1Carrier ModelingQuantization Conceptplank constantCore electronsValence electronsPeriodic Table of the Elements Group** Period 1 IA 1A 18 VIIIA8A 1 1 H 1.008 2 IIA 2A 13 IIIA3A 14 IVA4A 15 VA5A 16 VIA6A 17 VIIA7A 2 He4.003 2 3 Li 6.941 4 Be 9.012 5 B 10.816 C 12.017 N 14.018 O 16.009 F 19.0010 Ne20.18 8 9 10 3 11 Na 22.99 12 Mg 24.31 3 IIIB 3B 4 IVB 4B 5 VB 5B 6 VIB 6B 7 VIIB 7B ------- VIII ------- ------- 8 ------- 11 IB 1B 12 IIB2B 13 Al26.9814 Si28.0915 P 30.9716 S 32.0717 Cl35.4518 Ar39.954 19 K 39.10 20 Ca 40.08 21 Sc 44.96 22 Ti 47.88 23 V 50.94 24 Cr 52.00 25 Mn 54.94 26 Fe 55.85 27 Co 58.47 28 Ni 58.69 29 Cu63.5530 Zn65.3931 Ga69.7232 Ge72.5933 As74.9234 Se78.9635 Br79.9036 Kr83.80 5 37 Rb 85.47 38 Sr 87.62 39 Y 88.91 40 Zr 91.22 41 Nb 92.91 42 Mo 95.94 43 Tc (98) 44 Ru 101.1 45 Rh 102.9 46 Pd 106.4 47 Ag107.948 Cd112.449 In114.850 Sn118.751 Sb121.852 Te127.653 I 126.954 Xe131.3 6 55 Cs 132.9 56 Ba 137.3 57 La* 138.9 72 Hf 178.5 73 Ta 180.9 74 W 183.9 75 Re 186.2 76 Os 190.2 77 Ir 190.2 78 Pt 195.1 79 Au197.080 Hg200.581 Tl204.482 Pb207.283 Bi209.084 Po(210) 85 At(210) 86 Rn(222) 7 87 Fr (223) 88 Ra (226) 89 Ac~ (227) 104 Rf (257) 105 Db (260) 106 Sg (263) 107 Bh (262) 108 Hs (265) 109 Mt (266) 110 --- () 111 --- () 112---() 114---() 116---() 118 ---() 2s2p1sKLQuantization Concept¾ The shell model of the atom in which the electrons are confined to live within certain shells and in sub shells within shells. The Shell Model1s22s22p2or [He]2s22p2L shell with two sub shellsNucleus2rov+e- eQuantization ConceptyxxyzzxyzxyzStable orbit has radius r0The planetary model of hydrogen atom in which the negatively charged electron orbits the positively charged nucleus.Orbitals1s orbital 2pxorbital2pyorbital 2pzorbital (ml= 0)Atomic Bondinga. Ionic bonding (such as NaCl)b. Metallic bonding (all metals)c. Covalent bonding (typical Si)d. Van der Waals bonding (water…)e. Mixed bonding (GaAs, ZnSe…, ionic & covalent) Bonding forces in SolidsIonic Bonding Ionic BondingCl3pClosed K and L shellsNaClosed K and L shells3pNa+FArFANa+roCl-3s3s3s The origin of Ionic bonding¾ The formation of an ionic bond between Na and Cl atoms in NaCl.¾ The attraction is due to Coulombic forces.Cl-3Cl-Na+Na+Na+Cl-Cl-Cl-Na+Na+Na+Cl-Cl-Cl-Na+Na+Na+Cl-Cl-Cl-Na+Na+Na+Cl-Cl-Cl-Na+Na+Na+Cl-Cl-Cl-Na+Na+Na+Cl-Cl-Ionic Bonding Sodium Chloride¾ NaCl solid is made of Cl-and Na+ions arranged alternating so that the oppositely charged ions are closest to each other and attract each other. There are also repulsive force between the like-ions.¾ In equilibrium the net force acting on any ions is zero.¾ Zero energy corresponds to neutral Na and Cl atoms infinitely separated.Cl-Na+r0=0.28nm6-60-6.30.28 nmPotential energyE(r) [eV/(ion pair)]oSeparation re1.5 eVr=∞ClNar=∞Na+Cl-Cohesive energyIonic Bonding¾ Sketch of the potential energy per ion-pair in solid NaCl.