Chapter ISSUES TO ADDRESS... How are electrical conductance and resistance characterized ? What are the physical phenomena that distinguish conductors, semiconductors, and insulators? For metals, how is conductivity affected by imperfections, T, and deformation? For semiconductors, how is conductivity affected by impurities (doping) and T? Chapter 18: Electrical Properties

Chapter Scanning electron microscope images of an IC: A dot map showing location of Si (a semiconductor): -- Si shows up as light regions. A dot map showing location of Al (a conductor): -- Al shows up as light regions. Fig. (a), (b), (c) from Fig. 18.0, Callister 7e. Fig. (d) from Fig (a), Callister 7e. (Fig is courtesy Nick Gonzales, National Semiconductor Corp., West Jordan, UT.) (b) (c) View of an Integrated Circuit 0.5 mm (a) (d) 45  m Al Si (doped) (d)

Chapter Electrical Conduction Resistivity,  and Conductivity,  : -- geometry-independent forms of Ohm's Law E: electric field intensity resistivity (Ohm-m) J: current density conductivity -- Resistivity is a material property & is independent of sample Resistance: Ohm's Law:  V = I R voltage drop (volts = J/C) C = Coulomb resistance (Ohms) current (amps = C/s) I e - A (cross sect. area) VV L

Chapter Electrical Conduction When an electrical potential V [volts, J/C] is applied across a piece of material, a current of magnitude I [amperes, C/s] flows. In most metals, at low values of V, the current is proportional to V, and can be described by Ohm's law: I = V/R where R is the electrical resistance [ohms, Ω]. R depends on the intrinsic resistivity ρ of the material [Ω-m] and onthe geometry (length l and area A through which the current passes): R = ρl/A In most materials (e.g. metals), the current is carried by electrons (electronic conduction). In ionic crystals, the charge carriers are ions (ionic conduction).

Chapter Electrical Properties Which will conduct more electricity? Analogous to flow of water in a pipe So resistance depends on sample geometry, etc. D 2D2D

Chapter Definitions Further definitions J =   <= another way to state Ohm’s law J  current density   electric field potential = V/ or (  V/  ) Current carriers electrons in most solids ions can also carry (particularly in liquid solutions) Electron flux conductivity voltage gradient J =  (  V/  )

Chapter Room T values (Ohm-m) Selected values from Tables 18.1, 18.3, and 18.4, Callister 7e. Conductivity: Comparison Silver 6.8 x 10 7 Copper 6.0 x 10 7 Iron 1.0 x 10 7 METALS conductors Silicon 4 x Germanium 2 x 10 0 GaAs SEMICONDUCTORS semiconductors = (  - m) Polystyrene < Polyethylene Soda-lime glass 10 Concrete Aluminum oxide < CERAMICS POLYMERS insulators Up to 27 orders of magnitude, possibly widest variation in materials properties

Chapter Conductivity / Resistivity

Chapter What is the minimum diameter (D) of the wire so that  V < 1.5 V? Example: Conductivity Problem 100m Cu wire I = 2.5A - + e - VV Solve to get D > 1.87 mm < 1.5V 2.5A 6.07 x 10 (Ohm-m) 7 100m

Chapter Energy Band Structures in Solids Electrical conductivity in materials are strongly related to # of electrons available for conduction –Not all electrons will move in a material under an applied potential difference ! –More detail in Quantum Mechanics ! In an isolated atom electrons occupy well defined energy states, as discussed in Chapter 2. –Shells (1,2,3….), subshells (s,p,d,f…..), states in subshells, spin states When atoms come together to form a solid (N =12 atoms), a bonded regular atomic arrangement, their valence electrons interact with each other and with nuclei due to Coulombic forces. In addition, two specific quantum mechanical effects happen. –First, by Heisenberg's uncertainty principle, constraining the electrons to a small volume raises their energy, this is called promotion. –The second effect, due to the Pauli exclusion principle, limits the number of electrons that can have the same energy. As a result of these effects, the valence electrons of atoms at distinct energy states get split into closely spaced electron states and form wide electron energy bands when they form a solid. These bands are separated by gaps, where electrons cannot exist.

Chapter Energy Band Structures in Solids The extend of energy states splitting depends on inter-atomic distance Outermost shells start forming bands as atoms get closer, however core shells may not form bands as still far from each other. Band gaps, depending upon the inter-atomic distances also start forming

Chapter Electronic Band Structures Adapted from Fig. 18.2, Callister 7e. In solids gap between states could be eV apart

Chapter Band Structure Valence band – filled – highest occupied energy levels Conduction band – empty – lowest unoccupied energy levels valence band Conduction band Adapted from Fig. 18.3, Callister 7e.

