# Bài giảng Vật liệu học - Chapter 6: Electrical properties - Nguyễn Văn Dũng

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.

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1 Chapter 6 Electrical properties  Ohm’s law CuuDuongThanCong.com https://fb.com/tailieudientucntt 2 • Ohm's Law: V = I R voltage drop (volts = J/C) C = Coulomb resistance (Ohms) current (amps = C/s)    1  • Conductivity,  • Resistivity, : -- a material property that is independent of sample size and geometry    RA l surface area of current flow current flow path length CuuDuongThanCong.com https://fb.com/tailieudientucntt 3  Which will have the greater resistance?  Analogous to flow of water in a pipe  Resistance depends on sample geometry and size. D 2D  R1  2  D 2       2  8 D2   2  R2    2D 2       2   D2  R1 8 CuuDuongThanCong.com https://fb.com/tailieudientucntt 4 Further definitions J =  E <= another way to state Ohm’s law J  current density E  electric field potential = V/ flux a like area surface current A I  Electron flux conductivity voltage gradient J =  (V/ ) CuuDuongThanCong.com https://fb.com/tailieudientucntt 5 CuuDuongThanCong.com https://fb.com/tailieudientucntt 6 CuuDuongThanCong.com https://fb.com/tailieudientucntt 7 CuuDuongThanCong.com https://fb.com/tailieudientucntt 8 • Room temperature values (Ohm-m)-1 = ( m)-1= S m-1 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 10 -4 Germanium 2 x 10 0 GaAs 10 -6 SEMICONDUCTORS semiconductors Polystyrene <10 -14 Polyethylene 10 -15 -10 -17 Soda-lime glass 10 Concrete 10 -9 Aluminum oxide <10 -13 CERAMICS POLYMERS insulators -10 -10 -11 CuuDuongThanCong.com https://fb.com/tailieudientucntt 9 CuuDuongThanCong.com https://fb.com/tailieudientucntt 10 What is the minimum diameter (D) of the wire so that V < 1.5 V? (=6.07 x 107 (Ohm-m)-1) EXAMPLE: Cu wire I = 2.5 A - + V Solve to get D > 1.87 mm < 1.5 V 2.5 A 6.07 x 107 (Ohm-m)-1 100 m I V A R     4 2D  100 m CuuDuongThanCong.com https://fb.com/tailieudientucntt 11 Energy levels of an isolated atom CuuDuongThanCong.com https://fb.com/tailieudientucntt 12 CuuDuongThanCong.com https://fb.com/tailieudientucntt 13 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. CuuDuongThanCong.com https://fb.com/tailieudientucntt 14 ELECTRON ENERGY BAND STRUCTURES CuuDuongThanCong.com https://fb.com/tailieudientucntt 15 BAND STRUCTURE REPRESENTATION CuuDuongThanCong.com https://fb.com/tailieudientucntt 16 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. CuuDuongThanCong.com https://fb.com/tailieudientucntt 17 Metals Insulators Semiconductors CuuDuongThanCong.com https://fb.com/tailieudientucntt 18 CONDUCTION & ELECTRON TRANSPORT • Metals (Conductors): -- for metals empty energy states are adjacent to filled states. -- two types of band structures for metals -- thermal energy excites electrons into empty higher energy states. - partially filled band - empty band that overlaps filled band filled band Energy partly filled band empty band GAP fi lle d s ta te s Partially filled band Energy filled band filled band empty band fi lle d s ta te s Overlapping bands CuuDuongThanCong.com https://fb.com/tailieudientucntt 19 • Insulators: -- wide band gap (> 4 eV) -- few electrons excited across band gap Energy filled band filled valence band fi lle d s ta te s GAP empty band conduction • Semiconductors: -- narrow band gap (< 4 eV) -- more electrons excited across band gap Energy filled band filled valence band fi lle d s ta te s GAP ? empty band conduction CuuDuongThanCong.com https://fb.com/tailieudientucntt 20 where, E is the electron energy, EF is the Fermi energy, and T is the absolute temperature. Its physical meaning is that: f(E) is the probability of occupancy for an electron energy state at energy E by an electron. That is, the probability that this state is occupied by an electron is f(E), and the probability that it is vacant is 1 - f(E). The Fermi energy is the maximum energy occupied by an electron at 