2. Electronic levels in semiconductors 半导体内电子能级分布
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The Behavior of Electrons in aSemiconductoris a fascinating topic that has been the subject of much research over the years. Semiconductors are materials that can partially conduct electricity, and their behavior is dependent on the presence or absence of electrons in their crystal structure.One of the key features of a semiconductor is its energy band structure. In a semiconductor, there are two types of energy bands - the valence band and the conduction band. The valence band is where the electrons that are bound to the atoms in the crystal structure exist, while the conduction band is where the electrons that can move freely exist.is affected by a number of different factors. One important factor is the concentration of impurities in the material. Impurities are atoms that have been deliberately added to the semiconductor to change its electrical properties. For example, adding boron to silicon creates a p-type semiconductor, while adding phosphorus creates an n-type semiconductor.In a p-type semiconductor, the concentration of impurities is such that there is a relative shortage of electrons, and the holes left behind by the missing electrons behave as if they were positive charges. This has the effect of attracting electrons to the area, creating a flow of current. In contrast, in an n-type semiconductor, the concentration of impurities is such that there is an excess of electrons, which can move freely through the material.Another important factor that affects the behavior of electrons in a semiconductor is temperature. At low temperatures, the behavior of electrons is dominated by their interaction with the crystal lattice of the material. As the temperature increases, however, electrons can gain enough energy to move into the conduction band, where they can move freely and conduct electricity.In addition to temperature and impurities, the behavior of electrons in a semiconductor is also affected by the presence of electric fields. When an electric field is applied to a semiconductor, it can cause the electrons to move in a particular direction, which can be used to create a current, or to control the behavior of the material.is a complex topic, and there is still much to learn about the interactions between electrons and the crystal lattice of the material. However, the ability to control this behavior has led to the development of many of the technologies that we take for granted today, from computer chips to solar cells.In conclusion, the behavior of electrons in a semiconductor is a fascinating topic that has been the subject of much research over the years. Understanding the interaction between electrons and the crystal lattice of the material is key to our ability to control the behavior of semiconductors and to develop new technologies that rely on their unique properties.。
Semiconductor Manufacturing Technology半导体制造技术Instructor’s ManualMichael QuirkJulian SerdaCopyright Prentice HallTable of Contents目录OverviewI. Chapter1. Semiconductor industry overview2. Semiconductor materials3. Device technologies—IC families4. Silicon and wafer preparation5. Chemicals in the industry6. Contamination control7. Process metrology8. Process gas controls9. IC fabrication overview10. Oxidation11. Deposition12. Metallization13. Photoresist14. Exposure15. Develop16. Etch17. Ion implant18. Polish19. Test20. Assembly and packagingII. Answers to End-of-Chapter Review QuestionsIII. Test Bank (supplied on diskette)IV. Chapter illustrations, tables, bulleted lists and major topics (supplied on CD-ROM)Notes to Instructors:1)The chapter overview provides a concise summary of the main topics in each chapter.2)The correct answer for each test bank question is highlighted in bold. Test bankquestions are based on the end-of-chapter questions. If a student studies the end-of-chapter questions (which are linked to the italicized words in each chapter), then they will be successful on the test bank questions.2Chapter 1Introduction to the Semiconductor Industry Die:管芯 defective:有缺陷的Development of an Industry•The roots of the electronic industry are based on the vacuum tube and early use of silicon for signal transmission prior to World War II. The first electronic computer, the ENIAC, wasdeveloped at the University of Pennsylvania during World War II.•William Shockley, John Bardeen and Walter Brattain invented the solid-state transistor at Bell Telephone Laboratories on December 16, 1947. The semiconductor industry grew rapidly in the 1950s to commercialize the new transistor technology, with many early pioneers working inSilicon Valley in Northern California.Circuit Integration•The first integrated circuit, or IC, was independently co-invented by Jack Kilby at Texas Instruments and Robert Noyce at Fairchild Semiconductor in 1959. An IC integrates multiple electronic components on one substrate of silicon.•Circuit integration eras are: small scale integration (SSI) with 2 - 50 components, medium scale integration (MSI) with 50 – 5k components, large scale integration (LSI) with 5k to 100kcomponents, very large scale integration (VLSI) with 100k to 1M components, and ultra large scale integration (ULSI) with > 1M components.1IC Fabrication•Chips (or die) are fabricated on a thin slice of silicon, known as a wafer (or substrate). Wafers are fabricated in a facility known as a wafer fab, or simply fab.•The five stages of IC fabrication are:Wafer preparation: silicon is purified and prepared into wafers.Wafer fabrication: microchips are fabricated in a wafer fab by either a merchant chip supplier, captive chip producer, fabless company or foundry.Wafer test: Each individual die is probed and electrically tested to sort for good or bad chips.Assembly and packaging: Each individual die is assembled into its electronic package.Final test: Each packaged IC undergoes final electrical test.•Key semiconductor trends are:Increase in chip performance through reduced critical dimensions (CD), more components per chip (Moore’s law, which predicts the doubling of components every 18-24 months) andreduced power consumption.Increase in chip reliability during usage.Reduction in chip price, with an estimated price reduction of 100 million times for the 50 years prior to 1996.The Electronic Era•The 1950s saw the development of many different types of transistor technology, and lead to the development of the silicon age.•The 1960s were an era of process development to begin the integration of ICs, with many new chip-manufacturing companies.•The 1970s were the era of medium-scale integration and saw increased competition in the industry, the development of the microprocessor and the development of equipment technology. •The 1980s introduced automation into the wafer fab and improvements in manufacturing efficiency and product quality.•The 1990s were the ULSI integration era with the volume production of a wide range of ICs with sub-micron geometries.Career paths•There are a wide range of career paths in semiconductor manufacturing, including technician, engineer and management.2Chapter 2 Characteristics of Semiconductor MaterialsAtomic Structure•The atomic model has three types of particles: neutral neutrons(不带电的中子), positively charged protons(带正电的质子)in the nucleus and negatively charged electrons(带负电的核外电子) that orbit the nucleus. Outermost electrons are in the valence shell, and influence the chemical and physical properties of the atom. Ions form when an atom gains or loses one or more electrons.The Periodic Table•The periodic table lists all known elements. The group number of the periodic table represents the number of valence shell electrons of the element. We are primarily concerned with group numbers IA through VIIIA.•Ionic bonds are formed when valence shell electrons are transferred from the atoms of one element to another. Unstable atoms (e.g., group VIIIA atoms because they lack one electron) easily form ionic bonds.•Covalent bonds have atoms of different elements that share valence shell electrons.3Classifying Materials•There are three difference classes of materials:ConductorsInsulatorsSemiconductors•Conductor materials have low resistance to current flow, such as copper. Insulators have high resistance to current flow. Capacitance is the storage of electrical charge on two conductive plates separated by a dielectric material. The quality of the insulation material between the plates is the dielectric constant. Semiconductor materials can function as either a conductor or insulator.Silicon•Silicon is an elemental semiconductor material because of four valence shell electrons. It occurs in nature as silica and is refined and purified to make wafers.