PCS 224 - Solid State Physics
Semester: Fall 2024
Lecture 09
Topic: Doping in Semiconductors and Intro to Band Structure
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
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
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.
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.
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.
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).
N-Type Material:
More electrons (n0 > p0), electrons are majority charge carriers.
P-Type Material:
More holes (p0 > n0), holes are majority charge carriers.
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.
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.
Formulas and principles reviewed:
Binding energy and potential energy relations.
Key parameters from the Bohr model were discussed (energy levels, radii).
Energy level formulas and implications of orbital distances relative to atomic structures were reinforced.
Leftover electron interacts with the positively charged donor (e.g., from Phosphorous).
Ionization energy similar to that of hydrogen.
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.
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.
Impact of dielectric constant on binding energies was emphasized.
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.
Problem illustrating the adjustments in donor levels to achieve specific electrical properties in silicon.
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.
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.
Acceptor states become easily filled at room temperature, leading to increased hole concentration.
Denoted concentration typically as N_A in calculations.
Reevaluation of conductors, semiconductors, and insulators based on intrinsic properties.
Include relevant properties as required for semiconductor analysis.
Problem regarding calculations for determining donor concentrations and their impact on resistance.
Further exploration of acceptor states influence on resistance calculations.
Concept of electric neutrality within a semiconductor emphasizing the balance of charge carriers.
Simulation of extrinsic doping creating complex scenarios with balance across n-type and p-type within a single semiconductor.
Impact of disruptions leading to electric current and tendency toward reestablishment of neutrality.
Comprehensive review showing how donor and acceptor impurities affect conductivity and charge carrier concentrations under normal and doped conditions.
Transitioning to band structure concepts and understanding their implications in conductivity and insulator behavior from an energy level perspective.
Discussion about effective energy levels as dictated by quantum mechanics in multi-atom configurations related to conduction and valence bands.
Differentiation between classical and quantum mechanics as it pertains to electron behavior in solids.
Defining particles by their spatial probability distribution for energy states in solids.
Review of energy transitions in hydrogen and its quantum energy state variations with emission of light.
Review of how electrons are organized within shells, subshells, and their corresponding states.
Describing differences in electron likelihoods across various subshells in terms of spatial probability.
Describing orbital configurations and maximum capacity limits.
Illustrating the complexity arising from multiple electron interactions affecting energy states.
Principle emphasizing that no two electrons can occupy the same quantum state, establishing energy state occupancy rules.
Emphasizing energy preferences and how electrons fill from lowest to highest available states.
Dependency of atomic interactions on electron energy distributions across removed atom geometries.
How energy levels evolve as atoms approach, emphasizing complexity due to interactions.
Energy band formation due to atom proximity encouraging energy line redistributions and band structures forming.
Resulting continuum of energy states blending processes, becoming bands due to substantial atom aggregation.
Understanding defined conduction bands and valence bands within semiconductors, inclusive of forbidden energy gaps.
Characteristics of energy levels and their implications in charge density and stability.
Mechanisms for representing electron occupation states across energy levels, emphasizing the absence of states within gaps.
Distinction between filled and unfilled bands—fundamental to understanding conduction mechanisms.
Explicitly differentiating materials characterized by their conduction capabilities under ground state conditions.
Insight into semiconductors acting as insulators at low temperatures, with potential for conduction evolving as temperatures rise.
Understanding thermal excitation mechanisms contributing to semiconductor transitions between states at varying temperatures.
Identify nature of materials based on given data, categorizing them appropriately as conductors, insulators, or semiconductors.
Detailed exploration of conditions necessary for current flow in semiconductors at T=0.
Transaction requirements for electrons to move and overcome energy barriers for conduction.
Assessing difficulties faced by intrinsic semiconductors in facilitating current flow compared to conductive materials.
Understanding conceptually the dynamics of electron and hole interactions in semiconductor behaviors.
Understanding how light energy facilitates electron excitation in semiconductors across energy bands.
Estimating relevant wavelengths necessary for electron excitation across defined band gaps in materials.
Assessing photon energy numbers in relevance to conducting semiconductor energy transitions.
Understanding energy states unique to n-type and p-type semiconductors when at absolute zero temperature conditions.
Evaluating the charge carrier behaviors under typical operational temperatures with complete ionization considerations.
Visualization of energy states and their implications for conduction and carrier density in doped materials.
Description of how free electrons (n-carriers) migrate and conduct under applied fields in n-type semiconductors.
Understanding positional movements and implications of holes and their behaviors under electric fields as p-carriers.
Analyzing conceptual questions about intrinsic charge dynamics in semiconductors.
Consolidating knowledge on drawing and interpreting energy band diagrams relevant for conduction types.
Advanced exploration of temperature impacts on charge carrier distribution within semiconductors.
Recap of definitions and roles of energy bands and gaps within solid-state physics conventions.
Clarifying significance of Fermi energy as it relates to electron states occupancy at absolute zero.
Positioning of Fermi energy within band structures dictates a material’s conductive properties.
Overview of Fermi level differences in semiconductors versus metals and insulators.
Understanding the determination factors surrounding occupied states and their relation to the Fermi energy.
Recommended links for extended reading on semiconductor devices and energy band theory.
Importance of comprehending semiconductor engineering fundamentals.
Deepening comprehension of energy bands and their governing physics in current flow dynamics.
Encouragement for comprehending all discussed topics and preparation for future discussions on Band Structure and Fermi Energy.