FYS Vår 2015 (Kondenserte fasers fysikk)

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "FYS3410 - Vår 2015 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v15/index.html"

Transcription

1 FYS Vår 015 (Kondenserte fasers fysikk) Pensum: Introduction to Solid State Physics by Charles Kittel (Chapters 1-9 and 17, 18, 0, and Appendix D) Andrej Kuznetsov delivery address: Department of Physics, PB 1048 Blindern, 0316 OSLO Tel: , e-post: visiting address: MiNaLab, Gaustadaleen 3a

2 FYS3410 Lectures (based on C.Kittel s Introduction to SSP, Chapters 1-9, 17,18,0) Module I Periodic Structures and Defects (Chapters 1-3, 0) 6/1 Introduction. Crystal bonding. Periodicity and lattices, reciprocal space h 7/1 Laue condition, Ewald construction, interpretation of a diffraction experiment Bragg planes and Brillouin zones 4h 8/1 Elastic strain and structural defects in crystals h 30/1 Atomic diffusion and summary of Module I h Module II Phonons (Chapters 4 and 5) 09/ Vibrations, phonons, density of states, and Planck distribution h 10/ Lattice heat capacity: Dulong-Petit, Einstien and Debye models. Planck distribution. Comparison of different models 4h 11/ Thermal conductivity h 13/ Thermal expansion and summary of Module II. h Module III Electrons (Chapters 6, 7, 18 - pp , and Appendix D) 3/ Free electron gas (FEG) versus free electron Fermi gas (FEFG) h 4/ Effect of temperature Fermi- Dirac distribution. Heat capacity of FEFG. DOS in nanostructures. Origin of the band gap 4h 5/ Nearly free electron model. Kronig-Penney model. Empty lattice approximation. h 7/ Number of orbitals in a band. Summary of Module III. h Module IV Semiconductors and interfaces (Chapters 8, 9-pp 3-31, 17) 09/3 Recap of energy bands. Metals versus semiconductors. Surfaces and interfaces. h 10/3 Effective mass method. Intrinsic carrier generation elctrons and holes. Localized levels for hydrogen-like impurities donors and acceptors. Doping. 4h 11/3 Carrier statistics in semiconductors. h 13/3 p-n junctions. Examples of optoelectronic devices. Summary of Module IV. h

3 Lecture 13: Recap of energy bands. Metals versus semiconductors. Surfaces and interfaces. Introduction to the effective mass method Recap of energy bands Metals versus semiconductors Surfaces and interfaces Introduction to the effective mass method

4 Lecture 13: Recap of energy bands. Metals versus semiconductors. Surfaces and interfaces. Introduction to the effective mass method Recap of energy bands Metals versus semiconductors Surfaces and interfaces Introduction to the effective mass method

5 Why do we get a gap? Let us start with a free electron in a periodic crystal, but ignore the atomic potentials for now At the interface (BZ), we have two counter-propagating waves e ikx, with k = p/a, that Bragg reflect and form standing waves y E -p/a p/a k

6 Why do we get a gap? y+ ~ cos(px/a) peaks at atomic sites y - ~ sin(px/a) peaks in between y + y - E -p/a p/a k

7 Let s now turn on the atomic potential The y + solution sees the atomic potential and increases its energy The y - solution does not see this potential (as it lies between atoms) Thus their energies separate and a gap appears at the BZ This happens only at the BZ where we have standing waves U 0 y + y - -p/a p/a k

8 Lecture 13: Recap of energy bands. Metals versus semiconductors. Surfaces and interfaces. Introduction to the effective mass method Recap of energy bands Metals versus semiconductors Surfaces and interfaces Introduction to the effective mass method

9

10

11 Lecture 13: Recap of energy bands. Metals versus semiconductors. Surfaces and interfaces. Introduction to the effective mass method Recap of energy bands Metals versus semiconductors Surfaces and interfaces Introduction to the effective mass method

12

13

14

15

16

17

18

19

20 Lecture 13: Recap of energy bands. Metals versus semiconductors. Surfaces and interfaces. Introduction to the effective mass method Recap of energy bands Metals versus semiconductors Surfaces and interfaces Introduction to the effective mass method

21

22

23 Hole - an electron near the top of an energy band The hole can be understood as an electron with negative effective mass An electron near the top of an energy band with a negative curvature will have a negative effective mass A negatively charged particle with a negative mass will be accelerated like a positive particle with a positive mass (a hole!) E(K) F = m * a = QE p/a K Without the crystal lattice, the hole would not exist! The hole is a pure consequence of the periodic potential operating in the crystal!!!

24 E(K) and E(x) E(K) E(x) E C - conduction band K E V + valence band E g x p/a

25 Generation and Recombination of electron-hole pairs E(x) conduction band E C - - E V + valence band + x

26 Real 3D lattices, e.g. FCC, BCC, diamond, etc. a E(K x ) E(K y ) b y x p/a K x p/b K y Different lattice spacings lead to different curvatures for E(K) and effective masses that depend on the direction of motion.

27 Real 3D lattices, e.g. FCC, BCC, diamond, etc. m 1 1 c, ij E kk i j heavy m * (smaller d E/dK ) light m * (larger d E/dK )

28 Real 3D lattices, e.g. FCC, BCC, diamond, etc. Ge Si GaAs

29 Direct and inderect band gap in semiconductors energy (E) and momentum (ħk) must be conserved energy is released when a quasi-free electron recombines with a hole in the valence band: ΔE = E g does this energy produce light (photon) or heat (phonon)? indirect bandgap: ΔK is large but for a direct bandgap: ΔK=0 photons have very low momentum but lattice vibrations (heat, phonons) have large momentum Conclusion: recombination (e - +h + ) creates light in direct bandgap materials (GaAs, GaN, etc) heat in indirect bandgap materials (Si, Ge)

30 FYS Vår 015 (Kondenserte fasers fysikk) Pensum: Introduction to Solid State Physics by Charles Kittel (Chapters 1-9 and 17, 18, 0, and Appendix D) Andrej Kuznetsov delivery address: Department of Physics, PB 1048 Blindern, 0316 OSLO Tel: , e-post: visiting address: MiNaLab, Gaustadaleen 3a

31 FYS3410 Lectures (based on C.Kittel s Introduction to SSP, Chapters 1-9, 17,18,0) Module I Periodic Structures and Defects (Chapters 1-3, 0) 6/1 Introduction. Crystal bonding. Periodicity and lattices, reciprocal space h 7/1 Laue condition, Ewald construction, interpretation of a diffraction experiment Bragg planes and Brillouin zones 4h 8/1 Elastic strain and structural defects in crystals h 30/1 Atomic diffusion and summary of Module I h Module II Phonons (Chapters 4 and 5) 09/ Vibrations, phonons, density of states, and Planck distribution h 10/ Lattice heat capacity: Dulong-Petit, Einstien and Debye models. Planck distribution. Comparison of different models 4h 11/ Thermal conductivity h 13/ Thermal expansion and summary of Module II. h Module III Electrons (Chapters 6, 7, 18 - pp , and Appendix D) 3/ Free electron gas (FEG) versus free electron Fermi gas (FEFG) h 4/ Effect of temperature Fermi- Dirac distribution. Heat capacity of FEFG. DOS in nanostructures. Origin of the band gap 4h 5/ Nearly free electron model. Kronig-Penney model. Empty lattice approximation. h 7/ Number of orbitals in a band. Summary of Module III. h Module IV Semiconductors and interfaces (Chapters 8, 9-pp 3-31, 17) 09/3 Recap of energy bands. Metals versus semiconductors. Surfaces and interfaces. h 10/3 Effective mass method. Intrinsic carrier generation elctrons and holes. Localized levels for hydrogen-like impurities donors and acceptors. Doping. 4h 11/3 Carrier statistics in semiconductors. h 13/3 p-n junctions. Examples of optoelectronic devices. Summary of Module IV. h

