Semiconductor Physics - Linkأ¶ping University The Physics of Semiconductors – Grundmann . Basic Semiconductors

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  • 10p PhD Course 18 Lectures Nov-Dec 2011 and Jan – Feb 2012 Literature Semiconductor Physics – K. Seeger The Physics of Semiconductors – Grundmann Basic Semiconductors Physics - Hamaguchi Electronic and Optoelectronic Properties of Semiconductors - Singh Quantum Well Wires and Dots – Hartmann Wave Mechanics Applied to Semiconductor Heterostructures - Bastard Fundamentals of Semiconductor Physics and Devices – Enderlein & Horing Examination Homework Problems (6p) Written Exam (4p) Additionally Your own research area. Background courses (Solid State Physics, SC Physics, Sc Devices)

    Semiconductor Physics

  • 1. Introduction 2. Crystal and Energy Band structure 3. Semiconductor Statistics 4. Defects and Impurities 5. Optical Properties I : Absorption and Reflection 6. Optical Properties II : Recombinations 7. Carrier Diffusion 8. Scattering Processes 9. Charge Transport 10. Surface Properties 11. Low Dimensional Structures 12. Heterostructures 13. Quantum Wells/Dots 14. Organic Semiconductors 15. Graphene 16. Reserve and Summary

    Course Layout

  • Based on : The Physics of Semiconductors, Grundmann, Chapter 9. Semiconductor Optics, C.F. Klingshirn, Ch. 9-14 Lecture Anne Henry, IFM Lecture Ivan Ivanov, IFM Lecture Micheal Reshchikov, Virgina Commonwelth University, Richmond, USA

  • Lecture Layout Optical Techniques Photoluminscence Optical Recombinations Band-to-Band DAP Free Exciton Bound Exciton Temperature Dependence Internal Transitions Recombination Processes Time Resolved Photolumnscence

  • Optical techniques

    LUMINESCENCE: spontaneous emission of light in solids • Fluorescence: fast luminescence (electric-dipole allowed) • Phosphorescence: slow luminescence (electric-dipole forbidden) • Photo-luminescence (optical excitation) • Cathodo-luminescence (cathode ray (e-beam) excitation) • Electro-luminescence (electrical excitation) • Thermo-luminescence (heating) • Chemo-luminescence (chemical reaction)

    FTIR

    • Fourier Transform Infrared Reflectivity RAMAN

    • Phonon Scattering

  • PL : Photoluminscence

    Laser Excitation above bandgap, creates electrons and holes. Cryostat Normally Liquid He, < 2 K Detector PMT Photomultipliertube, scanning of monochromator CCD

  • FTIR – Fourier Transform Infrared Spectroscopy

    Michelson Interferometer Interference from fixed and moving mirror

    is converted by Fourir Transform to intensity spectrum

    Advantages: Improved Signal/Noise Improved resolution Disadvantages Requires internal light source to monitor

    mirror movement. Cannot use sensitive detectors in visible

    range. Mainly used for absorption and luminscence

    in the infrared. λ < 1 µm.

  • Recombination

    BB FE BE DAP IBE FB

    Excited electrons

    Created holes

    Excitation ħν

    D

    A

    R

    D

    A A

    IT

  • Recombination

    Energy and Momentum must be conserved

    Direct In-direct

  • Band-to-Band

    Spontaneous recombination rate dependent on electron and hole occupancy in each band

    PL Intensity

  • GaN From M. Reshchikov Virgina Commonwelyh Univ, Richmond USA

    Free-to-Bound

    Free-to-Bound (FB) recombinations dominates at higher temperatures, when Donors and Acceptors are ionized.

  • Free-to-Bound : Spectral Broadening

    At higher temperatures carriers are distributed in energy in the conduction band.

    Involvment of phonons in the recombination..

  • DAP : Donor-Acceptor-Pairs

    R a∼D A

    D

    A

    Remote pairs

    Close pairs

    VALENCE BAND

    CONDUCTION BAND

    R

    D

    A

  • DAP : Donor-Acceptor-Pairs

    Under certain conditions sharp lines related to specific Donor- Acceptor pair distance.

  • DAP : Donor-Acceptor-Pairs

    From Ivan Ivanov, IFM

  • DAP : Donor-Acceptor-Pairs

    Possible DAP arrangments:

    • Dh-Ah (hh set)

    • Dh-Ak (hk set)

    • Dk-Ah (kh set)

    • Dk-Ak (kk set)

    } equivalent structure

    In SiC two different donor and Acceptor positions Hexagonal (h) Cubic (k)

  • DAP : Donor-Acceptor-Pairs

    For deep donors and acceptors – involvment of phonons. For direct bandgap semiconductors mainly LO- phonons. Broadening dependent of number of involved phonons, N. S : Huang-Rhys factor (average number of involved phonons)

  • DAP : Donor-Acceptor-Pairs

    Huang Rhys Factor: Dependent on the displacement, q, in the configuration coordinate (CC) scheme. S 1 Strong coupling Broadening and shift toeards lower energies.

