Electrical Properties of Engineering Materials. Ohm s Law

Transcription

1 Electrical Properties of Engineering Materials (Callister: Chapter 18) Ohm s Law Electrical conductivity in metals and non-metals Band Structure of conductors, semi-conductors and insulators Intrinsic Semiconductors n-type and p-type Extrinsic Semiconductors Temperature dependence of conductivity in metals and and semiconductors. Semiconductor Devices ES 021 Electrical Properties 1 Ohm s Law Typical form of Ohm s Law V = IR Resistance is not a material property. It is a function of geometry. The material property is resistivity. Resistance l R = ρ or A Conductivity A σ = 1 ρ l There are similar, geometry independent expressions for current and voltage: I Current Density J = A V Electric Field Strength ξ = l Ohm s Law (independent of geometry) J = σξ ES 021 Electrical Properties 2

2 Ohm s Law Electrical charge is measured in units of coulombs. 1C =1A s The current density is also equal to the number of charge carriers multiplied by the charge on each carrier multiplied by the average velocity of each carrier, or J = n e v (The charge on one electron, e = C) Making the substitution into Ohm s Law, we can write: σξ = n e v or... σ = n e v ξ ES 021 Electrical Properties 3 Electrical Conductivity v σ = n e ξ v The term is called the mobility, µ ξ and so, finally, we have an expression for the conductivity of a material: σ = n e µ Because e is a constant, this equation implies that we can influence the conductivity of a material by changing the number of charge carriers, or influencing their mobility ES 021 Electrical Properties 4

3 Electrical Conductivity Charge carriers In metals and semiconductors and many insulators, electrons are the charge carriers Ions are the charge carriers in ionic compounds The mobility of the charge carriers depends on atomic bonding lattice defects microstructure diffusion rates (in ionic conductors) ES 021 Electrical Properties 5 Numerical Examples Calculate the number of charge carriers in a 1mm diameter copper wire 1m long. Since the valence of copper is one, there is one carrier per atom. Volume = l A = Weight = V density = g # Cu atoms = g mol 2 ( π 0.001[ m ]) 7 3 1[ m] = [ m ] 4 3 [ ] kg 3 m = [ kg] 7 m [ ] [ mol ] = [ atoms] Q the valence of Cu = 1, charge carriers ES 021 Electrical Properties 6

4 Numerical Examples Calculate the drift velocity in the wire under an applied voltage of 12V. (σ = Ω -1 m -1 ) n e v σξ σ v = ξ n e = V 12 V ξ = = = 12 [ V ] L 1m From the last example, the wire contains carriers 19 carriers n = = = [ m ] 2 volume π [ Ω m] 12 [ V ] v = V m m = 3 19 [ m ] [ C] Ω C m v σ = n e ξ σ n v ξ = 53 m s 1 1 [ Ω m ] [ carriers 3] [ m ] s [ V ] m m ES 021 Electrical Properties 7 Power Loss in Conductors The power used in an electrical circuit is given by: P = VI = I 2 R In the case of power transmission, this energy is lost as heat. Ordinarily, but not always, we want to minimize the power loss - consider: - an extension cord - toaster elements ES 021 Electrical Properties 8

5 Band Theory Pauli exclusion principle: No two electrons can be in the same place with the same energy state. For a single atom in a box each electron occupies a discrete energy level ONLY 2 electrons per level (±½ spins) The permissible energy levels are discrete. There is an energy gap between each level Energy E f Mg: 1s 2, 2s 2, 2p 6, 3s 2 ES 021 Electrical Properties 9 Fermi Energy At absolute zero (0K, -273 C) all electrons are at their minimum energy levels. This is what was always assumed but never talked about when you figured out which orbitals were occupied for different elements Mg:1s 2, 2s 2, 2p 6, 3s 2 O: 1s 2, 2s 2, 2p 4 etc. The Fermi Energy (E f ) is the energy of the most energetic electron when only the lowest energy levels are filled. Above absolute zero, some electrons will have enough thermal energy to jump the energy gap to the next higher energy level. ES 021 Electrical Properties 10

6 Band Theory When atoms come together to form a solid, the Pauli exclusion principle still forbids two electrons from having the same energy. Similar orbitals from neighbouring atoms are forced to have slightly different energies. A band of permissible energies is formed Conduction Band Valence Band Energy E f The electrons in the valence band are bound to the nucleus They will not take part in conduction unless they jump to the conduction band ES 021 Electrical Properties 11 Band Theory As atoms approach each other, it is the outer orbitals that form bands first. At the equilibrium spacing, the inner orbitals are far enough apart that they do not have to form bands In metals, the valence band and the conduction band overlap This is how the sea of electrons that we talked about in metallic bonding is formed. This is also what makes metals good electrical conductors. Mg atoms Conduction Band Valence Band ES 021 Electrical Properties 12

