Chapter 1 The Crystal Structure of Solids

Transcription

1 Chapter 1 The Crystal Structure of Solids In this chapter, (i) (ii) (iii) You should be able to sketch the atomic arrangement of atoms in the cubic lattices. You should be able to calculate the area and volume density of atoms. You should be able to identify the principal crystal directions and lattice planes in the cubic lattices. (iv) You should be able to acquire common senses of general semiconducting materials Crystal Structure of Solids 1

2 Types of Solids Amorphous Poly-crystalline Single-crystalline Have order only within a few atomic or molecular dimensions. Have a high degree of order over many atomic or molecular dimensions. Have a high degree of order,or regular geometric periodicity, throughout the entire volume of material. Grain Grain boundaries tend to degrade the electrical characteristics. Its electrical properties are superior to those of a non-single crystal material. Crystal Structure of Solids 2

3 Space Lattices The concern in this lecture will be the single crystal. A representative unit, or group of atoms, is repeated at regular intervals in each of the three dimensions to form the single crystal. The periodic arrangement of atoms in the crystal is called the lattice. Primitive and Unit Cell Lattice point( 格点 ): a representation of a particular atomic array by a dot. The simplest means of repeating an atomic array is by translation. Two-dimensional lattice can be translated a distance a1 in one direction and a distance b1 in a second noncolinear direction. A third noncolinear translation will produce the three-dimensional lattice. The translation directions need not be perpendicular. b 2 a 2 A b 3 B b 4 D a 4 a 3 b 1 a1 C Infinite two-dimensional lattice Various possible two-dimensional lattice/ unit cell Crystal Structure of Solids 3

4 We can see that single-crystal lattice is a periodic repetition of a group of atoms. Therefore, we do not need to consider the entire lattice. We just need to consider a fundamental unit. A unit cell is a small volume of the crystal that can be used to reproduce the entire crystal. A primitive unit cell A primitive cell is the smallest unit cell that can be repeated to form the lattice. In many cases, it is more convenient to use a unit cell that is not a primitive cell. Unit cells may be chosen that have orthogonal sides, whereas sides of a primitive cell may be nonorthogonal. This figure shows a generalized three-dimensional unit cell. The relationship between this cell and the lattice can be characterized by three vectors a, b and c, which need not be perpendicular and which may or may not be equal in length. r pa qb sc where p, q and s are integers. Crystal Structure of Solids 4

5 Basic Crystal Structures (a) Simple cubic : an atom located at each corner. (b) body-centered cubic (bcc) : has an additional atom at the center of the cube. (c) face-centered cubic (fcc) : has additional atoms on each face plane By knowing the crystal structure of a material and its lattice dimensions, we can determine several characteristics of the crystal. For example, we can determine the volume density of atoms. Crystal Structure of Solids 5

6 Basic Crystal Structures body-centered cubic (bcc) unit cell contains 2 atoms face-centered cubic (fcc) unit cell contains 4 atoms Crystal Structure of Solids 6

7 Example 1.1:To find the volume density of atoms in a crystal that is a body-centered cubic with a lattice constant a = 5 Å = 5 x 10-8 cm. Crystal Structure of Solids 7

8 Example 1.1:To find the volume density of atoms in a crystal that is a body-centered cubic with a lattice constant a = 5 Å = 5 x 10-8 cm. Solution: A corner atom is shared by eight unit cells which meet at each corner so that each corner atom effectively contributes one-eighth of its volume to each unit cell. The eight corner atoms then contribute an equivalent of one atom to the unit cell. If we add the body-centered atom to the corner atoms, each unit cell contains an equivalent of two atoms. The volume density of atoms is then found as Density 2atoms 5x x10 22 atoms / cm 3 Comment : The volume density of atoms just calculated represents the order of magnitude of density for most materials. The actual density is a function of the crystal type and crystal structure since the packing density number of atoms per unit cell- depends on crystal structure. Crystal Structure of Solids 8