•Pure silicon is intrinsic silicon. The silicon atoms bond together in covalent bonds, which defines many of silicon’s properties. Silicon atoms bond together in set, repeatable patterns, referred to asa crystal.•Germanium was the first semiconductor material used to make chips, but it was soon replaced by silicon. The reasons for this change are:Abundance of siliconHigher melting temperature for wider processing rangeWide temperature range during semiconductor usageNatural growth of silicon dioxide•Silicon dioxide (SiO2) is a high quality, stable electrical insulator material that also serves as a good chemical barrier to protect silicon from external contaminants. The ability to grow stable, thin SiO2 is fundamental to the fabrication of Metal-Oxide-Semiconductor (MOS) devices. •Doping increases silicon conductivity by adding small amounts of other elements. Common dopant elements are from trivalent, p-type Group IIIA (boron) and pentavalent, n-type Group VA (phosphorus, arsenic and antimony).•It is the junction between the n-type and p-type doped regions (referred to as a pn junction) that permit silicon to function as a semiconductor.4Alternative Semiconductor Materials•The alternative semiconductor materials are primarily the compound semiconductors. They are formed from Group IIIA and Group VA (referred to as III-V compounds). An example is gallium arsenide (GaAs).•Some alternative semiconductors come from Group IIA and VIA, referred to as II-VI compounds. •GaAs is the most common III-V compound semiconductor material. GaAs ICs have greater electron mobility, and therefore are faster than ICs made with silicon. GaAs ICs also have higher radiation hardness than silicon, which is better for space and military applications. The primary disadvantage of GaAs is the lack of a natural oxide.5Chapter 3Device TechnologiesCircuit Types•There are two basic types of circuits: analog and digital. Analog circuits have electrical data that varies continuously over a range of voltage, current and power values. Digital circuits have operating signals that vary about two distinct voltage levels – a high and a low.Passive Component Structures•Passive components such as resistors and capacitors conduct electrical current regardless of how the component is connected. IC resistors are a passive component. They can have unwanted resistance known as parasitic resistance. IC capacitor structures can also have unintentional capacitanceActive Component Structures•Active components, such as diodes and transistors can be used to control the direction of current flow. PN junction diodes are formed when there is a region of n-type semiconductor adjacent to a region of p-type semiconductor. A difference in charge at the pn junction creates a depletion region that results in a barrier voltage that must be overcome before a diode can be operated. A bias voltage can be configured to have a reverse bias, with little or no conduction through the diode, or with a forward bias, which permits current flow.•The bipolar junction transistor (BJT) has three electrodes and two pn junctions. A BJT is configured as an npn or pnp transistor and biased for conduction mode. It is a current-amplifying device.6• A schottky diode is formed when metal is brought in contact with a lightly doped n-type semiconductor material. This diode is used in faster and more power efficient BJT circuits.•The field-effect transistor (FET), a voltage-amplifying device, is more compact and power efficient than BJT devices. A thin gate oxide located between the other two electrodes of the transistor insulates the gate on the MOSFET. There are two categories of MOSFETs, nMOS (n-channel) and pMOS (p-channel), each which is defined by its majority current carriers. There is a biasing scheme for operating each type of MOSFET in conduction mode.•For many years, nMOS transistors have been the choice of most IC manufacturers. CMOS, with both nMOS and pMOS transistors in the same IC, has been the most popular device technology since the early 1980s.•BiCMOS technology makes use of the best features of both CMOS and bipolar technology in the same IC device.•Another way to categorize FETs is in terms of enhancement mode and depletion mode. The major different is in the way the channels are doped: enhancement-mode channels are doped opposite in polarity to the source and drain regions, whereas depletion mode channels are doped the same as their respective source and drain regions.Latchup in CMOS Devices•Parasitic transistors can create a latchup condition(???????) in CMOS ICs that causes transistors to unintentionally(无心的) turn on. To control latchup, an epitaxial layer is grown on the wafer surface and an isolation barrier(隔离阻障)is placed between the transistors. An isolation layer can also be buried deep below the transistors.Integrated Circuit Productsz There are a wide range of semiconductor ICs found in electrical and electronic products. This includes the linear IC family, which operates primarily with anal3og circuit applications, and the digital IC family, which includes devices that operate with binary bits of data signals.7Chapter 4Silicon and Wafer Preparation8z Semiconductor-Grade Silicon•The highly refined silicon used for wafer fabrication is termed semiconductor-grade silicon (SGS), and sometimes referred to as electronic-grade silicon. The ultra-high purity of semiconductor-grade silicon is obtained from a multi-step process referred to as the Siemens process.Crystal Structure• A crystal is a solid material with an ordered, 3-dimensional pattern over a long range. This is different from an amorphous material that lacks a repetitive structure.•The unit cell is the most fundamental entity for the long-range order found in crystals. The silicon unit cell is a face-centered cubic diamond structure. Unit cells can be organized in a non-regular arrangement, known as a polycrystal. A monocrystal are neatly arranged unit cells.Crystal Orientation•The orientation of unit cells in a crystal is described by a set of numbers known as Miller indices.The most common crystal planes on a wafer are (100), (110), and (111). Wafers with a (100) crystal plane orientation are most common for MOS devices, whereas (111) is most common for bipolar devices.Monocrystal Silicon Growth•Silicon monocrystal ingots are grown with the Czochralski (CZ) method to achieve the correct crystal orientation and doping. A CZ crystal puller is used to grow the silicon ingots. Chunks of silicon are heated in a crucible in the furnace of the puller, while a perfect silicon crystal seed is used to start the new crystal structure.• A pull process serves to precisely replicate the seed structure. The main parameters during the ingot growth are pull rate and crystal rotation. More homogeneous crystals are achieved with a magnetic field around the silicon melt, known as magnetic CZ.•Dopant material is added to the melt to dope the silicon ingot to the desired electrical resistivity.Impurities are controlled during ingot growth. A float-zone crystal growth method is used toachieve high-purity silicon with lower oxygen content.•Large-diameter ingots are grown today, with a transition underway to produce 300-mm ingot diameters. There are cost benefits for larger diameter wafers, including more die produced on a single wafer.Crystal Defects in Silicon•Crystal defects are interruptions in the repetitive nature of the unit cell. Defect density is the number of defects per square centimeter of wafer surface.•Three general types of crystal defects are: 1) point defects, 2) dislocations, and 3) gross defects.Point defects are vacancies (or voids), interstitial (an atom located in a void) and Frenkel defects, where an atom leaves its lattice site and positions itself in a void. A form of dislocation is astacking fault, which is due to layer stacking errors. Oxygen-induced stacking faults are induced following thermal oxidation. Gross defects are related to the crystal structure (often occurring during crystal growth).Wafer Preparation•The cylindrical, single-crystal ingot undergoes a series of process steps to create wafers, including machining operations, chemical operations, surface polishing and quality checks.