advertisement

HCMUT – FEEE – Electronic engineering department Instructor: Trần Hoàng Linh Chapter 1 Crystal Properties and Growth of Semiconductors Refs: 1. Solid State Electronic Devices, Ben G. Streetman and Sanjay Banerjee, Sixth Edition 2. Slides of Dr. Franklin D.Nkansah 3. Semiconductor Devices Physics and Technology 3E, S. M. Sze, Wiley 2010 1 Outline • • • • Semiconductor Materials Crystalline Lattices Bulk Crystal Growth Epitaxial Growth 2 Solid-state Material • Solid-state materials can be grouped into three classes—insulators, semiconductors, and conductors. – Insulators such as fused quartz and glass have very low conductivities, on the order of 10-18– 10-8S/cm – 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, magnetic field, and amounts of impurity atoms 3 4 Typical range of conductivities for insulators, semiconductors, and conductors. Note: , are functions of - Impurity - Temperature - Electric Field - Optical Excitation Semiconductors are not metals Semiconductor resistance decreases with temperature 5 Semiconductor materials 6 Element Semiconductors • Table 1-1 shows a portion of the periodic table related to semiconductors. • The element semiconductors, those composed of single species of atoms, such as silicon (Si) and germanium (Ge), can be found in Column IV. • In the early 1950s, germanium was the major semiconductor material. • Since the early 1960s silicon has become a practical substitute and has now virtually supplanted germanium as a semiconductor material. – Silicon is one of the most studied elements in the periodic table, and silicon technology is by far the most advanced among all semiconductor technologies. 7 Semiconductor materials – Si and Ge (1) • If we look at the periodic table, the element semiconductors, such as silicon (Si) or germanium (Ge), can be found in column IV of the table. • In the early 1950s, Ge was the most important semiconductor material, but, since the early 1960s, Si has played a major role and virtually displaced Ge as the main material for semiconductor material 8 Semiconductor materials – Si and Ge (2) • The reasons of that are: – Better properties at room temperature – High-quality silicon dioxide (SiO2) can be grown thermally. – Si is second only to oxygen in great quantity. – Devices made from Si cost less than any other semiconductor material – Silicon technology is by far the most advanced among all semiconductor technologies. 9 Compound Semiconductors • In recent years a number of compound semiconductors have found applications for various devices. – The important compound semiconductors as well as the twoelement-semiconductors are listed in Table 2. A binary compound semiconductor is a combination of two elements from the periodic table. – In addition to binary compounds, ternary compounds and quaternary compounds are made for special applications. • Compared with the element semiconductors, the preparation of compound semiconductors in single-crystal form usually involves much more complex processes. • Many of the compound semiconductors have electrical and optical properties that are different from those of silicon. – These semiconductors, especially GaAs, are used mainly for highspeed electronic and photonic applications. 10 Semiconductor Materials 11 Common Semiconductor Applications • Group IV – – – – Si for MOS, particularly CMOS digital logic and memory Si BJT for some logic and analog applications SiC for high power, high temperature applications Ge for diodes, BJTs • Group III/V – GaAs, GaAsP, InP for optoelectronic and high speed digital applications – InAs/GaInSb/AlInSb for long wavelength detectors – GaN, AlGaN for blue/white LEDs and high power devices • Group II/VI – CdTe, HgCdTe for long wavelength detectors Pronunciation: Generally, we can simply recite the name of each element, truncate the last one, and add “ide” to the end. For example, InGaAsP is “indium gallium arsenic phosphide”. 