Statistical Process Control for Censored Semiconductor Breakdown Data
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Solution Overview
Problem
Conventional statistical process control (SPC) methods for semiconductor integrated circuit manufacturing assume normal distribution and do not effectively handle censored data, leading to unreliable data collection and inadequate monitoring of process-related information, particularly in cases where voltage breakdown data is censored.
Innovation Solution
A method that determines minimum breakdown voltages for lots using order statistics, processes both censored and uncensored data points, and applies transformations like Box-Cox to normalize the data, enabling the calculation of control limits and anomaly detection in semiconductor integrated circuit manufacturing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional SPC methods assume normal distribution and directly apply control charts to observed data, then the process is simple and easy to implement, but the data collection becomes unreliable when censored data is present
Solution Approach 1:
The patent transforms the statistical parameters and data representation by introducing order statistics and handling censored data through specific statistical transformations. This allows the control chart to properly account for censored observations while maintaining the normal distribution assumption, thus resolving the contradiction between simplicity and reliability
Solution Approach 2:
The patent introduces an intermediary statistical framework that mediates between the simple control chart methodology and the complex reality of censored data. By using order statistics and transformation techniques as intermediaries, the system maintains ease of implementation while achieving reliable data collection
2Device complexity
If conventional SPC methods are used without handling censored data, then the monitoring process remains simple, but the control limits and anomaly detection become inaccurate
Solution Approach 1:
The patent changes the parameters used in control limit calculation by incorporating order statistics and censored data transformations. This allows accurate control limits to be established while keeping the overall monitoring process framework relatively simple, resolving the contradiction between complexity and precision
3Quantity of substance
If voltage breakdown data is collected with censored observations, then more complete data is obtained, but direct application of control charts becomes inadequate
Solution Approach 1:
The patent applies parameter transformations to handle censored data, converting the incomplete observations into a form suitable for control chart analysis. This maintains data completeness while reducing the difficulty of detection and measurement through systematic statistical handling
Solution Approach 2:
The patent implements a feedback mechanism where censored data information is fed back into the control chart methodology through order statistics. This allows the system to utilize the complete data set while the feedback loop ensures proper handling of censored observations in the analysis
Data Source
AI summary
A method for monitoring device characteristics of semiconductor integrated circuits. The device characteristics includes censored data and uncensored data. The method includes determining a plurality of minimum breakdown voltages numbered from 1 through N, respectively, for a plurality of lots (e.g., wafer fabrication lots) numbered from 1 through N. Each of the plurality of minimum breakdown voltages is respectively indicative of the plurality of samples through order statistics. One or more of the plurality of samples includes one or more uncensored data points and one or more censored data points. The method includes processing the minimum breakdown voltages, respectively, for the plurality of lots. Each of the minimum breakdown voltages is processed for the respective plurality of lots and is indicative of a population characteristic breakdown voltage numbered from 1 through N for the respective lot numbered from 1 through N. The method includes determining one or more anomalies based upon the processing of the minimum breakdown voltages. The one or more anomalies is associated with one or more processes associated with at least one of the lots.