•The first wafer preparation steps are the shaping operations: end removal, diameter grinding, and wafer flat or notch. Once these are complete, the ingot undergoes wafer slicing, followed by wafer lapping to remove mechanical damage and an edge contour. Wafer etching is done to chemically remove damage and contamination, followed by polishing. The final steps are cleaning, wafer evaluation and packaging.Quality Measures•Wafer suppliers must produce wafers to stringent quality requirements, including: Physical dimensions: actual dimensions of the wafer (e.g., thickness, etc.).Flatness: linear thickness variation across the wafer.Microroughness: peaks and valleys found on the wafer surface.Oxygen content: excessive oxygen can affect mechanical and electrical properties.Crystal defects: must be minimized for optimum wafer quality.Particles: controlled to minimize yield loss during wafer fabrication.Bulk resistivity(电阻系数): uniform resistivity from doping during crystal growth is critical. Epitaxial Layer•An epitaxial layer (or epi layer) is grown on the wafer surface to achieve the same single crystal structure of the wafer with control over doping type of the epi layer. Epitaxy minimizes latch-up problems as device geometries continue to shrink.Chapter 5Chemicals in Semiconductor FabricationEquipment Service Chase Production BayChemical Supply Room Chemical Distribution Center Holding tank Chemical drumsProcess equipmentControl unit Pump Filter Raised and perforated floorElectronic control cablesSupply air ductDual-wall piping for leak confinement PumpFilterChemical control and leak detection Valve boxes for leak containment Exhaust air ductStates of Matter• Matter in the universe exists in 3 basic states (宇宙万物存在着三种基本形态): solid, liquid andgas. A fourth state is plasma.Properties of Materials• Material properties are the physical and chemical characteristics that describe its unique identity.• Different properties for chemicals in semiconductor manufacturing are: temperature, pressure andvacuum, condensation, vapor pressure, sublimation and deposition, density, surface tension, thermal expansion and stress.Temperature is a measure of how hot or cold a substance is relative to another substance. Pressure is the force exerted per unit area. Vacuum is the removal of gas molecules.Condensation is the process of changing a gas into a liquid. Vaporization is changing a liquidinto a gas.Vapor pressure is the pressure exerted by a vapor in a closed container at equilibrium.Sublimation is the process of changing a solid directly into a gas. Deposition is changing a gas into a solid.Density is the mass of a substance divided by its volume.Surface tension of a liquid is the energy required to increase the surface area of contact.Thermal expansion is the increase in an object’s dimension due to heating.Stress occurs when an object is exposed to a force.Process Chemicals•Semiconductor manufacturing requires extensive chemicals.• A chemical solution is a chemical mixture. The solvent is the component of the solution present in larger amount. The dissolved substances are the solutes.•Acids are solutions that contain hydrogen and dissociate in water to yield hydronium ions. A base is a substance that contains the OH chemical group and dissociates in water to yield the hydroxide ion, OH-.•The pH scale is used to assess the strength of a solution as an acid or base. The pH scale varies from 0 to 14, with 7 being the neutral point. Acids have pH below 7 and bases have pH values above 7.• A solvent is a substance capable of dissolving another substance to form a solution.• A bulk chemical distribution (BCD) system is often used to deliver liquid chemicals to the process tools. Some chemicals are not suitable for BCD and instead use point-of-use (POU) delivery, which means they are stored and used at the process station.•Gases are generally categorized as bulk gases or specialty gases. Bulk gases are the relatively simple gases to manufacture and are traditionally oxygen, nitrogen, hydrogen, helium and argon.The specialty gases, or process gases, are other important gases used in a wafer fab, and usually supplied in low volume.•Specialty gases are usually transported to the fab in metal cylinders.•The local gas distribution system requires a gas purge to flush out undesirable residual gas. Gas delivery systems have special piping and connections systems. A gas stick controls the incoming gas at the process tool.•Specialty gases may be classified as hydrides, fluorinated compounds or acid gases.Chapter 6Contamination Control in Wafer FabsIntroduction•Modern semiconductor manufacturing is performed in a cleanroom, isolated from the outside environment and contaminants.Types of contamination•Cleanroom contamination has five categories: particles, metallic impurities, organic contamination, native oxides and electrostatic discharge. Killer defects are those causes of failure where the chip fails during electrical test.Particles: objects that adhere to a wafer surface and cause yield loss. A particle is a killer defect if it is greater than one-half the minimum device feature size.Metallic impurities: the alkali metals found in common chemicals. Metallic ions are highly mobile and referred to as mobile ionic contaminants (MICs).Organic contamination: contains carbon, such as lubricants and bacteria.Native oxides: thin layer of oxide growth on the wafer surface due to exposure to air.Electrostatic discharge (ESD): uncontrolled transfer of static charge that can damage the microchip.Sources and Control of Contamination•The sources of contamination in a wafer fab are: air, humans, facility, water, process chemicals, process gases and production equipment.Air: class number designates the air quality inside a cleanroom by defining the particle size and density.Humans: a human is a particle generator. Humans wear a cleanroom garment and follow cleanroom protocol to minimize contamination.Facility: the layout is generally done as a ballroom (open space) or bay and chase design.Laminar airflow with air filtering is used to minimize particles. Electrostatic discharge iscontrolled by static-dissipative materials, grounding and air ionization.Ultrapure deiniozed (DI) water: Unacceptable contaminants are removed from DI water through filtration to maintain a resistivity of 18 megohm-cm. The zeta potential represents a charge on fine particles in water, which are trapped by a special filter. UV lamps are used for bacterial sterilization.Process chemicals: filtered to be free of contamination, either by particle filtration, microfiltration (membrane filter), ultrafiltration and reverse osmosis (or hyperfiltration).Process gases: filtered to achieve ultraclean gas.Production equipment: a significant source of particles in a fab.Workstation design: a common layout is bulkhead equipment, where the major equipment is located behind the production bay in the service chase. Wafer handling is done with robotic wafer handlers. A minienvironment is a localized environment where wafers are transferred on a pod and isolated from contamination.Wafer Wet Cleaning•The predominant wafer surface cleaning process is with wet chemistry. The industry standard wet-clean process is the RCA clean, consisting of standard clean 1 (SC-1) and standard clean 2 (SC-2).•SC-1 is a mixture of ammonium hydroxide, hydrogen peroxide and DI water and capable of removing particles and organic materials. For particles, removal is primarily through oxidation of the particle or electric repulsion.•SC-2 is a mixture of hydrochloric acid, hydrogen peroxide and DI water and used to remove metals from the wafer surface.•RCA clean has been modified with diluted cleaning chemistries. The piranha cleaning mixture combines sulfuric acid and hydrogen peroxide to remove organic and metallic impurities. Many cleaning steps include an HF last step to remove native oxide.•Megasonics(兆声清洗) is widely used for wet cleaning. It has ultrasonic energy with frequencies near 1 MHz. Spray cleaning will spray wet-cleaning chemicals onto the wafer. Scrubbing is an effective method for removing particles from the wafer surface.•Wafer rinse is done with overflow rinse, dump rinse and spray rinse. Wafer drying is done with spin dryer or IPA(异丙醇) vapor dry (isopropyl alcohol).•Some alternatives to RCA clean are dry cleaning, such as with plasma-based cleaning, ozone and cryogenic aerosol cleaning.Chapter 7Metrology and Defect InspectionIC Metrology•In a wafer fab, metrology refers to the techniques and procedures for determining physical and electrical properties of the wafer.•In-process data has traditionally been collected on monitor wafers. Measurement equipment is either stand-alone or integrated.•Yield is the percent of good parts produced out of the total group of parts started. It is an indicator of the health of the fabrication process.Quality Measures•Semiconductor quality measures define the requirements for specific aspects of wafer fabrication to ensure acceptable device performance.•Film thickness is generally divided into the measurement of opaque film or transparent film. Sheet resistance measured with a four-point probe is a common method of measuring opaque films (e.g., metal film). A contour map shows sheet resistance deviations across the wafer surface.•Ellipsometry is a nondestructive, noncontact measurement technique for transparent films. It works based on linearly polarized light that reflects off the sample and is elliptically polarized.