  • FE : Free Excitons

    Electron – hole pair. Free to move in the lattice. Requires high purity material, and low temperatures. Binding energies ~5 – 50 meV

  • BE : Bound Excitons :

    The mechanism of binding exciton

  • Bound Excitons : Haynes Rules

    The empirical Haynes’ rule: The binding energy of an exciton to a shallow donor (acceptor) is proportional to some degree of the ground-state energy of this donor (acceptor).

  • Free Excitons : Direct Bandgap

    FE present in high quality materials. No-phonon line dominates. Weak coupling to optical phonons, LO

  • Excitons : Fine Structure

    In p-type layer relative intensity between Donor and Acceptor BE changes

  • Excitons : Fine Structure In HVP GaN Two different Donors. Splitting of valence band gives three different free excitons. XA, XB and XC Excited free exciton states XAn=2 Two-electron transitions ( )2e Electron-hole recombination leaves remaining electron in excited state

  • Excitons : Fine Structure

  • 2250230023502400

    PL In

    te ns

    ity (a

    .u )

    NP

    TA

    LA LO

    TO

    305031003150320032503300

    Photon Energy (meV)

    2.3 1014 cm-3

    1.8 1015 cm-3

    6.5 1017 cm-3

    P0

    Q0 P76

    I76

    NP

    TA

    LA

    LO TO

    3C 4H 6H

    SiC:N 1 NP 2 NP 3 NP + phonon replicas + phonon replicas + phonon replicas

    2850290029503000

    P0

    R I76

    NP

    TA

    LA LO

    TO

    S0

    1.5 1015 cm-3

    3C 4H 6H

    SiC:N 1 NP 2 NP 3 NP + phonon replicas + phonon replicas + phonon replicas

    Bound Excitons : Indirect Bandgap

    BE: ħω = Eg – EFE – EBE - Ephonon

  • BE : Local phonon spectrum

    DI and DII is a common but not identified defect in SiC:4H DI one defct in as-grown material. Local phonon replicas related to the defect distortion dependent of defect symmetri. DII several (?) defects in irradiated material with excited states and local phon replicas.

  • 305031003150320032503300

    Photon Energy (meV)

    2.3 1014 cm-3

    1.8 1015 cm-3

    6.5 1017 cm-3

    P0

    Q0 P76

    I76

    NP

    TA

    LA

    LO TO

    Bound Excitons : Relative Intensities

    Relative intensities between free exciton and bound exciton changes with donor doping. Lower doping gives increased FE recombination Can be used to determine doping level.

    SiC:4H T = 2K

  • Multiple Bound Excitons

    PNP

    BNP AsNP

    BTO

    PTO

    BTA

    FETO

    FELO

    NP TA TO LO LA

    P2 P3

    B2

    B3

    BMEC

    Si

    Multiple Bound Exciton Complexes: Multiple electron-hole pairs bound at neutral donor, seen in Si, GaP, CdSe and SiC

  • 3880 3884 3888

    PL in

    ten sit

    y (a

    rb . u

    ni ts) a) 4H-SiC: n = 8.1 10

    15 cm-3

    fit spectrum composing lines

    I 76.4

    P 68

    Q 51

    ++

    Wavelength (Å) 3880 3884 3888

    Wavelength (Å)

    b) 4H-SiC: n = 2.3 1014 cm-3

    fit spectrum composing lines

    I 76.4

    P 68Q

    51

    + +

    0.1

    1

    10

    100

    1E+14 1E+15 1E+16 1E+17

    Net carrier concentration (cm-3)

    R =

    B E

    /F E

    4H-SiC n = 5.2x1014 R (cm-3)

    1014 1015 1016 1017

    Q0

    I76.4

    (CV measurement)

    Bound Excitons : Doping Dependence

  • Bound Excitons : Doping Dependence

    At higher doping the BE line broadens and shift to lower energies due to bandgap narrowing. PL position used to determine doping.

  • PL : Temperature Dependence

  • PL : Temperature Dependence

  • PL : Temperature Dependence Spectra dominated by BE at low temperatures. These ionize and the FE intensity increases. Increased spectral broadening with temperature. Red-shift due to reduced bandgap with temperature. At room