electronic defects and calculation
Chapter 1: Introduction to Defects in Materials
Overview of ionic and electronic defects and their quantification.
Focus on electronic defects, which are intrinsic to materials.
Key concepts:
Generation of free electrons from the valence band to the conduction band.
Movement results in creation of electrons (free carriers) and holes (vacancies).
Equations for Concentration of Electronic Defects:
Concentration calculated using the same principles as ionic defects.
Activation energy (ΔG) corresponds to the band gap.
Important distinction in concepts between ionic and electronic defects:
Small n: Concentration of defects (electrons or holes).
Big N: Total lattice sites (relevant for ionic defects only).
Electronic defects use terms like density of states.
Each electron and hole occupies its own energy state due to Pauli Exclusion Principle.
Density of States Concepts:
Distribution of states around the conduction band (for electrons) and valence band (for holes).
Notation involves effective mass (m_e) and density states (N_c, N_v).
Equations for density of states to be acknowledged but not elaborated in this course.
Reaction Constants:
For electronic defects, reaction constant related to product of concentration of electrons and holes.
Chapter 2: Concentration of Electrons
Expressions for electron-hole symmetry:
Concentration of electrons (n) equals concentration of holes (p).
Such that their product leads to simpler calculations due to n=p.
Equation used for calculations:
Derived formulation relates to effective mass and thermal energy effects based on temperature.
Chapter 3: Constants and Temperature Effects
Application of constant values:
Schottky formation energy of magnesium oxide (MgO) = 7.7 eV, room temperature band gap = 7.65 eV.
Band gap changes with temperature: decreases by approximately 1 meV/K.
Setting up ionic defect calculations:
Methodology involves equality of magnesium and oxygen vacancy concentrations based on Schottky constant formation.
Chapter 4: Calculating Hole Concentration
Deriving electronic defect concentrations:
Focus on adjusting band gap based on temperature to calculate electron concentrations.
Effective masses of electrons and holes (m_e* and m_h*) are essential for calculating concentrations at elevated temperatures.
Long equation development:
Management of units according to Joules and electron volts.
Chapter 5: Comparing Concentrations
Calculating concentrations in cubic centimeters:
Transition from molar fractions to absolute numbers for direct comparisons.
Total lattice sites calculation through density of MgO and molecular weight consideration.
Final concentrations derived:
Ionic vacancy concentration and electronic disorder comparison reveal MgO acts as a mixed conductor.
Values suggest charge carriers include contributions from both ionic and electronic mechanisms.
Chapter 6: Conclusions on Conductivity
Example of sodium chloride (NaCl):
Demonstrates the contrasting behavior due to strong ionic character.
Schottky formation energy and ionic concentrations much higher, categorizing NaCl as an ideal ionic conductor.
Chapter 1: Introduction to Defects in Materials
Overview of ionic and electronic defects and their quantification. Focus on electronic defects, which are intrinsic to materials. Key concepts:
Generation of free electrons from the valence band to the conduction band.
Movement results in creation of electrons (free carriers) and holes (vacancies).
Equations
Concentration of Electronic Defects:
Concentration calculated using the same principles as ionic defects.
Activation energy (ΔG) corresponds to the band gap.
Expressions for Electron-Hole Symmetry:
Concentration of electrons (n) = Concentration of holes (p).
n * p leads to simpler calculations due to n=p.
Density of States:
Notation involves effective mass (m_e) and density states (N_c, N_v).
Reaction Constants:
For electronic defects, reaction constant related to product of concentration of electrons and holes.
Band Gap and Temperature Effects:
Band gap changes with temperature: decreases by approximately 1 meV/K.
Chapter 2: Concentration of Electrons
Expressions for electron-hole symmetry:
Concentration of electrons (n) equals concentration of holes (p).
Such that their product leads to simpler calculations due to n=p.
Chapter 3: Constants and Temperature Effects
Application of constant values:
Schottky formation energy of magnesium oxide (MgO) = 7.7 eV, room temperature band gap = 7.65 eV.
Setting up ionic defect calculations:
Methodology involves equality of magnesium and oxygen vacancy concentrations based on Schottky constant formation.
Chapter 4: Calculating Hole Concentration
Deriving electronic defect concentrations:
Focus on adjusting band gap based on temperature to calculate electron concentrations.
Effective masses of electrons and holes (m_e* and m_h*) are essential for calculating concentrations at elevated temperatures.
Long equation development:
Management of units according to Joules and electron volts.
Chapter 5: Comparing Concentrations
Calculating concentrations in cubic centimeters:
Transition from molar fractions to absolute numbers for direct comparisons.
Total lattice sites calculation through density of MgO and molecular weight consideration.
Final concentrations derived:
Ionic vacancy concentration and electronic disorder comparison reveal MgO acts as a mixed conductor.
Values suggest charge carriers include contributions from both ionic and electronic mechanisms.
Chapter 6: Conclusions on Conductivity
Example of sodium chloride (NaCl):
Demonstrates the contrasting behavior due to strong ionic character.
Schottky formation energy and ionic concentrations much higher, categorizing NaCl as an ideal ionic conductor.