MOSFET Substrate Doping Density Measurement via Iterative Surface Potential
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for determining substrate doping density in MOSFET devices are inaccurate due to the assumption of a constant surface potential, leading to erroneous results, as the surface potential actually depends on the substrate doping density.
Innovation Solution
A method that iteratively measures threshold voltage values for various source to substrate bias voltages, calculates the surface potential, and uses a least squares approach to determine a precise substrate doping density by adjusting the initial estimate until it meets a predetermined resolution value.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If the constant surface potential assumption is used in threshold voltage measurements, then the measurement process is simple, but the substrate doping density measurement precision deteriorates
Solution Approach 1:
The patent transforms the static assumption of constant surface potential into a dynamic model where surface potential is calculated as a function of substrate doping density. The measurement system iteratively adjusts the estimated substrate doping density, recalculates surface potential at each iteration, and updates the threshold voltage model until convergence is achieved. This dynamic approach resolves the contradiction by maintaining measurement simplicity while achieving high precision through iterative refinement.
Solution Approach 2:
The patent implements a feedback mechanism where the calculated substrate doping density from one iteration is used to update the surface potential calculation in the next iteration. The system continuously compares the measured threshold voltage with the calculated threshold voltage and adjusts the substrate doping density estimate accordingly. This feedback loop enables the system to achieve high measurement precision while maintaining the simplicity of the electrical measurement process.
2Measurement precision
If iterative calculation with variable surface potential is used, then the substrate doping density measurement precision is improved, but the calculation time increases
Solution Approach 1:
The patent applies preliminary action by first obtaining an initial estimate of substrate doping density before the iterative process begins. This initial estimate allows the system to start the iteration from a point close to the final solution, significantly reducing the number of iterations required for convergence. The preliminary estimation step prepares the system in advance, enabling high precision measurements while minimizing the time penalty associated with iterative calculations.
3Ease of operation
If electrical measurement methods are used, then the measurement process is non-destructive and convenient, but the accuracy deteriorates due to the constant surface potential assumption
Solution Approach 1:
The patent changes the parameter treatment from assuming surface potential is a constant to treating it as a variable that depends on substrate doping density. By modifying how the surface potential parameter is handled in the threshold voltage equation, the system maintains the convenience of electrical measurements while achieving high accuracy. The parameter change enables the electrical measurement method to account for the physical relationship between surface potential and substrate doping density without requiring destructive sample preparation.
Data Source
AI summary
A system and method are disclosed for very accurately determining a value of a substrate doping density in a metal oxide semiconductor device. A plurality of values of threshold voltage of a device under test are measured using a plurality of different values of source to substrate bias voltage. Then a linear relationship is determined between the plurality of values of threshold voltage and a plurality of different values of an expression that is a function of the source to substrate bias voltage and a function of a surface potential of the device. A very accurate value of the substrate doping density is reiteratively calculated from the linear relationship without assuming that the surface potential of the device has a constant value.