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Fundamentals of Semiconductor Optoelectronic Materials Jing Yang Materials Science & Engineering Tianjin University Nov.,2015 References Texts: P. Bhattacharya, Semiconductor Optoelectronic Devices, 2nd edition, Prentice Hall, 1997. 孟庆巨等，半导体器件物理（第2版），科学出版社，2009 刘恩科等，半导体物理学（第7版），电子工业出版社， 2011 Additional references: S. O. Kasap, Optoelectronic and Photonics: Principles and Practices, Prentice Hall, 2011. 曾谨言，量子力学导论，北京大学出版社, 1998 黄昆原著，固体物理学，高等教育出版社，1988 考核方式： 采取学术报告形式 分为5个小组(5,5,5,4,4)，每组选1人为组长。 从第2次课开始，每次最后两节课，由一个小组的组员轮流 讲解部分PPT课件内容。每人先讲解10分钟，然后回答同学 和老师的提问（5分钟）。组内分工合作、共同讨论课件内 容。主要参考中文版本课件，查阅参考书和文献，并适当增 加课件内容，如实例等。使用中文或英文课件讲解均可。 评分标准： PPT讲解及回答问题 —— 60% 小组内表现 —— 20%（组内成员互相排序） 提问 —— 20% （给讲PPT的同学提问，至少提问4次） 各小组课件讲解内容： 小组1：非平衡载流子、PN结部分内容 参考E-learning 课程中英文课件“半导体物理基础、PN结”， 2.6-3.3节，30-56页。 小组2：金属-半导体结 参考 E-learning 课程中英文课件“PN结、金属-半导体结”，第 四章，29-50页。查阅相关文献，适当增加实例 小组3：太阳能电池部分内容 参考E-learning 课程中英文课件“半导体异质结构、太阳能电池 和光电二极管”，6.1-6.4节，30-57页。查阅文献，增加实例 小组4：量子点太阳能电池、光电二极管 参考E-learning 课程中英文课件“半导体太阳能电池和光电二极 管”，6.10-6.12节，37-57页。查阅文献，增加实例 小组5：激光器、量子点生物荧光探针 参考E-learning 课程中英文课件“发光二极管和半导体激光器、 量子点生物荧光探针”，32-67页。查阅文献，增加实例 Outline Chap. 1 Introduction Chap. 2 Basics of Semiconductor Physics Chap. 3 P-N Junctions Chap. 4 Metal-Semiconductor Junctions Chap. 5 Semiconductor Heterojunctions Chap. 6 Semiconductor solar cells & Photodiodes Chap. 7 Light Emitting Diodes & Semiconductor Lasers Chap. 8 Quantum Dots for Biological Fluorescent Probes Chapter 1 Introduction 1.1 Semiconductor Optoelectronic Devices and Materials Semiconductor optoelectronic devices: Semiconductor functional devices in which the interaction of electronic processes with light and optical processes can suitably take place, usually accompanied by an energy conversion process (e.g., form electrical to optical, and vice). Common semiconductor optoelectronic devices: Optical Electrical: Photodetectors, solar cells. Electrical Optical: Light emitting diodes, injection lasers. Optical Optical: Optically-pumped semiconductor lasers, fluorescent quantum dos. Semiconductor optoelectronic materials: Semiconductor materials used for making the above devices. 1.2 Common Semiconductor Optoelectronic Materials Semiconductor Optoelectronic Materials IV or IV-IV compounds III-V compounds GaAs; GaP; GaN Ge Si SiC InAs; InP; InSb II-VI compounds ZnS; ZnO; ZnSe; ZnTe AlAs; AlP CdS; CdSe; CdTe GaAs1-xPx ;In1-xGaxP HgS; HgSe IV-VI compounds PbS; PbSe; PbSnTe; PbSnSe 1.3 Application of Some Semiconductor Optoelectronic Materials Germanium (Ge): Photodetectors. Silicon (Si): Photodetectors, solar cells. Silicon Carbide (SiC): Electroluminescent devices. Gallium Arsenide (GaAs): Lasers, light emitting diodes (LEDs), solar cells. Zinc Sulfide/Oxide (ZnS, ZnO): Electroluminescent and photoluminescent probes. Cadmium Sulfide (CdS): Solar cells, lasers. Cadmium Telluride (CdTe): Solar cells, IR photodetectors, fluorescent probes/bioimaging. Lead Sulfide/Selenide/Telluride (PbS, PbSe, PbTe): Solar cells, IR photodetectors, lasers. 1.4 Physics of Semiconductor Optoelectronic Devices The band gap energy normally determines the working wavelength of a semiconductor optoelectronic device. The conversion between electrical and optical energies usually relates to the electron transitions between the conduction band and valence band of a semiconductor. 