12 Outline • • • • Semiconductor Materials Crystalline Lattices Bulk Crystal Growth Epitaxial Growth 13 Classification of solids SOLID MATERIALS CRYSTALLINE POLYCRYSTALLINE AMORPHOUS (Non-crystalline) Single Crystal Crystal Structure 14 3 Types of Solids SOLIDS: [Single] Crystalline Atomic Arrangements: Periodic Amorphous Polycrystalline Random Grain Boundaries Materials used to fabricate integrated circuits include some from all three classifications. Amorphous: insulators (SiO2) Polycrystalline: MOS gates; contacts Crystalline: substrates 15 Crystalline Solid • Crystalline Solid is the solid form of a substance in which the atoms or molecules are arranged in a definite, repeating pattern in three dimension. Crystal Structure 17 Crystalline Solid • Single crystal has an atomic structure that repeats periodically across its whole volume. Even at infinite length scales, each atom is related to every other equivalent atom in the structure by translational symmetry Single Pyrite Crystal Amorphous Solid Single Crystal Crystal Structure 18 Polycrystalline Solid • • Polycrystal is a material made up of an aggregate of many small single crystals (also called crystallites or grains). The grains are usually 100 nm - 100 microns in diameter. Polycrystals with grains that are <10 nm in diameter are called nanocrystalline Polycrystalline Pyrite form (Grain) Polycrystal Crystal Structure 19 Amorphous Solid • Amorphous (non-crystalline) Solid is composed of randomly orientated atoms, ions, or molecules that do not form defined patterns or lattice structures. Crystal Structure 20 21 Unit Cell of Periodic Lattice Wigner-Seitz Primitive Cell • Choose a reference atom • Connect to all its neighbors by straight lines • Draw lines (in 2D) or planes (in 3D) normal to and at the midpoints of lines drawn in step 2 • Smallest volume enclosed is the Wigner-Seitz primitive cell Wigner-Seitz cell is ONE definition of a Unit Cell that always works There are other ways of construction! Crystal Lattices Bravais Lattices Non-Bravais Lattices (BL) (non-BL) All atoms are the same kind All lattice points are equivalent Atoms are of different kinds. Some lattice aren’t equivalent. Atoms are ofpoints different kinds. Some A combination 2 or more BL lattice points areofnot equivalent. 2 d examples Lattice Translation Vectors In General • Mathematically, a lattice is defined by 3 vectors called Primitive Lattice Vectors a1, a2, a3 are 3d vectors which depend on the geometry. • Once a1, a2, a3 are specified, the Primitive Lattice Structure is known. • The infinite lattice is generated by translating through a Direct Lattice Vector: T = n1a1 + n2a2 + n3a3 n1,n2,n3 are integers. T generates the lattice points. Each lattice point corresponds to a set of integers (n1,n2,n3). 2 Dimensional Lattice Translation Vectors Consider a 2-dimensional lattice (figure). Define the 2 Dimensional Translation Vector: Rn n1a + n2b a & b are 2 d Primitive Lattice Vectors, n1, n2 are integers. Point D(n1, n2) = (0,2) Point F(n1, n2) = (0,-1) • Once a & b are specified by the lattice geometry & an origin is chosen, all symmetrically equivalent points in the lattice are determined by the translation vector Rn. That is, the lattice has translational symmetry. Note that the choice of Primitive Lattice vectors is not unique! So, one could equally well take vectors a & b' as primitive lattice vectors. The Basis (or basis set) The set of atoms which, when placed at each lattice point, generates the Crystal Structure. Crystal Structure ≡ Primitive Lattice + Basis Translate the basis through all possible lattice vectors T = n1a1 + n2a2 + n3a3 to get the Crystal Structure or the Direct Lattice Crystal Structure Crystal structure can be obtained by attaching atoms or groups of atoms --basis-- to lattice sites. • The periodic lattice symmetry is such that the atomic arrangement looks the same from an arbitrary vector position r as when viewed from the point r' = r + T (1) where T is the translation vector for the lattice: T = n1a1 + n2a2 + n3a3 • Mathematically, the lattice & the vectors a1,a2,a3 are Primitive if any 2 points r & r' always satisfy (1) with a suitable choice of integers n1,n2,n3. • In 3 dimensions, no 2 of the 3 primitive lattice vectors a1,a2,a3 can be along the same