32 Lecture 14: Intrinsic and extrinsic semiconductors recap of the effective mass method analysis of E(k) and it s 1st and nd deriviates band-to-band transiotions: intrinsic semiconductors hydrogen-like impurities n- and p-type semiconductors equilibrium charge carrier concentration carriers in non-eqilibrium conditions: diffusion, generation and recombination

33 Lecture 14: Intrinsic and extrinsic semiconductors recap of the effective mass method analysis of E(k) and it s 1st and nd deriviates band-to-band transitions: intrinsic semiconductors hydrogen-like impurities n- and p-type semiconductors equilibrium charge carrier concentration carriers in non-eqilibrium conditions: diffusion, generation and recombination

34 Dynamics of electrons in a band The external electric field causes a change in the k vectors of all electrons: dk d k e E F ee dt dt E If the electrons are in a partially filled band, this will break the symmetry of electron states in the 1 st BZ and produce a net current. But if they are in a filled band, even though all electrons change k vectors, the symmetry remains, so J = 0. p a v p a k x k x When an electron reaches the 1 st BZ edge (at k = p/a) it immediately reappears at the opposite edge (k = -p/a) and continues to increase its k value. As an electron s k value increases, its velocity increases, then decreases to zero and then becomes negative when it re-emerges at k = -p/a!!

35 Dynamics of electrons in a band Negative effective mass!

36 Real 3D lattices, e.g. FCC, BCC, diamond, etc. a E(K x ) E(K y ) b y x p/a K x p/b K y Different lattice spacings lead to different curvatures for E(K) and effective masses that depend on the direction of motion.

37 Real 3D lattices, e.g. FCC, BCC, diamond, etc. m 1 1 c, ij E kk i j heavy m * (smaller d E/dK ) light m * (larger d E/dK )

38 Real 3D lattices, e.g. FCC, BCC, diamond, etc. Ge Si GaAs

39 Lecture 14: Intrinsic and extrinsic semiconductors recap of the effective mass method analysis of E(k) and it s 1st and nd deriviates band-to-band transisions: intrinsic semiconductors hydrogen-like impurities n- and p-type semiconductors equilibrium charge carrier concentration carriers in non-eqilibrium conditions: diffusion, generation and recombination

40 Band-to-band transitions 40

41 Band-to-band transitions valence band conduction band

42 Band-to-band transitions valence band conduction band gap size (ev) InSb 0.18 InAs 0.36 Ge 0.67 Si 1.11 GaAs 1.43 SiC.3 diamond 5.5 MgF 11

43 Band-to-band transitions valence band conduction band

44 Band-to-band transitions electrons in the conduction band (CB) missing electrons (holes) in the valence band (VB)

45 Band-to-band transitions

46 Band-to-band transitions free electrons VB maximum as E=0 conduction band valence band

47 Band-to-band transitions electrons in the conduction band (CB) missing electrons (holes) in the valence band (VB)

48 Band-to-band transitions for the conduction band for the valence band Both are Boltzmann distributions! This is called the non-degenerate case.

49 Band-to-band transitions

50 Band-to-band transitions CBM μ VBM

51 Band-to-band transitions In quantum wells

52 Lecture 14: Intrinsic and extrinsic semiconductors recap of the effective mass method analysis of E(k) and it s 1st and nd deriviates band-to-band transiotions: intrinsic semiconductors hydrogen-like impurities n- and p-type semiconductors equilibrium charge carrier concentration carriers in non-eqilibrium conditions: diffusion, generation and recombination

53 Hydrogen like impurities in semiconductors P donor in Si can be modeled d as hydrogen-like atom Hydrogen atom Hydrogen-like donor

54 Hydrogen atom - Bohr model ) (4 ) (4 energy: Total 4 1 Kineticenergy: 4 4 Potentialenergy: ) ( 4 4 1,,3..., for 4 1 n e mz E K r Ze V K E r Ze mv K r Ze dr r Ze V n Ze mr n v mze n r mr n mr n mr r mv Ze n n mvr L r v m r Ze r p p p p p p p p p p p

55 Hydrogen atom - Bohr model E 4 m0 q H. (4p0) 13 6 ev

56 Hydrogen like impurities in semiconductors Hydrogen-like donor Instead of m 0, we have to use m n*. Instead of o, we have to use K s o. K s is the relative dielectric constant of Si (K s, Si = 11.8). E 4 m0 q H. (4p0) 13 6 ev E d m * n 4 q (4π K ) s ev m * n m0 0 Ks ev

57 Hydrogen like impurities in semiconductors n 0 =0 n 0 E g E ID E g E ID E i E d n d E i E d p 0 =0 p 0

58 Lecture 14: Intrinsic and extrinsic semiconductors recap of the effective mass method analysis of E(k) and it s 1st and nd deriviates band-to-band transiotions: intrinsic semiconductors hydrogen-like impurities n- and p-type semiconductors equilibrium charge carrier concentration carriers in non-eqilibrium conditions: diffusion, generation and recombination

59 N- and p-type semiconductors Intrinsic semiconductor a) Energy level diagrams showing the excitation of an electron from the valence band to the conduction band. The resultant free electron can freely move under the application of electric field. b) Equal electron & hole concentrations in an intrinsic semiconductor created by the thermal excitation of electrons across the band gap

60 N- and p-type semiconductors n-type Semiconductor a) Donor level in an n-type semiconductor. b) The ionization of donor impurities creates an increased electron concentration distribution.

61 N- and p-type semiconductors p-type Semiconductor a) Acceptor level in an p-type semiconductor. b) The ionization of acceptor impurities creates an increased hole concentration distribution

62 N- and p-type semiconductors

63 N- and p-type semiconductors Intrinsic material: A perfect material with no impurities. n p n n& p & n i i E exp( k g B ) T are the electron, hole & intrinsic concentrations respectively. E g is the gap energy, T is Temperature. Extrinsic material: donor or acceptor type semiconductors. pn n i Majority carriers: electrons in n-type or holes in p-type. Minority carriers: holes in n-type or electrons in p-type.