Chapter Band Structure defines Electrical Properties Metals, single s valence electron N atoms => 4s band capable of 2N electrons => but only one s electron means half filled band structure. Metals with overlaping bands. Eg. Both s valence electrons exists in s subshell. In x’tal structure s and p subshells overlap, but p shell is empty. the valence band is filled, and no more electrons can be added (Pauli's principle). Electrical conduction requires that electrons be able to gain energy in an electric field. This is not possible in these materials because that would imply that the electrons are promoted into the forbidden band gap. <2eV insulator conductor >2eV

Chapter Energy States: Insulators & Semiconductors Insulators: -- Higher energy states not accessible due to gap (> 2 eV). Energy filled band filled valence band empty band filled states GAP Semiconductors: -- Higher energy states separated by smaller gap (< 2 eV). Energy filled band filled valence band empty band filled states GAP ?

Chapter Semiconductors and Insulators In semiconductors and insulators, electrons have to jump/move across the band gap into conduction band to find conducting states above E f The energy needed for the jump may originate from heat, or from irradiation at sufficiently small wavelength. The difference between semiconductors and insulators is that in semiconductors electrons can reach the conduction band at ordinary temperatures, where in insulators they cannot. E g is too large for insulators to have thermally or optically exited electrons promote to the conduction band. The probability that an electron reaches the conduction band is about exp(- E g /2kT) where E g is the band gap. If this probability is < one would not find a single electron in the conduction band in a solid of 1 cm 3. How come ? Remember N Av ~ This requires E g /2kT > 55. At room temperature, 2kT = 0.05 eV, E g > 2.8 eV corresponds to an insulator. An electron promoted into the conduction band leaves a hole (positive charge) in the valence band, that can also participate in conduction. Holes exist in metals as well, but are more important in semiconductors and insulators.

Chapter Charge Carriers Two charge carrying mechanisms Electron – negative charge Hole – equal & opposite positive charge Move at different speeds - drift velocity Higher temp. promotes more electrons into the conduction band    as T  Electrons scattered by impurities, grain boundaries, etc. Adapted from Fig (b), Callister 7e.

Chapter Conduction & Electron Transport Metals (Conductors): -- Thermal energy puts many electrons into a higher energy state. Energy States: -- for metals nearby energy states are accessible by thermal fluctuations filled band Energy partly filled valence band empty band GAP filled states Energy filled band filled valence band empty band filled states

Chapter Conduction in Metals In metals, highest occupied band is partially filled or bands overlap. Conduction occurs by promoting electrons into conducting states, that starts right above the Fermi level. The conducting states are separated from the valence band by an infinitesimal amount (~ eV). Energy provided by an electric field is sufficient to excite many electrons into conducting states. => High conductivity.

Chapter Summary Energy Band Structures and Bonding (metals, semiconductors, insulators) Relation to atomic bonding: –Insulators – valence electrons are tightly bound to (or shared with) the individual atoms – strongest ionic (partially covalent) bonding. Remember electro-negativity. –Semiconductors - mostly covalent bonding somewhat weaker bonding. Sharing of electrons. –Metals – valence electrons form an “electron gas” that are not bound to any particular ion.

Chapter Electron Mobility The force acting on the electron is -eE, where e is the electric charge and F=ma. As long as the electric field is present, in the absence of obstacles the electron is expected to speed up continuously in an electric field. –So, is the case in vacuum (e.g. inside a TV tube) or in a perfect crystal. –In a real solid, electrons motion are hindered by defects (dislocations, impurities, vacancies, etc), and even thermal vibrations of atoms. Electrons scatter by collisions with imperfections and due to atomic thermal vibrations. “frictional forces” => resistance => a net drift velocity of electron motion is established: where μ e – electron mobility [m 2 /V-s]. The “friction” transfers part of the energy supplied by the electric field into the lattice as heat. That is how electric heaters work.

