PCS224-Lecture09-Rebello-Student

Page 1

Course Information

• PCS 224 - Solid State Physics

• Semester: Fall 2024

• Lecture 09

• Topic: Doping in Semiconductors and Intro to Band Structure

Page 2

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

Page 3

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

Page 4

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.

Page 5

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.

Page 6

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.

Page 7

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).

Page 8

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.

Page 9

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.

Page 10

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.

Page 11

Lecture 08 Recap

• Formulas and principles reviewed:

  • Binding energy and potential energy relations.

  • Key parameters from the Bohr model were discussed (energy levels, radii).

Page 12

Recap: Orbital Radii

• Energy level formulas and implications of orbital distances relative to atomic structures were reinforced.

Page 13

Binding Energy of Donor Electron

• Leftover electron interacts with the positively charged donor (e.g., from Phosphorous).

• Ionization energy similar to that of hydrogen.

Page 14

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.

Page 15

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.

Page 16

Continue: Binding Energy of Donor Electron

• Impact of dielectric constant on binding energies was emphasized.

Page 17

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.

Page 18

Example Question for Donor Concentration

• Problem illustrating the adjustments in donor levels to achieve specific electrical properties in silicon.

Page 19

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.

Page 20

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.

Page 21

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.

Page 22

Properties of Silicon and Other Semiconductors

• Reevaluation of conductors, semiconductors, and insulators based on intrinsic properties.

  • Include relevant properties as required for semiconductor analysis.

Page 23

Example Question and Conceptual Questions

• Problem regarding calculations for determining donor concentrations and their impact on resistance.

Page 24

Continuing Example Questions

• Further exploration of acceptor states influence on resistance calculations.

Page 25

Electroneytrality Equation

• Concept of electric neutrality within a semiconductor emphasizing the balance of charge carriers.

Page 26

Compensated Semiconductors

• Simulation of extrinsic doping creating complex scenarios with balance across n-type and p-type within a single semiconductor.

Page 27

Violations of Electroneytrality

• Impact of disruptions leading to electric current and tendency toward reestablishment of neutrality.

Page 28

Overview of Doping Effects

• Comprehensive review showing how donor and acceptor impurities affect conductivity and charge carrier concentrations under normal and doped conditions.

Page 29

Lecture Goals Moving Forward

• Transitioning to band structure concepts and understanding their implications in conductivity and insulator behavior from an energy level perspective.

Page 30

Energy Levels within Solids

• Discussion about effective energy levels as dictated by quantum mechanics in multi-atom configurations related to conduction and valence bands.

Page 31

Quantum Physics Overview

• Differentiation between classical and quantum mechanics as it pertains to electron behavior in solids.

Page 32

Wave Functions in Quantum Mechanics

• Defining particles by their spatial probability distribution for energy states in solids.

Page 33

Energy Levels in Hydrogen Model

• Review of energy transitions in hydrogen and its quantum energy state variations with emission of light.

Page 34

Electron Orbitals and Quantum States

• Review of how electrons are organized within shells, subshells, and their corresponding states.

Page 35

Electron Orbital Characteristics

• Describing differences in electron likelihoods across various subshells in terms of spatial probability.

Page 36

Chemists’ Notation for Electron Configuration

• Describing orbital configurations and maximum capacity limits.

Page 37

Energy Levels in Multi-Electron Atoms

• Illustrating the complexity arising from multiple electron interactions affecting energy states.

Page 38

Pauli Exclusion Principle

• Principle emphasizing that no two electrons can occupy the same quantum state, establishing energy state occupancy rules.

Page 39

Filling Energy Levels

• Emphasizing energy preferences and how electrons fill from lowest to highest available states.

Page 40

Multiple Atoms and Energy Levels

• Dependency of atomic interactions on electron energy distributions across removed atom geometries.

Page 41

Energy Levels for Multiple Atomic Configurations

• How energy levels evolve as atoms approach, emphasizing complexity due to interactions.

Page 42

Level Splitting and Formation of Energy Bands

• Energy band formation due to atom proximity encouraging energy line redistributions and band structures forming.

Page 43

Energy Band Formation

• Resulting continuum of energy states blending processes, becoming bands due to substantial atom aggregation.