64 N- and p-type semiconductors donor: impurity atom that increases n acceptor: impurity atom that increases p N-type material: contains more electrons than holes P-type material: contains more holes than electrons majority carrier: the most abundant carrier minority carrier: the least abundant carrier intrinsic semiconductor: n = p = n i extrinsic semiconductor: doped semiconductor

65 Lecture 14: Intrinsic and extrinsic semiconductors recap of the effective mass method analysis of E(k) and it s 1st and nd deriviates band-to-band transiotions: intrinsic semiconductors hydrogen-like impurities n- and p-type semiconductors equilibrium charge carrier concentration carriers in non-eqilibrium conditions: diffusion, generation and recombination

66 Equilibrium charge carrier concentration in semiconductors Consider conditions for charge neutrality. The net charge in a small portion of a uniformly doped semiconductor should be zero. Otherwise, there will be a net flow of charge from one point to another resulting in current flow (that is against out assumption of thermal equilibrium). Charge/cm 3 = q p q n + q N D + q N A = 0 or p n + N D + N A = 0 where N D + = # of ionized donors/cm 3 and N A = # of ionized acceptors per cm 3. Assuming total ionization of dopants, we can write:

67 Equilibrium charge carrier concentration in semiconductors Assume a non-degenerately doped semiconductor and assume total ionization of dopants. Then, n p = n i ; electron concentration hole concentration = n i p n + N D N A = 0; net charge in a given volume is zero. Solve for n and p in terms of N D and N A We get: (n i / n) n + N D N A = 0 n n (N D N A ) n i = 0 Solve this quadratic equation for the free electron concentration, n. From n p = n i equation, calculate free hole concentration, p.

68 Equilibrium charge carrier concentration in semiconductors Intrinsic semiconductor: N D = 0 and N A = 0 p = n = n i Doped semiconductors where N D N A >> n i n = N D N A ; p = n i / n if N D > N A p = N A N D ; n = n i / p if N A > N D Compensated semiconductor n = p = n i when n i >> N D N A When N D N A is comparable to n i,, we need to use the charge neutrality equation to determine n and p.

69 Equilibrium charge carrier concentration in semiconductors Example Si is doped with As Atom/cm 3. What is the equilibrium hole concentra-tion p 0 at 300 K? Where is E F relative to E i ni p0 10 n cm 17 n 0 n e i ( E F E i ) kt 17 n 10 EF Ei ktln ln eV 10 n i

70 Equilibrium charge carrier concentration in semiconductors n N p N 0 a 0 d

71 Lecture 14: Intrinsic and extrinsic semiconductors recap of the effective mass method analysis of E(k) and it s 1st and nd deriviates band-to-band transiotions: intrinsic semiconductors hydrogen-like impurities n- and p-type semiconductors equilibrium charge carrier concentration carriers in non-eqilibrium conditions: diffusion, generation and recombination

72 Charge carriers in non-eqilibrium conditions Particles diffuse from regions of higher concentration to regions of lower concentration region, due to random thermal motion.

73 Charge carriers in non-eqilibrium conditions J n,diff qd n dn dx J p,diff qd p dp dx D is the diffusion constant, or diffusivity.

74 Charge carriers in non-eqilibrium conditions J J J n p J n J n, drift J n, diff qn ε n qd n dn dx J p J p, drift J p, diff qp ε p qd p dp dx

75 Charge carriers in non-eqilibrium conditions The position of E F relative to the band edges is determined by the carrier concentrations, which is determined by the net dopant concentration. In equilibrium E F is constant; therefore, the band-edge energies vary with position in a non-uniformly doped semiconductor: E c (x) E F E v (x)

76 The ratio of carrier densities at two points depends exponentially on the potential difference between these points: 1 i i1 1 1 i 1 i i i1 i F i i 1 F i1 i 1 i1 F ln 1 ln ln ln Therefore ln Similarly, ln ln n n q kt E E q V V n n kt n n n n kt E E n n kt E E n n kt E E n n kt E E Charge carriers in non-eqilibrium conditions

77 E v (x) Charge carriers in non-eqilibrium conditions E f E c (x) Consider a piece of a non-uniformly doped semiconductor: n-type semiconductor Decreasing donor concentration E c (x) E F E v (x) n dn dx Nc e kt N e c n kt n kt ( E E ( Ec EF ) / kt de dx c qε c F )/ kt de dx c

78 Charge carriers in non-eqilibrium conditions If the dopant concentration profile varies gradually with position, then the majority-carrier concentration distribution does not differ much from the dopant concentration distribution. N x) p( x) N ( x) n( x) D( A n-type material: p-type material: n( x) ND( x) NA p( x) NA( x) ND ( x) ( x) kt q 1 n dn dx kt q 1 N D dn dx D in n-type material

79 Charge carriers in non-eqilibrium conditions Band-to-Band R-G Center Impact Ionization

80 Charge carriers in non-eqilibrium conditions Direct R-G Center Auger

81 Charge carriers in non-eqilibrium conditions Energy (E) vs. momentum (ħk) Diagrams Direct: Indirect: Little change in momentum is required for recombination momentum is conserved by photon emission Large change in momentum is required for recombination momentum is conserved by phonon + photon emission

82 Charge carriers in non-eqilibrium conditions equilibrium values n n n 0 p p p 0 Charge neutrality condition: n p

83 Charge carriers in non-eqilibrium conditions Often the disturbance from equilibrium is small, such that the majority-carrier concentration is not affected significantly: For an n-type material: n p n0 so n n0 For a p-type material: n p p0 so p p0 However, the minority carrier concentration can be significantly affected.

84 Charge carriers in non-eqilibrium conditions Consider a semiconductor with no current flow in which thermal equilibrium is disturbed by the sudden creation of excess holes and electrons. n t n n for electrons in p-type material p t p p for holes in n-type material

85 Charge carriers in non-eqilibrium conditions Uniformly doped p-type and n- type semiconductors before the junction is formed. Internal electric-field occurs in a depletion region of a p-n junction in thermal equilibrium

FYS3410 - Vår 2015 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v15/index.html

FYS3410 - Vår 2015 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v15/index.html FYS3410 - Vår 2015 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v15/index.html Pensum: Introduction to Solid State Physics by Charles Kittel (Chapters 1-9 and 17, 18,

More information

FYS3410 - Vår 2014 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v14/index.html

FYS3410 - Vår 2014 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v14/index.html FYS3410 - Vår 2014 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v14/index.html Pensum: Solid State Physics by Philip Hofmann (Chapters 1-7 and 11) Andrej Kuznetsov delivery

More information

FYS3410 - Vår 2016 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v16/index.html

FYS3410 - Vår 2016 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v16/index.html FYS3410 - Vår 2016 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v16/index.html Pensum: Introduction to Solid State Physics by Charles Kittel (Chapters 1-9 and 17, 18,

More information

Module 6 : PHYSICS OF SEMICONDUCTOR DEVICES Lecture 34 : Intrinsic Semiconductors

Module 6 : PHYSICS OF SEMICONDUCTOR DEVICES Lecture 34 : Intrinsic Semiconductors Module 6 : PHYSICS OF SEMICONDUCTOR DEVICES Lecture 34 : Intrinsic Semiconductors Objectives In this course you will learn the following Intrinsic and extrinsic semiconductors. Fermi level in a semiconductor.

