Recap of Lecture #13: Thermodynamics III For a spontaneous process, ΔG = W max = The maximum work that can be obtained from a process at constant T and p For a non-spontaneous process, ΔG = W min = The minimum work that must be done to make a process go at constant T and p Lead acid battery Dry cell, alkaline cell Rechargeable Ni-Cd battery To get higher voltages, stack up cells in series (e.g., car battery 6 2 V = 12 V) Electrolysis: Driving non-spontaneous reactions by applying electrical energy The least unfavorable potential reaction goes first (there can be overlap) Overpotentials and concentrated reactants are used Recap of Lectures #14/15: Metals & Semiconductors Metals No band gap - HOMO, LUMO are at the same energy Electronic excitation is small vs. kt High electrical and thermal conductivity Conductivity decreases with increasing temperature because of electron scattering Semiconductors and Insulators Have a band gap between valence (lower) band and conduction (upper) band electronic excitation is >kt This determines insulator vs. semiconductor Direct band gap can be excited by photons (photons have very little momentum) Indirect band gap cannot be photoexcited efficiently Electrons (e ) and holes (h + ) can carry charge Differentiate with magnetic field (Hall effect) Energies of (dopant) states in the band gap determine conductivity and whether electrons or holes dominate current n- and p-type, respectively Conductivity increases with increasing temperature because of thermal excitation of carriers Semimetal Zero band gap, but no states at the Fermi energy 1
Recap of Lecture #15: Semiconductors, cont. Know: Valence and conduction bands Fermi energy (= Fermi level) Dopant energy Work function (= Ionization potential) Fabrication Steps Purify large crystal of semiconductor (e.g., silicon) Slice into wafers Polish wafers Use masks and lithography to sculpt wafer (remove material), to deposit material, and to do simple reactions Reactions in patterns: Oxidize Si to make insulator (or deposit insulator) React Si with metal to make conducting metal silicide (to connect devices) React Si to make doped volume of p- or n-type semiconductor more on this today Seal up devices to prevent further reactions Recap of Lecture #16: Semiconductors Semiconductor Manufacturing Purify large crystal of semiconductor (e.g., silicon) Slice into wafers Polish wafers Use masks and lithography to sculpt wafer (remove material), to deposit material, and to do simple reactions Reactions in patterns: Oxidize Si to make insulator (or deposit insulator) React Si with metal to make conducting metal silicide (to connect devices) React Si to make doped volume of p- or n-type semiconductor Seal up devices to prevent further reactions Dopants in semiconductors Do not form bands Set Fermi level and determine n- vs. p-type (by element) resistivity/conductivity (by concentration) 2
Requested Review Topics (reordered) Energy scales Gibbs free energy, spontaneity, entropy, standard states Acids and bases, including titrations Heat capacity Semiconductors: Density of states, dopants Redox reactions and oxidation states, electrolysis, voltaic cells (batteries) Energy distributions (statistical mechanics) Surface tension Carnot cycles and efficiency Thermodynamics ΔG, ΔH, ΔS Relate ΔG, K eq, E cell Convert from standard to arbitrary conditions Predict ΔG, ΔH, ΔS, K eq, E cell in many cases Electrochemistry Balance reactions LAnOx & GRedCat Relate to thermodynamics Electrolysis Relative ease of oxidation and reduction Batteries Corrosion 3
Materials Semiconductors Conduction and valence bands Band gap, Fermi level Density of states n- and p-type, semi-insulating Direct and indirect band gaps Reactions of Si to make: insulators, metals, and to add dopants Conductivity increases with increasing temperature thermal excitation to conduction band or from valence band Insulators Conductivity increases with increasing temperature Energy level diagram looks Metals No band gap Conductivity decreases with increasing temperature Energy scales Reactions, interactions vs. photon energies Measurements & spectroscopies Energies and wavelengths e.g., for diffraction, we match photon wavelength to bond length choose X-rays 4
Acid Strength Strong acids HCl, HBr, HI, HNO 3, HClO 4, H 2 SO 4 These dissociate completely to form H + + X - Other (weak) acids: Dissociate partially to H + + X - Rank by K a the highest K a is the strongest acid. Oxyacids: 1) The most highly charged center atom yields the strongest acid. 2) The most electronegative center element yields the strongest acid if the acids have the same structure. Lewis acid rules along above lines Polyprotic acids Lewis acid-base adducts 5
Base Strength Strong bases: LiOH, NaOH, KOH, RbOH, CsOH Ca(OH) 2, Sr(OH) 2, Ba(OH) 2 These dissociate completely to form OH - + M + Other (weak) bases: Rank by K b the highest K b is the strongest base The lowest K a for the conjugate acid is the strongest base Buffers HA H + + A - [H K a = + ][A - ] pk a = -log 10 K a [HA] ph = pk a log 10 [HA] [A - ] Surface tension Lower coordination of surface molecules Surfactants 6