ECE 440 Lecture 2 : Semiconductors And Crystal Structure

ECE 340Lecture 3 : Semiconductorsand Crystal StructureClass Outline: Semiconductor Crystal Lattices Semiconductor Crystal Growth

Things you should know when you leave Key Questions Why is crystal order important? How is a crystal defined? What are the most commontypes of crystal lattices used insemiconductor devices?M. J. GilbertECE 340 – Lecture 38/26/1 1

Semiconductor Crystal LatticesWhat is the crystal structure?CrystallinePolycrystallineAmorphous Crystal structures come in three basic kinds– In the CRYSTALLINE state the atoms are ordered into a well-defined lattice thatextends over very long distances .–POLYCRYSTALLINE materials consist of small crystallites that are embedded inAMORPHOUS regions of material.– In the AMORPHOUS state there is little or no evidence for long-range crystallineorder.M. J. GilbertECE 340 – Lecture 38/26/1 1

Semiconductor Crystal LatticesWhat does it matter if it is crystalline or not?CrystallineAmorphous We can get a lot of information from the unit cell:– Density of atoms– Distance between nearest atoms Calculate forces between atoms– Perform simple calculations Fraction of atoms filled in volume Density of atomsM. J. GilbertECE 340 – Lecture 38/26/1 1

Semiconductor Crystal LatticesSince we care about crystalline lattices, let’s examine the periodic lattice In the periodiclattice: 2D lattice where the greyballs denote lattice pointsM. J. Gilbert Basis2D Crystal– Symmetric arrayof points is thelattice.– We add the atomsto the lattice in anarrangement calleda basis.– We can define aset of primitivevectors which canbe used to traceout the entirecrystal structure.ECE 340 – Lecture 38/26/1 1

Semiconductor Crystal LatticesIn this section we consider some of the lattice types that will be importantfor our discussion of semiconductors Examine the simplecubic structure:azyxa1 axˆ(2.1)a 2 ayˆ(2.2)a3 azˆ(2.3)M. J. Gilbert– All primitivevectors are equal inall threedimensions.– Here again, theballs represent thelattice points, butno basis has beenadded.ECE 340 – Lecture 38/26/1 1

Semiconductor Crystal LatticesA simple variant on the cubic lattice is the body-centered cubic lattice Examine the body-centered cubic lattice (bcc):– Same as simple cubic but with an additional atom atthe center of the cell.– Primitive vectors are written in the more convenientsymmetric form but other representations exist.a1 a[xˆ yˆ zˆ ]2(2.4)a2 a[ xˆ yˆ zˆ ]2(2.5)a3 a[xˆ yˆ zˆ ]2(2.6)zayxM. J. GilbertECE 340 – Lecture 38/26/1 1

Semiconductor Crystal LatticesA final variant is the face-centered cubic lattice Examine the face-centered cubic lattice (fcc):– This is formed by adding an additional atom in the centerof each face of the simple cubic configuration.– This is the most important configuration we will consider.– The primitive vectors have been written again by usingsymmetry considerations.aa1 a[xˆ yˆ ]2(2.7)a2 a[yˆ zˆ ]2(2.8)a3 a[zˆ xˆ ]2(2.9)zyxM. J. GilbertECE 340 – Lecture 38/26/1 1

Semiconductor Crystal LatticesBut be careful There is a difference between unit cells andprimitive cells.– The primitive cell is the volume associated with onelattice point.– Often it is more convenient to use a unit cell that islarger than the primitive cell since such a cellillustrates the crystal symmetry in a clearer way.IN THIS FIGURE THE DOTTED LINES INDICATE THEUNIT CELL OF THE FACE-CENTERED CUBIC LATTICEaVunit a 3 a1 a 2 a 3(2.10)THE GRAY REGION DENOTES THE PRIMITIVE CELL FOR THIS LATTICEWHOSE VOLUME CAN BE DETERMINED FROM THE PRIMITIVE VECTORSINTRODUCED IN Eqns. 2.7 - 2.9V primitiveM. J. Gilberta3 a 3 (a1 a 2 ) 4ECE 340 – Lecture 3(2.11)8/26/1 1