1.4 Physics of Semiconductor Optoelectronic Devices Solar cells, optodetectors Absorption, photoconductive effect, photovoltaic effect LEDs, semiconductor lasers Carrier injection, radiative recombination Photoluminescent quantum dots for fluorescent probes Absorption, radiative recombination Chapter 2 Basics of Semiconductor Physics 2. Basics of Semiconductor Physics 2.1 Electron states in One Atom 2.2 Electron states and Band Structures in Semiconductors 2.3 Impurity and Defect Levels 2.4 Carrier Distribution in a Semiconductor 2.5 Conduction Processes in Semiconductors 2.6 Non-equilibrium Charge Carriers 2. Basics of Semiconductor Physics 2.1 Electron states in One Atom 2.2 Electron states and Band Structures in Semiconductors 2.3 Impurity and Defect Levels 2.4 Carrier Distribution in a Semiconductor 2.5 Conduction Processes in Semiconductors 2.6 Non-equilibrium Charge Carriers 2.1 Electron States in one atom The Earlier Proposal of Quantum Theory Probability Wave Schrödinger Equation Energy Eigenvalue and Eigenfunction of the Hydrogen Atom Model Electron Configuration The Earlier Proposal of Quantum Theory In 1900, Planck firstly proposed a hypothesis of “quantum”, and derived the blackbody formula, which perfectly matched the observation results. —— Discrete energy of electromagnetic radiation E h , p h In 1905, Einstein tried to explain the difficulties in the experiment of photoelectric effect, and put forward the concept of light quantum. —— Light is particulate. 19121913, Bohr proposed the quantum theory of atomic structure, which successively explained the line spectrum of hydrogen atom. —— Discrete energy levels and quantum transition Having limitations and problems！ The Duality of Matter Particles Wave-particle duality of light: Wavelike behavior: interference, diffraction, and polarization Particulate nature: blackbody radiation and photoelectric effect de Broglie wave (1924): In the atomic world, matter particles (electrons, protons, neutrons, atoms, etc) have wavelike properties, which have been verified by experiments, i.e., diffraction of electron beams by single crystals. E h, h p Wave mechanics of Schrödinger (1926) —— revealing the laws of particle movement in the microscopic systems. Statistical Explanation of Wave Functions —— Probability Wave Wave function ( r , t ) —— describes the quantum states of a microscopic particle. Probability wave (Born, 1926)：unifying the wavelike and particulate properties of microscopic particles. “Particulate” — microscopic particles have certain masses and charges, but different from classic particles. “Wavelike” — additivity of waves, but different from classic waves, not the fluctuations of physical quantities in the space. (r , t ) is also called amplitude of probability wave. Probability density * , the probability of finding the particle in a unit volume near the position r at time t. 2 Schrödinger Equation For a microscopic particle moving in a potential V ( r ) , 2 2 i (r , t ) V (r ) (r , t ) Hˆ (r , t ) t 2m 2 2 2 2 2 2 x y z 2 , Ĥ : Hamiltonian The Schrödinger equation, a fundamental equation in quantum mechanics, provides the basic laws of matter movement in the microscopic world. It’s actually a hypothesis, which needs to be verified by experiments. Energy Eigenequation If V ( r ) is independent of t, the solution (r , t ) can be obtained using the separation of variables (r , t ) E (r )e iEt / where E (r ) satisfies the time-independent Schrödinger equation, 2 2 2m V (r ) E (r ) E E (r ) E: energy of the system. In solving specific problems, the boundary conditions (bound states, periodic) requires that only certain values of E are acceptable, which are called the energy eigenvalues, and the corresponding solutions E (r ) are called energy eigenfunctions. Equation is the energy eigenequation of particles. Energy Eigenfunction of the Hydrogen Atom Model Only one electron outside the nucleus, so the energy z eigenfunctions can be accurately solved！ e2 Coulomb attraction: V (r ) 4 0 r 1 In spherical coordinates: (r ) + (r , , ) x r - The energy eigenequation of the electron in a hydrogen atom, me m p me m p , reduced effective mass of electron. (r , , ) R(r )( )( ) y d 2 2 m 0 2 ① d 1 d d m2 (sin ) [l (l 1) 2 ] 0 ② d sin sin d 1 d 2 dR 2 e2 l (l 1) (r ) 2 (E ) 2 R0 ③ 2 dr 4 0 r r r dr ①: Periodic boundary condition ( 2 ) ( ) ②: Finite solution m =0,±1,±2,… |m| l, l = 0,1,2,… ③: For E >0, solutions always exist. (continuum-states) For E <0, bound-states boundary condition (r , R n-l-1=0,1,2,… n=1,2,3,… The energy levels E are quantized. 