Thermal Donor Prediction in Silicon Wafers
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Solution Overview
Problem
Current methods fail to accurately predict thermal donor formation behavior in silicon wafers for both short-time and long-time heat treatments, which is crucial for semiconductor device manufacturing, especially in 3D NAND-type flash memories and DRAMs, where repeated low-temperature heat treatments are involved.
Innovation Solution
A method based on chemical kinetics using a bond-dissociation model and a bonding model for oxygen clusters, involving reaction rate equations to calculate the formation rate of oxygen clusters and subsequently thermal donors, allowing for precise prediction of thermal donor formation behavior.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional prediction methods are used for thermal donor formation, then prediction is possible for general cases, but prediction accuracy is insufficient for both short-time and long-time heat treatments
Solution Approach 1:
The patent divides the heat treatment time domain into two distinct segments: short-time heat treatment (up to several hours) and long-time heat treatment (several days or more). Different prediction methods are applied to each segment based on the dominant physical mechanisms at different times. This segmentation allows each method to be optimized for its specific time range, achieving high accuracy for both short and long durations without compromise.
Solution Approach 2:
The patent dynamically selects the prediction method based on the heat treatment time parameter. For short-time treatments, a method based on oxygen diffusion and cluster formation kinetics is used. For long-time treatments, a method accounting for thermal donor annihilation and equilibrium behavior is applied. This dynamic adaptation ensures the most appropriate model is used for each specific condition, maximizing prediction accuracy across the full range of heat treatment durations.
2Quantity of substance
If heat treatment time is extended to ensure complete thermal donor formation, then maximum thermal donor concentration is achieved, but prediction becomes inaccurate due to thermal donor annihilation
Solution Approach 1:
The patent performs preliminary identification of the heat treatment duration category (short-time vs. long-time) before applying the prediction calculation. By determining in advance which time regime the treatment falls into, the appropriate prediction model is selected beforehand, avoiding the application of incorrect models that would lead to inaccurate predictions of thermal donor concentration.
Solution Approach 2:
The patent changes the prediction model parameters based on heat treatment time. For short-time treatments, parameters related to oxygen diffusion coefficients and cluster formation rates are used. For long-time treatments, parameters accounting for thermal donor annihilation kinetics and equilibrium concentrations are applied. This parameter adaptation allows accurate prediction of thermal donor concentration across different time scales.
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 enables accurate prediction of thermal donor formation in silicon wafers for both short-time and long-time heat treatments, improving the evaluation and production of silicon wafers by determining thermal donor concentration and resistivity, thus enhancing semiconductor device characteristics.
Implementation Method 1
when the silicon wafer is subjected to heat treatment at a relatively low temperature of approximately less than 600° C. (hereinafter referred to as low-temperature heat treatment). These oxygen clusters are donors that release electrons and are called thermal donors.
Implementation Method 2
When thermal donors are subjected to high-temperature heat treatment at approximately 650° C. or more, they become electrically neutral; such a high-temperature heat treatment is called donor killer heat treatment (donor killer annealing).
Implementation Method 3
A method based on chemical kinetics using a bond-dissociation model and a bonding model for oxygen clusters, involving reaction rate equations to calculate the formation rate of oxygen clusters
Data Source
AI summary
Provided is a method of accurately predicting the thermal donor formation behavior in a silicon wafer, a method of evaluating a silicon wafer using the prediction method, and a method of producing a silicon wafer using the evaluation method. The method of predicting the formation behavior of thermal donors, includes: a first step of setting an initial oxygen concentration condition before performing heat treatment on the silicon wafer for reaction rate equations based on both a bond-dissociation model of oxygen clusters associated with the diffusion of interstitial oxygen and a bonding model of oxygen clusters associated with the diffusion of oxygen dimers; a second step of calculating the formation rate of oxygen clusters formed through the heat treatment using the reaction rate equations; and a third step of calculating the formation rate of thermal donors formed through the heat treatment based on the formation rate of the oxygen clusters.