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The fraction of impurities equation calculates the ratio of crystal lattice sites occupied by impurities to the total number of crystal lattice sites. It's based on the Boltzmann distribution and describes how impurities distribute in a crystal lattice at thermal equilibrium.
The calculator uses the formula:
Where:
Explanation: The exponential function describes the probability of impurity occupation based on the energy barrier and thermal energy available at a given temperature.
Details: Calculating the fraction of impurities is crucial for understanding material properties, semiconductor doping efficiency, crystal purity assessment, and predicting material behavior in various applications.
Tips: Enter energy required per impurity in joules and temperature in kelvin. Both values must be positive numbers.
Q1: What does the fraction of impurities represent?
A: It represents the probability that a given lattice site will be occupied by an impurity atom at thermal equilibrium.
Q2: Why is the exponential function used?
A: The exponential form comes from the Boltzmann distribution, which describes how particles distribute among energy states at thermal equilibrium.
Q3: What are typical values for energy required per impurity?
A: This varies by material system but typically ranges from 0.1 eV to several eV (1 eV = 1.602 × 10⁻¹⁹ J).
Q4: How does temperature affect impurity fraction?
A: Higher temperatures generally increase the fraction of impurities as thermal energy helps overcome the energy barrier for impurity incorporation.
Q5: What are the limitations of this model?
A: This assumes ideal conditions and doesn't account for impurity-impurity interactions, lattice strain effects, or non-equilibrium conditions.