Mapping Atomic-Scale Wave Functions to Effective Mass Models
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Solution Overview
Problem
Current methods struggle to accurately extract effective mass models from complex band structure data of confined nanodevices, as existing systems cannot handle the interleaved band structures of these devices, making it difficult to simulate their behavior effectively in TCAD tools.
Innovation Solution
A method is developed to generate an approximate band structure model by mapping atomic-scale wave functions and eigenenergies from First Principles Methods to effective mass models, using a curve-fitting process to match and identify interleaved band ladders, enabling a more precise simulation of confined nanodevices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If effective mass approximation is used to describe band structure, then computational speed is improved, but accuracy deteriorates for confined nanodevices
Solution Approach 1:
The method segments the complex band structure into multiple interleaved band ladders, each representing a subset of bands. By treating each ladder separately with effective mass approximation while maintaining the ability to combine them, the method achieves both computational efficiency and accuracy for confined nanodevices where single-parabola approximations fail.
Solution Approach 2:
The patent employs a composite modeling approach by combining multiple effective mass models (one for each band ladder) to represent the overall band structure. This composite model captures the complex behavior of confined systems while retaining the computational advantages of effective mass approximation, unlike single-model approaches.
2Ease of manufacture
If bulk material parameters are used for confined devices, then ease of manufacture is improved, but reliability deteriorates
Solution Approach 1:
The method applies local quality by assigning different effective mass parameters to different band ladders based on their specific characteristics. Each band ladder receives customized parameters fitted to its local band structure features, rather than using uniform bulk material parameters, thereby improving simulation reliability for confined devices while maintaining practical parameter extraction procedures.
3Measurement precision
If atomic-scale modeling is used to generate band structure data, then measurement precision is improved, but device complexity increases
Solution Approach 1:
The patent segments the complex atomic-scale band structure data into multiple manageable band ladders. This segmentation reduces the complexity of processing by organizing the data into distinct groups that can be treated separately, while preserving the high precision information from atomic-scale calculations.
Solution Approach 2:
The method extracts key parameters (effective mass, band edges, non-parabolicity coefficients) from the complex atomic-scale band structure data for each band ladder. By extracting only the essential parameters needed for device simulation rather than processing the complete atomic-scale data, the method reduces computational complexity while maintaining precision.
4Measurement precision
If multiple band ladders are present in confined systems, then accuracy is improved, but difficulty of detecting and measuring increases
Solution Approach 1:
The patent addresses the difficulty of analyzing interleaved band structures by segmenting them into distinct band ladders. Each ladder is identified and characterized separately, making the detection and measurement process manageable despite the complexity of having multiple interleaved bands in confined systems.
Data Source
AI summary
Computer-aided methods for simulating confined nanodevices are disclosed. In example implementations, atomic-scale model of the nanodevices are generated so that dimensions and materials are specified. Then, band structures which comprise wave functions and Eigen energies are calculated using First Principles Methods (FPM). Effective mass modeled which comprise wave functions and Eigen energies are generated. After that, spatial wave functions of the calculated FPM band structures are mapped to the generated effective mass band structures wave functions by considering global behavior. In response to the mapping, generated effective mass models are fitted to calculated FPM energies so that approximate electronic band structures of the confined nanodevices are modeled. Computer programs for carrying out the methods, data media and computer systems are also disclosed.