PCS224-Lecture09-Rebello-Student
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Course Information
PCS 224 - Solid State Physics
Semester: Fall 2024
Lecture 09
Topic: Doping in Semiconductors and Intro to Band Structure
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Covered Topics
Electrostatics (Lec 01 & 02)
Electric Force and Electric Field
Charge Distribution (i.e. parallel plate)
Electric Potential Energy and Potential Difference
Capacitance
Photoelectric Effect (Lec 03, Lec 04)
Introduction to Semiconductors (Lec 04, Lec 05)
Intrinsic vs. Extrinsic Semiconductors
Holes as Charge Carriers
Fundamental Equation of Semiconductors: n0 = ni^2
Current and Conductivity (Lec 06)
Current, Conductivity, Resistance, Drift Speed, Current Density, Hall Effect
Bohr’s Model of the Atom (Lec 08)
Overview of previously covered material
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Lecture Goals
Review Bohr’s Model of the Atom
Topic Focus: Doping in Semiconductors
Understanding how semiconductors are engineered (p-type and n-type)
Introduction of new terminology: dielectric constant, donors, acceptors, compensated semiconductors
Conceptual understanding of the usefulness of doping in engineering
Reference: Neamen 4.2
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Naturally Occurring Semiconductors
Silicon (Si) and Germanium (Ge) are intrinsic semiconductors.
Intrinsic Semiconductors: Naturally occurring, defined by their pure state without impurities.
Extrinsic Semiconductors: Engineered by adding impurities to modify electrical properties.
Valence Electrons: Crucial for forming covalent bonds in semiconductors.
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Electron and Hole Concentration
Definitions:
n0: Free electron concentration (number density) in thermal equilibrium.
p0: Hole concentration (number density) in thermal equilibrium.
Why are two variables necessary?
Expectation is that number of electrons does not equal number of holes due to doping and thermal motion.
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Intrinsic Concentration
For intrinsic semiconductors: n0 = p0 = ni (where ni is the intrinsic carrier concentration).
Table 1.2: Intrinsic Carrier Concentrations @ 300 K
Silicon: n_i = 1.02 x 10^10 cm^-3
Gallium Arsenide (GaAs): n_i = 2.1 x 10^6 cm^-3
Germanium (Ge): n_i = 2.4 x 10^13 cm^-3
Key Takeaway: ni is a property of the material, affects its carrier dynamics when doped.
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What is Doping?
Doping Definition:
Adding impurities (different types of atoms) into semiconductor.
Donors vs. Acceptors:
Donors: Atoms that provide extra free electrons (denoted as N_D).
Acceptors: Atoms that create holes (denoted as N_A).
Impact of impurities: Enhance electrical properties by increasing charge carriers (electrons or holes).
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N-Type and P-Type Materials
N-Type Material:
More electrons (n0 > p0), electrons are majority charge carriers.
P-Type Material:
More holes (p0 > n0), holes are majority charge carriers.
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N-Type Doping
Replacement of Silicon atom with a Group V atom (e.g., Phosphorus).
Phosphorus atoms have five valence electrons, four are utilized in covalent bonding.
Leads to extra free electron and increases n0 in semiconductor.
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N-Type Semiconductor Formation
Phosphorus impurity: Substitutes a Silicon atom, leading to excess electrons.
For N-type semiconductors, approximately: n0 = N_D
Conceptual analogy: Similar to adding acid to water, resulting in a large concentration of hydrogen ions.
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Lecture 08 Recap
Formulas and principles reviewed:
Binding energy and potential energy relations.
Key parameters from the Bohr model were discussed (energy levels, radii).
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Recap: Orbital Radii
Energy level formulas and implications of orbital distances relative to atomic structures were reinforced.
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Binding Energy of Donor Electron
Leftover electron interacts with the positively charged donor (e.g., from Phosphorous).
Ionization energy similar to that of hydrogen.
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Dielectrics
The polarization of molecules occurs when an external electric field is applied, resulting in a change in dielectric behavior.
