AMHS 26 | March 2025 Semiconductor Digest www.semiconductordigest.com Chaos and AMHS methodologies AMHS systems are physical dynamic systems acting on the wafer-lot state space outside of process tools. But we are not modeling AMHS. Instead, we model the inter process wafer-lot state space comprising of multitudes of wafer lots on the move or in dynamic storage. Our model is the state space of the inter process moves with parameters of de- livery time T n , velocity V n , and distance D n , of each wafer lot. And then define a mathematical map for this which relates delivery time of a wafer lot move to the next process and beyond. The map on the Conveyor Moves As a wafer lot advances through the manufacturing process its T n accu- mulates according to the time series, iterating the steps from tool to tool. Each step starting with the previously accumulated T n-1 , and then calculating the next value of T n . This process is linear, modeling Conveyor logistics as linear dynamic systems. The variance of and S n of each move is linearly additive for the final outcome, of total transfer time T of the lot. Similarly, we model the inter process state space of the wafer lots when dis- crete vehicle systems are acting on it. The map via vehical moves P(t) being a stochastic vehicle arrival time after request to move. The probable value of arrival time of a vehicle, after a request-to-move can be modeled as an exponential P(t) shape factor for the exponential probability of t. It may be assigned a value meaning the mean rate of stepping. The point, however, is that the series ( T n ) j , is nonlinear as the wafer-lot-moves iterate the formula. The growth of uncertainty in the cumulative time of wafer lot transits between multiple fabricating processes is subject to exponential growth. This fact is clear, as only the probability of time is inserted in place of T n-1 before calculating the newly accumu- lated time for transits. Then, adding probabilities inside the formula the algebra of probabilities dictates a multiplication (ref. Towards Clean Frontend Manufacturing, Horn, IEEE Transactions, 2022 CSTIC). Resulting in exponential growth. This dynamic system, or rather our map imitating it, is chaotic. Meaning, that forward predictions, forecasting arrival times between processes, and cycle time for the lot, have severe limitations. We can only forecast a very near future. Then, to prevent the uncontrolled growth of uncertainty, the wafer lot transfer process itself is sometimes suspended (stockers/buffers) and restarted. Overall, chaotic behavior limits the forecast horizon for the state when moving via discrete vehicle type AMHS. Machine learning (AI) How would machine learning operate in the inter process wafer moves state space? In the iterative process of observing values of parameters in that space, i.e. observing its state, based on which an action set is computed by the agent, followed by rapid de- livery of the action to the system (ref. AMHS in the Reinforced Dispatch Learning Environment of IC Fabs. Horn, Semiconductor Digest, January 2024) The parameters to observe in the inter process wafer state space are the accumulated vectors ( T n ) j resulting from move distances, times for inter process transits and times in dynamic storage. Suggesting routing algorithms to improve over all time T to transit the fabrication process. Such algorithms would comprise the Agent. And Rewards for learning be calculated for improved average delivery times. By default, a sub- stantial part of learning would be the minimizing of S j , the stocker times of routes. Conclusions There are caveats to this learning process. Such as steady state wafer starts, defined to-from process flow tables, and a data base for historic (T n ) j . Then a most serious question is the ability of the Machine Learning scheme to work with the uncertainty in the current computations of (T n ) j . As shown above for the discrete vehicle AMHS systems this uncertainty is great. How would the agent create an action based on uncertainty in the measurement of the state? Nonlinearity of the AMHS models for current 300 mm, and also for the legacy 200 mm fabrication thus represent difficulties for oncoming AI applications. Early demonstrations of AI were applied to Dispatch models which neglected considerations of realistic AMHS. No application of AI for reducing the substrate content (cycle time) in the inter process state space, i.e. the pure AMHS case, are known in literature. But we antic- ipate that the linearity of conveyor transport nets would offer an easier way for machine learning and so offer a longer horizon for forecasting. And, at the same time, the likelihood of voiding the chaotic growth of uncer- tainty. Considering the exponential growth of uncertainty of the vehicle model, the wisdom of maintaining our current discrete vehicle based AMHS design, as is, becomes questionable. Installations already exist where the inter process transport assignment of the vehicles is transferred to con- veyors, while maintaining the vehi- cle’s vertical service assignments to the tool port.