line. But, DO NOT think of a1,a2,a3 as a mutually orthogonal set! Often, they are neither mutually perpendicular nor all the same length! • For examples, see Fig. 3a (2 dimensions): The Primitive Lattice Vectors a1,a2,a3 aren’t necessarily a mutually orthogonal set! Often, they are neither mutually perpendicular nor all the same length! • For examples, see Fig. 3b (3 dimensions): Crystal Lattice Types Bravais Lattice An infinite array of discrete points with an arrangement & orientation that appears exactly the same, from whichever of the points the array is viewed. A Bravais Lattice is invariant under a translation T = n1a1 + n2a2 + n3a3 Nb film Non-Bravais Lattices •In a Bravais Lattice, not only the atomic arrangement but also the orientations must appear exactly the same from every lattice point. 2 Dimensional Honeycomb Lattice • The red dots each have a neighbor to the immediate left. The blue dot has a neighbor to its right. The red (& blue) sides are equivalent & have the same appearance. But, the red & blue dots are not equivalent. If the blue side is rotated through 180º the lattice is invariant. The Honeycomb Lattice is NOT a Bravais Lattice!! Honeycomb Lattice Geometry of Lattice Points In a Bravais lattice, • every point in the lattice can be “reached” by integer translation of unit vectors • every point has the same environment as every other point (same number of neighbors, next neighbors, …) Not a Bravais Lattice … Not a Bravais Lattice … ….but these can be converted into Bravais lattice Not a Bravais Lattice … Two different unit cells in random order … these CANNOT be transformed to Bravais lattice ex. Aluminum-Manganese compounds, non-sticky coats Unit Cells in One-dimensional Crystals There is exactly ONE primitive unit cell in a 1D system No system truly 1-D, but …. • 1D properties dominate behavior in some material • e.g.: polymers, DNA, 1D heterostructures (lasers, RTDs) • Can often be solved analytically, many properties have 2D/3D analogs Unit Cell in 2D (all sites are equivalent) It can be shown that, in 2 Dimensions, there are Five (5) & ONLY Five Bravais Lattices! 2-Dimensional Unit Cells Unit Cell The Smallest Component of the crystal (group of atoms, ions or molecules), which, when stacked together with pure translational repetition, reproduces the whole crystal. b S a S S S S S S S S S S S S S S Unit Cell The Smallest Component of the crystal (group of atoms, ions or molecules), which, when stacked together with pure translational repetition, reproduces the whole crystal. Note that the choice of unit cell is not unique! S S S 2-Dimensional Unit Cells – Artificial Example: “NaCl” Lattice points are points with identical environments. 2-Dimensional Unit Cells: “NaCl” Note that the choice of origin is arbitrary! the lattice points need not be atoms, but The unit cell size must always be the same. 2-Dimensional Unit Cells: “NaCl” These are also unit cells! It doesn’t matter if the origin is at Na or Cl! 2-Dimensional Unit Cells: “NaCl” These are also unit cells. The origin does not have to be on an atom! 2-Dimensional Unit Cells: “NaCl” These are NOT unit cells! Empty space is not allowed! 2-Dimensional Unit Cells: “NaCl” In 2 dimensions, these are unit cells. In 3 dimensions, they would not be. 2-Dimensional Unit Cells Why can't the blue triangle be a unit cell? Example: 2 Dimensional, Periodic Art! A Painting by Dutch Artist Maurits Cornelis Escher (1898-1972) Escher was famous for his so called “impossible structures”, such as Ascending & Descending, Relativity,.. Can you find the “Unit Cell” in this painting? 