Principles of electronic materials PYL-102

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1 Principles of electronic materials PYL-102 P. Das Broad Research Area: Nanoscale magnetism, electronic transport fluctuations

2 Course objective - providing basic foundation/training to understand electronic, optoelectonic and other solid state devices

3 Course-Content Energy bands in solids Classification of electronic materials: metals, semiconductors, insulators Free electron model. conductivity, concepts of Fermi surface Effective mass and holes Concepts of phonons Thermoelectricity Intrinsic, extrinsic semiconductors, degenerate semiconductors Metal-semiconductor junctions, p-n junctions Diffusion and drift transport - carrier lifetime and diffusion length Direct and Indirect band gaps Optical transitions, photon absorption, Exciton Photovoltaic effect Dielectrics and electrical polazation, depolarization field Piezoelectricity, Pyroelectricity and ferroelectricity Magnetism in metals - types of interactions, Magnetic susceptibility, Domains Magnetic anisotropies, Spin-orbit interactions

4 Suggested books Semiconductor Physics and Devices, by D. A. Neamen, McGraw Hill publishers Band theory and electronic properties of solids, by John Singleton, Oxford University Press Introduction to Solid State Physics, by Charles Kittel, Wiley publishers Solid State Physics by N. Aschcroft and N. Mermin

5 PYL-102 Course evaluation and attendance policy Attendance: Full attendance required, No entry after 5 minutes of the class. Grading/Evaluation: 1. Minor-I: 25 points 2. Minor II: 25 points 3. Major: 50 points No re-minor, No re-major!

6 Metallic state favoured by most elements

8 Metals Tightly bound ion cores Surrounded by a more loosly-bound valence electrons Large no. of nearest neighbor (hcp, fcc, bcc, etc.) -e Z - e( Z c - Z) - e( Z c - Z) - e( Z c - Z) - e( Z c - Z) Nucleus Core electrons Valence electrons Ionf Nucleus Core Conduction electrons

9 Array of widely spaced, small ion cores Mobile electrons move through the volume between the cores 0 (a) (b) Energy/V 0-1

10 The Drude model Electrons collide only with ion cores and nothing else! No interaction with each other (independent electron approximation) or with ions (free electron approximation) between collisions! collisions are instantaneous, results in change in velocity Electron experiences a collision a rate 1 (scattering rate) electrons achieve thermal equilibrium with surroundings only through collisions

11 Failure of Drude s model Drude s results (equipartition of energy) C = 3 2 nk B C (obtained from M-B statistics for classical gas of density n) Sp. heat is T-independent T

12 Failure of Drude s model Experimental heat capacity Drude s results (equipartition of energy) 0.2 Sample: Co A C = 3 2 nk B Sp. heat is T-independent -1-1 C (J mol K ) 0.1 C B T (K) Ref.: G. Duyckaerts, Physica 6, 817 (1939).

13 Failure of Drude s model Drude s results (equipartition of energy) C = 3 2 nk B -1-1 C (J mol K ) A C B Sp. heat is T-independent T (K) C V = T + T 3 Electrons Phonons Ref.: G. Duyckaerts, Physica 6, 817 (1939).

14 Specific heat of Cu c/t (10 4 J Mol 1 K 2 )

15 Quantum mechanical treatment of electrons in solids

16 position coordinate X

17 Filling of quantized energy states E N klein E F E n 0 x

18 k y Area per point = (2 ) 2 L x L y k x No. of states per unit k-space area = L x L y (2 ) 2

20 Density of states, F-D distribution function, etc.. a) f(e) n(e) D(E) 1 T = 0 b) 0 E F E

21 F-D distribution function T = 0 T 0

22 T- dependence of F-D distribution function 6/kB, in units of K

24 k x =2 /L

25 Radial Probability density function of hydrogen atom/s Isolated atom Two atoms Splitting of states

26 Formation of energy bands

27 Potential energy for an isolated atom (e.g., hydrogen atom) U ( r) e r 2

28 Potential energy for a multiple atoms (periodically placed) PE(r) U r 0 V(x) a a x = 0 a 2a 3a x = L

29 Kronig-Penney simplification of 1D potential 0 V(x) a a x = 0 a 2a 3a x = L Ψ I Ψ II

30 U, potential energy I Bloch function k(x) =u k (x) e ik xx

31 k x =2 /L

32 P sin a a Energy band in Kronnig Penney model + cos a = cos ka P sin a a + cos a E t (PI&) sin Ka + cos Ka Allowed Forbidden +1-1 a