9 Crystal Planes and Miller Indices Surfaces, or planes through the crystal, can be described by considering the intercepts of the plane along the, b and axes used to describe the lattice. a c Three basic planes that are commonly considered in a cubic crystal are shown below. (100) (110) (111) Fig.(a): The plane is parallel to the b and c axes so the intercepts are given as p=1, q=infinity and s=infinity. Taking the reciprocal, we obtain the Miller indices as (1,0,0), so the plane is referred to as the (100) plane. Note: Any plane parallel to the one shown in Fig.(a) and separated by an integral number of lattice constants is equivalent and is referred to as the (100) plane. One advantage to taking the reciprocal of the intercepts to obtain the Miller indices is that the use of infinity is avoided when describing a plane that is parallel to an axis. Crystal Structure of Solids 9

10 Crystal Direction The direction can be expressed as a set of three integers which are the components of a vector in that direction. For example, the body diagonal in a simple cubic lattice is composed of a vector components 1,1,1. The body diagonal is then described as the [111] direction. (110) (111) (100) Note: The brackets are used to designate direction as distinct from the parentheses used for the crystal planes. In the simple cubic lattices, the [hkl] direction is perpendicular to the (hkl) plane. This perpendicularity may not be true in noncubic lattices. Crystal Structure of Solids 10

11 Crystal Structure of Solids Michael Tan 11

12 Atomic Bonding The type of bond, or interaction, between atoms depends on the particular atom or atoms in the crystal. If there is not a strong bond between atoms, they will not stick together to create a solid. (i) Ionic Bonding : A coulomb interaction between oppositely charged ions. Ex: Sodium chloride (NaCl) Materials of Group I and VII. (ii) Covalent Bonding : Sharing of electrons between two atoms, so that in effect the valence energy shell of each atoms is full. Materials of Group IV. (iii) (iv) Metallic Bonding Van der Waals Bonding Crystal Structure of Solids 12

13 Imperfections and Impurities in Solids In a real crystal, the lattice is not perfect. It contains imperfections (defects) and impurities. Imperfections (defects); that is, the perfect geometric periodicity is disrupted in some manner. Imperfections tend to alter the electrical properties of a material. Imperfections in Solids (i) Lattice Vibrations : due to thermal energy which is a function of temperature. (ii) Point Defects Interstitial (a) Vacancy (b) Interstitial Crystal Structure of Solids 13

14 (iii) Line Defects Line Dislocation (a) Line dislocation Effects of defects: Disruption of the normal geometric periodicity of the lattice and the ideal atomic bonds in the crystal. The change of electrical properties of materials. Impurities in Solids Crystal Structure of Solids 14

15 Semiconductor Materials High Conductivity Low Conductor/Metal Semiconductor Insulator III IV V B C Al Si P Ga Ge As In Sb Periodic table Elemental Group IV of periodic table Silicon (Si) Germanium (Ge) Carbon (C) Compound Combinations of Group III and Group V Elements Binary: GaAs, AlAs,AlP,GaN, GaP, InP etc. Ternary: AlGaAs, InGaAs, InGaP etc. Combinations of Group IV and Group IV Elements SiC, SiGe etc. Silicon is the most common material for ICs. Crystal Structure of Solids 15

16 Group IV Crystalline Materials Elemental Semiconductors formed from atoms in Column IV C (carbon): Different Crystalline Phases Diamond Structure: Diamond Graphite: Metallic An insulator or semiconductor. The most common carbon solid. Fullerenes: Based on Buckminsterfullerene: Bucky Balls, Nanotubes, Graphene, Insulators, Semiconductors, or Metals depending on preparation. Clathrates: Possible new forms of C solids? Semiconductors or Semimetals, Compounds Crystal Structure of Solids 16