More information

FYS3410 - Vår 2014 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v14/index.html

FYS3410 - Vår 2014 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v14/index.html FYS410 - Vår 014 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys410/v14/index.html Pensum: Solid State Physics by Philip Hofmann (Chapters 1-7 and 11) Andrej Kuznetsov delivery

More information

Semiconductor Physics

Semiconductor Physics 10p PhD Course Semiconductor Physics 18 Lectures Nov-Dec 2011 and Jan Feb 2012 Literature Semiconductor Physics K. Seeger The Physics of Semiconductors Grundmann Basic Semiconductors Physics - Hamaguchi

More information

Solid State Detectors = Semi-Conductor based Detectors

Solid State Detectors = Semi-Conductor based Detectors Solid State Detectors = Semi-Conductor based Detectors Materials and their properties Energy bands and electronic structure Charge transport and conductivity Boundaries: the p-n junction Charge collection

More information

Doped Semiconductors. Dr. Katarzyna Skorupska

Doped Semiconductors. Dr. Katarzyna Skorupska Doped Semiconductors Dr. Katarzyna Skorupska 1 Doped semiconductors Increasing the conductivity of semiconductors by incorporation of foreign atoms requires increase of the concentration of mobile charge

More information

FYS Vår 2012 (Kondenserte fasers fysikk)

FYS Vår 2012 (Kondenserte fasers fysikk) FYS3410 - Vår 2012 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/index-eng.xml Based on Introduction to Solid State Physics by Kittel Course content Periodic structures,

More information

Intrinsic and Extrinsic Semiconductors, Fermi-Dirac Distribution Function, the Fermi level and carrier concentrations

Intrinsic and Extrinsic Semiconductors, Fermi-Dirac Distribution Function, the Fermi level and carrier concentrations ENEE 33, Spr. 09 Supplement I Intrinsic and Extrinsic Semiconductors, Fermi-Dirac Distribution Function, the Fermi level and carrier concentrations Zeynep Dilli, Oct. 2008, rev. Mar 2009 This is a supplement

More information

MCEN Fall 2003.

MCEN Fall 2003. Basic types of solid materials. Overview The theory of bands provides a basis for understanding the classification and physical properties of solid materials such as electrical conductivity, optical behavior

More information

Lecture 8: Extrinsic semiconductors - mobility

Lecture 8: Extrinsic semiconductors - mobility Lecture 8: Extrinsic semiconductors - mobility Contents Carrier mobility. Lattice scattering......................... 2.2 Impurity scattering........................ 3.3 Conductivity in extrinsic semiconductors............

More information

SEMICONDUCTOR I: Doping, semiconductor statistics (REF: Sze, McKelvey, and Kittel)

SEMICONDUCTOR I: Doping, semiconductor statistics (REF: Sze, McKelvey, and Kittel) SEMICONDUCTOR I: Doping, semiconductor statistics (REF: Sze, McKelvey, and Kittel) Introduction Based on known band structures of Si, Ge, and GaAs, we will begin to focus on specific properties of semiconductors,

More information

3. Diodes and Diode Circuits. 3. Diodes and Diode Circuits TLT-8016 Basic Analog Circuits 2005/2006 1

3. Diodes and Diode Circuits. 3. Diodes and Diode Circuits TLT-8016 Basic Analog Circuits 2005/2006 1 3. Diodes and Diode Circuits 3. Diodes and Diode Circuits TLT-8016 Basic Analog Circuits 2005/2006 1 3.1 Diode Characteristics Small-Signal Diodes Diode: a semiconductor device, which conduct the current

More information

This is the 11th lecture of this course and the last lecture on the topic of Equilibrium Carrier Concentration.

This is the 11th lecture of this course and the last lecture on the topic of Equilibrium Carrier Concentration. Solid State Devices Dr. S. Karmalkar Department of Electronics and Communication Engineering Indian Institute of Technology, Madras Lecture - 11 Equilibrium Carrier Concentration (Contd.) This is the 11th

More information

- thus the electrons are free to change their energies within the 3s band

- thus the electrons are free to change their energies within the 3s band Allowed and Forbidden Energy Bands - allowed energy bands associated with different atomic orbitals may overlap, as in (a) - the regions between allowed energy bands are called forbidden bands or band

More information

Analog & Digital Electronics Course No: PH-218

Analog & Digital Electronics Course No: PH-218 Analog & Digital Electronics Course No: PH-218 Lecture 1: Semiconductor Materials Course Instructors: Dr. A. P. VAJPEYI Department of Physics, Indian Institute of Technology Guwahati, India 1 Semiconductors

More information

Lecture 2: Semiconductors: Introduction

Lecture 2: Semiconductors: Introduction Lecture 2: Semiconductors: Introduction Contents 1 Introduction 1 2 Band formation in semiconductors 2 3 Classification of semiconductors 5 4 Electron effective mass 10 1 Introduction Metals have electrical

More information

Definition : Characteristics of Metals :

Definition : Characteristics of Metals : Metallic Bond Definition : It may be defined as, 1. The force that binds a metal ion to a number of electrons with in its sphere of influence. 2. The attractive force which holds the atoms of two or more

More information

First Time User Guide to Carrier Statistics Lab on nanohub.org Ver. 2

First Time User Guide to Carrier Statistics Lab on nanohub.org Ver. 2 Network for Computational Nanotechnology (NCN) UC Berkeley, Univ.of Illinois, Norfolk State, Northwestern, Purdue, UTEP First Time User Guide to Carrier Statistics Lab on nanohub.org Ver. 2,Saumitra Raj

More information

1.5 Light absorption by solids

1.5 Light absorption by solids 1.5 Light absorption by solids Bloch-Brilloin model L e + + + + + allowed energy bands band gaps p x In a unidimensional approximation, electrons in a solid experience a periodic potential due to the positively

More information

Semiconductor Detectors Calorimetry and Tracking with High Precision

Semiconductor Detectors Calorimetry and Tracking with High Precision Semiconductor Detectors Calorimetry and Tracking with High Precision Applications 1. Photon spectroscopy with high energy resolution. Vertex detection with high spatial resolution 3. Energy measurement

More information

Lecture 2 Semiconductor Physics (I)

Lecture 2 Semiconductor Physics (I) Lecture 2 Semiconductor Physics (I) Outline Intrinsic bond model : electrons and holes Generation and recombination Intrinsic semiconductor Doping: Extrinsic semiconductor Charge Neutrality Reading Assignment:

More information

Applied Quantum Mechanics for Electrical Engineers Workshop II Energy Band Model and Doping

Applied Quantum Mechanics for Electrical Engineers Workshop II Energy Band Model and Doping Applied Quantum Mechanics for Electrical Engineers Workshop II Energy Band Model and Doping 95 pts Objective: Explore the effect of doping on the energy band diagram and the carrier concentration. Instructions:

More information

NORGES TEKNISK- NATURVITENSKAPELIGE UNIVERSITET INSTITUTT FOR FYSIKK. Eksamen i Emne TFY4220 Faste Stoffers Fysikk

