半导体物理学半导体 (2).pdf
Basic Concepts in CrystalsClassification of solids01Point group、Space group、7 crystal systems02Concepts of unit cell、Crystal planes、Crystal axis03Surface and volume density of atoms04Classification of solidsSchematic of three general types of crystals:(a)Amorphous（无定形）,(b)polycrystalline（多晶）,(c)single crystal（单晶）.Amorphous glassPolycrystalline silicon waferMonocrystalline silicon waferAmorphous materials have order only within a few atomic or molecular dimensions.An ordered area is a spatial volume in which atoms or molecules have a regular geometric arrangement or periodicity.Single-crystal regions are the ordered spatial regions within many atomic or molecular dimensions,also called as grains.Polycrystalline materials compose of multiple ordered regions,which are separated from one another by grain boundaries.Single crystal materials have a regular geometric periodicity throughout the entire volume of the material.Classification of solidsPoint Group(点群，Symmetry Class)A combination of all macroscopic symmetry elements of the crystal.Point group(Emphasize symmetry operations)Symmetry class(Emphasize symmetry elements)Definition：Name：Total：Although there are many combinations of symmetry elements,there are only 32 reasonable combinations,called 32 point groups or symmetry classes.Point group、Space group、7 crystal systems Space group（点群）is a combination of all symmetry elements in the internal structure of the crystal,specifically a combination of all symmetry elements in the unit cell.The crystal structure is regarded as an infinite figure,and its symmetry is characterized by the unit cell.Besides the macroscopic symmetry elements,there are microscopic symmetrical elements such as translation axis,slip axis,and spiral axis.1,2,3,4,6,-3,-4,-6,m,C form 32 Point groups.1，2，3，4，6，-3，-4，-6，21，31，32，41，42，43，61，62，63，64，65，m,a,b,c,n,d,C,and P(H,R),C(A,B),F,I form 230 Space groups.Point group、Space group、7 crystal systemsCrystal Classes（晶类）：Crystals with the same point group are classified into one crystal class,with a total of 32 crystal classes.That is,each symmetry type corresponds to a crystal class.Crystal System（晶系）：According to the symmetries,32 crystal classes are divided into 7 crystal systems:Triclinic,monoclinic,orthorhombic,rhombohedral,tetragonal,hexagonal,cubic.Point group、Space group、7 crystal systemsCrystal Family（晶族）：According to the presence and absence of the higher order axis of the point group,the 7 crystal systems are divided into 3 crystal families:low-level crystal families,intermediate-level crystal families,and high-level crystal families.Point group、Space group、7 crystal systems3 crystal familiesAffiliated crystal systemslow-level crystal familiestriclinic,monoclinic,orthorhombicintermediate-level crystal familiesrhombohedral,tetragonal,hexagonalhigh-level crystal familiescubicConcepts of unit cell、Crystal planes、Crystal axisUnit and Primitive CellA unit cell is a small volume of the crystal that can be used to reproduce the entire crystal.A unit cell is not a unique entity；A primitive cell is the smallest unit cell that can be repeated to form the lattice;Basic Crystal StructuresSC,Simple CubicBCC,Body-Centered CubicFCC,Face-Centered CubicThree lattice types:(a)simple cubic,(b)body-centered cubic,(c)face-centered cubic.Concepts of unit cell、Crystal planes、Crystal axisThree lattice planes:(a)(100)plane,(b)(110)plane,(c)(111)plane.Crystal Planes and Miller IndicesConcepts of unit cell、Crystal planes、Crystal axisDirections in CrystalsThree lattice directions and planes:(a)(100)plane and 100 direction,(b)(110)plane and 110 direction,(c)(111)plane and 111 direction.Concepts of unit cell、Crystal planes、Crystal axisSurface and volume density of atomsSurface density of atomsSC,Simple CubicBCC,Body-Centered CubicFCC,Face-Centered Cubicvolume density of atoms in crystal：body-centered cubicAssume the lattice constant a=0.5nm=5*10-8cmVolume Density atoms/cm3223810*6.110*5181*8Surface and volume density of atoms