0K. Fermi function CuuDuongThanCong.com https://fb.com/tailieudientucntt 21 CuuDuongThanCong.com https://fb.com/tailieudientucntt 22 CuuDuongThanCong.com https://fb.com/tailieudientucntt 23 CHARGE CARRIERS IN INSULATORS AND SEMICONDUCTORS Two types of electronic charge carriers: Free Electron – negative charge – in conduction band Hole – positive charge – in valence band Move at different speeds - drift velocities CuuDuongThanCong.com https://fb.com/tailieudientucntt 24 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. CuuDuongThanCong.com https://fb.com/tailieudientucntt 25 INTRINSIC SEMICONDUCTION IN TERMS OF ELECTRON AND HOLE MIGRATION electric field electric field electric field • Electrical Conductivity given by: # electrons/m3 electron mobility # holes/m3 hole mobility he epen   Concept of electrons and holes: + - electron hole pair creation + - no applied applied valence electron Si atom applied electron hole pair migration CuuDuongThanCong.com https://fb.com/tailieudientucntt 26 26 NUMBER OF CHARGE CARRIERS Intrinsic Conductivity   )s/Vm 45.085.0)(C10x6.1( m)(10 219 16         he i e n For GaAs ni = 4.8 x 10 24 m-3 For Si ni = 1.3 x 10 16 m-3 • Ex: GaAs he epen  • for intrinsic semiconductor n = p = ni   = ni|e|(e + h) CuuDuongThanCong.com https://fb.com/tailieudientucntt 27 INTRINSIC SEMICONDUCTORS: CONDUCTIVITY VS T • Data for Pure Silicon: --  increases with T -- opposite to metals material Si Ge GaP CdS band gap (eV) 1.11 0.67 2.25 2.40 Selected values from Table 18.3, Callister & Rethwisch 8e.  ni e E gap / kT    ni e e  h  CuuDuongThanCong.com https://fb.com/tailieudientucntt 28 Intrinsic semiconductor - A semiconductor in which properties are controlled by the element or compound that makes the semiconductor and not by dopants or impurities. Extrinsic semiconductor - A semiconductor prepared by adding dopants, which determine the number and type of charge carriers. Doping - Deliberate addition of controlled amounts of other elements to increase the number of charge carriers in a semiconductor. CuuDuongThanCong.com https://fb.com/tailieudientucntt 29 Extrinsic semiconductor (doped with an electron donor) Without thermal excitation With thermal excitation CuuDuongThanCong.com https://fb.com/tailieudientucntt 30 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. CuuDuongThanCong.com https://fb.com/tailieudientucntt 31 Energy bands Intrinsic semiconductor Extrinsic semiconductor (doped with an electron donor) CuuDuongThanCong.com https://fb.com/tailieudientucntt 32 Extrinsic semiconductor (doped with an electron acceptor) Without thermal excitation With thermal excitation CuuDuongThanCong.com https://fb.com/tailieudientucntt 33 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. CuuDuongThanCong.com https://fb.com/tailieudientucntt 34 Energy bands Intrinsic semiconductor Extrinsic semiconductor (doped with an electron acceptor) material Si Ge band gap (eV) 1.11 0.67 CuuDuongThanCong.com https://fb.com/tailieudientucntt 35 CuuDuongThanCong.com https://fb.com/tailieudientucntt 36 Defect semiconductor (excess semiconductor Zn1+xO) Zn+ ion serves as an electron donor. CuuDuongThanCong.com https://fb.com/tailieudientucntt 37 Energy bands of Zn1+xO CuuDuongThanCong.com https://fb.com/tailieudientucntt 38 Defect semiconductor (deficit semiconductor Ni1-xO) Ni3+ ion serves as an electron acceptor. CuuDuongThanCong.com https://fb.com/tailieudientucntt 39 Energy bands of Ni1-xO CuuDuongThanCong.com https://fb.com/tailieudientucntt 40 CuuDuongThanCong.com https://fb.com/tailieudientucntt 41 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. CuuDuongThanCong.com https://fb.com/tailieudientucntt 42 Temperature Effect - When the temperature of a metal increases, thermal energy causes the atoms to vibrate Effect of Atomic Level Defects - Imperfections in crystal structures scatter electrons, reducing the mobility and conductivity of the metal CuuDuongThanCong.com https://fb.com/tailieudientucntt 43 CuuDuongThanCong.com https://fb.com/tailieudientucntt 44 T     where = temperature coefficient of electrical resistivity Change of resistivity with temperature for a metal CuuDuongThanCong.com https://fb.com/tailieudientucntt 45 CuuDuongThanCong.com https://fb.com/tailieudientucntt 46 © 2 0 0 3 B ro o k s/ C o le , a d iv is io n o f T h o m so n L ea rn in g , In c. T h o m so n L ea rn in g ™ i s a tr ad em ar k u se d h er ei n u n d er l ic en se . CuuDuongThanCong.com https://fb.com/tailieudientucntt 47  = q n  For a metal, σ decreases with increasing temperature because μ decreases with increasing temperature. For a semiconductor, σ increases with increasing temperature because n and/or p increases with increasing temperature. CuuDuongThanCong.com https://fb.com/tailieudientucntt 48 where Eg = energy band gap between conduction and valence bands, k = Boltzmann's constant, and T = temperature in K. The factor of 2 in the exponent is because the excitation of an electron across Eg produces an intrinsic conduction electron and an intrinsic hole. ,en /2kTEg For a semiconductor CuuDuongThanCong.com https://fb.com/tailieudientucntt 49 Taking natural logarithms, Changing the natural logarithms to logarithms of base 10, .eσσ /2kTE o g . 2kT E σlnσln g o  . (2.3)2kT E σlogσlog g o  CuuDuongThanCong.com https://fb.com/tailieudientucntt 50 Conductivity of an ionic solid , )A + C(n q = An q + Cn q =  where n = number of Schottky defects per unit volume C = mobility of cations, A = mobility of anions. CuuDuongThanCong.com https://fb.com/tailieudientucntt 51 ,nnn ei  where n = total concentration of conduction electrons, ni = concentration of intrinsic conduction electrons, ne = concentration of extrinsic conduction electrons. An n-type semiconductor CuuDuongThanCong.com https://fb.com/tailieudientucntt 52 ,eDD   , +N = n De . e n kT2/Eg- i  . e n /kTE- D e . < < nn ei .pp i CuuDuongThanCong.com https://fb.com/tailieudientucntt 53 However , .pp i No extrinsic holes, thus pi = ni Thus, p = ni CuuDuongThanCong.com https://fb.com/tailieudientucntt 54 enn  . 0 p  . qp + qn = pn  nqn   CuuDuongThanCong.com https://fb.com/tailieudientucntt 55 , p + p = p ei where p = total concentration of conduction holes pi = concentration of intrinsic holes, pe = concentration of extrinsic holes. A p-type semiconductor CuuDuongThanCong.com https://fb.com/tailieudientucntt 56 , A - e - +A  , h + + A - A  , N = p Ae  , e p kT2/Eg- i . e - p /kTEA e CuuDuongThanCong.com https://fb.com/tailieudientucntt 57 p < < p ei .nn i . p =n i p p e . 0n  . qp + qn = pn  qn  p CuuDuongThanCong.com https://fb.com/tailieudientucntt 58 THE MASS-ACTION LAW Product of n and p is a constant for a particular semiconductor at a particular temperature CuuDuongThanCong.com https://fb.com/tailieudientucntt 59 .ppnn ii  .nnp 2i Siforcm101.5n 310i  .Geforcm102.5n 313i  Intrinsic semiconductor This equation applies whether the semiconductor is doped or not. CuuDuongThanCong.com https://fb.com/tailieudientucntt 60  De Nnn DD NN  .Nn D . N n = n n = p D 2 i 2 i Consider an n-type semiconductor. (Donor exhaustion) CuuDuongThanCong.com https://fb.com/tailieudientucntt 61  ANpp e A-A NN  .Np A . N n = n = 2 i 2 i Ap n Consider an p-type semiconductor. (Donor exhaustion) CuuDuongThanCong.com https://fb.com/tailieudientucntt 62 Conducting polymers THE NOBEL PRIZE IN CHEMISTRY, 2000: CONDUCTIVE POLYMERS  Professor Alan J. Heeger at the University of California at Santa Barbara, USA  Professor Alan G. MacDiarmid at the University of Pennsylvania, USA and  Professor Hideki Shirakawa at the University of Tsukuba, Japan rewarded the Nobel Prize in Chemistry for 2000 “for the discovery and development of electrically conductive polymers”. Conjugated polymers are organic macromolecules that are characterized by a backbone chain of alternating double- and single-bonds. Their overlapping p-orbitals create a system of delocalised π-electrons, which can result