•Reflectometry is used to measure a film thickness based on how light reflects off the top and bottom surface of the film layer. X-ray and photoacoustic technology are also used to measure film thickness.•Film stress is measured by analyzing changes in the radius of curvature of the wafer. Variations in the refractive index are used to highlight contamination in the film.•Dopant concentration is traditionally measured with a four-point probe. The latest technology is the thermal-wave system, which measures the lattice damage in the implanted wafer after ion implantation. Another method for measuring dopant concentration is spreading resistance probe. •Brightfield detection is the traditional light source for microscope equipment. An optical microscope uses light reflection to detect surface defects. Darkfield detection examines light scattered off defects on the wafer surface. Light scattering uses darkfield detection to detectsurface particles by illuminating the surface with laser light and then using optical imaging.•Critical dimensions (CDs) are measured to achieve precise control over feature size dimensions.The scanning electron microscope is often used to measure CDs.•Conformal step coverage is measured with a surface profiler that has a stylus tip.•Overlay registration measures the ability to accurately print photoresist patterns over a previously etched pattern.•Capacitance-voltage (C-V) test is used to verify acceptable charge conditions and cleanliness at the gate structure in a MOS device.Analytical Equipment•The secondary-ion mass spectrometry (SIMS) is a method of eroding a wafer surface with accelerated ions in a magnetic field to analyze the surface material composition.•The atomic force microscope (AFM) is a surface profiler that scans a small, counterbalanced tip probe over the wafer to create a 3-D surface map.•Auger electron spectroscopy (AES) measures composition on the wafer surface by measuring the energy of the auger electrons. It identifies elements to a depth of about 2 nm. Another instrument used to identify surface chemical species is X-ray photoelectron spectroscopy (XPS).•Transmission electron microscopy (TEM) uses a beam of electrons that is transmitted through a thin slice of the wafer. It is capable of quantifying very small features on a wafer, such as silicon crystal point defects.•Energy-dispersive spectrometer (EDX) is a widely used X-ray detection method for identifying elements. It is often used in conjunction with the SEM.• A focused ion beam (FIB) system is a destructive technique that focuses a beam of ions on the wafer to carve a thin cross section from any wafer area. This permits analysis of the wafermaterial.Chapter 8Gas Control in Process ChambersEtch process chambers••The process chamber is a controlled vacuum environment where intended chemical reactions take place under controlled conditions. Process chambers are often configured as a cluster tool. Vacuum•Vacuum ranges are low (rough) vacuum, medium vacuum, high vacuum and ultrahigh vacuum (UHV). When pressure is lowered in a vacuum, the mean free path(平均自由行程) increases, which is important for how gases flow through the system and for creating a plasma.Vacuum Pumps•Roughing pumps are used to achieve a low to medium vacuum and to exhaust a high vacuum pump. High vacuum pumps achieve a high to ultrahigh vacuum.•Roughing pumps are dry mechanical pumps or a blower pump (also referred to as a booster). Two common high vacuum pumps are a turbomolecular (turbo) pump and cryopump. The turbo pump is a reliable, clean pump that works on the principle of mechanical compression. The cryopump isa capture pump that removes gases from the process chamber by freezing them.。
半导体分离芯材料英语Semiconductor Materials for Isolation Cores.Semiconductor materials play a crucial role in modern electronics, particularly in the fabrication of isolation cores. Isolation cores are essential components in integrated circuits, ensuring that different sections of the circuit operate independently without interference. This article delves into the world of semiconductor materials suitable for isolation cores, discussing their properties, applications, and challenges.1. Introduction to Semiconductor Materials.Semiconductors are materials that have an electrical conductivity falling between that of conductors and insulators. They exhibit unique electronic properties, making them ideal for use in electronic devices. Silicon (Si) and germanium (Ge) are the most commonly used semiconductors, but others such as gallium arsenide (GaAs)and silicon carbide (SiC) are also finding applications in specific areas.2. Properties of Semiconductor Materials.Bandgap Energy: The bandgap energy is a measure of the energy required to excite an electron from the valence band to the conduction band. Materials with larger bandgap energies are better suited for high-temperature applications.Doping: Semiconductors can be doped with impurities to alter their conductivity. Dopants such as boron (B) or phosphorus (P) are introduced to create p-type or n-type semiconductors, respectively.Lattice Structure: The atomic lattice structure of semiconductors determines their physical and electrical properties. Silicon and germanium have diamond-like lattice structures, which contribute to their widespread use.3. Isolation Cores and Their Importance.Isolation cores are critical in integrated circuits, where they prevent electrical signals from leaking between different circuit sections. This isolation ensures that signals are contained within their designated paths, preventing crosstalk and noise. Isolation cores are typically made from insulating materials, but semiconductor materials can also be used to achieve isolation.4. Semiconductor Materials for Isolation Cores.Silicon-on-Insulator (SOI): SOI technology involves a thin layer of silicon sandwiched between two layers of insulating material, such as silicon dioxide or sapphire. This structure provides excellent isolation between different circuit sections. SOI wafers are widely used in high-performance microelectronics, as they offer reduced parasitic capacitance and improved thermal performance.Silicon Carbide (SiC): SiC is a wide-bandgap semiconductor material with excellent thermal conductivity and chemical stability. It is suitable for high-temperatureand high-power applications. SiC-based isolation cores can withstand extreme operating conditions, making them idealfor use in power electronics and aerospace applications.Gallium Arsenide (GaAs): GaAs has a smaller bandgap than silicon but offers higher electron mobility and saturation velocity. GaAs-based isolation cores are commonly used in high-frequency applications such as microwave and millimeter-wave circuits. GaAs also finds applications in optoelectronics due to its ability to emit and detect light.5. Challenges and Future Outlook.Despite the many advantages of semiconductor materials for isolation cores, there are still challenges to overcome. One major challenge is the scalability of these materialsfor smaller and more complex integrated circuits. Another challenge lies in the fabrication process, which requires precise control over doping levels, lattice structures, and defect densities.Future research in this area will focus on developing new semiconductor materials with improved properties and on optimizing fabrication processes for better scalability and performance. Materials such as two-dimensional semiconductors and topological insulators are beingactively explored for their potential in next-generation electronics.Conclusion.Semiconductor materials play a pivotal role in the fabrication of isolation cores, enabling the reliable operation of integrated circuits. Silicon, silicon carbide, and gallium arsenide are among the most commonly used semiconductors for this purpose, each offering its unique advantages and applications. Future research in this field will focus on addressing challenges related to scalability and fabrication processes while exploring novel materials with improved properties.。