17 Si (silicon): Different Crystalline Phases Diamond Structure: A Semiconductor. The most common Si solid. Clathrates: New forms of Si solids.( 硅笼化合物 ) Semiconductors, Semimetals, Compounds Ge (germanium): Different Crystalline Phases Diamond Structure: A Semiconductor. The most common Ge solid. Clathrates: New forms of Ge solids. Semiconductors, Semimetals, Compounds Crystal Structure of Solids 17

18 Sn (tin): Different Crystal Phases Diamond Structure: Gray tin or α-sn. A Semimetal! Body Centered Tetragonal Structure( 体心四方 ): White tin or β-sn. A Metal. The most common Sn solid. Clathrates: New forms of Sn solids. Semiconductors, Semimetals, Compounds, Recent Research Pb (lead): Face Centered Cubic Structure: A Metal. Crystal Structure of Solids 18

19 Group IV Materials A Chemical Trend Material Bandgap as a function of Near-Neighbor Distance for Diamond Structure Solids Decreasing Bandgap E g correlates with Increasing Nearest-Neighbor Bond Length d Atom E g (ev) d (Å) C Si Ge Sn (a semimetal) Pb (a metal) Not the diamond structure! Crystal Structure of Solids 19

20 Elemental Semiconductors Mainly, these are from the Column IV elements C (diamond), Si,Ge, Sn (gray tin or α-sn) The atoms are tetrahedrally bonded in the diamond crystal structure and each atom has 4 nearest-neighbors. Bonding: sp 3 covalent bonds. Some Column V & Column VI elements are semiconductors: P - A 3-fold coordinated lattice. S, Se, Te 5-fold coordinated lattices. Crystal Structure of Solids 20

21 III-V Compounds Periodic Table Columns III & V Thallium 铊 Column III B Al Ga In Column V N P As Sb Tl not used Bi Some possible compounds which are semiconductors are: BN, BP, BAs, AlN, AlP, AlAs, AlSb, GaN GaP, GaAs, GaSb, InP, InAs, InSb,. Crystal Structure of Solids 21

22 Some Applications of III-V Materials IR detectors, LED s, solid state lasers, switches,. BN, BP, BAs, AlN, AlP, AlAs, AlSb, GaN GaP, GaAs, GaSb; InP, InAs, InSb,. A Chemical Trend The bandgap decreases & the interatomic distance increases going down the periodic table. There is tetrahedral coordination of the atoms. Many III-V compounds have the zincblende crystal structure ( 闪锌矿 ). Some (B compounds & N compounds) have the wurtzite crystal structure ( 纤锌矿 ). Interatomic Bonding: The bonds are not purely covalent! The charge separation due to the valence differences leads to Partially Ionic bonds. Crystal Structure of Solids 22

23 II-VI Compounds Periodic Table Columns II & VI Column II Zn Cd Hg Column VI O S Se Mn sometimes Te not used Po Some possible compounds which are semiconductors or semimetals are: ZnO, ZnS, ZnSe, ZnTe, CdS, CdSe, CdTe, HgS, HgSe, HgTe, + some compounds with Mn. Crystal Structure of Solids 23

24 IV- IV Compounds Periodic Table Column IV Column IV Binary combinations of C, Si, Ge, Sn SiC Other compounds: GeC, SnC, SiGe, SiSn, GeSn,.. Cannot be made or cannot be made without species segregation or are not semiconductors. Two common crystalline phases for SiC are zincblende (a semiconductor), & hexagonal close packed (a large gap insulator). ( 六方密排 ) There are also MANY other crystal structures for SiC! Crystal Structure of Solids 24

25 IV- VI Compounds Periodic Table Columns IV & VI Column IV Column VI C O Si S Ge Se Sn Te Pb Some possible compounds which are semiconductors are: PbS, PbTe, PbSe, SnS. Other compounds: SnTe, GeSe,.. can t be made, can t be made without segregation, or aren t binary compounds, or aren t semiconductors. Crystal Structure of Solids 25