7 Electrical Conductivity in Metals Remember that we control the conductivity in any material either by changing the number of carriers or influencing the mobility. We can t do much about the number of carriers in metals (There are already lots adding more won t accomplish anything) However, we can influence the mobility. Temperature Lattice Defects Cold Working Impurities Second phases ES 021 Electrical Properties 13 Electrical Conductivity in Metals Temperature Lattice vibrations reduce mobility of conduction electrons Defects Lattice imperfections also reduce mobility ES 021 Electrical Properties 14

8 Second phase particles Electrical Conductivity in Metals ES 021 Electrical Properties 15 Electrical Conductivity in Metals Cold working (increasing the dislocation content) decreases the conductivity somewhat. Impurity atoms can have a significant effect on conductivity ES 021 Electrical Properties 16

9 Intrinsic Semiconductors Materials like silicon and germanium are intrinsic semiconductors: the valence band and conduction band do not overlap, but the energy gap is small and so, even at room temperature, some electrons have enough thermal energy to enter the conduction band. When an electron moves up to the conduction band, it leaves a hole behind in the valence band. As electrons move in one direction, the holes move in the opposite direction ES 021 Electrical Properties 17 Intrinsic Semiconductors The conductivity is determined by the mobility of the electrons and the holes. σ = n e µ + p e µ e h For intrinsic semiconductors: n = p Therefore: ( µ + µ ) = p e ( µ ) σ = n e + µ e h e h ES 021 Electrical Properties 18

10 Intrinsic Semiconductors The number of electrons in the conduction band (and the number of holes in the valence band) increases with temperature. n = p = n 0 Eg exp 2kT and therefore the conductivity also increases with temperature. σ = n e E g ( µ + ) e h exp 2kT 0 µ ES 021 Electrical Properties 19 Intrinsic Semiconductors The conductivity of semiconductors is controlled by the number of carriers. ES 021 Electrical Properties 20

11 Extrinsic Semiconductors Because intrinsic semiconductors are so temperature sensitive, it is difficult to accurately control their conductivity. By intentionally adding a small number of impurities (doping) we produce extrinsic semiconductors. The conductivity of extrinsic semiconductors is controlled primarily by the concentration of the dopant atoms. ES 021 Electrical Properties 21 n-type Semiconductors If we add an impurity atom with a valence of 5 (e.g. P, As, Sb) to silicon (valence = 4), we are also adding an extra electron. 4 electrons participate in the covalent bonding, 1 electron enters a donor state just below the conduction band This is an n-type semiconductor. (extra negative charge) ES 021 Electrical Properties 22

12 n-type Semiconductors The extra electron is not tightly bound to the atoms and only requires a small increase in energy to enter the conduction band At low temperatures, the donor electrons dominate the conductivity extrinsic semiconduction As the temperature increases, eventually all of the donor electrons are in the conduction band donor exhaustion and the conductivity is constant At higher temperatures, silicon valence electrons begin to contribute to conduction intrinsic semiconduction ES 021 Electrical Properties 23 n-type Semiconductors The total number of charge carriers is equal to: n total dopant intrinsic intrinsic ntotal = ne + ne + nh E E d g = n0d exp + 2n0 exp kt 2kT We use these materials below the intrinsic range, so the number of carriers is: Ed ntotal n d exp In the exhaustion range, 0 kt where the electrical characteristics are most and, therefore, the conductivity is: stable, the number of carriers is equal to the σ n µ number of impurity atoms d e e ES 021 Electrical Properties 24

13 p-type Semiconductors If we add an impurity atom with a valence of 3 (e.g. B, Al, Ga, In) to silicon (valence = 4), we create an extra hole in the valence band. These holes can be filled by other electrons in the valence band and, therefore, the hole can move. The energy required to move an adjacent electron into the hole is much less than E g This is an p-type semiconductor. (extra positive charge) ES 021 Electrical Properties 25 p-type Semiconductors Like n-type semiconductors, p-type semiconductors also go through Extrinsic, Exhaustion, and Intrinsic semiconduction phases as the temperature is increased. We choose the dopant concentration to give us the desired conductivity in the exhaustion range where the conductivity is approximately constant. σ = p e µ h where p is the number of acceptor levels or holes introduced by the dopant. ES 021 Electrical Properties 26

