Properties of Materials

Tao Deng, dengtao@sjtu.edu.cn 1 1896 1920 1987 2006 Properties of Materials Chapter 3 Electrical Properties of Materials Tao Deng

3.1.4.4 The superconducting tunneling effect (Josephson effect) Tao Deng, dengtao@sjtu.edu.cn 2 In the 1960s, Josephson effect in weakly connected superconductors is one of the significant breakthroughs in the research of superconductivity. Weakly connected superconductors have a sandwich structure of superconducting - insulator - superconductor (SIS) with a nanometer insulating film in the middle of the two superconductors. Josephson junction Josephson effect:for the S-I-S structure with current < I C,there is no voltage through the dielectric layer. The weakly connected superconductors have a zero resistance, i.e. the insulating (vacuum, normal) layer between two superconductors can also pass the superconducting current.

Josephson junctions Possible Josephson junctions: (1) Superconductor- insulator - Superconductor; (2) Superconductor - normal metal - Superconductor; (3) Superconductor - vacuum - Superconductor (STM); (4) two superconductors contacted by point; (5) Two superconductor contacted by microbridge; (a) Tunnel junction (b) Proximity effect bridge (c) One-dimensional micro-bridge (d) Twodimensional micro-bridge (e) Three-dimensional micro-bridge (f) the micro-bridge with thickness changing (g) Point contact Tao Deng, dengtao@sjtu.edu.cn 3

3.1.5 Measurement of electrical resistance Tao Deng, dengtao@sjtu.edu.cn 4 3.1.5.1 (1) Measurement of resistance in metals Adjusting the current and four variable resistors, so that the electric potentials of point f and point c in the bridge circuit are equal. The bridge is in equilibrium: R x R n I I 1 1 R R 1 2 I I 2 2 R R 3 4 If R1 = R3, then R2 and R4 can be adjusted with R2 = R4 in the double bridge measurement. In other words, the equilibrium of the bridge can be achieved by adjusting R3 and R4 only: R x R n R R 1 2 Measurement through double bridge

Tao Deng, dengtao@sjtu.edu.cn 5 2)The resistance measurements of semiconductors V I S l 3 2 2 1 3 1 1 1 1 1 2 l l l l l l V I lv I 2 The two-probe method The four-probe method

3) The resistance measurements of insulators Ballistic galvanometer can be used in the measurement of the resistance of an insulator. When the switch K is switched to 1 and after a time of t: R x Ut Q Where U is the voltage of DC supply ; t is the charging time; Q is the electric charge on the capacitor after a charging time t, which can be measured by ballistic galvanometer. When the switch K is switched to 2, we have Q C b m where C b is the impact constant of ballistic galvanometer; α m is the maximum offset of the galvanometer (direct readout). Therefore : R x Ut C b m Tao Deng, dengtao@sjtu.edu.cn 6

3 The electrical properties Tao Deng, dengtao@sjtu.edu.cn 7 Electrical conductivity

Tao Deng, dengtao@sjtu.edu.cn 8 3 The electrical properties Electrical conductivity Dielectric property

3.2 The dielectric property Tao Deng, dengtao@sjtu.edu.cn 9 3.2.1 Dielectric property and polarization of dielectric media 3.2.1.1 Concept and characterization of dielectric property Under an applied electric field, the property of inducing charges on the surface of material is called the dielectric property. Such material is referred to the dielectric body (dielectric media). (a) Vacuum plate capacitor (b) A dielectric material between the capacitor plates

The permittivity The quantity used to measure the capacity of induced charge in a material is called the permittivity ε. For a Simple capacitor with only two plates, the capacity (C) is proportional to the plate area (A), and inversely proportional to the distance (d) between the plates: C A d If it s vacuum between plates, then A C 0 0 d ε 0 -The permittivity of vacuum Relative permittivity (dielectric constant): r C C 0 0 The polarization of the media in the electrostatic field so: C r 0 A d Tao Deng, dengtao@sjtu.edu.cn 10

3.2.1.2 The concept of the polarization Tao Deng, dengtao@sjtu.edu.cn 11 1.The basic concept of the polarization Under the action of an external electric field, the particles (ions, atoms, molecules) in the medium or the positive and negative charge centers in different regions are separated to form the electric dipole moment (dipole) inside the medium. This process is called polarization. If the relative displacement vector of positive charge to the negative charge is u, then the electric dipole moment is qu The direction is from the negative to the positive, the same as that of the external electric field. The magnitude of the electric dipole moment can also be described by "the particle polarization coefficient α" : E loc where,e loc -The local electric field acting on the particles.