Chapter Electron Mobility Electrical conductivity is proportional to number of free electrons and electron mobility: σ = N e |e| μ e N e - number of “free” or conduction electrons per unit volume e is the absolute charge on a free electron x C

Chapter Metals: Resistivity vs T, Impurities Read pages Imperfections increase resistivity -- grain boundaries -- dislocations -- impurity atoms -- vacancies These act to scatter electrons so that they take a less direct path. Resistivity increases with: -- temperature -- wt% impurity -- %CW Adapted from Fig. 18.8, Callister 7e. (Fig adapted from J.O. Linde, Ann. Physik 5, p. 219 (1932); and C.A. Wert and R.M. Thomson, Physics of Solids, 2nd ed., McGraw-Hill Book Company, New York, 1970.)  =  thermal +  impurity +  deformation deformed Cu at%Ni T (°C) Cu at%Ni Cu at%Ni Resistivity,  (10 -8 Ohm-m) 0 Cu at%Ni “Pure” Cu

Chapter Estimating Conductivity Adapted from Fig. 7.16(b), Callister 7e. Question: -- Estimate the electrical conductivity  of a Cu-Ni alloy that has a yield strength of 125 MPa. Yield strength (MPa) wt. %Ni, (Concentration C) wt%Ni Adapted from Fig. 18.9, Callister 7e. wt. %Ni, (Concentration C) Resistivity,  (10 -8 Ohm-m) C Ni = 21 wt%Ni From step 1: 30

Chapter Pure Semiconductors: Conductivity vs T Data for Pure Silicon: --  increases with T -- opposite to metals Adapted from Fig , Callister 5e. (Fig adapted from G.L. Pearson and J. Bardeen, Phys. Rev. 75, p. 865, 1949.) electrical conductivity,  (Ohm-m) pure (undoped) T(K) electrons can cross gap at higher T material Si Ge GaP CdS band gap (eV) Selected values from Table 18.3, Callister 7e. Energy filled band filled valence band empty band filled states GAP ?

Chapter Semiconductivity Semiconductor do have a lower conductivity than metals but unique properties of semiconductors make them very useful materials. Electrical properties of semiconductors are very sensitive to the presence of impurities: Intrinsic semiconductors - electrical conductivity is based on the electronic structure of pure material. Extrinsic semiconductors - electrical conductivity is dictated by impurity atoms. WHY ?

Chapter Conduction in Terms of Electron and Hole Migration Adapted from Fig , Callister 7e. electric field Electrical Conductivity given by: # electrons/m 3 electron mobility # holes/m 3 hole mobility Concept of electrons and holes: + - electron hole pair creation + - no appliedapplied valence electron Si atom applied electron hole pair migration

Chapter Intrinsic Semiconductors Number of electrons in conduction band increases exponentially with temperature: C is a material constant E g is the bandgap width 0 K RT ~ 300 K EgEg Thermally excited conductions electrons Holes left behind An electron promoted into the conduction band leaves a hole (positive charge) in the valence band. In an electric field, electrons and holes move in opposite direction and participate in conduction In Si (E g = 1.1 eV) one out of every atoms contributes an electron to the conduction band at room temperature.

Chapter Intrinsic Semiconductors Since both electrons and holes conduct the conductivity of an intrinsic semiconductor is Electrons are more mobile than holes, μ e > μ h In an intrinsic semiconductor, a hole is produced by the promotion of each electron to the conduction band. Therefore, n = p and n (and p) increase exponentially with temperature, whereas μ e and μ h decrease (about linearly) with temperature. Conductivity of intrinsic semiconductors increase with temperature (different from metals!)

Chapter Intrinsic Semiconductors

Chapter Extrinsic Semiconductors Extrinsic semiconductors - electrical properties (conductivity) is dictated by impurity atoms. Example: Si is considered to be extrinsic at room T if impurity concentration is one atom per (remember our estimation of the number of electrons promoted to the conduction band by thermal fluctuations at 300 K) –Unlike intrinsic semiconductors, an extrinsic semiconductor may have different concentrations of holes and electrons. It is called p-type if p > n and n-type if n > p. –One can engineer conductivity of extrinsic semiconductors by controlled addition of impurity atoms – doping (addition of a very small concentration of impurity atoms). –Two common methods of doping are diffusion and ion implantation.

Chapter n-type Extrinsic SMs When excess electron carriers are produced by substitutional impurities that have more valence electron per atom than the semiconductor matrix. Example: phosphorus (or As, Sb..) with 5 valence electrons, is an electron donor in Si since only 4 electrons are used to bond to the Si lattice when it substitutes for a Si atom. Fifth outer electron of P atom is weakly bound in a donor state (~ 0.01 eV) and can be easily thermally promoted to the conduction band. Impurities which produce extra conduction electrons are called donors, N D = N Phosphorus ~ n Elements in columns V and VI of the periodic table are donors for semiconductors in the IV column such as Si and Ge.

