems [
10
,
11
]. Under this
interpretation, the HS-NH regime corresponds to full-wafer optical alignment in a matter
of minutes, whereas the LS-H regime would translate into a multi-hour process devoted
only to optical alignment. This difference clearly shows that high-speed actuation is not
merely beneficial, but fundamentally necessary for meeting the throughput requirements
of high-volume PIC and co-packaged optics manufacturing [1,3].
Overall, these results validate the importance of integrating high-speed piezoelectric
drive electronics directly into the probe-card architecture. They also show that, when
combined with an efficient search strategy such as Fix-Grad, the Eclipse Dynamic platform
can achieve alignment times consistent with the fastest per-die coupling results reported in
the recent literature [10,11].
5.5. Impact of Hysteresis
Hysteresis imposes a severe temporal penalty due to mandatory reset-to-zero motions,
inflating high-speed execution times by 130% for the Fix-Grad algorithm (from 1.44 to
3.32 a.u.) and by 92% for the Global BO method (from 2.24 to 4.29 a.u.). Despite this
near-halving of throughput, robust algorithms maintain highly stable alignment quality:
Fix-Grad retains a constant 99.4% accuracy and 95.8% reliability regardless of hysteresis.
Conversely, the Global BO approach experiences a reliability degradation from 90.3% to
88.9%, indicating that uncompensated hysteresis distorts the coupling landscape sufficiently
to trap pure probabilistic exploration in local maxima. Ultimately, the business case for
implementing feedforward hysteresis compensation, such as inverse P-I models [
14
,
16
], is
highly compelling. Mitigating these nonlinearities effectively doubles system throughput
and tester capacity, thoroughly justifying the initial software development investment.
https://doi.org/10.3390/mi17050592