NORGES TEKNISK- NATURVITENSKAPELIGE UNIVERSITET INSTITUTT FOR FYSIKK. Eksamen i Emne TFY4220 Faste Stoffers Fysikk Page of 5 NORGES TEKNISK- NATURVITENSKAPELIGE UNIVERSITET INSTITUTT FOR FYSIKK Fagleg kontakt under eksamen: Institutt for fysikk, Gløshaugen Professor Steinar Raaen, 4896758 Eksamen i Emne TFY40 Faste

More information

Semiconductors Band Formation & direct and indirect gaps. Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India

Semiconductors Band Formation & direct and indirect gaps. Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India Semiconductors Band Formation & direct and indirect gaps 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India http://folk.uio.no/ravi/semi2013 Review of Energy Bands (1)

More information

Semiconductors, Insulators and Metals

Semiconductors, Insulators and Metals CHAPTER 2 ENERGY BANDS AND EFFECTIVE MASS Semiconductors, insulators and metals Semiconductors Insulators Metals The concept of effective mass Prof. Dr. Beşire GÖNÜL Semiconductors, Insulators and Metals

More information

University of Toronto Department of Electrical and Computer Engineering. ECE 330F SEMICONDUCTOR PHYSICS Eng. Annex 305

University of Toronto Department of Electrical and Computer Engineering. ECE 330F SEMICONDUCTOR PHYSICS Eng. Annex 305 University of Toronto Department of Electrical and Computer Engineering ECE 330F SEMICONDUCTOR PHYSICS Eng. Annex 305 Experiment # 1 RESISTIVITY AND BAND GAP OF GERMANIUM TA: Iraklis Nikolalakos OBJECTIVE

More information

DO PHYSICS ONLINE. conduction band. ~ 6 ev. Fig. 1. Energy band diagram for diamond (insulator) and silicon (semiconductor).

DO PHYSICS ONLINE. conduction band. ~ 6 ev. Fig. 1. Energy band diagram for diamond (insulator) and silicon (semiconductor). DO PHYSIS ONLINE FROM IDEAS TO IMPLEMENTATION 9.4.3 ATOMS TO TRANSISTORS SEMIONDUTORS ENERGY BANDS Diamond is a very good insulator. The electronic configuration in the ground state is 1s 2 2s 2 2. It

More information

Solid-State Physics: The Theory of Semiconductors (Ch. 10.6-10.8) SteveSekula, 30 March 2010 (created 29 March 2010)

Solid-State Physics: The Theory of Semiconductors (Ch. 10.6-10.8) SteveSekula, 30 March 2010 (created 29 March 2010) Modern Physics (PHY 3305) Lecture Notes Modern Physics (PHY 3305) Lecture Notes Solid-State Physics: The Theory of Semiconductors (Ch. 10.6-10.8) SteveSekula, 30 March 2010 (created 29 March 2010) Review

More information

Chapter 5. Second Edition ( 2001 McGraw-Hill) 5.6 Doped GaAs. Solution

Chapter 5. Second Edition ( 2001 McGraw-Hill) 5.6 Doped GaAs. Solution Chapter 5 5.6 Doped GaAs Consider the GaAs crystal at 300 K. a. Calculate the intrinsic conductivity and resistivity. Second Edition ( 2001 McGraw-Hill) b. In a sample containing only 10 15 cm -3 ionized

More information

ENEE 313, Spr 09 Midterm II Solution

ENEE 313, Spr 09 Midterm II Solution ENEE 313, Spr 09 Midterm II Solution PART I DRIFT AND DIFFUSION, 30 pts 1. We have a silicon sample with non-uniform doping. The sample is 200 µm long: In the figure, L = 200 µm= 0.02 cm. At the x = 0

More information

Lecture 2 - Semiconductor Physics (I) September 13, 2005

Lecture 2 - Semiconductor Physics (I) September 13, 2005 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-1 Lecture 2 - Semiconductor Physics (I) September 13, 2005 Contents: 1. Silicon bond model: electrons and holes 2. Generation and recombination

More information

Lecture Light Emitting Diodes.

Lecture Light Emitting Diodes. Lecture 19-20 Light Emitting Diodes. Today: 1. Carrier recombination in semiconductors. 2. p-n junctions with carrier injection. Light-emitting diodes (LEDs). Questions you should be able to answer by

More information

Silicon Basics -- General Overview. File: ee4494 silicon basics.ppt revised 09/11/2001 copyright james t yardley 2001 Page 1

Silicon Basics -- General Overview. File: ee4494 silicon basics.ppt revised 09/11/2001 copyright james t yardley 2001 Page 1 Silicon Basics -- General Overview. File: ee4494 silicon basics.ppt revised 09/11/2001 copyright james t yardley 2001 Page 1 Semiconductor Electronics: Review. File: ee4494 silicon basics.ppt revised 09/11/2001

More information

ELECTRONIC DEVICES MENJANA MINDA KREATIF DAN INOVATIF

ELECTRONIC DEVICES MENJANA MINDA KREATIF DAN INOVATIF INTRODUCTION TO ELECTRONIC DEVICES MENJANA MINDA KREATIF DAN INOVATIF Introduction What is Electronics? Electronic Devices? Electronic Systems? introduction Electronics: The branch of physics that deals

More information

Free Electron Fermi Gas (Kittel Ch. 6)

Free Electron Fermi Gas (Kittel Ch. 6) Free Electron Fermi Gas (Kittel Ch. 6) Role of Electrons in Solids Electrons are responsible for binding of crystals -- they are the glue that hold the nuclei together Types of binding (see next slide)

More information

Basic laws and electrical properties of metals (I) Electrical properties. Basic laws and electrical properties of metals (II)

Basic laws and electrical properties of metals (I) Electrical properties. Basic laws and electrical properties of metals (II) Electrical properties Electrical conduction How many moveable electrons are there in a material (carrier density)? How easily do they move (mobility)? Semiconductivity Electrons and holes Intrinsic and

More information

Section A5: Current Flow in Semiconductors

Section A5: Current Flow in Semiconductors Section A5: Current Flow in Semiconductors Conductive behaviors in materials, defined by the parameter conductivity, are a primary factor in the development of electronic and optoelectronic devices. Electrical

More information

The Physics of Energy sources Renewable sources of energy. Solar Energy

The Physics of Energy sources Renewable sources of energy. Solar Energy The Physics of Energy sources Renewable sources of energy Solar Energy B. Maffei Bruno.maffei@manchester.ac.uk Renewable sources 1 Solar power! There are basically two ways of using directly the radiative

More information

Electrical Properties

Electrical Properties Electrical Properties Outline of this Topic 1. Basic laws and electrical properties of metals 2. Band theory of solids: metals, semiconductors and insulators 3. Electrical properties of semiconductors

More information

Semiconductors, diodes, transistors

Semiconductors, diodes, transistors Semiconductors, diodes, transistors (Horst Wahl, QuarkNet presentation, June 2001) Electrical conductivity! Energy bands in solids! Band structure and conductivity Semiconductors! Intrinsic semiconductors!