in interesting and useful optical and electronic properties. CuuDuongThanCong.com https://fb.com/tailieudientucntt 63 Conductivity of conductive polymers compared to those of other materials, from quartz (insulator) to copper (conductor). Polymers may also have conductivities corresponding to those of semiconductors. CuuDuongThanCong.com https://fb.com/tailieudientucntt 64 CuuDuongThanCong.com https://fb.com/tailieudientucntt Chemical structures of some conductive polymers. From top left clockwise: polyacetylene; polyphenylene vinylene; polypyrrole (X = NH) and polythiophene (X = S); and polyaniline (X = NH/N) and polyphenylene sulfide (X = S). A key property of a conductive polymer is the presence of conjugated double bonds along the backbone of the polymer. In conjugation, the bonds between the carbon atoms are alternately single and double. The presence of C5 makes it impossible for the π electrons of the C6-C7 pi bond to join the conjugated system on the first four carbons. CuuDuongThanCong.com https://fb.com/tailieudientucntt 66 CuuDuongThanCong.com https://fb.com/tailieudientucntt 67 Conjugation is not enough to make the polymer material conductive. In addition – and this is what the dopant does – charge carriers in the form of extra electrons or ”holes” have to be injected into the material. The “doped” form of polyacetylene had a conductivity of 105 Siemens per meter, which was higher than that of any previously known polymer. As a comparison, Teflon has a conductivity of 10–16 S.m–1and silver and copper 108 S.m–1. CuuDuongThanCong.com https://fb.com/tailieudientucntt 68 • The halogen doping that transforms polyacetylene to a good conductor of electricity is oxidation (or p-doping). • Reductive doping (called n-doping) is also possible using, e.g., an alkali metal. The doped polymer is thus a salt. However, it is not the counter ions, I3 – or Na+, but the charges on the polymer that are the mobile charge carriers. Mechanism of polymer conductivity – role of doping CuuDuongThanCong.com https://fb.com/tailieudientucntt 69 Dielectric materials CuuDuongThanCong.com https://fb.com/tailieudientucntt 70 CuuDuongThanCong.com https://fb.com/tailieudientucntt 71 CuuDuongThanCong.com https://fb.com/tailieudientucntt 72 CuuDuongThanCong.com https://fb.com/tailieudientucntt 73  Dielectric strength is defined as the maximum voltage required to produce a dielectric breakdown through the material and is expressed as Volts per unit thickness. The higher the dielectric strength of a material the better its quality as an insulator.  Electrical breakdown or dielectric breakdown is when current flows through an electrical insulator when the voltage applied across it exceeds the breakdown voltage. This results in the insulator becoming electrically conductive. CuuDuongThanCong.com https://fb.com/tailieudientucntt 74 CuuDuongThanCong.com https://fb.com/tailieudientucntt 75 CuuDuongThanCong.com https://fb.com/tailieudientucntt 76 CuuDuongThanCong.com https://fb.com/tailieudientucntt 77 CuuDuongThanCong.com https://fb.com/tailieudientucntt 78 CuuDuongThanCong.com https://fb.com/tailieudientucntt 79 CuuDuongThanCong.com https://fb.com/tailieudientucntt 80 Ferroelectric - A material that shows spontaneous and reversible dielectric polarization. Piezoelectric – A material that develops voltage upon the application of a stress and develops strain when an electric field is applied. CuuDuongThanCong.com https://fb.com/tailieudientucntt 81 CuuDuongThanCong.com https://fb.com/tailieudientucntt ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. 82 The (a) direct and (b) converse piezoelectric effect. In the direct piezoelectric effect, applied stress causes a voltage to appear. In the converse effect (b), an applied voltage leads to development of strain. CuuDuongThanCong.com https://fb.com/tailieudientucntt 83 CuuDuongThanCong.com https://fb.com/tailieudientucntt 84 CuuDuongThanCong.com https://fb.com/tailieudientucntt