Chapter n-type Extrinsic SMs The hole created in donor state is far from the valence band and is immobile upon the promotion of the donated electron to the conduction band. n >>p Conduction occurs mainly by the donated electrons (thus n-type). σ ~ N D |e| μ e

Chapter Intrinsic: # electrons = # holes (n = p) --case for pure Si Extrinsic: --n ≠ p --occurs when impurities are added with a different # valence electrons than the host (e.g., Si atoms) Intrinsic vs Extrinsic Conduction n-type Extrinsic: (n >> p) no applied electric field Phosphorus atom valence electron Si atom conduction electron hole p-type Extrinsic: (p >> n) no applied electric field Boron atom Adapted from Figs (a) & 18.14(a), Callister 7e.

Chapter Intrinsic Semiconductors Pure material semiconductors: e.g., silicon & germanium –Group IVA materials Compound semiconductors – III-V compounds Ex: GaAs & InSb – II-VI compounds Ex: CdS & ZnTe – The wider the electronegativity difference between the elements the wider the energy gap.

Chapter Doped Semiconductor: Conductivity vs. T Data for Doped Silicon: --  increases doping -- reason: imperfection sites lower the activation energy to produce mobile electrons. Adapted from Fig , Callister 5e. (Fig adapted from G.L. Pearson and J. Bardeen, Phys. Rev. 75, p. 865, 1949.) doped at%B at%B electrical conductivity,  (Ohm-m) pure (undoped) T(K) Comparison: intrinsic vs extrinsic conduction extrinsic doping level: /m 3 of a n-type donor impurity (such as P). -- for T < 100 K: "freeze-out“, thermal energy insufficient to excite electrons. -- for 150 K < T < 450 K: "extrinsic" -- for T >> 450 K: "intrinsic" Adapted from Fig , Callister 7e. (Fig from S.M. Sze, Semiconductor Devices, Physics, and Technology, Bell Telephone Laboratories, Inc., 1985.) conduction electronconcentration (10 21 /m 3 ) T(K) freeze-out extrinsic intrinsic doped undoped

Chapter Number of Charge Carriers Intrinsic Conductivity  = n|e|  e + p|e|  e For GaAsn = 4.8 x m -3 For Si n = 1.3 x m -3 for intrinsic semiconductor n = p  = n|e|(  e +  n ) Ex: GaAs

Chapter Allows flow of electrons in one direction only (e.g., useful to convert alternating current to direct current. Processing: diffuse P into one side of a B-doped crystal. Results: --No applied potential: no net current flow. --Forward bias: carrier flow through p-type and n-type regions; holes and electrons recombine at p-n junction; current flows. --Reverse bias: carrier flow away from p-n junction; carrier conc. greatly reduced at junction; little current flow. p-n Rectifying Junction p-typen-type p-typen-type Adapted from Fig , Callister 7e p-type n-type -+

Chapter Properties of Rectifying Junction Fig , Callister 7e.Fig , Callister 7e.

Chapter Transistor MOSFET MOSFET (metal oxide semiconductor field effect transistor) Fig , Callister 7e.

Chapter Integrated Circuit Devices Integrated circuits - state of the art ca. 50 nm line width –1 Mbyte cache on board –> 100,000,000 components on chip –chip formed layer by layer Al is the “wire” Fig , Callister 6e.

Chapter Ferroelectric Ceramics Ferroelectric Ceramics are dipolar below Curie T C = 120ºC cooled below T c in strong electric field - make material with strong dipole moment Fig , Callister 7e.

Chapter Piezoelectric Materials at rest compression induces voltage applied voltage induces expansion Adapted from Fig , Callister 7e. Piezoelectricity – application of pressure produces current

Chapter Electrical conductivity and resistivity are: -- material parameters. -- geometry independent. Electrical resistance is: -- a geometry and material dependent parameter. Conductors, semiconductors, and insulators differ in accessibility of energy states for conductance electrons. For metals, conductivity is increased by -- reducing deformation -- reducing imperfections -- decreasing temperature. For pure semiconductors, conductivity is increased by -- increasing temperature -- doping (e.g., adding B to Si (p-type) or P to Si (n-type). Summary

Chapter Core Problems: Self-help Problems: ANNOUNCEMENTS Reading: