Semiconductor Leakage Distribution Estimation via Gaussian Mixed Model
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Solution Overview
Problem
Current leakage estimation methods for semiconductor devices, particularly for DRAM, are inefficient as they require a large number of data points and are mainly performed at the gate level, whereas accurate estimation at the transistor level is necessary due to increasing power consumption concerns in mobile devices.
Innovation Solution
A leakage distribution estimation system that includes a parameter sampling unit, data transformation unit, leakage data generation unit, and a Gaussian mixed model (GMM) modeling unit to efficiently estimate circuit leakage currents at the transistor level by selecting sample values, transforming them into Gaussian values, generating leakage data, and clustering it to determine the leakage distribution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If leakage estimation is performed at gate level or higher level, then the analysis can be performed more easily, but the accuracy is insufficient for DRAM devices with single-transistor cell structures operating in analog range
Solution Approach 1:
The patent segments the leakage estimation problem into transistor-level analysis components. It divides the DRAM cell into individual switching elements (transistors) and analyzes leakage currents at each transistor level separately, then combines the results. This segmentation enables accurate analog-range analysis of single-transistor structures while maintaining systematic ease of operation through modular processing steps.
2Measurement precision
If a large number of leakage data points are collected for accurate distribution estimation, then the estimation accuracy improves, but the analysis time and computational resources increase significantly
Solution Approach 1:
The patent performs preliminary actions by collecting and organizing transistor-level leakage data and bias information before the actual distribution estimation. It pre-processes the data by extracting relevant leakage components and organizing them by transistor type and operating conditions. This preliminary preparation enables accurate distribution estimation using fewer data points, as the data is already structured for efficient Gaussian mixed model fitting.
Solution Approach 2:
The patent changes the parameter space by transitioning from gate-level abstract parameters to transistor-level physical parameters (threshold voltage, channel width, channel length, bias conditions). It also transforms the estimation approach from requiring large Monte-Carlo sample sets to using structured transistor-level data with Gaussian mixed modeling. This parameter transformation achieves accurate leakage distribution estimation with reduced data requirements and computational time.
3Measurement precision
If Monte-Carlo simulations are used for leakage distribution estimation, then statistical accuracy can be achieved, but the method suffers from local minima issues and requires extensive computation
Solution Approach 1:
The patent substitutes the mechanical Monte-Carlo simulation approach with a statistical modeling approach based on Gaussian mixed models. Instead of relying on random sampling and iterative convergence that can trap in local minima, it uses deterministic statistical methods that fit leakage data to Gaussian distributions with multiple components. This substitution eliminates local minima issues while maintaining statistical accuracy and reducing computational complexity.
Data Source
AI summary
A semiconductor device includes a leakage distribution estimation system. The system includes: a parameter sampling unit suitable for selecting sample values for parameters, which are changed according to a process variation of the semiconductor device; a data transformation unit suitable for transforming the sample values selected by the parameter sampling unit into Gaussian sample values; a leakage data generation unit suitable for generating leakage data of the semiconductor device by performing a leakage simulation using node bias information on switching elements included in the semiconductor device, information extracted for leakage components of the switching elements, and the Gaussian sample values; and a Gaussian mixed model (GMM) modeling unit suitable for clustering the leakage data into a plurality of clusters, generating Gaussian components corresponding to the respective clusters using the leakage data of the clusters and mixing the Gaussian components thereby to determine a leakage distribution of the semiconductor device.