Multicarrier Mobility Spectrum Analysis via Hall Effect
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional methods for analyzing semiconductor materials using Hall effect measurements often favor narrow mobility peaks, excluding other valid solutions and neglecting noise uncertainties, leading to misleading results and incomplete characterization of carrier properties in electronic devices.
Innovation Solution
A method is developed to determine a two-dimensional spectrum of carrier mobility and density by performing magnetic field-dependent Hall measurements, incorporating noise uncertainties, and using statistical analysis to classify matrices as physical or unphysical, thereby extracting precise carrier properties and their uncertainties.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional Hall effect measurement methods are used, then the measurement process is simple, but the results are misleading due to favoring narrow mobility peaks and excluding other valid solutions
Solution Approach 1:
The patent changes the analysis parameters by introducing a probability density function approach that considers multiple carrier types simultaneously. Instead of using conventional single-peak fitting methods, the patent transforms the problem into determining a distribution of carrier mobilities and densities, allowing multiple valid solutions to coexist rather than forcing a single narrow peak fit.
Solution Approach 2:
The patent introduces a probability density function as an intermediary between the raw Hall effect measurements and the final carrier property determination. This intermediary function allows the system to account for measurement uncertainties and multiple carrier types without requiring complex direct analysis, bridging the gap between simple measurements and accurate multi-carrier characterization.
2Measurement precision
If conventional methods exclude solutions with broad mobility peaks, then narrow mobility peaks are favored, but valid multi-carrier solutions are lost
Solution Approach 1:
The patent adds another dimension to the analysis by considering both mobility and density as simultaneous variables in a probability density function. Instead of analyzing mobility peaks in one dimension, the patent transforms the problem into a two-dimensional space of mobility-density pairs, allowing broad and narrow peaks to coexist as part of a multi-carrier distribution without excluding valid solutions.
Solution Approach 2:
The patent treats the semiconductor material as a composite system with multiple carrier types, each characterized by their own mobility and density parameters. By using a probability density function that sums contributions from multiple carrier ensembles, the patent preserves information about all carrier types rather than forcing the data into a single homogeneous carrier model.
3Device complexity
If noise uncertainties are not considered in the analysis, then the analysis is simpler, but the user has no idea of the uncertainty in the derived carrier properties
Solution Approach 1:
The patent incorporates feedback by using the probability density function to continuously account for measurement uncertainties throughout the analysis process. The measurement errors are propagated through the probability density calculation, providing continuous feedback about the reliability of each determined carrier property. This allows the system to maintain simplicity while quantifying uncertainties in the final results.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach allows for accurate characterization of individual layers or multiple carrier types within semiconductor materials, providing a robust and reliable method for determining carrier properties and their uncertainties, enhancing the understanding of electronic device performance.
Implementation Method 1
One method that may be used in the characterization of semiconductor materials is a Hall effect measurement. The Hall effect measurement measures the transverse and longitudinal voltages created when a magnetic field is applied perpendicular to a current through the material under study.
Data Source
AI summary
A method for determining a two-dimensional spectrum of a specified carrier having a specified mobility and density in a material of an electronic device, the method including performing a magnetic field-dependent Hall measurement on the material of the electronic device; determining, using the magnetic field-dependent Hall measurement, a probability density function of a conductance of the material of the electronic device, wherein the probability density function describes a spectrum of a plurality of m-carriers, wherein the plurality of m-carriers includes the specified carrier having the specified mobility and density; and determining an electrical transport of a plurality of electrons and holes inside the material of the electronic device by observing a variation of the probability density function with any of the specified mobility and density of the specified carrier.