26 Some Applications of IV-VI Materials: IR detectors, switches, PbS, PbTe have the zincblende crystal structure Most others have 6-fold coordinated lattices. The bonding is ~ 100% ionic These materials have very small bandgaps, which makes them very useful as IR detectors Crystal Structure of Solids 26

27 Some Applications of IV-VI Materials: IR detectors, switches, PbS, PbTe have the zincblende crystal structure Most others have 6-fold coordinated lattices. The bonding is ~ 100% ionic These materials have very small bandgaps, which makes them very useful as IR detectors Crystal Structure of Solids 27

28 I-VII Compounds Periodic Table Columns I & VII These materials are mostly Ionic Insulators: NaCl, KCl, CsCl, Their lattices do not have tetrahedral coordination. Most of them are 6- or 8-fold coordinated and have the NaCl or CsCl crystal structures (discussed in any elementary Solid State Physics book). The bonding is ~ 100% ionic Their bandgaps are large (which is why they are insulators!) Crystal Structure of Solids 28

29 Oxide Compounds These are a category all their own Most of these materials are good insulators with large bandgaps. A few are Semiconductors: CuO, Cu 2 O, ZnO Many of their properties are not very well understood. Partially as a result of this there are relatively few applications. An exception to this is ZnO, which has wide use in ultrasonic transducers. At low T, some oxides are superconductors Many high T c superconductors are based on La 2 CuO 4 (T c ~ 135K) Crystal Structure of Solids 29

30 Some Other Semiconductor Materials Alloy mixtures of elemental materials (binary alloys): Si x Ge 1-x,... (0 x 1) Alloy mixtures of binary compounds (ternary alloys): Ga 1-x Al x As, GaAs 1-x P x, (0 x 1) Alloy mixtures of binary compounds with mixtures on both sublattices (quaternary alloys): Ga 1-x Al x As 1-y P y,.., (0 x 1, 0 y 1) In the growth process, x & y can be varied, which varies the material bandgap & other properties. BANDGAP ENGINEERING! Crystal Structure of Solids 30

31 Exotic Semiconductors Layered Compounds: PbI 2, MoS 2, PbCl 2, These materials have strong Covalent Bonding within each layer & weak Van Der Waals bonding between layers. This means that they are effectively 2 dimensional solids That is, their electronic & vibrational properties have a ~ 2 dimensional character. Organic Semiconductors:Polyacetylene (CH 2 ) n and other polymers These materials show great promise for future applications ( for 35 years!) Many of these materials are not well understood Crystal Structure of Solids 31

32 Other Semiconductors Magnetic Semiconductors Compounds with Mn and/or Eu (& other magnetic ions) These are simultaneously semiconducting & magnetic EuS, Cd x Mn 1-x Te, Optical modulators, Others I-II-(VI) 2 & II-IV-(V) 2 compounds AgGaS 2, ZnSiP 2,., Tetrahedral bonding V 2 -(VI) 3 compounds As 2 Se 3. Crystal Structure of Solids 32

33 Many Materials of Interest in This Course: Have crystal lattice structures Diamond or Zincblende (These will be discussed in detail again later!) In these structures, each atom is tetrahedrally coordinated with four (4) nearest-neighbors. The bonding between neighbors is (mostly) sp 3 hybrid bonding (strongly covalent). There are 2 atoms/primitive cell (repeated to form an infinite solid). Crystal Structure of Solids 33

34 Diamond Structure Silicon and Germanium are two examples of semiconductor materials that have a diamond crystal structure. A unit cell of the diamond structure is more complicated than the simple cubic structures. A unit cell of diamond structure An important characteristic of the diamond lattice is that any atom within the diamond structure will have four nearest neighboring atoms. The diamond structure refers to the particular lattice in which all atoms are of the same species such as silicon or germanium. Crystal Structure of Solids 34

