7.1 Band structure and electronic properties of semiconductors
3 min read•august 9, 2024
Semiconductors are the backbone of modern electronics. Their unique band structure, with valence and conduction bands separated by a gap, determines their electrical properties. Understanding these bands is crucial for designing efficient thermoelectric devices.
Electronic properties like and are key to semiconductor performance. These factors, influenced by and temperature, affect how well a material can conduct electricity and heat. Mastering these concepts is essential for optimizing thermoelectric materials.
Band Structure
Valence and Conduction Bands
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- represents the highest occupied energy level in a semiconductor at absolute zero temperature
- in the valence band participate in bonding between atoms in the crystal structure
- denotes the lowest unoccupied energy level where electrons can move freely through the material
- Electrons excited from the valence band to the conduction band contribute to electrical conductivity
- Energy difference between the top of the valence band and the bottom of the conduction band defines the band gap
- Band gap determines the electrical and optical properties of semiconductors (silicon: 1.12 eV, germanium: 0.67 eV)
Direct and Indirect Bandgaps
- Direct occurs when the minimum of the conduction band aligns vertically with the maximum of the valence band in k-space
- Direct bandgap materials facilitate efficient electron transitions without phonon involvement (gallium arsenide)
- Indirect bandgap materials have misaligned conduction band minimum and valence band maximum in k-space
- Indirect bandgap transitions require phonon assistance, resulting in less efficient optical processes (silicon)
- Direct bandgap semiconductors excel in optoelectronic applications (LEDs, lasers)
- Indirect bandgap materials find use in electronic devices and solar cells due to their longer carrier lifetimes
Electronic Properties
Fermi Level and Carrier Concentration
- Fermi level represents the energy at which the probability of electron occupation equals 0.5 at thermal equilibrium
- Fermi level position relative to the band edges determines the semiconductor's electrical characteristics
- In intrinsic semiconductors, the Fermi level lies near the middle of the band gap
- Doping shifts the Fermi level closer to the conduction band (n-type) or valence band (p-type)
- Carrier concentration describes the number of free electrons or per unit volume
- Intrinsic carrier concentration depends on temperature and band gap (silicon at room temperature: ~1.5 × 10^10 cm^-3)
- Extrinsic carrier concentration controlled by doping levels (typical range: 10^15 to 10^19 cm^-3)
Effective Mass and Density of States
- accounts for the interaction between electrons and the crystal lattice
- Electrons in a crystal behave as if they have a different mass than free electrons due to lattice interactions
- Effective mass influences carrier mobility and transport properties
- Lighter effective mass results in higher mobility and better transport characteristics (electrons in GaAs: 0.067m0)
- Density of states (DOS) quantifies the number of available energy states per unit energy and volume
- DOS depends on the band structure and effective mass of the carriers
- Higher DOS near the band edges enhances carrier concentration and electrical conductivity
- 3D density of states for parabolic bands follows the equation:
Carrier Transport
Mobility and Scattering Mechanisms
- Mobility measures how easily charge carriers move through a semiconductor under an applied electric field
- Higher mobility leads to better electrical conductivity and faster device operation
- Mobility depends on various factors (effective mass, temperature, doping concentration)
- Electron mobility typically exceeds hole mobility due to lower effective mass (silicon: μe ≈ 1400 cm^2/V·s, μh ≈ 450 cm^2/V·s)
- Scattering mechanisms limit carrier mobility (lattice vibrations, impurity scattering, carrier-carrier scattering)
- dominates at high temperatures, while impurity scattering prevails at low temperatures
- Matthiessen's rule combines different scattering mechanisms:
Electron and Hole Transport Characteristics
- Electrons and holes exhibit different transport properties due to their distinct effective masses and scattering cross-sections
- Drift current results from carrier motion under an applied electric field
- Drift velocity relates to mobility and electric field strength:
- Diffusion current arises from carrier concentration gradients
- Einstein relation connects diffusion coefficient and mobility:
- Ambipolar transport occurs when both electrons and holes contribute significantly to current flow
- Recombination and generation processes influence carrier lifetimes and transport dynamics
- Minority carrier diffusion length impacts device performance (solar cells, bipolar transistors)
Key Terms to Review (18)
Angle-resolved photoemission spectroscopy (ARPES): Angle-resolved photoemission spectroscopy (ARPES) is a powerful experimental technique used to study the electronic structure of materials by measuring the energy and momentum of electrons ejected from a sample when it is illuminated with light. This technique allows researchers to create detailed maps of the electronic band structure and provides insights into the behavior of electrons in various materials, particularly semiconductors.
Band structure calculations: Band structure calculations are computational methods used to determine the electronic energy levels and the arrangement of these levels in a solid, specifically in semiconductors. These calculations help in understanding the behavior of electrons in materials, such as their conductivity and other electronic properties, by mapping out how energy levels change with respect to momentum. This information is crucial for predicting how materials will perform in applications like thermoelectrics and semiconductors.