半导体器件英文版Semiconductor devices are electronic components thatutilize the unique properties of semiconductors to perform various functions in electronic circuits. These devices playa crucial role in modern technology and are essential for the operation of almost all electronic devices.One of the most common types of semiconductor devices is the diode, which allows current to flow in only one direction. Diodes are used in rectifiers to convert alternating current (AC) to direct current (DC) and in circuits to protect components from reverse voltage.Transistors are another important semiconductor devicethat are used to amplify or switch electronic signals. There are two main types of transistors: bipolar junctiontransistors (BJTs) and field-effect transistors (FETs). BJTsuse a current to control the flow of another current, while FETs use an electric field to control the flow of current.Integrated circuits (ICs) are semiconductor devices that contain thousands or even millions of individual components, such as transistors, diodes, and resistors, all embedded on a single semiconductor chip. ICs are the building blocks of most electronic devices and can be found in smartphones, computers, televisions, and many other electronic gadgets.Another important semiconductor device is the light-emitting diode (LED), which emits light when an electric current passes through it. LEDs are widely used in displays, indicators, and lighting applications due to their energy efficiency and long lifespan.Semiconductor devices have revolutionized the electronics industry and have enabled the development of advanced technologies such as computers, smartphones, and renewable energy systems. As semiconductor technology continues toevolve, new devices with improved performance and capabilities are being developed to meet the increasing demands of modern electronics.。
半导体的原理与应用英语1. Introduction to SemiconductorsSemiconductors are materials that have electrical conductivity between conductors (such as metals) and insulators (such as ceramics). They have unique electronic properties that make them essential in various electronic devices. This article aims to provide an overview of the principles and applications of semiconductors in English.2. Basic Principles of SemiconductorsSemiconductors rely on the behavior of electrons and holes within their crystalline structure. The key principle is the band gap, which is the energy difference between the valence band (electron-rich) and the conduction band (electron-poor). At absolute zero temperature, semiconductors have a fully occupied valence band and an empty conduction band. However, at higher temperatures or with external energy input, electrons can be excited to the conduction band, creating a conductive pathway.3. Types of SemiconductorsThere are two main types of semiconductors: intrinsic and extrinsic. Intrinsic semiconductors are pure semiconducting materials, such as silicon (Si) and germanium (Ge). Extrinsic semiconductors are doped with impurities to alter their electrical properties. Two common types of extrinsic semiconductors include n-type (electron-doped) and p-type (hole-doped) semiconductors.4. Doping Process in SemiconductorsDoping introduces impurities into the semiconductor crystal, which modifies its electrical conductivity. For n-type doping, atoms with more valence electrons, such as phosphorus (P), are added. These extra electrons become the majority charge carriers, increasing conductivity. In contrast, p-type doping involves adding atoms with fewer valence electrons, such as boron (B). These。
半导体英文词汇SemiconductorA semiconductor is a material that has electrical conductivity between that of a conductor and that of an insulator. This means that it can conduct some electricity under certain conditions, but not as much as a conductor. Semiconductors are essential components of electronic devices, such as diodes, transistors, and integrated circuits.半导体半导体是一种在导体和绝缘体之间具有电导性的材料。
这意味着在某些条件下它可以导电,但不像导体那样能够导电。
半导体是电子器件的基本组成部分,如二极管、晶体管和集成电路。
DiodeA diode is a semiconductor device that allows current to flow in only one direction. It has two terminals, an anode and a cathode. When a positive voltage is applied to the anode and a negative voltage to the cathode, the diode conducts electricity. However, if the polarity of theapplied voltage is reversed, the diode blocks the flow of current.二极管二极管是一种只允许电流在一个方向中流动的半导体器件。
电子信息技术专业英语习题答案电子信息技术专业英语第2版习题答案Exercise AnswersPart one ElectronicsUnit 1 Electronic ComponentsExercises1.(1)the simplest components in any circuit(2)converting electrical energy into heat.(3)仅沿单向流动(4)on or off switch(5)称为电绝缘的绝缘材料2. (1)current(2)circuit(3)charge(4)conductors(5)Transistors3. (1)which ---atoms(2)it---balloon(3)it---The unit of voltage, or potential difference(4)which---a wall or the ceiling(5)it---the charge of an electron is a negative one of 1.60218x10-19 coulombs4. (1)constitute(2)consists of(3)is composed of(4)makes up(5)constitute5. (1) Resistors can reduce the flow of current.(2) Capacitors consist of two pieces of conducting materials separated by a non-conducting material called a dielectric.(3)The function of a transistor is similar to a switch.Unit 2 SemiconductorExercises1.(1)集成电路(2)半导体的导电性(3)positive type material semiconductor(4)forward bias(5)每秒可完成上百万的简单指令操作2.(1)---(a)(2)---(c)(3)---(b)(4)---(e)(5)---(d)3. (1)√(2)x (3)x (4)√ (5) √4.(1)只要加很小的电压就能让电流流动的材料称为导体。
第一单元 元件与定律A .课文译文电阻器、电容器和电感器在电子电路中,电阻器、电容器和电感器是非常重要的元件。
电阻器和电阻电阻器是二端口元件。
电阻是阻止电流流动,更确切地说,是阻止电荷流动的能力。
在国际单位制中,电阻用欧姆来度量。
希腊字母Ω是欧姆的标准符号。
较大的电阻一般用千欧和兆欧来表示。
模拟这种特性常用的电路元件是电阻器。
图1.1表示电阻器的电路符号,R 表示电阻器的电阻值。
图1.1 电阻器的电路符号为了进行电路分析,我们必须在电阻器中指明电流和电压的参考方向。
如果我们选择关联参考方向,那么电压和电流之间的关系是:v =iR (1.1)这里 v 是电压,其单位是伏特, i 是电流,其单位是安培, R 是电阻,其单位是欧姆。
如果选择非关联参考方向,我们必须写成:v =-iR (1.2)用在公式(1.1)和(1.2)中的代数式就是著名的欧姆定律。
欧姆定律表示了电压作为电流的函数。
然而,要表示电流是电压的函数也是非常方便的。
欧姆定律是电阻两端的电压和电流间的代数关系。
电容器和电容电能可以存储在电场中,存储电能的装置叫电容器。
电容器存储电能的能力叫做电容。
图1.2表示电容器的电路符号。
电容的电路参数用字母C 表示,用法拉来度量。
因为法拉是相当大的电容量,实际上电容值通常位于皮法和微法之间。
图1.2 电容器的电路符号当电压随时间变化时,电荷的位移也随时间变化,引起了众所周知的位移电流。
在终端,位移电流和传导电流没有区别。
当电流参考方向和电压参考方向是关联参考方向时,电流正比于电容两端电压随时间的变化率的数学表达式为:dtdv C i = (1.3) 这里 i 的单位是安培,C 的单位是法拉,v 的单位是伏特, t 的单位是秒。
电感器和电感众所周知,电感是电子电路中的模块之一。
所有的线圈都有电感。
电感是抵抗流过线圈电流的任何变化的性质。
电感用字母L 表示,其单位是亨利。
图1.3表示一个电感器。
图1.3 电感器的电路符号当电流和电压的参考方向关联时,有dt diL v = (1.4)这里v 的单位是伏特,L 的单位是亨利,i 的单位是安培,t 的单位是秒。
——电材专业英语课文翻译Semiconductor Materials• 1.1 Energy Bands and Carrier Concentration• 1.1.1 Semiconductor Materials•Solid-state materials can be grouped into three classes—insulators(绝缘体), semiconductors, and conductors. Figure 1-1 shows the electrical conductivities δ(and the corresponding resistivities ρ≡1/δ)associated with(相关)some important materials in each of three classes. Insulators such as fused(熔融)quartz and glass have very low conductivities, in the order of 1E-18 to 1E-8 S/cm;固态材料可分为三种:绝缘体、半导体和导体。
图1-1 给出了在三种材料中一些重要材料相关的电阻值(相应电导率ρ≡1/δ)。
绝缘体如熔融石英和玻璃具有很低电导率,在10-18 到10-8 S/cm;and conductors such as aluminum and silver have high conductivities, typically from 104 to 106 S/cm. Semiconductors have conductivities between those of insulators and those of conductors. The conductivity of a semiconductor is generally sensitive to temperature, illumination(照射), magnetic field, and minute amount of impurity atoms. This sensitivity in conductivity makes the semiconductor one of the most important materials for electronic applications.导体如铝和银有高的电导率,典型值从104到106S/cm;而半导体具有的电导率介乎于两者之间。
第2单元电子基础第3课半导体材料通常,根据材料导电性能的不同,可分为三种类型——导体,半导体和绝缘体。
半导体是一种导电能力介于导体和绝缘体之间的材料,其导电性在外部电场的作用下是变化的。
半导体材料的导电性能比导体差,但是相对于绝缘体来说其导电性能比较好。
早在19世纪就开始对半导体材料进行研究,多年以来,许多半导体材料已经开发。
表1-1为半导体化学元素周期表的一部分。
元素半导体是由单一元素制成的半导体材料。
例如IV族元素硅、锗和锡和VI族元素硒和锑。
大多数化合物半导体材料由两种或两种以上元素组成。
如砷化镓是III-V族化合物。
它是由III族的镓元素和V族的砷元素组成。
由半导体材料制成的电子器件非常微小。
利用半导体材料的性质可以制造出功能多样的半导体器件。
另外,半导体器件和其他电子器件相比有很多优点,它们体积小、重量轻而且功耗小。
与其他电子器件一样,半导体器件有控制电子移动的能力。
可用作整流器、探测器、放大器、振荡器、电子开关、混频器和调制器等。
通常用于半导体器件的半导体材料是锗和硅,它们是应用最广的半导体材料。
锗和硅都属于金刚石晶格结构,这种结构同时也属于立方晶体族结构。
地球上超过90%的成分由二氧化硅和硅酸盐组成。
硅元素储量丰富,占地球上第二位。
在沙滩上闪闪发亮的就是硅石。
在自然界和工业的许多化合物中均发现有硅成份组成。
对工业技术来讲,最重要的就是硅是半导体器件的基础平台。
大多数的半导体器件都是由硅材料制造的,尤其是集成电路和微芯片。
在集成电路制造中,硅材料是形成单晶硅片的基础。
为了跟上集成电路制造工艺、芯片尺寸和电路复杂程度的步伐,硅晶体和晶圆也必须在增加直径的同时改善其性能。
现在普遍制造的硅片直径已经足够大,可以达到300mm也就是12inch。
图3-1中显示的是一片硅晶圆。
现代的特大规模集成电路,其设计工艺已经要求达到60纳米,这都是由于硅单晶具有非常良好的性质,而且这些硅片都是应用坩埚直拉法形成的。
Chapter2ELECTRONIC LEVELSIN SEMICONDUCTORS2.1INTRODUCTIONSemiconductor electronic and optoelectronic devices depend upon how electrons inside ma-terials behave and how they are influenced by external perturbations which may be electrical, electromagnetic,mechanical,or magnetic,etc.The simplest approach to understanding such properties would be to use classical physics.Based on classical physics the general problem could be solved by using Newton’s equationd p=e(E+v×B)dtwhere p is the electron momentum,v the velocity,and E and B are the electrical and magnetic fields,respectively.Additional forces,if present,can be added on the right-hand side of the equa-tion.Although classical physics has been successful in describing many of nature’s phenomena, it fails completely when it is used to describe electrons in solids.To understand the underlying physical properties that form the basis of modern intelligent information devices,we need to use quantum mechanics.According to quantum mechanics particles such as electrons behave as waves while waves such as electromagnetic waves behave as particles.The wave nature of particles is manifested for electrons in solids.To the level needed in device physics,the electronic properties are described by the Schr¨o dinger equation.However,It turns out we can develop effective descriptions for the behavior of electrons and then use simple classical physics.Of course to develop this effective description we have to solve the Schr¨o dinger equation.But once this description is developed we can use Newton’s equation to understand how electrons respond to external forces.This allows us to use simple models to describe electronic devices.In this chapter we will review a few important outcomes of quantum mechanics.In particular we will discuss the following:282.2.PARTICLES IN AN ATTRACTIVE POTENTIAL:BOUND STATES29•Electronic properties in an atom:All solids are made up of atoms and the properties of electrons in atoms allows us to develop insight into the electronic properties of solids.We will discuss the hydrogen atom problem since it is the simplest atom and captures the useful physics needed to understand the theory of doping.