35 <100> flat at 180 deg for n-type and 90 deg for p-type. <111> flat at 45 deg for n-type, no secondary for p-type. Crystal Structure of Solids 35

36 The Zincblende Structure ( 闪锌矿 ) The zincblende structure differs from the diamond structure only in that there are two different types of atoms in the lattice. Compound semiconductors, such gallium arsenide (GaAs) have the zincblende structure. Note: The atoms in both the diamond and zincblende structures are joined together to form a tetrahedron. A unit cell of zincblende structure. Ex: GaAs lattice Crystal Structure of Solids 36

37 Some Materials of Interest in This Course have crystal lattice structures Wurtzite Structure This is similar to the Zincblende structure, but it has hexagonal symmetry instead of cubic. In these structures, each atom is tetrahedrally coordinated with four (4) nearest-neighbors. The bonding between neighbors is (mostly) sp 3 hybrid bonding (strongly covalent). There are 2 atoms/primitive cell (repeated to form an infinite solid). Wurtzite crystals can (and generally do) have properties such as piezoelectricity and pyroelectricity Crystal Structure of Solids 37

38 Wurtzite Lattice Crystal Structure of Solids 38

39 Growth Techniques Czochralski Method (LEC) (Bulk Crystals) Dash Technique Bridgeman Method Chemical Vapor Deposition (CVD) (Thin films; epitaxial film growth) Metal-Organic Chemical Vapor Deposition (MOCVD) Molecular Beam Epitaxy (MBE) (Thin films) Liquid Phase Epitaxy (LPE) (Thin films) Crystal Structure of Solids 39

40 GROWTH of SEMICONDUCTOR MATERIALS Success in fabricating very large scale integrated (VLSI) circuits /ultra large scale integrated ( ULSI) circuits is a result of pure single-crystal semiconductor materials. Presently, Silicon, has concentrations of most impurities of less than 1 part in 10 billion. To get high purity of semiconductor materials, we need; (i) Extreme care in the growth processes, (ii) High growth technologies, (iii) Extreme care at each step of the fabrication processes. Container (1) Growth from a Melt A common technique for growing single-crystal materials such as silicon, is called Czochralski method. Chuck Seed Crystal Heater Tube Melt Crucible Crystal Structure of Solids 40

41 Czochralski Method Bridgeman Method a temperature gradient along the crucible growth speed ~ 2-3 mm/minute O, C are contaminants! Crystal Structure of Solids 41

42 (2) Epitaxial Growth Epitaxial growth is a process whereby a thin, single-crystal layer of material is grown on the surface of a single-crystal substrate. Epitaxial layer(algaas) Epitaxial layer (Si) Substrate (GaAs) Substrate (Si) Heteroepitaxial Growth Homoepitaxial Growth Epitaxial Growth Technique (i) Chemical Vapor Deposition (CVD) (ii) Liquid Phase Epitaxy (LPE) (iii) Molecular Beam Epitaxy (MBE) (iv) Metal Organic Vapor Phase Epitaxy (MOVPE)/ Metal Organic Chemical Vapor Epitaxy (MOCVD) Crystal Structure of Solids 42

43 Epitaxial films can be grown from solid, liquid, or gas phases. It is easier to control the growth rate in gas phase epitaxy by controlling the flow of gases. In CVD, gases containing the required chemical elements are made to react in the vicinity of the substrate inside the reactor. Example reaction. Chemical Vapor Deposition (CVD) (The temperature of the substrate plays an important role). SiH 4 (heat) Si + 2 H 2 (Silane gas) (on the substrate) (H 2 gas) The reaction occurs in a sealed container (reactor) NOTE!! Silane gas is highly toxic & highly explosive!! NOTE!! Hydrogen gas is highly explosive!!!! Crystal Structure of Solids 43