Bandgap: The bandgap is the energy difference between the top of the valence band and the bottom of the conduction band in a semiconductor, determining its electrical conductivity. It plays a crucial role in defining whether a material behaves as a conductor, insulator, or semiconductor based on how easily electrons can jump from the valence band to the conduction band when energy is supplied. This transition is influenced by temperature and material composition, affecting the electronic properties and overall performance of semiconductor devices.
Carrier Concentration: Carrier concentration refers to the number of charge carriers, such as electrons or holes, per unit volume in a material. It plays a crucial role in determining the electrical and thermal transport properties of thermoelectric materials, influencing their efficiency and performance in converting heat into electricity or vice versa.
Conduction Band: The conduction band is a range of energy levels in a solid where electrons can move freely, allowing for electrical conduction. In semiconductors, the conduction band plays a crucial role in determining electronic properties, as electrons within this band can contribute to current flow when they are excited from the valence band, which is lower in energy. The ability of electrons to transition between these bands is essential for understanding how semiconductors conduct electricity and how they can be manipulated for various applications.
Doping: Doping refers to the intentional introduction of impurities into a semiconductor material to modify its electrical properties. This process is crucial in tailoring the charge carrier concentration, which directly influences the thermoelectric performance of materials used in devices like thermoelectric generators and coolers.
Effective mass: Effective mass is a parameter that characterizes the response of charge carriers, like electrons and holes, to external forces in a material. It reflects how the motion of these carriers behaves as if they were free particles but modified by the material's band structure. This concept is crucial for understanding transport properties and influences factors like thermoelectric efficiency and ZT.
Electrons: Electrons are negatively charged subatomic particles that orbit the nucleus of an atom and are fundamental to the electrical properties of materials. Their movement and interactions play a key role in determining how charge carriers transport through materials and the electronic behavior of semiconductors, impacting conductivity, band gaps, and overall material performance.
Energy Filtering: Energy filtering is a process in thermoelectric materials where charge carriers with higher energy are selectively transmitted, while lower energy carriers are blocked or scattered. This mechanism enhances the thermoelectric performance by improving the quality of carriers that contribute to electrical conductivity while minimizing thermal conductivity, ultimately leading to increased efficiency in energy conversion.
Extrinsic semiconductor: An extrinsic semiconductor is a type of semiconductor that has been doped with specific impurities to enhance its electrical conductivity. This doping introduces additional charge carriers, either electrons or holes, which significantly alter the material's electronic properties and performance. By controlling the type and amount of dopant added, extrinsic semiconductors can be engineered to have tailored conductivity, making them essential for various electronic applications.
Holes: Holes are the absence of electrons in a semiconductor, acting as positive charge carriers that facilitate electrical conduction. In a semiconductor's band structure, when electrons move from the valence band to the conduction band, they leave behind these vacant spots or holes. These holes behave as if they have a positive charge and play a crucial role in charge carrier transport mechanisms, impacting how electricity flows through semiconductor materials.
Intrinsic semiconductor: An intrinsic semiconductor is a pure semiconductor material that has no significant impurities and exhibits electrical conductivity based solely on its own charge carriers, namely electrons and holes. The unique band structure of intrinsic semiconductors shows a valence band fully occupied with electrons and a conduction band that is empty at absolute zero, allowing for conductivity to increase as temperature rises due to thermally generated electron-hole pairs.
Metal-insulator transition: The metal-insulator transition is a phenomenon where a material changes from a metallic state, characterized by high electrical conductivity, to an insulating state with very low conductivity, often due to changes in temperature, pressure, or doping levels. This transition is crucial for understanding the electronic properties of materials and plays a significant role in the behavior of semiconductors and their applications in electronic devices.
Mobility: Mobility refers to the ability of charge carriers, such as electrons and holes, to move through a material when an electric field is applied. This property is crucial in determining how effectively a semiconductor can conduct electricity and thus influences the overall performance of thermoelectric materials. Higher mobility leads to better electrical conductivity, which directly impacts the efficiency of thermoelectric devices by optimizing their power generation and heat management capabilities.
Phonon Scattering: Phonon scattering refers to the process where phonons, the quantized modes of vibrations in a material, interact with various defects, impurities, or other phonons, leading to a change in their direction and energy. This phenomenon is crucial in determining the thermal conductivity of materials, impacting their efficiency in thermoelectric applications as it affects how heat is transported and managed within these systems.
Seebeck Coefficient: The Seebeck coefficient is a measure of the thermoelectric voltage generated in response to a temperature difference across a material. It indicates how effectively a material can convert heat energy into electrical energy and is fundamental to understanding the performance of thermoelectric devices.
Thermoelectric figure of merit (zt): The thermoelectric figure of merit (zt) is a dimensionless parameter that measures the efficiency of thermoelectric materials in converting heat into electrical energy. A higher zt value indicates better performance, which is influenced by the material's electrical conductivity, thermal conductivity, and Seebeck coefficient. Understanding zt helps in assessing how well a material can be used for applications like power generation and refrigeration.
Valence Band: The valence band is the highest energy band in a semiconductor that is fully occupied by electrons at absolute zero temperature. It plays a crucial role in determining the electrical and optical properties of semiconductors, as it contains the electrons involved in bonding and conduction processes when energy is supplied.