¾ Zero energy corresponds to neutral Na and Cl atoms infinitely separated.Metallic Bonding Metallic Bonding¾ In metallic bonding the valence electrons from the metal atoms form a “clouds of electrons” which fills the space between the metal ions and “glues” the ions together through the Coulombic attraction between the electron gas and positive metal ions. The origin of Metallic bondingFree valence electrons forming an electron gasPositive metal ion cores4Covalent BondingInteratomic separation, r+AttractionRepulsion0FA=Attractive forceFR=Repulsive forceFN=Net forceror=∞MoleculeSeparated atomsror+RepulsionAttraction0EA=Attractive PEER=Repulsive PEE=Net PEForcePotential Energy,oE(r)Covalent BondingPotential energyvs.Interatomic separationForcevs.Interatomic separationEoor1s1122121sCovalent Bonding¾ Formation of covalent bondbetween two H atoms leads to the H2molecule.¾ Electrons spend majority of their time between the two nuclei which results in a net attractionbetween the electrons and the two electrons and the two nuclei which is the origin of the covalent bond.H-H moleculeH-atomH-atomElectron shellCovalent bondHCHHHHHHHL shell K shellCCHHHHCovalent BondingIn three dimensions, due to symmetry, the bonds are directed towards the corners of a tetrahedron.Covalent bonding in methane, CH4 , involves four hydrogen atoms sharing electrons with one carbon atom. Each covalent bond has two shared electrons. The four bonds are identical and repel each other. MethaneCovalent bondCovalent bond109.5°5Covalent Bonding¾ The diamond crystal is a covalently bonded network of carbon atoms. ¾ Each carbon atoms is bonded covalently to four neighbors forming a regular 3-dim. pattern of atoms which constitutes the diamond crystal. Diamond CrystalABAB′HClVan der Waals BondingA permanently polarized moleculeis called an electric dipole moment.Dipoles can attract or repeleach other depending on their relative orientations.Suitably oriented dipoles attract each other to form Van der Waals bonds. The origin of Van der Waals bonding between water moleculesHOHVan der Waals Bonding The origin of Van der Waals bonding between water moleculesThe H2O molecule is polar and has a net permanent dipole moment.Attraction between the various dipole moment in water gives rise to Van der Waals bonding.Time averaged electron (negative charge) distribution Ionic cores(Nucleus + K shells)NeABSynchronized fluctuation of the electronsVan der Waals forceVan der Waals BondingClosed L shellsInstantaneous electron (negative charge) distribution fluctuates about the nucleus  Induced dipole-interaction and the resulting Van der Waals force.6Energy Band Formation (I)¾ Strongly bonded materials: small interatomic distances. ¾ Thus, the strongly bonded materials can have larger energy bandgaps than do weakly bonded materials.Energy Bandgapwhere ‘no’ states existAs atoms are brought closer towardsone another and begin to bond together, their energy levels mustsplit into bands of discrete levelsso closely spaced in energy, theycan be considered a continuum ofallowed energy.Pauli Exclusion PrincipleOnly 2 electrons, of spin+/-1/2, can occupy the same energy state at the same point in space.Energy Band Formation (I)Fig 2.5 p28 Conceptual development of the energy band model.Electron energyThe 2N electrons in the 3s sub-shell and the 2N electrons in the 3p sub-shell undergo sp3hybridization.Energy Band Formation (Si) Energy levels in Si as a function of inter-atomic spacingThe core levels (n=1,2) in Si are completely filled