44 Metal-Organic Chemical Vapor Deposition (MOCVD) Example reaction: (Trimethal gallium gas) (Methane gas) Ga(CH 3 ) 3 + AsH 3 (Arsene gas) 3CH 4 + GaAs (on the substrate) The reaction occurs in a sealed container (reactor) NOTE!! Arsene gas is highly toxic & highly flammable! Trimethal gallium gas is highly toxic!! Methane gas is highly explosive! Crystal Structure of Solids 44

45 MOCVD Dopants are introduced in precisely controlled amounts! Crystal Structure of Solids 45

46 Molecular Beam Epitaxy (MBE) Thin film growth under ultra high vacuum (~10-10 torr) Reactants introduced by molecular beams. Create beams by heating source of material in an (or Knudsen) cell. Several sources, several beams of different materials aimed at substrate Can deposit 1 atomic layer or less! A very precisely defined mixture of atoms to give EXACTLY the desired material composition! Crystal Structure of Solids 46

47 MBE Source molecular beam comes out here Source is in here r r Crystal Structure of Solids 47

48 MBE Setup complex & expensive! Crystal Structure of Solids 48

49 RHEED: Used with MOCVD & MBE electron beam probe to monitor surface film quality One period of oscillation growth of one atomic layer of GaAs (or whatever material) Crystal Structure of Solids 49

50 MOCVD vs. MBE MBE Mainly useful for research lab experiments. Not efficient for mass production! MOCVD Useful for lab experiments & for mass production! MANY MILLIONS OF $$$$ FOR BOTH!!!!! Crystal Structure of Solids 50

51 MOCVD vs. MBE Molecular Beam Expitaxy (MBE) Metal-Organic Chemical Vapor Deposition (MOCVD) Both of these techniques allow crystals to be deposited on a substrate one monolayer at a time with great precision. These techniques are very useful for artificial crystal structures such as superlattices and quantum wells. Differences between MBE and MOCVD MOCVD Gases are let into the reactor at high pressure ~ 1 torr MBE Always done under UHV conditions, with pressures below 10-8 torr Crystal Structure of Solids 51

52 Crystal Structure of Solids 52 52

53 Liquid Phase Epitaxy (LPE) (GaAs & other III-V materials) A group III metal utilized as a solvent for As The solvent is cooled in contact with (GaAs) substrate. Becomes saturated with As. Nucleation of GaAs on the substrate. A slider, containing different solutes, can grow precise compositions of material. Crystal Structure of Solids 53

54 LPE Crystal Structure of Solids 54

55 Summary The properties of semiconductors and other materials are determined to a large extent by the single-crystal lattice structure. The unit cell is a small volume of the crystal that is used to reproduce the entire crystal. Three basic unit cells are the simple cubic, body-centered cubic (bcc) and face-centered cubic (fcc). Miller indices are used to describe planes in a crystal lattice. These planes may be used to describe the surface of a semiconductor material. The Miller indices are also used to describe directions in a crystal. Imperfections do exist in semiconductor materials. A few of these imperfections are vacancies, substitutional impurities, and interstitial impurities. Small amounts of controlled substitutional impurities can favorably alter semiconductor properties. A few of the most common semiconductor materials were listed. Silicon has the diamond crystal structure. Atoms are formed in a tetrahedral configuration with four nearest neighbor atoms. Most binary semiconductors have a zincblende or Wurtzite lattice, that is basically the same as the diamond lattice. Crystal Structure of Solids 55

56 Summary (cont.) A brief description of semiconductor growth methods was given. Bulk growth produces the starting semiconductor material or substrate. Epitaxial growth can be used to control the surface properties of a semiconductor. Most semiconductor devices are fabricated in the epitaxial layer. Glossary of Important Terms Binary semiconductor Ternary semiconductor Covalent Bonding Ion Bonding Doping Elemental semiconductor Compound semiconductor Epitaxial layer Ion Implantation Lattice Miller Indices Primitive Cell Unit Cell Substrate Zincblende Lattice Wurtzite Lattice Diamond Lattice Crystal Structure of Solids 56