EELE408 Photovoltaics Lecture 05: Semiconductor 05...آ  EELE408 Photovoltaics Lecture 05: Semiconductor

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  • 1

    EELE408 Photovoltaics Lecture 05: Semiconductor Basics

    Dr. Todd J. Kaiser tjkaiser@ece.montana.edu

    Department of Electrical and Computer Engineering Montana State University - Bozeman

    Bond Model

    Silicon Atom

    Si

    14 electrons with 4 valence

    3

    Filled orbitals do not interact The four outer

    valence electrons interact

    Semicconductors

    4

    Elements around Silicon

    III IV V

    5

    Si

    Si

    SiSi Si

    SiSi

    Si

    Si

    Si

    Si

    Si

    SiSi

    Si

    Si

    Si

    Si

    Si

    SiSi

    Si

    Si

    Si Si

    Si

    Si

    SSi

    Si

    Si

    Si Si

    Si

    SSi

    Si

    Si Si

    SSi

    Si SSi

    6

    Si Si

    Si

    Si SiSi

    Si Si

    Si

    Si

    Si

    Si

    Si

    Si

    Si

    Si Si

    Si

    Si

    SiSi

    Si

    Si

    Si S

    Si

    Si

    SiSi

    Si

    Si

    Si

    S

    Si

    SiSi

    Si

    Si

    S

    SiSi

    Si

    SSi

    Covalent Bonds:

    Shared electrons to fill orbital

  • 2

    Intrinsic Silicon

    Si Si Si Si Si Si Si

    Si Si Si Si Si Si Si

    Si Si Si Si Si Si Si

    7

    Si Si Si Si Si Si Si

    Si Si Si Si Si Si Si

    Poor conductor: No free electrons to carry current Need to engineer electrical properties (conduction)

    Valence V: n-type doping

    III IV V

    8

    Extra Negative Electrons

    Si Si Si Si Si Si Si

    Si Si As Si Si Si Si

    Si Si Si Si Si As Si

    9

    Si Si Si Si Si As Si

    Si As Si Si Si Si Si

    Si Si Si Si Si Si Si

    Each N‐type dopant brings an extra electron to the lattice

    Valence III: p-type doping

    III IV V

    10

    Extra Positive Holes

    Si Si Si Si Si Si Si

    Si B Si Si B Si Si

    Si Si Si Si Si Si Si

    11

    Si Si Si Si Si Si Si

    Si Si Si B Si Si Si

    Si Si Si Si Si Si Si

    Each P‐type dopant is short an electron, creating a hole in the lattice

    Bond Model

    • Electrons from broken bonds are free to move • Electrons from neighboring bonds can also move into the

    ‘hole’ created by a broken bond, allowing the broken bond or ‘hole’ to propagate as if had a positive charge – Bubble in a liquid

    12

  • 3

    Band Model

    Orbital Shells

    • The positions of the electrons around the nucleus are quantized to specific energy levels or Shells

    • The orbital determines the energy of the electron

    r qV

    0

    2

    4 

    14

    n = 1

    n = 2

    n = 3

    0

    Energy of Electrons

    Energy

    M 4d

    4f

    N

    5s 5p

    5d

    5f

    O

    5g

    2s 2pLower Electron 

    Energy: More  Tightly Bound  to Nucleus

    15

    n

    1s

    n=1

    K

    2s 2p

    L

    n=2

    3s 3p

    3d

    n=3

    4s 4p

    n=4 n=5 n=6

    Higher Electron  Energy: Less Bound  to Nucleus

    Orbitals fill from  the bottom up.

    Silicon Electron Configuration

    [Ne]3s23p2

    M

    (n=3)

    s

    (l = 0)

    p

    (l = 1)

    d

    (l = 2) (m = ‐1) (m = 0) (m = 1)(m = ‐2) (m = 2)

    16

    K

    (n=1)

    L

    (n=2)

    s

    (l = 0)

    s

    (l = 0)

    p

    (l = 1)

    Splitting of Energy Levels in a Crystalline Lattice

    Energy Discrete Energy States

    Continuum of Energy States

    Allowed

    Forbidden

    S i

    S i

    17

    Interatomic Distance d

    Band gaps

    Allowed

    Allowed

    Forbidden

    Forbidden

    Allowed and forbidden energy levels at atomic spacing

    Energy

    Energy Gap

    Conduction Band

    Valence Band

    Band Diagram

    This corresponds to an electron jumping from the valence band to the conduction b d