The relationship between polarization and the induced charges on the surface Tao Deng, dengtao@sjtu.edu.cn 12 Polar plate Dielectric medium Polar plate - - - - - - - + - + - + - + - + - + - + - + - + + + + + + + + - + - + - + - + - + - + - + - Positive induced charge External electric field Negative induced charge Bound charge Free charge

3.2.1.3 Measure of the polarization The intensity of polarization: The sum of the electric dipole moment in the medium per unit volume : P n 0 or: where,n 0 -The Number of dipole per unit volume; -The average electric dipole moment. The polarization of the medium is proportional to the external electric field strength E: E loc P n0e loc For the linear polarization,average electric dipole moment is proportional to the strength of the local electric field E loc P 0 E P V ε 0 -The permittivity of vacuum;χ-the electric susceptibility Tao Deng, dengtao@sjtu.edu.cn 13

The permittivity ε under DC electric field Tao Deng, dengtao@sjtu.edu.cn 14 The density of free charge on the surface of a plate in a vacuum capacitor is described by vector D (the electric displacement). According to the theory of the electrostatic field, we have: D 0 E When the dielectric material is filled between the plates of a capacitor, due to the polarization: D E P P 0 E 0 D E 1 0 So: 1 0 1 r ( the permittivity) ( the relative permittivity) D E

Tao Deng, dengtao@sjtu.edu.cn 15 Basic magnetic parameters Magnetization (Intensity) M: M H Magnetic susceptibility χ:magnetization intensity under the action of an unit of the external magnetic field M H Magnetic induction B:in Vacuum: In a magnetic medium: B0 0H B H M H 0 0 1 Permeability of vacuum μ 0 : 0 B 0 H Relative permeability μ r : r ( 1 ) Magnetic permeabilityμ: 0 r B H

3.2.1.4 The basic forms of dielectric polarization Tao Deng, dengtao@sjtu.edu.cn 16 (1) Polarization forms 1)The electronic polarization The relative displacement of the electron cloud related to the nucleus. 2)The ionic polarization The relative displacement between the positive and negative ions. 3)Molecular polarization The rotation of the inherent dipole moment of polar molecules. 4)The interfacial polarization The charge separation at the boundary/interfaces due to the displacement of the movable ions (charged).

3.2.1.4 The basic forms of dielectric polarization Tao Deng, dengtao@sjtu.edu.cn 17 (a) The electronic: the nonoverlapping of the center of the electron cloud and that of the positive charge. (b) The ionic: the change of the relative position between positive and negative changes. (c) The molecular: orientation of permanent dipole along the external field. (d) The interface: charges aggregate at internal interface and move in the external field

Tao Deng, dengtao@sjtu.edu.cn 18 (2) The polarization type The polarization of elastic displacement Elastic polarization achieved instantaneously, without consumption of energy; disappears immediately when the electric field is removed. The polarization of electronic displacement (10-14 ~ 10-16 s) The polarization of ionic displacement (10-12 ~ 10-13 s) The relaxed polarization That s related to the thermal motion, inelastic, and consumes energy. The relaxation polarization of electrons (weakly bound electrons, 10-2 ~ 10-9 s) The relaxation polarization of ions (weakly bound ions) (10-2 ~ 10-5 s) The polarization of molecular (10-2 ~ 10-10 s) The polarization of space charge (10-2 s)

3.2.1.5 Clausius-Mosotti equation D E E P 0 P n E loc r n E E 1 loc 0 According to Lorentz relationship : Clausius-Mosotti equation 1 Eloc E P 3 r 1 n 1 3 Applicable in the weakly interaction molecular gas, non-polar liquids and non-polar solids, as well as some ionic crystals. For media with two or more polarized particles,: r 0 0 r 1 1 1 3 r 0 i n i i Tao Deng, dengtao@sjtu.edu.cn 19

3.2.1.6 The temperature coefficient of permittivity Tao Deng, dengtao@sjtu.edu.cn 20 Permittivity has a linear relationship with temperature: T 1 T 0 T 0 Where,T 0 -The initial temperature (usually room temperature); T -The actual temperature; ε 0 ε T -The permittivity at the temperature T 0 and T; ν-temperature coefficient of permittivity T T T T 0 0 0 0