The dielectric constant expresses how much the electric field is reduced in the material.
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Dielectric Properties of Semiconductors
Property Table for Silicon, Gallium Arsenide, and Germanium at T=300 K:
Silicon (Si):
Atoms: 5.0 x 10^22 cm^-3
Dielectric Constant: 11.7
Bandgap Energy: 1.12 eV
Influence of dielectric constants expressed in effective density of states.
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Continue: Binding Energy of Donor Electron
Impact of dielectric constant on binding energies was emphasized.
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Summary of Donor (N-Type)
Binding energy for donor electrons lower than intrinsic energy levels.
Key Aspect: Donor electrons are easily freed at room temperature.
Concentration denoted as N_D; typically assume all donors are ionized.
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Example Question for Donor Concentration
Problem illustrating the adjustments in donor levels to achieve specific electrical properties in silicon.
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P-Type Doping
Replacement of Silicon with a Group III atom (e.g., Boron).
Boron lacks a full complement of valence electrons, resulting in the formation of holes.
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Extrinsic P-Type Semiconductor
Boron substitutes Si atom, creating holes that can lead to better charge carrier mobility.
Understanding of mobility in discussing how electrons move to fill these holes.
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Summary of Acceptor Behavior
Acceptor states become easily filled at room temperature, leading to increased hole concentration.
Denoted concentration typically as N_A in calculations.
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Properties of Silicon and Other Semiconductors
Reevaluation of conductors, semiconductors, and insulators based on intrinsic properties.
Include relevant properties as required for semiconductor analysis.
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Example Question and Conceptual Questions
Problem regarding calculations for determining donor concentrations and their impact on resistance.
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Continuing Example Questions
Further exploration of acceptor states influence on resistance calculations.
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Electroneytrality Equation
Concept of electric neutrality within a semiconductor emphasizing the balance of charge carriers.
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Compensated Semiconductors
Simulation of extrinsic doping creating complex scenarios with balance across n-type and p-type within a single semiconductor.
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Violations of Electroneytrality
Impact of disruptions leading to electric current and tendency toward reestablishment of neutrality.
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Overview of Doping Effects
Comprehensive review showing how donor and acceptor impurities affect conductivity and charge carrier concentrations under normal and doped conditions.
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Lecture Goals Moving Forward
Transitioning to band structure concepts and understanding their implications in conductivity and insulator behavior from an energy level perspective.
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Energy Levels within Solids
Discussion about effective energy levels as dictated by quantum mechanics in multi-atom configurations related to conduction and valence bands.
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Quantum Physics Overview
Differentiation between classical and quantum mechanics as it pertains to electron behavior in solids.
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Wave Functions in Quantum Mechanics
Defining particles by their spatial probability distribution for energy states in solids.
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Energy Levels in Hydrogen Model
Review of energy transitions in hydrogen and its quantum energy state variations with emission of light.
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Electron Orbitals and Quantum States
Review of how electrons are organized within shells, subshells, and their corresponding states.
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Electron Orbital Characteristics
Describing differences in electron likelihoods across various subshells in terms of spatial probability.
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Chemists’ Notation for Electron Configuration
Describing orbital configurations and maximum capacity limits.
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Energy Levels in Multi-Electron Atoms
Illustrating the complexity arising from multiple electron interactions affecting energy states.
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Pauli Exclusion Principle
Principle emphasizing that no two electrons can occupy the same quantum state, establishing energy state occupancy rules.
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Filling Energy Levels
Emphasizing energy preferences and how electrons fill from lowest to highest available states.
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Multiple Atoms and Energy Levels
Dependency of atomic interactions on electron energy distributions across removed atom geometries.
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Energy Levels for Multiple Atomic Configurations
How energy levels evolve as atoms approach, emphasizing complexity due to interactions.
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Level Splitting and Formation of Energy Bands
Energy band formation due to atom proximity encouraging energy line redistributions and band structures forming.