Semiconductor Crystal LatticesNow let’s look at the silicon crystal To discuss the crystal structure of different semiconductors wewill need to account for the basis unit that is added to eachlattice point.– Elemental semiconductors such as silicon and germanium both exhibitthe diamond structure.– Named after one of the two crystalline forms of carbon. Here we display the siliconunit cell. The balls each representone silicon atom. The solid lines representchemical bonds. Note how the bonds form atetrahedron. How many atoms per unitcell?M. J. GilbertECE 340 – Lecture 38/26/1 1

Semiconductor Crystal LatticesLooks confusing, but it’s not so bad It is really just two inter-penetrating fcc lattices with a diatomic basis. It looks more complex because we do not show atoms extending beyondthe unit cell by convention. In the figure below, each different color represents pairs of atomsfrom the same basis. The black balls represent atoms with one atom in their basis outside theunit cell.a(xˆ , yˆ , zˆ )4(0, 0, 0)LATTICEM. J. GilbertBASISECE 340 – Lecture 3UNIT CELL8/26/1 1

Semiconductor Crystal LatticesWhat about compound semiconductors?Gallium Many compoundsemiconductors suchas Gallium Arsenide(GaAs) exhibit thezincblende crystalstructure.Arsenide– The atomicconfiguration is thesame as diamond.– The difference lies inthat each successiveatom is from adifferent chemicalelement.M. J. GilbertUseful questions to ask: How many atoms per unit cell? Avogadro’s number: NA # atoms / mole Atomic mass: A grams / mole Atom counting in unit cell: atoms / cm3 How do you calculate density?ECE 340 – Lecture 38/26/1 1

Crystal Growth - SiliconM. J. GilbertECE 340 – Lecture 38/26/1 1

Crystal Growth – Compound Semiconductors Heterojunctions are typically produced by aprocess known as MOLECULAR-BEAM EPITAXY– This is performed in an ultra-high vacuum (UHV)evaporation chamber working at pressures of 10-11 Torr.– The materials to be grown are provided from heatedKNUDSEN CELLS in which the individual elements areindividually EDWITH LIQUIDNITROGEN600 CKNUDSEN CELLSCONTAININGGa, Al, As & SiELECTRONDIFFRACTIONDETECTORUHV PUMPA SCHEMATIC DIAGRAM SHOWING THE KEY COMPONENTSOF A MOLECULAR-BEAM EPITAXY SYSTEMM. J. GilbertECE 340 – Lecture 38/26/1 1

Crystal Growth – Compound Semiconductors Careful control of the deposition rates and the substratetemperature are required to realize heterojunctions with welldefined interfaces.– In order to achieve high uniformity the substrate is heated toapproximately 600 ºC and is slowly rotated in the vacuum chamber.– The growth rate of the epitaxial layer is of order several MICRONSPER HOUR which allows for ATOMIC level resolution in the growthprocess.– The growth is monitored in situ using electron diffraction and massspectroscopy.TEM IMAGES OF EPITAXIALLY GROWN GaAs/AlGaAsM. J. GilbertECE 340 – Lecture 38/26/1 1

Example ProblemTreating atoms as rigid spheres with radii equal to ½ the distance betweenthe nearest neighbors, show that the ratio of the volume occupied by atoms tothe total available volume in an FCC is 74%.M. J. GilbertECE 340 – Lecture 38/26/1 1

M.J. Gilbert ECE 340 –Lecture 3 8/26/11. Semiconductor Crystal Lattices To discuss the crystal structure of different semiconductors we will need to account for the . basis. unit that is added to each . lattice. point. – Elemental semiconductors such as silicon and germaniu