14 p-type Semiconductors ES 021 Electrical Properties 27 Semiconductor Devices Thermistors: These are temperature measuring devices that take advantage of the predictable variation of conductivity with temperature in intrinsic semiconductors Pressure Transducers The band gap of a semiconductor is dependent (in part) upon the spacing between atoms. Compressing a semiconductor reduces the spacing between atoms. The energy gap decreases and the conductivity increases. ES 021 Electrical Properties 28

15 Diodes When an n-type and a p-type semiconductor are physically joined, a diode is formed. Electrons are concentrated on the n side and holes are concentrated on the p side Current will flow through the device if the holes and electrons are able to recombine at the interface. Forward Bias Current flows Reverse Bias No current flows current ES 021 Electrical Properties 29 Rectifiers Diodes If you apply an alternating voltage to a diode, it will only conduct when it is in forward bias. Forward Reverse ES 021 Electrical Properties 30

16 Diodes Breakdown Voltage If the reverse voltage is high enough (Breakdown voltage) a very large current will flow. The breakdown voltage can be controlled by choosing appropriate dopants and their concentrations. These devices are called Zener diodes ES 021 Electrical Properties 31 Solar Cells If we shine a light on a p-n junction, the absorbed photons create electron-hole pairs. The electrons are attracted to the p-side, the holes are attracted to the n-side, and a current flows. The energy obtained from this phenomenon depends on the band gap energy and the wavelength of light absorbed: λ = hc E g where: λ = the wavelength of light absorbed h = Planck's constant c = the speed of light E g = the band gap energy ES 021 Electrical Properties 32

17 Light Emitting Diodes When holes and electrons recombine at the interface, energy is released (according to the same formula) If the wavelength of the energy is in the visible range, we can see it. a Light Emitting Diode By tailoring the band gap of the p-n junctions, we can obtain LEDs of different colours. What band gap is required to produce red (λ=0.656µm), yellow (λ=0.574µm), and blue (λ=0.0.49µm) LEDs? Red - E g = 6 = 1.88 ev [ ev s] 3 10 [ m / s] [ ev s] 3 10 [ m / s] Yellow - E [ m] g = [ m] Blue- E g = = 2.52 ev = 2.15 ev 8 [ ev s] 3 10 [ m / s] 10 [ m] ES 021 Electrical Properties 33 Transistors A Bipolar Junction Transistor (BJT) is a sandwich of n-p-n or p-n-p semiconductors. They are used as amplifiers and switches in electronic circuits. They allow a relatively small input signal to control a large output signal B Emitter E Collector C Base ES 021 Electrical Properties 34

18 Transistors Consider the p-n-p case: When the transistor is on : a small forward bias is applied to the emitter side a larger reverse bias (but less than the breakdown voltage) is applied to the collector side Look at each side separately ES 021 Electrical Properties 35 Transistors If we apply a small forward bias (0.7V is typical) to the emitter side of the transistor only: E no current flows from E (or B) to C because there is no voltage. (The holes have no reason to enter the p-type collector) the emitter behaves as a diode and a proportionally small current flows through the device from E to B (holes move from the p-type emitter to the n- type base) + - i p B h + h + h + h + e - h + h + e - h + h + n ES 021 Electrical Properties 36 p C

19 Transistors If we apply a large reverse bias (e.g. 20V) to the collector side of the transistor only: no current flows between E and B or C because there is no voltage. the collector behaves as a (reverse bias) diode and no current flows from C to B + - B E h + h + e - h + h + C h + h + h + h + p e - n ES 021 Electrical Properties 37 p Now for the good part Transistors If we now apply both voltages to the device, what should happen? You would expect that every thing would operate as the individual halves, But you would be wrong + - i B + - E h + h + h + h + e - h + h + e - h + h + p n ES 021 Electrical Properties 38 p C

20 Transistors The trick to making a BJT is to make the base very thin compared to its height and to dope it less than the emitter and collectors. Holes from the emitter cross the junction into the base, but almost all of them are pulled into the collector before they can leave through the B terminal. Almost all of the current entering the base leaves through the collector. Since the collector voltage is higher, the input power is amplified i B i E h + h + h + h + e - h + h + e - h + h + p n ES 021 Electrical Properties 39 p C Field Effect Transistors A field effect transistor (FET) achieves the same effect in a different manner. The source and drain are physically placed far enough apart that the output voltage cannot draw a significant number of carriers across the gap. A signal voltage provides an electric field that draws the carriers towards the gate, bringing them closer to the drain. The SiO 2 insulator prevents them from reaching the gate. ES 021 Electrical Properties 40

21 Manufacturing Semiconductor Devices ES 021 Electrical Properties 41