3-Dimensional Unit Cells 3-Dimensional Unit Cells 3-Dimensional Unit Cells 3 Common Unit Cells with Cubic Symmetry Simple Cubic (SC) Body Centered Cubic (BCC) Face Centered Cubic (FCC) Conventional & Primitive Unit Cells Unıt Cell Types Primitive Conventional (Non-primitive) A single lattice point per cell More than one lattice point per cell The smallest area in 2 dimensions, or The smallest volume in 3 dimensions Volume (area) = integer multiple of that for primitive cell Simple Cubic (SC) Conventional Cell = Primitive cell Body Centered Cubic (BCC) Conventional Cell ≠ Primitive cell Face Centered Cubic (FCC) Structure Conventional Unit Cells • A Conventional Unit Cell just fills space when translated through a subset of Bravais lattice vectors. • The conventional unit cell is larger than the primitive cell, but with the full symmetry of the Bravais lattice. • The size of the conventional cell is given by the lattice constant a. FCC Bravais Lattice The full cube is the Conventional Unit Cell for the FCC Lattice Conventional & Primitive Unit Cells Face Centered Cubic Lattice Primitive Unit Cell (Shaded) Lattice Const. Primitive Lattice Vectors a1 = (½)a(1,1,0) a2 = (½)a(0,1,1) a3 = (½)a(1,0,1) Note that the ai’s are Conventional Unit Cell (Full Cube) NOT Mutually Orthogonal! Elements That Form Solids with the FCC Structure Body Centered Cubic (BCC) Structure Conventional & Primitive Unit Cells Body Centered Cubic Lattice Primitive Lattice Primitive Unit Cell Vectors a1 = (½)a(1,1,-1) a2 = (½)a(-1,1,1) Lattice a3 = (½)a(1,-1,1) Constant Conventional Unit Cell (Full Cube) Note that the ai’s are NOT mutually orthogonal! Elements That Form Solids with the BCC Structure Conventional & Primitive Unit Cells Cubic Lattices Simple Cubic (SC) c b Primitive Cell = Conventional Cell Fractional coordinates of lattice points: 000, 100, 010, 001, 110,101, 011, 111 a b c Body Centered Cubic (BCC) Primitive Cell Conventional Cell a b c Fractional coordinates of the lattice points in the conventional cell: 000,100, 010, 001, 110,101, 011, 111, ½ ½ ½ a Primitive Cell = Rombohedron Conventional & Primitive Unit Cells Cubic Lattices Face Centered Cubic (FCC) Primitive Cell Conventional Cell The fractional coordinates of lattice points in the conventional cell are: 000,100, 010, 001, 110,101, 011, 111, ½ ½ 0, ½ 0 ½, 0 ½ ½, ½ 1 ½, 1 ½ ½ , ½ ½ 1 b c a Simple Hexagonal Bravais Lattice Conventional & Primitive Unit Cells Points of the Primitive Cell Hexagonal Bravais Lattice Primitive Cell = Conventional Cell c b a Fractional coordinates of lattice points in conventional cell: 100, 010, 110, 101, 011, 111, 000, 001 Hexagonal Close Packed (HCP) Lattice: A Simple Hexagonal Bravais Lattice with a 2 Atom Basis The HCP lattice is not a Bravais lattice, because the orientation of the environment of a point varies from layer to layer along the c-axis. General Unit Cell Discussion • For any lattice, the unit cell &, thus, the entire lattice, is UNIQUELY determined by 6 constants (figure): a, b, c, α, β and γ which depend on lattice geometry. • As we’ll see, we sometimes want to calculate the number of atoms in a unit cell. To do this, imagine stacking hard spheres centered at each lattice point & just touching each neighboring sphere. Then, for the cubic lattices, only 1/8 of each lattice point in a unit cell is assigned to that cell. In the cubic lattice in the figure, Each unit cell is associated with (8) (1/8) = 1 lattice point. Primitive Unit Cells & Primitive Lattice Vectors • In general, a Primitive Unit Cell is determined by the parallelepiped formed by the Primitive Vectors a1 ,a2, & a3 such that there is no cell of smaller volume that can • The Primitive Unit Cell volume can be found by • As we’ve discussed, a Primitive vector manipulation: V = a1(a2 a3) Unit Cell can be repeated to fill space by periodic repetition of it • For the cubic unit cell in through the translation vectors the figure, V = a3 be used as a building block for the crystal structure. T = n1a1 + n2a2 + n3a3. Primitive Unit Cells • Note that, by definition, the Primitive Unit Cell must contain ONLY ONE lattice point. • There can be different choices for the Primitive Lattice Vectors, but the Primitive Cell volume must be independent of that choice. 2 Dimensional Example! j P = Primitive Unit Cell NP = Non-Primitive Unit Cell Bravais lattices in 3D: 14 types, 7 classes Bravais lattices in 3D: 14 types, 7 classes 72 3 Dominant Bravais Lattices a (SC ) a a (BCC ) (FCC ) a = lattice constant, lattice parameter the spacing between atoms at one side of a cubic unit cell (~5-6 Å for typical semiconductors) 74 Surface Reconstruction 76 Miller-Indices and Definition of Planes 78 Miller Indices: Rules Miller Indices: Rules Where does Miller Indices come from ? Specification of vectors normal to a particular plane! Bravais-Miller Indices Direction Indices 83 84 Example of Miller indices for planes Note: If a plane passes through the origin, translate it to a parallel position. Intercept at negative branch minus sign: (h -k l ) (h k l) 85 Why Are Crystal Planes Important? • real crystals are eventually terminate at a surface • Semiconductor devices are fabricated at or near a surface • many of a single crystal's structural and electronic properties are highly anisotropic 86 Equivalent Planes: {h k l} 87 Crystallographic Notation Miller Indices: Notation (hkl) Interpretation crystal plane {hkl} [hkl] <hkl> equivalent planes crystal direction equivalent directions h: inverse x-intercept of plane k: inverse y-intercept of plane l: inverse z-intercept of plane (Intercept values are in multiples of the lattice constant; h, k and l are reduced to 3 integers having the same ratio.) Crystal Structure Model Characteristics of Cubic Lattices Simple BCC FCC Volume of cubic cell Volume of primitive cell Type of primitive cell Lattice points per cubic cell a3 a3 SC 1 a3 1/2a3 a3 1/4a3 Lattice points per unit cell Nearest neighbour distance # of nearest neighbours Next nearest neighbour distance 1/a3 a 6 2 a # of next nearest neighbours 12 rhombohedral rhombohedral 2 2/a3 1/23a 8 a 6 4 4/a3 1/22a 12 a 6 89 Close Packing: Close packing (closest packing) is the most efficient arrangement of spheres. For crystals it is envisioned as the spheres representing the atoms at the bases touch each other. Packing of a unit cell: Packing fraction: The ratio of the total volume of a set of objects packed into a space to the volume of that space. 90 Lattices: Diamond & Zincblende a(x + y + z)/4 (a) a unit cell of the diamond lattice constructed by placing atoms (1/4, 1/4, 1/4) from each atom in an FCC. (b) top view (along any <100> direction) of an extended diamond lattice. The colored circles indicate one FCC sublattice and black circles indicate the interpenetrating FCC. 91 Lattices: Si (Diamond) & GaAs (Zincblende) 92 Silicon 93 Another way to think of the diamond lattice is this: Imagine that the fcc lattice (top figure) has attached to it, at the bottom right corner, the two atoms indicated in red below. If we attach these two atoms to each of the fcc lattice sites, the result is the diamond lattice. (We call this “lattice with a basis”, where the basis is the two red atoms.) 94 Si Crystal: Diamond Lattice 95 Crystallographic Planes and Si Wafers Silicon wafers are usually cut along a {100} plane with a flat or notch to orient the wafer during IC fabrication: 97 Which solid state material for electronic devices? • Why semiconductors? vs. conductors or insulators Bandgap Elemental (Si) vs. compound (GaAs) Resistivity () control over 1010 range. • Why (usually) crystalline? polycrystalline amorphous crystalline pure repeatable easy to cleave • Why silicon? cheap SiO2 is very good insulator good at room temperature 98 Outline • • • • Semiconductor Materials Crystalline Lattices Bulk Crystal Growth Epitaxial Growth 99 Crystal growth 100 Crystal Growth (Si) 101 Czochralski method 102 Czochralski method 103 Float-zone crystal growth 104 Procedure of Silicon Wafer Production Raw material ― Polysilicon nuggets purified from sand Si crystal ingot Crystal pulling A silicon wafer fabricated with microelectronic circuits Final wafer product after polishing, cleaning and inspection Slicing into Si wafers using a diamond saw 105 106 Outline • • • • Semiconductor Materials Crystalline Lattices Bulk Crystal Growth Epitaxial Growth 107 Epitaxial growth Epitaxis: epi - on taxis - arrangement 108 Epitaxial Growth (on substrate) 109 110 111 Liquid-Phase Epitaxy (LPE) 112 Molecular Beam Epitaxy (MBE) 113 Molecular Beam Epitaxy (MBE) 114 Chemical Vapor Deposition (CVD) or Vapor-Phase Epitaxy (VPE) 115 Metal-Organic Chemical Vapor Deposition (MOCVD) 116 Metal-Organic Chemical Vapor Deposition (MOCVD) 117