Non-local Scattering Modeling in Quantum Devices
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Solution Overview
Problem
Current numerical techniques for solving Non-equilibrium Green's Function (NEGF) are limited in studying non-local scattering due to computational constraints, particularly in modeling realistic quantum devices, as they require significant memory and time, restricting the investigation to small non-locality ranges.
Innovation Solution
A physics-based local approximation method using Fermi's golden rule is developed, which considers the dimensionality, size dependence, and energy dependence of devices to efficiently model non-local scattering, reducing computational resources and memory usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a full inversion method is used to model complete non-locality range, then measurement precision of non-local scattering is improved, but quantity of substance (memory consumption) increases significantly
Solution Approach 1:
The Green's function matrix is divided into diagonal blocks and off-diagonal blocks. The method computes only the required diagonal blocks (and minimal off-diagonal blocks for current density), rather than inverting the entire matrix. This segmentation allows solving for local density of states efficiently while avoiding the memory burden of full matrix inversion.
Solution Approach 2:
The patent applies a diagonal approximation with a scaling factor to treat population scattering, which is a partial action that captures the essential physics without computing all off-diagonal elements. This partial computation approach provides sufficient accuracy for many applications while dramatically reducing memory requirements compared to full inversion.
2Productivity
If a diagonal approximation with scaling factor is used to treat population scattering, then productivity is improved, but measurement precision of non-local scattering deteriorates
Solution Approach 1:
The patent introduces a scaling factor parameter that can be adjusted to account for non-local effects in the diagonal approximation. By tuning this parameter, the method maintains computational efficiency while improving accuracy for population scattering processes. The scaling factor effectively compensates for the simplified diagonal-only approach.
3Measurement precision
If non-local recursive Green's function technique is used to study long-ranged scattering, then measurement precision of non-local scattering is improved, but quantity of substance (memory consumption) increases
Solution Approach 1:
The NL-RGF technique segments the computation into local and non-local components, allowing the method to handle long-ranged scattering by systematically including off-diagonal blocks only when necessary. This segmented approach enables studying larger non-locality ranges than full inversion while maintaining better accuracy than simple local approximation.
4Adaptability or versatility
If device size is increased to model realistic quantum devices, then adaptability is improved, but quantity of substance (memory consumption) increases
Solution Approach 1:
The method segments the device into smaller computational units (diagonal blocks) that can be processed independently or in small groups. This block-diagonal approach allows the simulation of larger devices by dividing them into manageable segments, reducing the memory footprint compared to treating the entire device as a single large matrix.
Data Source
AI summary
A non-transitory machine-readable storage medium is disclosed, which stores a program for modeling a many particle system. When executed on a processing system, the program causes the processing system to (1) determine a compensation function that, when applied to a plurality of interaction equations, compensates for errors introduced by an approximation included in at least one of the plurality of interaction equations, (2) determine an uncompensated solution of the many particle system by solving the many particle system without the plurality of interaction equations, (3) calculate a plurality of observables in the many particle system by solving the many particle system with the plurality of interaction equations by a first iteration, and (4) model the many particle system based on the plurality of observables.