0) e2 2 2 E En , a 4 e 0 2an 2 (Bohr radius) nlm (r , , ) Rnl (r )Ylm ( , ) Three Quantum Numbers 1. Principal quantum number n, n＝1, 2, 3,… 2. Orbital angular momentum quantum number l， l =0, 1, 2,…, (n – 1) 3. Magnetic quantum number m, m＝0, 1, 2，…, l Each set of quantum numbers n, l, m determines a wave function of electron or an atomic orbital, and represent a state of motion of atomic electron, different from the concept of Bohr’s “atomic orbital”. Electron cloud: describe the area around a nucleus where an electron will probably be, with density of dots representing the probability density ||2. 1. Principal quantum number n Determining the energy levels of hydrogen atom. n are positive integers, and the energy levels are quantized. A larger n means the electron is most likely to be found farther from the nucleus. 2 The most probable radius, rn n a, n 1, 2,3,... Atomic orbitals with the same principal quantum number n are called one “electronic shell or shell”. The shells corresponding to n=1, 2, 3, 4, 5, 6, etc. are represented by labels K, L, M, N, O, P, etc. 2. Orbital angular momentum quantum number l Determining the value of orbital angular momentum vector L of electrons, L l (l 1) l 0,1,2,, (n 1) Quantized orbital angular momentum Describing the shape of atomic orbitals and electron clouds. The orbitals with l=0,1, 2,3, are represented by s,p,d,f. Wave functions with the same l are called one “subshell”. In multi-electron atoms, l also determines the energy of electrons. 3. Magnetic quantum number m The orientation of orbital angular momentum vector is quantized. The projection of orbital angular momentum in zaxis is: Lz m m＝0,1,2，…,l Describing the orientation of atomic orbitals and electron clouds. For s-orbital, l=0, m=0. The electron cloud is spherical about the nucleus, no orientation. For p-orbital, l=1, m=0,±1. The electron cloud has three different orientations. For d-orbital, l=2, m=0,±1,±2. The electron cloud has five different orientations. 1s, 2p, 3d Electron Clouds of Hydrogen Atom 1s: n=1, l=0, m=0 2p: n=2, l=1, m=±1, 0 3d: n=3, l=2, m=±2, ±1, 0, Spin Angular Momentum Quantum Number ms The fourth quantum number, describing the electron state of motion (the spin orientation of the electron). Not deriving from the Schrödinger equation, and not related to n, l, m. Spin is the intrinsic property of electrons. The spin angular momentum is, Ls s(s 1) s=1/2 The projection of electron spin in certain direction is, Lsz ms ms=1/2, the spin quantum number. A Complete Description of the Motion States of Electrons Each set of n, l, m quantum numbers describes all the characteristics of one wave function, and thus determines the characteristics of the electron cloud. However, in order to completely describe the motion states of atomic electrons, the spin quantum number ms is also need to be nailed down. Electron Configuration Aufbau Principle (Lowest-energy principle) Electrons enter orbitals of lowest energy first. Pauli exclusion principle Within an orbital there can only be two electrons and each should have opposite spins. (One spins clockwise and one spins counterclockwise.) Hund’s rule When electrons occupy orbitals of the same energy, electrons will enter empty orbitals first, and with the same spins. 