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Energy Band Formation
Resulting continuum of energy states blending processes, becoming bands due to substantial atom aggregation.
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Solid-State Energy Bands
Understanding defined conduction bands and valence bands within semiconductors, inclusive of forbidden energy gaps.
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Energy Band Components
Characteristics of energy levels and their implications in charge density and stability.
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Energy Level (Band) Diagrams
Mechanisms for representing electron occupation states across energy levels, emphasizing the absence of states within gaps.
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Conduction and Valence Bands Described
Distinction between filled and unfilled bands—fundamental to understanding conduction mechanisms.
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Conductors vs Insulators
Explicitly differentiating materials characterized by their conduction capabilities under ground state conditions.
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Semiconductor Behavior at Low Temperature
Insight into semiconductors acting as insulators at low temperatures, with potential for conduction evolving as temperatures rise.
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Semiconductor Temperature Responses
Understanding thermal excitation mechanisms contributing to semiconductor transitions between states at varying temperatures.
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Inquiry on Material Classification
Identify nature of materials based on given data, categorizing them appropriately as conductors, insulators, or semiconductors.
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Current Flow Generation
Detailed exploration of conditions necessary for current flow in semiconductors at T=0.
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Conditions for Current Flow
Transaction requirements for electrons to move and overcome energy barriers for conduction.
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Challenges in Non-Metal Conductivity
Assessing difficulties faced by intrinsic semiconductors in facilitating current flow compared to conductive materials.
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Hall Effect Inquiry
Understanding conceptually the dynamics of electron and hole interactions in semiconductor behaviors.
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Energy of a Photon Overview
Understanding how light energy facilitates electron excitation in semiconductors across energy bands.
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Photon Energy for Excitation
Estimating relevant wavelengths necessary for electron excitation across defined band gaps in materials.
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Homework Problem - Photon Energy
Assessing photon energy numbers in relevance to conducting semiconductor energy transitions.
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Doped Semiconductors at Absolute Zero
Understanding energy states unique to n-type and p-type semiconductors when at absolute zero temperature conditions.
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Above Absolute Zero Conditions
Evaluating the charge carrier behaviors under typical operational temperatures with complete ionization considerations.
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Energy Band Diagrams for Doped Semiconductors
Visualization of energy states and their implications for conduction and carrier density in doped materials.
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Role of Free Electrons
Description of how free electrons (n-carriers) migrate and conduct under applied fields in n-type semiconductors.
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Holes as Current Carriers
Understanding positional movements and implications of holes and their behaviors under electric fields as p-carriers.
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Questions on Intrinsic Semiconductor Behavior
Analyzing conceptual questions about intrinsic charge dynamics in semiconductors.
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Summary of the Energy Level Diagram
Consolidating knowledge on drawing and interpreting energy band diagrams relevant for conduction types.
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Progression of Semiconductor Behavior with Temperature
Advanced exploration of temperature impacts on charge carrier distribution within semiconductors.
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Elaborating on Solid Energy Bands
Recap of definitions and roles of energy bands and gaps within solid-state physics conventions.
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Fermi Energy and Its Role
Clarifying significance of Fermi energy as it relates to electron states occupancy at absolute zero.
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Fermi Energy Position in Bands
Positioning of Fermi energy within band structures dictates a material’s conductive properties.
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Fermi Energy Across Material Types
Overview of Fermi level differences in semiconductors versus metals and insulators.
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Vacancy in States vs. Probability
Understanding the determination factors surrounding occupied states and their relation to the Fermi energy.
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Additional Resources and References
Recommended links for extended reading on semiconductor devices and energy band theory.
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Key Attributes to Retain
Importance of comprehending semiconductor engineering fundamentals.
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Advanced Understanding Goals
Deepening comprehension of energy bands and their governing physics in current flow dynamics.
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Questions and Student Engagement
Encouragement for comprehending all discussed topics and preparation for future discussions on Band Structure and Fermi Energy.