•Electrons in a quantum well:Quantum wells,both naturally occurring and artificially cre-ated in semiconductor structures are very important in modern technology.In devices such as MOSFETs,lasers,modulators etc.electrons are in quantum wells of various sizes and shapes.•Electrons in free space and in crystalline materials:Most high performance semiconductor devices are based on high quality crystals.In these periodic structures electrons have allowed energies that form bands separated from each other(in energy)by gaps.Almost every semicon-ductor property depends upon these bands.Once we understand the band theory,i.e properties of electrons in crystalline solids we can develop the effective description mentioned above and use simple classical concepts.•Occupation of electronic states:Quantum mechanics has very specific rules on the actual occupation of energies allowed by Schr¨o dinger equation.This occupation theory is central to understanding solid state physics and device behavior.Once we have developed the basic quantum theory structure we will discuss properties of various semiconductors and their heterostructures.2.2PARTICLES IN AN ATTRACTIVE POTENTIAL:BOUND STATESWe will now examine several important quantum problems that have impact on materials and physical phenomena useful for device applications.The Schr¨o dinger equation for electrons canbe written in as−22m0∇2+V(r,t)Ψ(r,t)=EΨ(r,t)where m0is the mass of the electron and V(r,t)is the potential energy.This is a differential equation with solutionsΨ.Once the equation is solved we get a series of allowed energies and wavefunctions.Energies are allowed while others not consistent with the equation are forbidden. The band theory that forms the basis of all semiconductor devices is based on energy bands and gaps.2.2.1Electronic levels in a hydrogen atomThe hydrogen atom problem is of great relevance in understanding dopants in semiconductors. We will briefly summarize thesefindings.The hydrogen atom consists of an electron and a pro-ton interacting with the Coulombic interaction.The problem can be solved exactly and provides insight into how electrons behave inside atoms.Wavefunctions in the H-atom problem have the following term:ψn m(r,θ,φ)=R n (r)F m(θ)G m(φ)30CHAPTER2.ELECTRONIC LEVELS IN SEMICONDUCTORS The symbols n, ,m are the three quantum numbers describing the solution.The three quantum numbers have the following allowed values:principle number,n:Takes values1,2,3,...angular momentum number, :Takes values0,1,2,...n−1magnetic number,m:Takes values− ,− +1,...The principle quantum number specifies the energy of the allowed electronic levels.The energy eigenvalues are given byE n=−μe42(4π 0)2 2n2(2.2.1)The spectrum is shown schematically infigure2.1.Due to the much larger mass of the nucleus as compared with the mass of the electron,the reduced massμis essentially the same as the electron mass m0.The ground state of the hydrogen atom is given byψ100=1πa3e−r/a0(2.2.2)The parameter a0appearing in the functions is called the Bohr radius and is given bya0=4π 0 2=0.53˚A(2.2.3)It roughly represents the spread of the ground state.As noted earlier the dopant problem is addressed by using the potential of the H-atom2.2.2Electrons in a quantum wellAs noted in the previous chapter,using semiconductor heterostructures it is possible to fab-ricate quantum well systems.These systems are used for high-performance devices,such as transistors,lasers and modulators.The quantum well problem can also be used to understand how defects create trap levels.A quantum well potential profile is shown infigure2.2.The well(i.e.,region where potential energy is lower)is described by a well size W=2a as shown and a barrier height V0.In general the potential could be confining in one dimension with uniform potential in the other two directions(quantum well),or it could be confining in two dimensions(quantum wire)or in all three dimensions(quantum dot).As discussed later in this chapter such quantum wells are formed in semiconductor structures and we can use the results discussed in this section to understand these problems.We assume that the potential has a formV(r)=V(x)+V(y)+V(z)2.2.PARTICLES IN AN ATTRACTIVE POTENTIAL:BOUND STATES31116E 11 9E 11 4E 1E 11s2s3s 4s 5s= 0Figure 2.1:Allowed energy levels of electrons in a hydrogen atom .32CHAPTER 2.ELECTRONIC LEVELS IN SEMICONDUCTORS2a V 0V –W 2W 2x = 00x Figure 2.2:Schematic of a quantum well of width 2a and infinite barrier height or barrier height V 0.so that the wavefunction is separable and of the formψ(r )=ψ(x )ψ(y )ψ(z )We will briefly discuss the problem of the square potential well,and in section 2.10we will use the quantum well physics to discuss semiconductor quantum wells of importance in devices.The simplest form of the quantum well is one where the potential is zero in the well and infinite outside.The equation to solve then is (the wave function is non-zero only in the well region)− 22m d 2ψdx 2=Eψ(2.2.4)which has the general solutionsψ(x )=B cos nπx 2a ,n odd =A sin nπx 2a ,n even (2.2.5)The energy is E =π2 2n 28ma 2(2.2.6)Note that the well size is 2a .The normalized particle wavefunctions areψ(x )= W cos nπx W ,n odd = 2W sin nπx W ,n even (2.2.7)2.3.ELECTRONS IN CRYSTALLINE SOLIDS 33If the potential barrier is not infinite,we cannot assume that the wavefunction goes to zero at the boundaries of the well.Let us define two parameters.α= 2mE 2β= 2m (V 0−E )(2.2.8)The conditions for the allowed energy levels are given by the transcendental equations αW 2tan αW 2=βW 2(2.2.9)and αW 2cot αW 2=−βW 2(2.2.10)An important outcome of these solutions is that as in the H-atom case,only some energies are allowed for the electron.This result is of importance in electronic devices as will be discussed in section 2.10.2.3ELECTRONS IN CRYSTALLINE SOLIDSThe devices discussed in this text are made from crystalline materials.It is,therefore,impor-tant to understand the electronic properties of these materials.Let us first examine the simpler problem of electrons in free space.It turns out that electrons in crystals can be considered to behave as if they are in free space except they have a different “effective properties”.In the free space problem the background potential energy is uniform in space.The time-independent equation for the background potential in a solid equal to V 0is − 22m ∂2∂x +∂2∂y +∂2∂zψ(r )=(E −V 0)ψ(r )(2.3.1)A general solution of this equation isψ(r )=1√Ve ±i k ·r(2.3.2)and the corresponding energy isE = 2k 22m +V 0(2.3.3)where the factor 1√V in the wavefunction occurs because we wish to have one particle per volume V orVd 3r |ψ(r )|2=1(2.3.4)We assume that the volume V is a cube of side L .Note that if we assign the momentum of the electron as k the energy-momentum relation of free electrons is the same as that in classical ter we will see that in crystalline material one can use a similar relationship except the mass of the electron is modified by an effective mass.34CHAPTER2.ELECTRONIC LEVELS IN SEMICONDUCTORS Density of states for a three-dimensional systemWe will now discuss the extremely important concept of density of states.The concept of density of states is extremely powerful,and important physical properties in materials,such as optical absorption,transport,etc.,are intimately dependent upon this concept.Density of states is the number of available electronic states per unit volume per unit energy around an energy E. If we denote the density of states by N(E),the number of states in a unit volume in an energy interval dE around an energy E is N(E)dE.Accounting for spin,the density of states can be shown to be(see Appendix C)N(E)=√2m3/2(E−V0)1/2π(2.3.5)Infigure2.4a we show the form of the three-dimensional density of states.Density of states in sub-three-dimensional systemsThe use of heterostructures has allowed one to make sub-three-dimensional-systems.In these systems the electron can be confined in two-dimensions(forming a quantum well)or in one-dimensional(quantum wire)and zero-dimensional(quantum dot)space.The two-dimensional density of