2. Basics of Semiconductor Physics 2.1 Electron states in One Atom 2.2 Electron States and Band Structures in Semiconductors 2.3 Impurity and Defect Energy Levels 2.4 Carrier Distribution in a Semiconductor 2.5 Conduction Processes in Semiconductors 2.6 Non-equilibrium Charge Carriers 2.2 Electron states and Band Structures in Semiconductors Electron Sharing —— Qualitative explanation Band Theory —— Quantitative explanation Interpretation of Metals, Semiconductors, and Insulators with Band Theory Quantum Confinement Effect Electron Sharing and Formation of Band The periodicity in the structure of single crystals. Periodic potential Under single-electron approximation, the potential V ( r ) for every electron in the single crystals is regarded as periodic V (r ) V (r ') V (r Rm ) Rm arbitrary lattice vector. Electron Sharing and Formation of Band V(r) r One dimensional periodic potential ATOM Electron Sharing and Formation of Band Electron sharing Due to the overlap of electronic shells between adjacent atoms that constitute a single crystal, electrons are not confined to a certain atom, and can transfer to the neighboring atom. So, electrons can move in the whole crystals, which is called electron sharing. The extent of overlap is larger for outer shells, therefore, the electron sharing is more prominent in the ourtermost shell, i.e. valence electrons. Electron Sharing and Formation of Band Electron sharing —— by Quantum Mechanics Based on the tunneling effect of quantum mechanics, electrons can cross the barrier between atoms and transfer to another atom, leading to the electron sharing in the whole crystal. Electron Sharing and Formation of Band Splitting of energy levels Due to the potentials of other atoms, the energy of shared electrons changes. The energy levels of isolated atoms will split. H2 molecule The closer of atoms, the stronger interaction between them, and the wider of band. Electron Sharing and Formation of Band Band structure General rules: The band related to the outer shell is wider. Smaller lattice constants lead to wider band. Bands can overlap. Atomic level Allowed band Forbidden band Forbidden band Atomic orbit Electron Sharing and Formation of Band Band structure The number of energy levels in each band is N(2l+1). N the number of atoms, (2l+1) the degree of degeneracy of the atomic level of isolated atoms. E.g., If spin is ignored, since s-level is non-degenerate (m=0), when N atoms form a crystal, the s-level splits into N close levels. While, the degree of degeneracy of p-level is 3 (m=0,1), so a p-level splits into 3N close energy levels. In practice, N~1023, energy levels in each band get so close, that each band is considered as continuous, the so called “quasicontinuous”. Electron Sharing and Formation of Band Band structure In practice, each band usually does not simply correspond to each energy level of isolated atoms. E.g., for Si and Ge, each atom has four valence electrons (2 selectron, 2 p-electrons). When crystals form, due to orbital hybridization, the two bands do not correspond to s- and p-level, respectively, but both contains 2N levels. Each band could take in 4N electrons. Upper band: empty band Lower band: filled band Electron Sharing and Formation of Band Electron configuration in band Configuration rule: Lowest-energy principle Pauli exclusion principle Band related terms: Filled band：electron states are completely occupied by Valence band: the uppermost filled band of semiconductors, electrons. ---- Non-conductive filled by valence electrons. Partially-occupied band: parts of the states are occupied. Conduction band: the empty band above the valence band. ---- Conductive Empty band: none of the states are occupied. ---- Nonconductive Conductive! Band Theory Quantitatively solving the electron states in single crystals by using quantum mechanics. The fundamental theory in current research of electron movements in solids. Clarifying the general rule of electron movements in single crystals. Demonstrating the differences among metals, semiconductors, and insulators. Band Theory Approximate theory Since a single crystal is consist of periodically arranged atoms, each of which contains many electrons, the problem of electron movements in crystals is a many-body problem, which could not precisely solved. Adiabatic