More information

4.1 SOLAR CELL OPERATION. Y. Baghzouz ECE Department UNLV

4.1 SOLAR CELL OPERATION. Y. Baghzouz ECE Department UNLV 4.1 SOLAR CELL OPERATION Y. Baghzouz ECE Department UNLV SOLAR CELL STRUCTURE Light shining on the solar cell produces both a current and a voltage to generate electric power. This process requires a material

More information

Semiconductor lasers and LEDs read Agrawal pp

Semiconductor lasers and LEDs read Agrawal pp Semiconductor lasers and LEDs read Agrawal pp. 78-116 Objectives, understand the following: Stimulated emission, spontaneous emission, and absorption in semiconductors Design of an LED and laser diode:

More information

Crystalline solids. A solid crystal consists of different atoms arranged in a periodic structure.

Crystalline solids. A solid crystal consists of different atoms arranged in a periodic structure. Crystalline solids A solid crystal consists of different atoms arranged in a periodic structure. Crystals can be formed via various bonding mechanisms: Ionic bonding Covalent bonding Metallic bonding Van

More information

Energy band diagrams. Single atom. Crystal. Excited electrons cannot move. Excited electrons can move (free electrons)

Energy band diagrams. Single atom. Crystal. Excited electrons cannot move. Excited electrons can move (free electrons) Energy band diagrams In the atoms, the larger the radius, the higher the electron potential energy Hence, electron position can be described either by radius or by its potential energy In the semiconductor

More information

Condensed Matter Physics Prof. G. Rangarajan Department of Physics Indian Institute of Technology, Madras. Lecture - 36 Semiconductors

Condensed Matter Physics Prof. G. Rangarajan Department of Physics Indian Institute of Technology, Madras. Lecture - 36 Semiconductors Condensed Matter Physics Prof. G. Rangarajan Department of Physics Indian Institute of Technology, Madras Lecture - 36 Semiconductors We will start a discussion of semiconductors one of the most important

More information

CHAPTER - 45 SEMICONDUCTOR AND SEMICONDUCTOR DEVICES

CHAPTER - 45 SEMICONDUCTOR AND SEMICONDUCTOR DEVICES 1. f = 101 kg/m, V = 1 m CHAPTER - 45 SEMCONDUCTOR AND SEMCONDUCTOR DEVCES m = fv = 101 1 = 101 kg No.of atoms = 101 10 6 10 = 64.6 10 6. a) Total no.of states = N = 64.6 10 6 = 58.5 = 5. 10 8 10 6 b)

More information

CHAPTER 1: Semiconductor Materials & Physics

CHAPTER 1: Semiconductor Materials & Physics Chapter 1 1 CHAPTER 1: Semiconductor Materials & Physics In this chapter, the basic properties of semiconductors and microelectronic devices are discussed. 1.1 Semiconductor Materials Solid-state materials

More information

High Open Circuit Voltage of MQW Amorphous Silicon Photovoltaic Structures

High Open Circuit Voltage of MQW Amorphous Silicon Photovoltaic Structures High Open Circuit Voltage of MQW Amorphous Silicon Photovoltaic Structures ARGYRIOS C. VARONIDES Physics and EE Department University of Scranton 800 Linden Street, Scranton PA, 18510 United States Abstract:

More information

Electrical Conductivity

Electrical Conductivity Advanced Materials Science - Lab Intermediate Physics University of Ulm Solid State Physics Department Electrical Conductivity Translated by Michael-Stefan Rill January 20, 2003 CONTENTS 1 Contents 1 Introduction

More information

Types of Epitaxy. Homoepitaxy. Heteroepitaxy

Types of Epitaxy. Homoepitaxy. Heteroepitaxy Epitaxy Epitaxial Growth Epitaxy means the growth of a single crystal film on top of a crystalline substrate. For most thin film applications (hard and soft coatings, optical coatings, protective coatings)

More information

INSTITUTE FOR APPLIED PHYSICS Physical Practice for Learners of Engineering sciences Hamburg University, Jungiusstraße 11

INSTITUTE FOR APPLIED PHYSICS Physical Practice for Learners of Engineering sciences Hamburg University, Jungiusstraße 11 INSTITUTE FOR APPIED PHYSICS Physical Practice for earners of Engineering sciences Hamburg University, Jungiusstraße 11 Hall effect 1 Goal Characteristic data of a test semiconductor (Germanium) should

More information

FUNDAMENTAL PROPERTIES OF SOLAR CELLS

FUNDAMENTAL PROPERTIES OF SOLAR CELLS FUNDAMENTAL PROPERTIES OF SOLAR CELLS January 31, 2012 The University of Toledo, Department of Physics and Astronomy SSARE, PVIC Principles and Varieties of Solar Energy (PHYS 4400) and Fundamentals of

More information

The nearly-free electron model

The nearly-free electron model Handout 3 The nearly-free electron model 3.1 Introduction Having derived Bloch s theorem we are now at a stage where we can start introducing the concept of bandstructure. When someone refers to the bandstructure

More information

Chapter 1. Semiconductors

Chapter 1. Semiconductors THE ELECTRON IN ELECTRIC FIELDS Semiconductors If we were to take two parallel plates and connect a voltage source across them as shown in Figure 1, an electric field would be set up between the plates.

More information

Imperfections in atomic arrangements

Imperfections in atomic arrangements MME131: Lecture 8 Imperfections in atomic arrangements Part 1: 0D Defects A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Occurrence and importance of crystal defects Classification

More information

The Illuminated p-n Junction. ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner

The Illuminated p-n Junction. ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner The Illuminated p-n Junction The Illuminated pn Junction Generation re-visited Basic requirements Optical Generation Absorption Coefficient Optical Generation Rate The Illuminated pn Junction IV equation

More information

Processing of Semiconducting Materials Prof. Pallab Banerji Metallurgy and Material Science Indian Institute of Technology, Kharagpur

Processing of Semiconducting Materials Prof. Pallab Banerji Metallurgy and Material Science Indian Institute of Technology, Kharagpur Processing of Semiconducting Materials Prof. Pallab Banerji Metallurgy and Material Science Indian Institute of Technology, Kharagpur Lecture - 25 Carrier Transport in P - N Junction In my last lecture,

More information

Physics 551: Solid State Physics F. J. Himpsel

Physics 551: Solid State Physics F. J. Himpsel Physics 551: Solid State Physics F. J. Himpsel Background Most of the objects around us are in the solid state. Today s technology relies heavily on new materials, electronics is predominantly solid state.

