Semiconductor Model Parameter Generation for Trapped-Charge Variability
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Solution Overview
Problem
Existing semiconductor device models fail to accurately capture time-dependent degradation and reliability, particularly due to interactions between bias temperature instability (BTI) and intrinsic parameter fluctuations from random discrete dopants, line edge roughness, and metal gate granularity, which limits their effectiveness in modeling the performance of semiconductor devices over time.
Innovation Solution
A method for generating semiconductor device model parameters that involves receiving performance data from statistical instances of semiconductor devices, extracting model parameters, modeling statistics to determine moments and correlations, and generating parameters using these determinations for specific areal trapped charge densities, incorporating techniques like the Generalized Lambda Distribution and Probability Integral Transform to account for non-normal distributions and variability sources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional uniform model fitting is used to model average device performance, then model simplicity is maintained, but accuracy in capturing time-dependent degradation and reliability is insufficient
Solution Approach 1:
The model parameters are segmented into two categories: (1) parameters that remain constant across statistical instances, and (2) parameters that vary between instances due to random variability sources. This segmentation allows the model to capture both average performance and device-to-device variations without requiring complete re-extraction of all parameters for each instance.
Solution Approach 2:
The invention changes the parameter extraction approach from fitting uniform models to average performance to re-extracting specific parameters for individual statistical instances. This parameter change enables accurate modeling of time-dependent degradation by capturing the interactions between BTI and intrinsic parameter fluctuations specific to each device instance.
2Measurement precision
If one model card is created for each transistor instance, then individual device variations are captured, but the problem space scales up significantly with measurement and simulation requirements
Solution Approach 1:
A small set of re-extracted parameters serves multiple functions: they capture intrinsic parameter fluctuations, model time-dependent degradation effects, and represent device variations across different stress conditions. This universal parameter set eliminates the need to create completely separate model cards for each device instance while maintaining accuracy.
Solution Approach 2:
Instead of creating unique model cards for each transistor instance through extensive measurement and simulation, the invention uses statistical copying by generating parameters from fitted distributions based on a limited set of measured or simulated data points. This copying approach efficiently generates representative model parameters for individual instances without requiring complete characterization of each device.
3Reliability
If statistical distributions are used to model parameter variations, then device variability is captured, but handling non-normal distributions and correlations between parameters becomes complex
Solution Approach 1:
The invention transforms the statistical modeling approach by using the Generalized Lambda Distribution (GLD) to represent non-normal parameter distributions. The GLD parameters are fitted to the statistical moments of the measured data, enabling accurate representation of skewed and non-Gaussian distributions while maintaining computational tractability.
Solution Approach 2:
The Generalized Lambda Distribution serves as an intermediary between the raw measured parameter variations and the final model parameters. By fitting GLD to the statistical moments and using probability integral transforms, the invention mediates the complexity of non-normal distributions and correlations, converting them into manageable parameter sets that can be efficiently used in circuit simulations.
Data Source
AI summary
A method for generating semiconductor device model parameters includes receiving semiconductor device performance data of statistical instances of semiconductor devices, for a plurality of areal trapped charge densities Model parameters are extracted to produce individual model instances, each corresponding to the respective statistical instances for the areal trapped charge densities. Statistics of the extracted model parameters are modeled by processing the individual model instances to determine, for each areal trapped charge density, moments describing non-normal marginal distributions of the extracted model parameters and correlations between the extracted model parameters. Semiconductor device model parameters are generated for use in simulating a circuit using the determined moments and the determined correlations, for a selected areal trapped charge density.