approximation Single-electron approximation Nearly free electron approximation Tight binding approximation Band Theory Adiabatic approximation Ignore the lattice vibration. Every ion core is fixed at its equilibrium position. （1927, Born-Oppenheimer） Single-electron approximation Every electron is considered to move in an effective potential, and the movement of every electron is independent (Hartree-Fock) . For ideal single crystals, the effective potential is periodic. Band Theory Wave equation of electrons in crystal 2 2 2m V r (r ) E (r ) where V (r ) V (r Rn ) Rn arbitrary lattice vector. Band Theory Wave function of electrons in crystal ( r ) Bloch theorem —— if the potential is periodic, the solution of the wave equation should have the following form: r e u r where Another expression: i k r u r u r Rn —— Bloch function k wave vector Rn arbitrary lattice vector r Rn eik R r n Band Theory Bloch function Expression 1: r e u r i k r Plane wave modulated by periodic potential. Expression 2: r Rn e r ik Rn The electron wave functions for equivalent sites in different unit cells are differentiated by one factor with modulus of 1. The probability of finding electrons at equivalent sites in different unit cells is same. Band Theory Wave function of free electrons For one freely moving electron with mass m, velocity v , its momentum p and energy E: 2 1 p p mv, E 2 m de Broglie wave , for free electrons, plane wave with frequency , and wavelength : r , t Ae k E h , p h 2 i k r 2t k wave vector Band Theory Wave function of free electrons | (r ) |2 A2 --- The probability of finding (r ) Ae ik r the electron at different places are the same --freely moving. p mv 2 1 p E 2 m E h p h 2 k E k v m 2 Wave vector k describes the electron states. 2 k E 2m k Band Theory r e u r i k r Periodic boundary condition and the value of k For a finite crystal in a cuboid shape, which has N1, N2, N3 unit cells along directions of a1 , a2 , a3 , so the Bloch function should satisfied the following periodic boundary condition: k (r Ni ai ) k (r ) ai (i 1, 2,3) —— lattice primitive vector Band Theory r e i k r u r Periodic boundary condition and the value of k Due to the periodic boundary condition, the wave vector k should take some discrete values. l3 l1 l2 k b1 b2 b3 N1 N2 N3 li integers, bi (i 1, 2,3) reciprocal lattice primitive vector. Wave vector k represents the motion state of electrons in crystals. k is not the momentum any more. Band Theory General conclusions for electron motion states in crystals. The states of Bloch electrons are decided by the two quantum numbers n and k , and the corresponding energy eigenvalue and wave function are E n (k ) and (r ) nk For given n, E n (k ) is a periodic function of k , which has upper and lower limits. Different n represents different bands. E n (k ) Constitutes the band structure of crystals. r e i k r u r Band Theory Brillouin zone 3rd 2nd 1st 2nd 3rd k E n (k ) as a function of k k 2π Energy Band 2π Reduced Brillouin Zone Band Theory Generally, in order to determine an electron state, one should tell: （1）Which band does it belong to (n=?） （2）What is the reduced wave vector k? To solve the wave function of electrons in crystals, different approximations should be adopted with respect to different cases. Band Theory Nearly free electron approximation For metals, the valence electrons are weakly bounded to the positively-charged core, so the periodically varied part in V(r) is very small compared to the average kinetic energy. Consequently, the motion of electrons is very close to that of free electrons, but affected by the periodic potential. (Kronig-Penny) Band Theory Nearly free electron approximation Replace V(r) with V , the average potential, and treat V r V as perturbation. 