More information

ELE2110A Electronic Circuits

ELE2110A Electronic Circuits Chinese University of Hong Kong Department of Electronic Engineering Second Term 07/08 ELE2110A Electronic Circuits Prof. Pun Kong Pang Email: kppun@ee.cuhk.edu.hk Lecture 01-1 Course Information Homepage:

More information

Conduction in Semiconductors

Conduction in Semiconductors Chapter 1 Conduction in Semiconductors 1.1 Introduction All solid-state devices, e.g. diodes and transistors, are fabricated from materials known as semiconductors. In order to understand the operation

More information

Chapter No: 14 Chapter: Semiconductor Electronics: Materials, Devices And Simple Circuits (ONE MARK QUESTIONS)

Chapter No: 14 Chapter: Semiconductor Electronics: Materials, Devices And Simple Circuits (ONE MARK QUESTIONS) Chapter No: 14 Chapter: Semiconductor Electronics: Materials, Devices And Simple Circuits (ONE MARK QUESTIONS) 1. What is an electronic device? It is a device in which controlled flow of electrons takes

More information

Fall 2004 Ali Shakouri

Fall 2004 Ali Shakouri University of California at Santa Cruz Jack Baskin School of Engineering Electrical Engineering Department EE-145L: Properties of Materials Laboratory Lab 5b: Temperature Dependence of Semiconductor Conductivity

More information

VIII.4. Field Effect Transistors

VIII.4. Field Effect Transistors Field Effect Transistors (FETs) utilize a conductive channel whose resistance is controlled by an applied potential. 1. Junction Field Effect Transistor (JFET) In JFETs a conducting channel is formed of

More information

Electrons and Holes in Semiconductors

Electrons and Holes in Semiconductors Hu_ch01v4.fm Page 1 Thursday, February 12, 2009 10:14 AM 1 Electrons and Holes in Semiconductors CHAPTER OBJECTIVES This chapter provides the basic concepts and terminology for understanding semiconductors.

More information

Chapter Outline. Diffusion - how do atoms move through solids?

Chapter Outline. Diffusion - how do atoms move through solids? Chapter Outline iffusion - how do atoms move through solids? iffusion mechanisms Vacancy diffusion Interstitial diffusion Impurities The mathematics of diffusion Steady-state diffusion (Fick s first law)

More information

The General Properties of Si, Ge, SiGe, SiO 2 and Si 3 N 4 June 2002

The General Properties of Si, Ge, SiGe, SiO 2 and Si 3 N 4 June 2002 The neral Properties of,,, O 2 and 3 N 4 June 2002 Virginia Semiconductor 1501 Powhatan Street, Fredericksburg, VA 22401-4647 USA Phone: (540) 373-2900, FAX (540) 371-0371 www.virginiasemi.com, tech@virginiasemi.com

More information

Lecture 3: Optical Properties of Bulk and Nano. 5 nm

Lecture 3: Optical Properties of Bulk and Nano. 5 nm Lecture 3: Optical Properties of Bulk and Nano 5 nm First H/W#1 is due Sept. 10 Course Info The Previous Lecture Origin frequency dependence of χ in real materials Lorentz model (harmonic oscillator model)

More information

Materials Science and Engineering Department MSE , Sample Test #1, Spring 2010

Materials Science and Engineering Department MSE , Sample Test #1, Spring 2010 Materials Science and Engineering Department MSE 200-001, Sample Test #1, Spring 2010 ID number First letter of your last name: Name: No notes, books, or information stored in calculator memories may be

More information

6.772/SMA Compound Semiconductors Lecture 20 - Laser Diodes 1 - Outline Stimulated emission and optical gain

6.772/SMA Compound Semiconductors Lecture 20 - Laser Diodes 1 - Outline Stimulated emission and optical gain 6.772/SMA5111 - Compound Semiconductors Lecture 20 - Laser Diodes 1 - Outline Stimulated emission and optical gain Absorption, spontaneous emission, stimulated emission Threshold for optical gain Laser

More information

- in a typical metal each atom contributes one electron to the delocalized electron gas describing the conduction electrons

- in a typical metal each atom contributes one electron to the delocalized electron gas describing the conduction electrons Free Electrons in a Metal - in a typical metal each atom contributes one electron to the delocalized electron gas describing the conduction electrons - if these electrons would behave like an ideal gas

More information

A. X-ray diffraction B. elemental analysis C. band gap energy measurement based on absorption of light D. none of the above

A. X-ray diffraction B. elemental analysis C. band gap energy measurement based on absorption of light D. none of the above LED Review Questions 1. Consider two samples in the form of powders: sample A is a physical mixture comprising equal moles of pure Ge and pure Si; sample B is a solid solution of composition Si0.5Ge0.5.

More information

phys4.17 Page 1 - under normal conditions (pressure, temperature) graphite is the stable phase of crystalline carbon

phys4.17 Page 1 - under normal conditions (pressure, temperature) graphite is the stable phase of crystalline carbon Covalent Crystals - covalent bonding by shared electrons in common orbitals (as in molecules) - covalent bonds lead to the strongest bound crystals, e.g. diamond in the tetrahedral structure determined

More information

Lecture 3: Optical Properties of Bulk and Nano. 5 nm

Lecture 3: Optical Properties of Bulk and Nano. 5 nm Lecture 3: Optical Properties of Bulk and Nano 5 nm The Previous Lecture Origin frequency dependence of χ in real materials Lorentz model (harmonic oscillator model) 0 e - n( ) n' n '' n ' = 1 + Nucleus

More information

Understanding the p-n Junction by Dr. Alistair Sproul Senior Lecturer in Photovoltaics The Key Centre for Photovoltaic Engineering, UNSW

Understanding the p-n Junction by Dr. Alistair Sproul Senior Lecturer in Photovoltaics The Key Centre for Photovoltaic Engineering, UNSW Understanding the p-n Junction by Dr. Alistair Sproul Senior Lecturer in Photovoltaics The Key Centre for Photovoltaic Engineering, UNSW The p-n junction is the fundamental building block of the electronic

More information

Lecture 3: Electron statistics in a solid

Lecture 3: Electron statistics in a solid Lecture 3: Electron statistics in a solid Contents Density of states. DOS in a 3D uniform solid.................... 3.2 DOS for a 2D solid........................ 4.3 DOS for a D solid........................

More information

A Program for Calculating Mobility and Carrier Density in Bulk Semiconductors

A Program for Calculating Mobility and Carrier Density in Bulk Semiconductors A Program for Calculating Mobility and Carrier Density in Bulk Semiconductors Dan Barrett, Electrical Engineering, University of Notre Dame Contents 1 Introduction A - 1 2 Theory A - 2 3 The Program A

More information

Chapter 16. Diodes and Applications. Objectives

Chapter 16. Diodes and Applications. Objectives Chapter 16 Diodes and Applications Objectives Understand the basic structure of semiconductors and how they conduct current Describe the characteristics and biasing of a pn junction diode Describe the

More information

Spring 2002 Dawn Hettelsater, Yan Zhang and Ali Shakouri, 05/09/2002

Spring 2002 Dawn Hettelsater, Yan Zhang and Ali Shakouri, 05/09/2002 University of California at Santa Cruz Jack Baskin School of Engineering Electrical Engineering Department EE-145L: Properties of Materials Laboratory Lab 7: Solar Cells Spring 2002 Dawn Hettelsater, Yan

More information

Classical Theory Expectations. Heat Capacity: Real Metals

Classical Theory Expectations. Heat Capacity: Real Metals Classical Theory Expectations Equipartition: 1/k B T per degree of freedom In 3-D electron gas this means 3/k B T per electron In 3-D atomic lattice this means 3k B T per atom (why?) So one would expect:

More information

Semiconductor Laser Diode

Semiconductor Laser Diode Semiconductor Laser Diode Outline This student project deals with the exam question Semiconductor laser diode and covers the following questions: Describe how a semiconductor laser diode works What determines

More information

Electronic Structure and the Periodic Table Learning Outcomes

Electronic Structure and the Periodic Table Learning Outcomes Electronic Structure and the Periodic Table Learning Outcomes (a) Electronic structure (i) Electromagnetic spectrum and associated calculations Electromagnetic radiation may be described in terms of waves.