states is defined as the number of available electronic states per unit area per unit energy around an energy E.It can be shown that the density of states for a parabolic band(for energiesgreater than V0)is(seefigure2.3b)N(E)=m0π(2.3.6)Finally,we can consider a one-dimensional system often called a“quantum wire.”The one-dimensional density of states is defined as the number of available electronic states per unit length per unit energy around an energy E.In a1D system or a“quantum wire”the density of states is(including spin)(seefigure2.3c)N(E)=√2m1/20(E−V)−1/2(2.3.7)Notice that as the dimensionality of the system changes,the energy dependence of the density of states also changes.As shown infigure2.3,for a three-dimensional system we have(E−V0)1/2dependence,for a two-dimensional system we have no energy dependence,and for a one-dimensional system we have(E−V0)−1/2dependence.We will see later in the next section that when a particle is in a periodic potential,its wave-function is quite similar to the free particle wavefunction.Also,the particle responds to external forces as if it is a free particle except that its energy-momentum relation is modified by the presence of the periodic potential.In some cases it is possible to describe the particle energy bythe relationE= 2k22m∗+E edge(2.3.8)where m∗is called the effective mass in the material and E edge is the bandedge energy.The ef-fective mass in general summarizes the appropriate way to modify the free electron mass based2.3.ELECTRONS IN CRYSTALLINE SOLIDS35N(E)E(a) E02D systemE(b)(c)V0Figure2.3:Energy dependence of the density of states in:(a)three-dimensional,(b)two-dimensional,and(c)one-dimensional systems.on the physical property being characterized.Appendix C describes the various forms of effec-tive mass in detail.The expressions derived for the free electron density of states can then be carried over to describe the density of states for a particle in a crystalline material(which has a periodic potential)by simply replacing m0by m∗.36CHAPTER2.ELECTRONIC LEVELS IN SEMICONDUCTORS EXAMPLE2.1Calculate the density of states of electrons in a3D system and a2D system at an energy of1.0eV.Assume that the background potential is zero.The density of states in a3D system(including the spin of the electron)is given by(E is the energy inJoules)N(E)=√2(m0)3/2E1/2π=√2(0.91×10−30kg)(E1/2)π2(1.05×10−34J·s)3=1.07×1056E1/2J−1m−3Expressing E in eV and the density of states in the commonly used units of eV−1cm−3,we getN(E)=1.07×1056×(1.6×10−19)3/2(1.0×10−6)E1/2=6.8×1021E1/2eV−1cm−3At E=1.0eV we getN(E)=6.8×1021eV−1cm−3For a2D system the density of states is independent of energy and isN(E)=m0π 2=4.21×1014eV−1cm−22.3.1Particle in a periodic potential:Bloch theoremBand theory,which describes the properties of electrons in a periodic potential arising from the periodic arrangement of atoms in a crystal,is the basis for semiconductor technology.The Schr¨o dinger equation in the crystal− 2 2m0∇2+U(r)ψ(r)=Eψ(r)(2.3.9)where U(r)is the background potential seen by the electrons.Due to the crystalline nature of the material,the potential U(r)has the same periodicityU(r)=U(r+R)We have noted earlier that if the background potential is V0,the electronic function in a volumeV isψ(r)=e i k·r √Vand the electron momentum and energy arep= kE=2k2+V02.3.ELECTRONS IN CRYSTALLINE SOLIDS37 The wavefunction is spread in the entire sample and has equal probability(ψ∗ψ)at every point in space.In the periodic crystal electron probability is the same in all unit cells of the crystal2.4.because each cell is identical.This is shown schematically infigureU|ψFigure2.4:A periodic potential,|ψ|2has the same spatial periodicity as the potential. Bloch’s theorem states the eigenfunctions of the Schr¨o dinger equation for a periodic potential are the product of a plane wave e i k·r and a function u k(r),which has the same periodicity as the periodic potential.Thusψk(r)=e i k·r u k(r)(2.3.10) is the form of the electronic function.The periodic part u k(r)has the same periodicity as the crystal,i.e.u k(r)=u k(r+R)(2.3.11) The wavefunction has the propertyψk(r+R)=e i k·(r+R)u k(r+R)=e i k·r u k(r)e i k·R=e i k·Rψk(r)(2.3.12) To obtain the allowed energies,i.e.the band structure,computer techniques are used to solve the Schr¨o dinger equation.One obtains a series of allowed energy bands separated by bandgaps as shown schematically infigure2.5.Each band has an E vs.k relation Examples of such relations called bandstructure will be shown later in section2.6.The product of and the k-vector behaves like an effective momentum for the electron inside the crystal.The smallest k-values lie in a k-space called the Brillouin zone(seefigure2.6).If the k-value is chosen beyond the Brillouin zone values,the energy values are simply repeated.The concept38CHAPTER 2.ELECTRONIC LEVELS INSEMICONDUCTORSFree st a tes B o u n d s t a t e s E 1E 2E 3E 4E vFree st a tes}}..Figure 2.5:A schematic description of allowed energy levels and energy bands in an atom and in crystalline materials.of allowed bands of energy separated by bandgaps is central to the understanding of crystalline materials.Near the bandedges it is usually possible to define the electron E –k relation asE = 2(k −k o )22m ∗where k o is the k -value at the bandedge and m ∗is the effective mass.The concept of an effective mass is extremely useful,since it represents the response of the electron–crystal system to the outside world.k -vector According to the Bloch theorem,in the perfectly periodic background potential that the crystal presents,the electron propagates without scattering.The electronic state ∼exp (i k ·r )is an extended wave which occupies the entire crystal.To describe the response of the electron waves to external forces one uses the wavepacket description.The equation of motion for electrons in2.3.ELECTRONS IN CRYSTALLINE SOLIDS39(a)(b)Figure2.6:Brillouin zone of(a)the face centered cubic lattice and(b)the hexagonal lattice.40CHAPTER2.ELECTRONIC LEVELS IN SEMICONDUCTORS general isd pdt=F ext+F intHowever this is not very useful for a meaningful description of the electron because it includes the internal forces on the electron.We need a description which does not include the evaluation of the internal ing a wavepacket description of electrons as with any wave phenomena it is the wave group velocity that represents the propagation of wave energy.In the case of a particle wave the group velocity represents the particle velocity.The group velocity of this wavepacket isv g=dωd k(2.3.13) whereωis the frequency associated with the electron of energy E;in quantum mechanics,ω=E/ :v g=1dE d k=1∇k E(k)If we have an electricfield E present,the work done on the electron during a time intervalδt isδE=−e E·v gδt(2.3.14) We may also write,in generalδE=dEδk= v g·δk(2.3.15) Comparing the two equations forδE,we getδk=−e E δtgiving us the relationd kdt=−e E(2.3.16) In general,we may writed kdt=F ext(2.3.17) The term k responds to the external forces as if it is the momentum of the electron,although, as can be seen by comparing the true Newtons equation of motion,it is clear that k contains the effects of the internal crystal potentials and is therefore not the true electron momentum. The quantity k is called the crystal momentum.We can,for all practical purposes,treat the electrons as if they are free and obey the effective Newtons equation of motion.This physical picture is summarized infigure2.7.2.4.OCCUPATION OF STATES:DISTRIBUTION FUNCTION 41++++++++++++Figure 2.7:Electrons in a periodic potential can be treated as if they are in free space except that their energy–momentum relation is modified because of the potential.Near the bandedges the electrons respond to the outside world as if they have an effective mass m ∗.The effective mass can have a positive or negative value.2.4OCCUPATION OF STATES:DISTRIBUTION FUNCTIONBandstructure calculations give us the allowed energies for the electron.How will the particles distribute among the allowed states?To answer this question we need to use quantum statistical physics.According to quantum mechanics particles (this term includes classical particles and classical waves which are represented by particles)have an intrinsic angular momentum called42CHAPTER 2.ELECTRONIC LEVELS IN SEMICONDUCTORS spin.The spin of particles can take a value of 0,1/2 , ,3/2 ,etc.Particles which have inte-gral spins (in units of )are called bosons,while those that have half-integral spins are called fermions.According to thermodynamics,a system with a large number of particles can be described by macroscopic properties such as temperature,pressure,volume,etc.Under equilibrium condi-tions (no exchange of net energy with other systems)the system is described by a distribution function,which gives us the occupation number for any energy level.To find this occupation we have to minimize the free energy F of the system subject to any constraints from quantum mechanics (such as the Pauli exclusion principle).The following distribution functions are ob-tained for equilibrium:•For fermions such as electronsf (E )=1exp E −E F k B T +1Here f (E )is the occupation function;E F is the Fermi energy and its value depends upon particle density).In classical physics the occupation function for electrons isf (E )=1exp E −E F k B T (2.4.1)Note that if E −E F k B T ;i.e.,f (E ) 1,the classical function approaches the quantum Fermi distribution function.For completeness we note the distributed function for bosons as well.