2 0 2 0 0 V E 2m (1) The solution of (1) is that for free electrons moving in a constant potential V : 1 ikr 0 k r e , Rn 2 2 k 0 Ek V 2m Band Theory Nearly free electron approximation Due to the perturbation in potential, E(k) abruptly changed at k =n/a：the original higher energy level rises, while the original lower level falls. —— Repulsion Band Theory Nearly free electron approximation E n (k ) as a function of k Energy Band Band Theory Tight binding approximation The 3d electrons in transition metals and the core electrons in solids are tightly bound to the atoms. Put isolated atoms onto the lattice points. The motion of electrons is similar to that of bound electrons in isolated atoms, but affected by the perturbation induced by the potentials from other atoms . Consider the electron wave function in crystals as a linear combination of N degenerate atomic wave functions. Band Theory Primary conclusions for tight binding approx. When N atoms compose a crystal, due to the overlap between the wave functions of neighboring atoms, the N degeneracy is released, and form a band. Interpretation of Metals, Semiconductors, and Insulators with Band Theory T=0 K Fermi Energy EF Empty Band Partiallyoccupied Band Valence Band Filled Band Empty Band Conduction Band Eg Eg Filled Band Filled Band Filled Band Filled Band Metal Filled Band Semiconductor Insulator Quantum Confinement Effect The quantum confinement effect (QCE) can be observed once the dimension of the material is of the same magnitude as the wavelength of the electron wave function. The electronic and optical properties deviate substantially from those of bulk materials. The confinement of the electron motion leads to discrete energy spectrum and the band gap becomes size dependent. 0D quantum materials: quantum dots, clusters. 1D: nanowires, nanorods. 2D: quantum wells. For semiconductors, the QCE occurs only when the dimension of the material is smaller than the exciton Bohr radius. Quantum Confinement Effect The variation of band gap with the size of PbS quantum dots. Bulk Quantum dot Molecule ACS Nano 3, 3023（2009） Quantum Confinement Effect QCE ultimately results in a blue shift in optical illumination as the size of the particles decreases. CdS CdSe/ZnS 2. Basics of Semiconductor Physics 2.1 Electron states in One Atom 2.2 Electron states and Band Structures in Semiconductors 2.3 Impurity and Defect Levels 2.4 Carrier Distribution in a Semiconductor 2.5 Conduction Processes in Semiconductors 2.6 Non-equilibrium Charge Carriers 2.3 Impurity and Defect Levels Formation of Impurity and Defect Levels Impurity Levels Impurities in III-V Compound Semiconductors Deep Levels Defect Levels 2.3.1 Formation of Impurity and Defect Levels In real semiconductors, various types of defects or impurities exist, which will induce additional potentials in semiconductors, and thus result in localized electronic states. Therefore, the electrons and holes can be bound to the vicinity of the impurities or defects, corresponding to impurity or defect levels inside the forbidden band. —— Extrinsic semiconductors. Intrinsic semiconductors: semiconductors without any impurities and defects. 2.3.2 Impurity Levels Ionization energy of donor Ec Ed Ei Ev Energy in the middle of the forbidden band Donor level Electrons in the conduction band Ionized donor (a) Donor impurity in a Si single crystal. (b) Donor level and ionization. Donor impurities are those which offer energy levels containing electrons in the forbidden band. Group V atoms are donors in Si and Ge. Semiconductors with donor impurities are referred to as n-type semiconductors, since electrons are the charge carriers. 2.3.2 Impurity Levels Ec Ei Ea Ev Energy in the middle of the forbidden band Ionization energy of acceptor Acceptor level Holes in the valence band Ionized acceptor (a) Acceptor impurity in a Si single crystal. (b) Acceptor level and ionization. Acceptor impurities are those which offer empty energy levels in the forbidden band. Group III atoms are donors in Si and Ge. Semiconductors with acceptor impurities are referred to as p-type semiconductors, since holes are the charge carriers. 