Page 44

Solid-State Energy Bands

• Understanding defined conduction bands and valence bands within semiconductors, inclusive of forbidden energy gaps.

Page 45

Energy Band Components

• Characteristics of energy levels and their implications in charge density and stability.

Page 46

Energy Level (Band) Diagrams

• Mechanisms for representing electron occupation states across energy levels, emphasizing the absence of states within gaps.

Page 47

Conduction and Valence Bands Described

• Distinction between filled and unfilled bands—fundamental to understanding conduction mechanisms.

Page 48

Conductors vs Insulators

• Explicitly differentiating materials characterized by their conduction capabilities under ground state conditions.

Page 49

Semiconductor Behavior at Low Temperature

• Insight into semiconductors acting as insulators at low temperatures, with potential for conduction evolving as temperatures rise.

Page 50

Semiconductor Temperature Responses

• Understanding thermal excitation mechanisms contributing to semiconductor transitions between states at varying temperatures.

Page 51

Inquiry on Material Classification

• Identify nature of materials based on given data, categorizing them appropriately as conductors, insulators, or semiconductors.

Page 52

Current Flow Generation

• Detailed exploration of conditions necessary for current flow in semiconductors at T=0.

Page 53

Conditions for Current Flow

• Transaction requirements for electrons to move and overcome energy barriers for conduction.

Page 54

Challenges in Non-Metal Conductivity

• Assessing difficulties faced by intrinsic semiconductors in facilitating current flow compared to conductive materials.

Page 55

Hall Effect Inquiry

• Understanding conceptually the dynamics of electron and hole interactions in semiconductor behaviors.

Page 56

Energy of a Photon Overview

• Understanding how light energy facilitates electron excitation in semiconductors across energy bands.

Page 57

Photon Energy for Excitation

• Estimating relevant wavelengths necessary for electron excitation across defined band gaps in materials.

Page 58

Homework Problem - Photon Energy

• Assessing photon energy numbers in relevance to conducting semiconductor energy transitions.

Page 59

Doped Semiconductors at Absolute Zero

• Understanding energy states unique to n-type and p-type semiconductors when at absolute zero temperature conditions.

Page 60

Above Absolute Zero Conditions

• Evaluating the charge carrier behaviors under typical operational temperatures with complete ionization considerations.

Page 61

Energy Band Diagrams for Doped Semiconductors

• Visualization of energy states and their implications for conduction and carrier density in doped materials.

Page 62

Role of Free Electrons

• Description of how free electrons (n-carriers) migrate and conduct under applied fields in n-type semiconductors.

Page 63

Holes as Current Carriers

• Understanding positional movements and implications of holes and their behaviors under electric fields as p-carriers.

Page 64

Questions on Intrinsic Semiconductor Behavior

• Analyzing conceptual questions about intrinsic charge dynamics in semiconductors.

Page 65

Summary of the Energy Level Diagram

• Consolidating knowledge on drawing and interpreting energy band diagrams relevant for conduction types.

Page 66

Progression of Semiconductor Behavior with Temperature

• Advanced exploration of temperature impacts on charge carrier distribution within semiconductors.

Page 67

Elaborating on Solid Energy Bands

• Recap of definitions and roles of energy bands and gaps within solid-state physics conventions.

Page 68

Fermi Energy and Its Role

• Clarifying significance of Fermi energy as it relates to electron states occupancy at absolute zero.

Page 69

Fermi Energy Position in Bands

• Positioning of Fermi energy within band structures dictates a material’s conductive properties.

Page 70

Fermi Energy Across Material Types

• Overview of Fermi level differences in semiconductors versus metals and insulators.

Page 71

Vacancy in States vs. Probability

• Understanding the determination factors surrounding occupied states and their relation to the Fermi energy.

Page 72

Additional Resources and References

• Recommended links for extended reading on semiconductor devices and energy band theory.

Page 73

Key Attributes to Retain

• Importance of comprehending semiconductor engineering fundamentals.

Page 74

Advanced Understanding Goals

• Deepening comprehension of energy bands and their governing physics in current flow dynamics.

Page 75

Questions and Student Engagement

• Encouragement for comprehending all discussed topics and preparation for future discussions on Band Structure and Fermi Energy.