3.2.1.7 Permittivity under AC electric field Assuming the AC electric field as a sine wave: E E 0 e it The electric displacement vector with a phase angle difference (δ) behind the electric field vector: D D0e According to D E, the complex permittivity under the alternating electric field is: D E D E 0 0 e i where, e s s D E i 0 0 cos s sin s s cos isin i is the static permittivity Tao Deng, dengtao@sjtu.edu.cn 21 i t is the real part of the complex permittivity. is the imaginary part of the complex permittivity

Tao Deng, dengtao@sjtu.edu.cn 22 3.2.2.2 Complex permeability and energy loss Assume H changes with a sinusoidal function ~ it it H H m e So: B ~ B m e Permeability with a complex form: ~ i where, Bm cos m 0H Bm sin m 0H m m cos sin The real part The imaginary part The loss tangent : tan 1 Q Q-The quality factor The energy loss for a period of dynamic magnetization: W ~ ~ T t d t HdB H cos sin sin m tbm H mbm 0 0 H 2 m

3.2.2 Dielectric loss Tao Deng, dengtao@sjtu.edu.cn 23 3.2.2.1 The concept of dielectric loss Under the external field, dielectric materials will consume energy through heat generation. The power loss of dielectric materials is the heat generation within unit time; it s also referred as the dielectric loss.

Tao Deng, dengtao@sjtu.edu.cn 24 3.2.2.2 Dielectric loss (1)The loss through conduction (the conductance leakage) For an ideal dielectric material, the conductance should not exist, i.e., the loss through conductance does not exist. There are always more or less charged particles (or vacancies) in the dielectric materials. These charged particles under external electric field move along the direction parallel to the field throughout the electrodes, resulting in the leakage of current and the loss of energy. There are conductance leakages in all dielectric materials.

Tao Deng, dengtao@sjtu.edu.cn 25 (2)Polarization loss When the medium polarizes slowly (relaxed polarization, space charge polarization, etc.), the energy loss is caused by the thermal motion of charged particles under the action of the electric field. It's a relative long for the establishment of relaxed polarization (about 10-2 to 10-3 seconds), so the electric moment caused by the polarization usually lags behind the applied electric field, which generates the loss. If the frequency of the applied voltage is so low that the polarization in the medium can completely match the change of the external electric field, it does not generate the polarization loss. If the frequency of the applied voltage too high, it will generate the polarization loss.

Tao Deng, dengtao@sjtu.edu.cn 26 (3)The ionization loss The ionization loss is caused by the gas in the dielectric. When the strength of the applied electric field is stronger than the ionization of the gas contained in the pores of a medium, the energy absorbed during the ionization of the gas is the ionization loss.

Tao Deng, dengtao@sjtu.edu.cn 27 (4)The structural loss In a high-frequency electric fields or at a low temperatures, there is a dielectric loss closely related to the tightness of the structure in medium; It s the structural loss, and has little relationship with temperature. It increases with the increase of the frequency.

5)Inhomogeneity of the macro structure Tao Deng, dengtao@sjtu.edu.cn 28 Most of engineering dielectric materials are not homogeneous. For example, ceramic materials that usually contain crystal phase, glass phase and gas phase, and have statistical distribution of these phases in the medium. Due to the difference of dielectric properties of each phase, there may be more free charges accumulated between phases, causing the uneven distribution of electric field, and leading to high electric field strength in a certain location and the higher losses.

3.2.2.3 Characterization of dielectric loss Conductive leakage flow is equivalent to a resistance inside the material. The loss is due to the resistive heating: W V R 2 1 V E 2 Sd The energy consumption in the medium in unit volume is : ~ W E V 2 V E 2 Sd With the increases of temperature, the volume conductivity of medium rises exponentially: ~ ~ W e W 0 at e T 0 Tao Deng, dengtao@sjtu.edu.cn 29

3.2.2.4 Influence of frequency on dielectric loss If the polarization is fast enough to match the changes of electric field all the time, there will be no loss. Otherwise there will be a current flow (absorption current) in the medium, with an equivalent resistance of ρ a, permittivity ε a. The dielectric loss per unit volume is: ~ W 2 2 g 2 2 1 where - The frequency of external electric field ; E - The strength of external electric field ; E 2 g 1 a -The initial conductivity of absorption current ; a 4k a k = 9 10-11,is a constant Tao Deng, dengtao@sjtu.edu.cn 30

Tao Deng, dengtao@sjtu.edu.cn 31 3.2.3 Dielectric strength 3.2.3.1 Characterization of dielectric strength When the voltage is above a critical value of V b, insulator will lose the insulating properties. V b ---breakdown voltage. Dielectric strength E b V b d

Tao Deng, dengtao@sjtu.edu.cn 32 3.2.3.2 The form of breakdown (1)Electric breakdown When the applied voltage is high enough, the speed of free of electrons is above a certain critical value and these electrons will enable the ionization of the ion to generate secondary electron. Those secondary electrons will accelerate and generate more electrons avalanche This process probably only need 10-7 ~ 10-8 seconds, so the electric breakdown is instant.

Tao Deng, dengtao@sjtu.edu.cn 33 3.2.3.2 The form of breakdown (1)Electric breakdown From the band theory, the electron energy increases with the increase of electric field intensity. When there are enough electrons gaining enough energy over the forbidden band and into the conduction band, the breakdown will happen.

(2)Thermal breakdown Tao Deng, dengtao@sjtu.edu.cn 34 During the process, part of the electrical energy transfers into heat energy and the temperature rises. The loss increases with the rise of temperature completely lose of insulation.

Tao Deng, dengtao@sjtu.edu.cn 35 (3)Chemical breakdown Related to irreversible change of electrolysis, chemical corrosion, oxidation, reduction and ionization of gas in porous material A slow process (aging)

3.2.3.3 The factors that influence the dielectrical strength Tao Deng, dengtao@sjtu.edu.cn 36 Temperature has small influence on the electric breakdown Temperature has a great influence on thermal breakdown Temperature promotes the chemical breakdown Frequency (ω) has a great influence on the dielectric loss, so it has a great influence on the thermal breakdown. E b A Where, A depends on the shape and size, cooling conditions and dielectric constant

3.3 Thermoelectricity Tao Deng, dengtao@sjtu.edu.cn 37 Thermal Magnetic Electromagnetic Electrical Optical

Tao Deng, dengtao@sjtu.edu.cn 38 3.3 Thermoelectricity 8.3.1 Thermoelectric effect and its nature There are connections between the potential difference, temperature difference, electrical current and heat flow. The first thermoelectric effect-seebeck effect The second thermoelectric effect-peltier effect The third thermoelectric effect-thomson effect

3.3.1.1 The first thermoelectric effect-seebeck effect When two different metals are connected to form a closed path, with a temperature difference between two ends, an electric current will be generated inside this circuit. Thermoelectric potential caused by Seebeck effect: 12 S T 12 Where S 12 -The seebeck coefficient,its value is: k N S12 ln e N N 1 N 1 The free electron density in metal 1,2 1 2 Tao Deng, dengtao@sjtu.edu.cn 39

(1)Contact Potential & Thermoelectric Potential Tao Deng, dengtao@sjtu.edu.cn 40 Due to the differences of work function and concentration of electron in metals, electrons will redistribute at the boundary layer when metals contact, and a electrostatic potential is created, which is called Contact Potential (V). 1 2 The diagram of potential at a metal contact V kt N 12 V 2 V1 ln N e Where V 1,V 2 - Escape potential of metal 1 and metal 2 respectively; 1 2

(1)Contact Potential & Thermoelectric Potential Tao Deng, dengtao@sjtu.edu.cn 41 The thermoelectric Potential of this circuit is : T V 12 V12 1 12 T2 kt N kt 1 1 2 12 V2 V1 ln V2 V1 ln e N2 e N N 1 2 k N 12 T1 T2 ln N e 1 2

(2)Thermal potential The temperature gradient will make electrons move from the high temperature end to the low temperature end, so an electric field will be formed, which is against the further diffusion of electrons. When the electric force F e equals to the thermal diffusion force F T, a static thermoelectric field V 1 (T 1,T 2 )was formed between two ends of Metal 1. V 2 (T 1,T 2 ) is also formed between ends of Metal 2 Tao Deng, dengtao@sjtu.edu.cn 42

Tao Deng, dengtao@sjtu.edu.cn 43 (2)Thermal potential For the circuit formed by Metal 1 & Metal 2, the directions of thermoelectric potentials are opposite. Even if the temperature difference between the ends of these two metals is the same, the two thermoelectric potentials won t be the same because of the difference of materials. The thermal potential of the circuit is : T V T V T, T V T T 12 V12 1 12 2 2 1 2 1 1, 2