    Si Si Si Si Si Si Si

    Si Si Si Si Si Si Si

    Si Si Si Si Si Si Si

    Position

    Thermal energy causes an electron to break its bond to the silicon lattice

    band

    The electron is now free to move through the silicon lattice

  • 4

    Energy

    Energy Gap

    Conduction Band

    Valence Band

    Band Diagram

    Additional current is caused by the movement of the “hole”

    Si Si Si Si Si Si Si

    Si Si Si Si Si Si Si

    Si Si Si Si Si Si Si

    Position

    Other electrons can then move into the voids or holes in the lattice left by the released electron

    Energy

    Energy Gap

    Conduction Band

    Valence

    Band Diagram

    Position

    Band

    It is easier to think of a positive hole moving in the valence band

    Energy

    Energy Gap

    Conduction Band

    Valence Band

    Intrinsic Concentration

    There is an intrinsic concentration of electrons that are able to move that is a function of

    Si Si Si Si Si Si Si

    Si Si Si Si Si Si Si

    Si Si Si Si Si Si Si

    Position

    At absolute zero there is insufficient thermal energy to break any bonds so no electrons are in the conduction band

    temperature

    As the temperature rises electrons escape the silicon lattice

    21

    Energy

    Energy

    Conduction Band

    Intrinsic Concentration As the temperature rises more and more electrons are excited into the  conduction band and the silicon becomes more conductive with an equal  concentration of electrons in the valence band and holes in the conduction  band

    22

    Position

    gy Gap

    Valence Band

     

     310

    2 19

    /101)300(

    6884exp 300

    1038.9375275

    cmKTn T

    TKKTn

    i

    i

    

      

      

     

      Empirical equation for

    near room temperature

    Energy

    Energy

    Conduction Band

    N-Type Doping Doping the silicon lattice with atoms with 5 valence electrons (V) create sites in the band diagram that require little energy to break the bond to the dopant atom and become free to move in the lattice or in other words move into the conduction band.

    23

    Position

    gy Gap

    Valence Band

    As As As As As As As As As As As As As

    N type Material

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    Majority Charge Carriers are Negative electrons

    24

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    +

    Few holes

  • 5

    Energy

    Energy

    Conduction Band

    P-Type Doping Doping the silicon lattice with atoms with 3 valence electrons (III) create sites  in the band diagram that require little energy to trap an electron into the  dopant atom. Holes are created in the valence band that are free to move.

    25

    Position

    gy Gap

    Valence Band

    B B B B B B B B B B B B B

    P type Material

    -------

    Majority Charge Carriers are Positive holes

    26

    -

    -

    -

    -

    -

    -

    -

    -

    -

    -

    -

    -

    -

    -

    -

    -

    -

    -

    -

    -

    -

    Few electrons

    Equilibrium Carrier Concentration

    • Law of Mass Action – At equilibrium the product of the majority and minority carrier

    concentration is a constant

    – n0 is the equilibrium electron concentration – p0 is the equilibrium hole concentration

    2 00 inpn 

    27

    – ni is the intrinsic concentration

    N-Type Carrier Concentration

    • At room temperature in an N-type material, the electron concentration is approximately the donor doping concentration

    D

    i

    D

    N np

    Nn 2

    0

    0

    28

    – ND is the donor doping concentration

    P-Type Carrier Concentration

    • At room temperature in a P-type material, the hole concentration is approximately the acceptor doping concentration

    A

    i

    A

    N nn

    Np 2

    0

    0

    29

    – NA is the acceptor doping concentration

    Energy

    Energy

    Conduction Band

    Minority Concentration Dependence

    Low Doping High Doping

    30

    Position

    gy Gap

    Valence Band

    Montana State University 30

    As the doping concentration increases the concentration of minority carriers decreases.

  • 6

    Energy Levels of Elements in the Band Gap of Silicon (Traps)

    Li Sb P As S Pt Mn Ag Hg

    0.033 0.039 0.044 0.049

    0.18

    0.37 0.37 0.33 0.33

    31

    B Al Ga In Co Z