•Massless bosons (like photons)f (E )=1exp Ek B T −1(2.4.2)•Bosons with mass (this applies to electron pairs that occur in superconductors)f (E )=1exp E −μk B T −1(2.4.3)where μis an energy determined from the particle density.•There is a distribution function that proves to be useful in solid state devices.When solving the Schr¨o dinger equation we can get more than one solution with the same energy.This is the degeneracy g d of a state.Consider a case where a state has a degeneracy g i and can,in principle,be occupied by g d electrons.However,for dopants and defect levels,when one electron is placed in the allowed state,the next one cannot be placed because of the Coulombic repulsion.This happens for some states,such as those states associated with donors or acceptors,traps,etc.2.5.METALS AND INSULATORS43Figure2.8:Schematic of the Fermi function for electrons and other fermions.In general the position of E F is dependent on temperature.The occupation probability is at0.5at the Fermi energy.Thus,even though Pauli exclusion principle would allow two(or more)electrons to reside on the state,the repulsion would not.In such cases the occupation function can be shown to bef(E)=11g dexpE−E Fk B T+1(2.4.4)Infigure2.8we show a schematic of the Fermi function for electrons and its dependence on temperature.It is important to note that at E=E F,f(E)=0.5regardless of the temperature. At zero temperature,the Fermi function becomes a step function with f(E<E F)=1.0and f(E)>E F=0.0.2.5METALS AND INSULATORSBand theory shows that the allowed energy states of electrons in a crystalline material are de-scribed by a series of allowed bands separated by forbidden bandgaps.Two important situations44CHAPTER 2.ELECTRONIC LEVELS IN SEMICONDUCTORSV ac uum energyCore levelCore levelHighesto cc upiedba nd isp a rti a llyfilled Highest o cc upied ba nd is c ompletely filled E g : B a ndg a p Inertba ndsFigure 2.9:Electron occupation of the bands in a metal and semiconductor (or insulator).In a metal,the highest occupied band at 0K is partially filled with electrons.In a semiconductor at 0K,the highest occupied band is completely filled with electrons and the next band is completely empty.The separation between the two bands is the bandgap E g .arise when we examine the electron occupation of allowed bands.As shown in figure 2.9we can have a situation where an allowed band is completely filled with electrons,while the next allowed band is separated in energy by a gap E g and is completely empty at 0K.In a second case,the highest occupied band is only half full (or partially full).When an allowed band is completely filled with electrons,the electrons in the band cannot conduct any current.Since electrons are fermions they cannot carry any net current in a filled band since an electron can only move into an empty state.Because of this effect,when we have a material in which a band is completely filled,while the next allowed band is separated in energy and empty,the material has,in principle,infinite resistivity and is an insulator or a semiconductor.The material in which a band is only half full with electrons has a very low resistivity and is a metal.The band that is normally filled with electrons at 0K in semiconductors is called the valence band,while the upper unfilled band is called the conduction band .The energy difference be-tween the vacuum level and the highest occupied electronic state in a metal is called the metal work function .The energy between the vacuum level and the bottom of the conduction band is called the electron affinity.2.5.METALS AND INSULATORS45Ele c c torted withFilled ba ndΣk= 0V a len c e ba ndTot a l momentum b e c omes –k ehole k ve c tor is –k eFigure2.10:Illustration of the wavevector of afilled valence band with a missing electron k e. The wavevector is−k e,which is associated with the hole.Semiconductors have zero conductivity at0K and quite low conductivity atfinite temper-atures,but it is possible to alter their conductivity by orders of magnitude through doping or applied electric potentials.This makes semiconductors useful for active devices.2.5.1Electrons and HolesIn semiconductors the valence band is full of electrons and the conduction band is empty at0K.Atfinite temperatures some of the electrons leave the valence band and occupy the conduction band.Electrons in the conduction band can carry current.When electrons leave the valence band there are unoccupied states.Consider the situation as shown infigure2.10,where an electron with momentum k e is missing from the valence band.When all of the valence band states are occupied,the sum of the total momentum is zero;i.e.k i=0=k i=k ek i+k e(2.5.1)This result is just an indication that there are as many positive k states occupied as there are negative ones.Now,in the situation where the electron at wavevector k e is missing,the total wavevector isk i=k ek i=−k e(2.5.2)The missing state is called a hole and the wavevector of the system−k e is attributed to it.It is important to note that the electron is missing from the state k e and the momentum associated with the hole is at−k e.The position of the hole is depicted as that of the missing electron.But in reality the hole wavevector k h is−k e,as shown infigure2.10and we havek h=−k e(2.5.3) If an electricfield is applied,all the electrons move in the direction opposite to the electricfield. This results in the unoccupied state moving in thefield direction.The hole thus responds as if46CHAPTER2.ELECTRONIC LEVELS IN SEMICONDUCTORS it has a positive charge.It therefore responds to external electric and magneticfields E and B, respectively,according to the equation of motiond k hdt=e[E+v h×B](2.5.4) where k h and v h are the momentum and velocity of the hole.Thus the equation of motion of holes is that of particles with a positive charge e.The mass of the hole has a positive value,although the electron mass in its valence band is negative.When we discuss the valence band properties,we refer to holes.This is because in the valence band only the missing electrons or holes lead to charge transport and currentflow.2.6BANDSTRUCTURE OF SOME IMPORTANTSEMICONDUCTORSIn this section we will examine the band structure near the band edges for several important materials.To represent the bandstructure on afigure that is two-dimensional,we draw the E-k diagram in several panels where k goes from zero to its maximum value along the(100)direction or the(111)direction,etc within the Brillouin zone.As shown infigure2.6for the fcc lattice, the maximum k-value along the(100)direction is2π/a(1,0,0).This point is called the X-point and there arefive other equivalent points,due to the cubic symmetry of the lattice.Similarly, along the(111)direction,the maximum k-point isπ/a(1,1,1)and seven other similar points. This point is called the L-point.Thus we commonly display the E-k diagram with k going from the origin(called theΓ-point)to the X-point and from the origin to the L-point.2.6.1Direct and indirect semiconductorsTwo types of band structures arise in semiconductors-direct and indirect.The top of the valence band of most semiconductors occurs at effective momentum equal to zero.A typical bandstructure of a semiconductor near the top of the valence band is shown infigure2.11.We notice the presence of three bands near the valence bandedge.These curves or bands are labeled I,II,and III in thefigure and are called the heavy hole(HH),light hole(LH),and the split off hole bands.The bottom of the conduction band in some semiconductors occurs at k=0.Such semicon-ductors are called direct bandgap materials.Semiconductors,such as GaAs,InP,GaN,InN,etc., are direct bandgap semiconductors.In other semiconductors,the bottom of the conduction band does not occur at the k=0point,but at certain other points.Such semiconductors are called indirect semiconductors.Examples are Si,Ge,AlAs,etc.Due to the law of momentum conservation,direct gap materials have a strong interaction with light.Indirect gap materials have a relatively weak interaction with electrons.When the bandedges are at k=0it is possible to represent the bandstructure by a simplerelation of the formE(k)=E c+ 2k2∗(2.6.1)。