2.3.2 Impurity Levels • If a semiconductors has both donor and acceptor impurities, the electrons in the donor level must firstly fill the acceptor level, and the rest can be excited to the conduction band. • The cancellation between donor and acceptor impurities are named impurity compensation. • The type of conduction of a compensated semiconductor is determined by the impurity with a higher concentration. 2.3.3 Impurities in III-V Compound Semiconductors The numbers of valence electrons in the impurity and lattice atom determine the impurity behavior. For III-V compounds (i.e., GaAs), group VI atoms (Se, Te) replace group V atoms (As), and are donor impurity. While, group II atoms (Zn, Cd) replace group III atoms (Ga), and are acceptor impurity. The group IV atoms can replace groups III and V atoms. The concentration of group IV atoms and temperature determine the impurity behavior. 2.3.4 Deep Levels The ionization energy of the donors and acceptors, in Si or Ge doped with P or B atoms, or in GaAs doped with Se or Zn atoms, is around 0.01eV, and the impurity levels are called shallow levels. Deep levels: impurity levels located close to the center of the forbidden band. Due to the large ionization energies, deep levels make no contributions to the carrier density under thermal equilibrium. But they might become combination centers of electrons and holes, which reduce the lift time of non-equilibrium carriers. 2.3.4 Deep Levels A deep-level impurity may have several different ionized states, corresponding to multi impurity levels in the forbidden band. Impurities that can become both donors and acceptors are named amphoteric impurity. • One valence electron for Energy levels of Au atoms in germanium. each Au atom. ---- 3 holes • The Au atom in Ge can accept 1,2,3 electrons and becomes Au-,Au2-,Au3-, corresponding to three acceptor levels Ea1, Ea2, Ea3. • The Au atom is also able to offer the outermost electron, and becomes Au+, corresponding to one donor level Ed.. 2.3.5 Defect Levels —— Point Defect Example 1: Vacancy and interstitial atom P-type PbS can be obtained by manipulating PbS in a high ionic crystals (oxides, partialFor pressure of sulfur, whichsulfides, leads to selenides) Pb vacancies. Example Positive2:center: cations as interstitial atoms, or anion vacancies ZnO can beanions obtained by deoxidizing in vacuum, N-type Negative center: as interstitial atoms,ZnO or cation vacancies which induces O vacancies. Point defects in ionic crystals Positive centers are donors which can provide electrons. Negative centers are acceptors. The conduction type of semiconductors can be controlled by nonstoichiometric ratio method. 2.3.5 Defect Levels —— Point Defect Vacancy and interstitial atom For covalence crystals —— Si or Ge The vacancy is an acceptor, since the four nearest neighbors of it have one unpaired electron for each, which tend to accept electrons. The interstitial atom is a donor, for it has four unpaired electrons which could be lost. Vacancies in Si and Ge crystals 2.3.5 Defect Levels —— Point Defect Vacancy and interstitial atom For covalence crystals —— III-V compounds (GaAs, etc.) There is no definite answer for whether the vacancies and interstitial atoms are donors or acceptors, which should be determined by the experiments. Point defects in GaAs 2.3.5 Defect Levels —— Point Defect Substitutional atom For covalence crystals ——III-V compounds (GaAs, etc.) Substitutional atoms in binary compounds Two types of substitutional atoms: A substitute B (AB), B substitute A (BA). AB is an acceptor, while BA is a donor. E.g., GaAs behaves like an acceptor, and AsGa is a donor. The substitutional atoms almost don’t exist in compounds with high ionicity.