Tao Deng, dengtao@sjtu.edu.cn 44 (3)Application of Seebeck effect Semiconductor Seebeck effect is larger than that of metals so semiconductors are used for thermoelectric power generation, and metals are used mainly for measuring temperatures; (1)Temperature measurement Pt Rh-Pt: can measure the temperature as high as 1700 ; Ni Cr-Ni Si:has a high sensitivity Cu- konstantan alloy :is used in the range from 15K to room temperature; (2) Thermoelectric power generation small, light weight, simple; suitable for spacecrafts, undersea cables system, lighthouse on the sea, oil wells, the assistant power source for stations on uninhabited islands, cardiac pacemaker.

3.3.1.2 The 2 nd Effect-Peltier Effect Tao Deng, dengtao@sjtu.edu.cn 45 When a return circuit is consist of two different kinds of metals with a current, one of the joints will releases heat, and another absorbs heat -- Peltier Effect. The heat released or taken in at the joints is called Peltier heat(q P ): Q P P AB It Where, P AB -Peltier Coefficient Peltier Effect is applied in electrical cooling.

3.3.1.3 The 3 rd Effect- Thomson Effect Thomson Effect: Absorption of heat or release of heat when there are both an electric current and a temperature field (heat current) inside a homogeneous conductor. When the direction of current and temperature field are the same, heat will be released. When the two directions are inverse, heat will be absorbed. Electrons are accelerated; Release heat Electrons are slowed down; Absorb heat Thomoson Heat Q T : Q T SItT Where S -Thomoson Coefficient (a) No external current. (b) External current has the same direction as the heat flow (c) External current has the opposite direction as the heat flow Tao Deng, dengtao@sjtu.edu.cn 46

3.3.2. Figure of merit Tao Deng, dengtao@sjtu.edu.cn 47 The comprehensive thermoelectric property of materials can be described by Figure of merit Z. Z S S 2 2 Where, S is the coefficient of the thermoelectric potential; σ, the conductivity; λ, the conductivity of heat; ρ, the resistivity. So Z is determined by both the electric and thermal properties, where the electric part(s 2 σ) is called power factor. The relationship between temperature and figure of merit of commercial thermoelectric material.

3.3.2. Piezoelectricity Tao Deng, dengtao@sjtu.edu.cn 48 Piezoelectricity is the electric charge that accumulates in certain solid materials] in response to applied mechanical stress Piezoelectric plate used to convert audio signal to sound waves

3.3.2. Pyroelectric Tao Deng, dengtao@sjtu.edu.cn 49 Pyroelectricity is the ability of certain materials to generate a temporary voltage when they are heated or cooled. Pyroelectricity vs. Thermoelectricity??

3.3.2. Ferroelectric Tao Deng, dengtao@sjtu.edu.cn 50 Ferroelectricity is a property of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. Or relating to a crystalline dielectric that can be given a permanent electric polarization through the application of an electric field.

The key concept of this chapter Tao Deng, dengtao@sjtu.edu.cn 51 Resistivity Electric conductivity Conductor Semiconductor Insulator Carrier Mobility Energy band theory Matthiessen law Electric conductance Ionic conductance Conductance of impurity ion Intrinsic ionic conductivity Intrinsic carrier Majority carrier Minority carrier Superconductivity Meissner effect Josephson effect BCS Theory Soliton Dielectric property Dielectric media Dielectric constant Polarization Electron triggered polarization relaxation Polarizability Dipole polarization Intensity of polarization Polarization of space charge Displacement polarization Complex permittivity Dielectric loss Conductance loss Polarization loss Loss of ionization Structural lose Loss angle tangent value Dielectric breakdown strength Electric breakdown Thermal breakdown Chemical breakdown Ferroelectricity Thermoelectric effect Seebeck effect Peltier effect Thomson effect Figure of merit Piezoelectricity Piezoelectric effect Pyroelectric property Photoconductivity

Homework Tao Deng, dengtao@sjtu.edu.cn 52 Read one paper related to flexible electronics, thermoelectric or piezoelectric that s published in Science, Nature, Advanced Materials, Nano Letters or other top English journals. Write one or two paragraphs of your learning in English after reading the paper.