More information

Introduction To Materials Science FOR ENGINEERS, Ch. 5. Diffusion. MSE 201 Callister Chapter 5

Introduction To Materials Science FOR ENGINEERS, Ch. 5. Diffusion. MSE 201 Callister Chapter 5 Diffusion MSE 21 Callister Chapter 5 1 Goals: Diffusion - how do atoms move through solids? Fundamental concepts and language Diffusion mechanisms Vacancy diffusion Interstitial diffusion Impurities Diffusion

More information

SMA5111 - Compound Semiconductors Lecture 2 - Metal-Semiconductor Junctions - Outline Introduction

SMA5111 - Compound Semiconductors Lecture 2 - Metal-Semiconductor Junctions - Outline Introduction SMA5111 - Compound Semiconductors Lecture 2 - Metal-Semiconductor Junctions - Outline Introduction Structure - What are we talking about? Behaviors: Ohmic, rectifying, neither Band picture in thermal equilibrium

More information

Characteristic curves of a solar cell

Characteristic curves of a solar cell Related Topics Semi-conductor, p-n junction, energy-band diagram, Fermi characteristic energy level, diffusion potential, internal resistance, efficiency, photo-conductive effect, acceptors, donors, valence

More information

Semiconductor p-n junction diodes

Semiconductor p-n junction diodes Semiconductor p-n junction diodes p n p-n junction formation p-type material Semiconductor material doped with acceptors. Material has high hole concentration Concentration of free electrons in p-type

More information

Processing of Semiconducting Materials Prof. Pallab Banerji Department of Metallurgy and Material Science Indian Institute of Technology, Kharagpur

Processing of Semiconducting Materials Prof. Pallab Banerji Department of Metallurgy and Material Science Indian Institute of Technology, Kharagpur Processing of Semiconducting Materials Prof. Pallab Banerji Department of Metallurgy and Material Science Indian Institute of Technology, Kharagpur Lecture - 8 Diffusion and Ion Implantation II (Refer

More information

Diode Applications. This chapter teaches the employment of pn-junction diodes in various applications.

Diode Applications. This chapter teaches the employment of pn-junction diodes in various applications. Diode Applications This chapter teaches the employment of pn-junction diodes in various applications. Rectifier diodes Rectifier diodes are used, for example, in power supplies, AC-to-DC converters, and

More information

Electronic Transport in Solar Cells and DFT Calculations for Si and GaAs

Electronic Transport in Solar Cells and DFT Calculations for Si and GaAs Electronic Transport in Solar Cells and DFT Calculations for Si and GaAs Jean Diehl Institut für Theoretische Physik Goethe-Universität, Frankfurt June 24th, 211 1 / 24 Contents 1 Introduction to Solar

More information

6-2. A quantum system has the following energy level diagram. Notice that the temperature is indicated

6-2. A quantum system has the following energy level diagram. Notice that the temperature is indicated Chapter 6 Concept Tests 6-1. In a gas of hydrogen atoms at room temperature, what is the ratio of atoms in the 1 st excited energy state (n=2) to atoms in the ground state(n=1). (Actually H forms H 2 molecules,

More information

Physics Notes Class 12 Chapter 14 Semiconductor Electronics, Materials, Devices and Sample Circuits

Physics Notes Class 12 Chapter 14 Semiconductor Electronics, Materials, Devices and Sample Circuits 1 P a g e Physics Notes Class 12 Chapter 14 Semiconductor Electronics, Materials, Devices and Sample Circuits It is the branch of science which deals with the electron flow through a vacuum, gas or semiconductor.

More information

University of California at Santa Cruz Electrical Engineering Department EE-145L: Properties of Materials Laboratory

University of California at Santa Cruz Electrical Engineering Department EE-145L: Properties of Materials Laboratory University of California at Santa Cruz Electrical Engineering Department EE-145L: Properties of Materials Laboratory Lab 8: Optical Absorption Spring 2002 Yan Zhang and Ali Shakouri, 05/22/2002 (Based

More information

Ch. 4: Imperfections in Solids Part 1. Dr. Feras Fraige

Ch. 4: Imperfections in Solids Part 1. Dr. Feras Fraige Ch. 4: Imperfections in Solids Part 1 Dr. Feras Fraige Outline Defects in Solids 0D, Point defects vacancies Interstitials impurities, weight and atomic composition 1D, Dislocations edge screw 2D, Grain

More information

Metals, Semiconductors, and Insulators

Metals, Semiconductors, and Insulators Metals, Semiconductors, and Insulators Every solid has its own characteristic energy band structure. In order for a material to be conductive, both free electrons and empty states must be available. Metals

More information

CONTENTS. Preface. 1.1.2. Energy bands of a crystal (intuitive approach)

CONTENTS. Preface. 1.1.2. Energy bands of a crystal (intuitive approach) CONTENTS Preface. Energy Band Theory.. Electron in a crystal... Two examples of electron behavior... Free electron...2. The particle-in-a-box approach..2. Energy bands of a crystal (intuitive approach)..3.

More information

THE CURRENT-VOLTAGE CHARACTERISTICS OF AN LED AND A MEASUREMENT OF PLANCK S CONSTANT Physics 258/259

THE CURRENT-VOLTAGE CHARACTERISTICS OF AN LED AND A MEASUREMENT OF PLANCK S CONSTANT Physics 258/259 DSH 2004 THE CURRENT-VOLTAGE CHARACTERISTICS OF AN LED AND A MEASUREMENT OF PLANCK S CONSTANT Physics 258/259 I. INTRODUCTION Max Planck (1858-1947) was an early pioneer in the field of quantum physics.

More information

CHEM 10113, Quiz 7 December 7, 2011

CHEM 10113, Quiz 7 December 7, 2011 CHEM 10113, Quiz 7 December 7, 2011 Name (please print) All equations must be balanced and show phases for full credit. Significant figures count, show charges as appropriate, and please box your answers!

More information

1. Degenerate Pressure

1. Degenerate Pressure . Degenerate Pressure We next consider a Fermion gas in quite a different context: the interior of a white dwarf star. Like other stars, white dwarfs have fully ionized plasma interiors. The positively

More information

Lecture 19: Solar cells

Lecture 19: Solar cells Lecture 19: Solar cells Contents 1 Introduction 1 2 Solar spectrum 2 3 Solar cell working principle 3 4 Solar cell I-V characteristics 7 5 Solar cell materials and efficiency 10 1 Introduction Solar cells

More information