33 Energy band in Kronnig Penney model

34 Energy band in Kronnig Penney model E 8mw2 h 2

35 Energy band in Kronnig Penney model

36 Energy band in Kronnig Penney model Extended zone scheme Reduced zone scheme

37 E 8mw2 h 2 Energy band in Kronnig Penney model Reduced zone scheme

38 Energy band in weak periodic potential Reduced zone scheme G E E 2 (k) 1 E 1 (k) E 3 (k) -2π/a -π/a 0 π/a 2π/a k x Abb. 7.2.

39 Energy band in weak periodic potential Reduced zone scheme V ~ 0 Reduced zone scheme V ~ finite E (a) E (b) E G Free electrons freie Elektronen 2. Band Bandlücke gap -2π/a E 2 (k) -π/a 1 0 E 1 (k) π/a E 3 (k) 2π/a k x Band- Elektronen Band electrons -π/a 1. Band 0 π/a k x -π/a 0 π/a k x

40 Energy band in weak periodic potential Reduced zone scheme Repeated Zone Scheme (a) E (b) E Free electrons freie Elektronen 2. Band Bandlücke gap Band- Elektronen Band electrons -π/a 1. Band 0 π/a k x -π/a 0 π/a k x

41 Band structure of Cu Text Wave vector

42 Velocity and effective mass of Bloch electrons

43 Metal and insulator: band structure conduction band Valence band Metal Valence band Valence band conduction band Valence band Insulator 0 a Valence band

44 electrical resistivity Electrical conductivity semiconductor (insulator for T 0) superconductor metal temperature Temperature

45 Wigner Seitz cell for 2D lattices

46 Wigner Seitz cell for 3D (BCC) lattices

47 Resistivity of materials H. Queisser et al., Science, 1998

48 Energy bands in metal, semiconductor and insulators Energy metal T=0 semi conductor Insulator EC EC Fermi energy EC EC Valence bands Abb

49 Energy bands in metal, semiconductor and insulators Energy metal semi conductor Insulator EC EC Fermi energy EC EC Valence bands Abb

50 Energy bands in metal, semiconductor and insulators Energy metal semi conductor Insulator EC EC Fermi energy EC EC Valence bands Abb

51 electrical resistivity Electrical conductivity semiconductor (insulator for T 0) superconductor metal temperature Temperature

52 Semiconducting materials III IV V VI VII Material Stoff / Band E g gap ev (ev) 5 B 6 C 7 N 8 O 9 F 13 Al 14 Si 15 P 16 S 17 Cl 31 Ga 32 Ge 33 As 49 In 50 Sn 51 Sb 52 Te 34 Se 35 Br 53 I Abb Elemente im Periodensy Diamond Diamant 5,60 Si 1,11 Ge 0,66 GaAs InSb GaN InP CdS

53 Energy bands in metal, semiconductor and insulators 4+ 2e 4+ 2e 4+ 2e 4+ 2e 4+ 2e 4+ 2e Abb

54 Energy bands for Si, Ge Energy Energy Wave vector Wave vector

55 Energy bands for Si, Ge Energy Energy [000] [100] Wave vector [111] [000] Wave vector

56 Energy bands for GaAs

57 Energy bands for Si, Ge Light holes Heavy holes

58 Intrinsic carrier concentration - T dependence

59 Doping for Si

60 ( ) Energy bands and carrier concentration in Semi Cond. Conduction band Fermi energy Valence band Abb Zur Erklärung der temperaturunabhängigen

61 Doping in semiconductor e e e e e e e e 4+ e e e e e 4+ e e As e e e e e 4+ e e 4+ e e

62 Ionization energy (mv) Impurity Si Ge P As B Al Donors Acceptors Impurity GaAs Se 6 Te 5.8 Si* 5.8 Ge 6.1 Be 28 Si 34.5 Ge* 40.4

63 Extrinsic semiconductor

64 Extrinsic semiconductor

65 Extrinsic semiconductor

66 Temperature dependence of carrier concentration ln n e a) Intrinsic n e = N D Saturation/ Störstellenerschöpfung Extrinsic Eigenleitung Störstellenreserve Partial ionization n e<nd 1/T

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