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  • Lecture 2

    Semiconductor Physics

    Semiconductor Physics 1-1

  • Outline Bond model: electrons and holes

    Electron-hole pair generation and recombination

    Intrinsic semiconductor

    Doping: Extrinsic semiconductor

    Charge Neutrality

    Introduction to Charge Carrier Transport

    Semiconductor Physics 1-2

  • Test Yourself

    Can you differentiate between: Semiconductors



    What is the difference between charge carriers and free charge carriers ?

    Semiconductor Physics 1-3

  • Semiconductor Materials

    Three most used semiconductors: carbon (C), silicon (Si) and germanium (Ge)

    Semiconductor Physics 1-4

    Carbon Silicon Germanium

  • Silicon (most common semiconductor material)

    Bond Model

    Si is column IV of the periodic table

    Electronic structure of silicon atom: 10 core electrons (tightly bound)

    4 valence electrons (loosely bound, responsible for most of the chemical properties

    Other semiconductors: Single crystal: Ge, C (diamond form)

    Compound: GaAs, InP, InGaAs, InGaAsP, GaP, ZnSe, CdTe (on the average, 4 valence electrons per atom)

    Semiconductor Physics 1-5

  • Silicon crystal structure

    Semiconductor Physics 1-6

    Diamond structure: atoms tetrahedrally bonded by sharing valence electrons

    covalent bonding

    Each atom shares 4 electrons

    eight covalent electrons associated with each atom

    Si atomic density:

    5 x 1022 cm-3

  • Simple “flattened” model of Si crystal

    This bonding of atoms, strengthened by the sharing of

    electrons, is called covalent bonding

    Molecules or ions tend to be more stable when the outermost electron shells of their constituent atoms contain eight electrons

    Semiconductor Physics 1-7

    At 0 oK: • All bonds are satisfied (all valence electrons engaged in

    bonding) • No “free” electrons (or holes)

  • Creation of electron-hole pair At room temperature (default 27 oC or 300 oK),

    approximately 1.5X 1010 free carriers in 1 cm3 of intrinsic silicon material Intrinsic semiconductor material means material has

    been refined to a very low level of impurities

    Semiconductor Physics 1-8

  • Creation of electron-hole pair Electron-hole pairs in a silicon crystal. Free

    electrons are being generated continuously while some recombine with holes

    Electrons and holes

    in semiconductors are

    “fuzzier”: they span

    many atomic sites

    Semiconductor Physics 1-9

    At finite temperature, some bonds are broken • “free” electrons – Mobile negative charge -1.6 x 10-19 C • “free” holes – Mobile positive charge, +1.6 x 10-19 C

  • Definitions

    “electron” means free electron Not concerned with bonding electrons or

    core electrons

    Define: n ≡ free electron concentration [cm-3] p ≡ free hole concentration [cm-3] Mass action law (at thermal equilibrium)

    Where ni ≡ intrinsic carrier concentration [cm−3 ]

    Semiconductor Physics 1-11

    pnni .2

  • Generation and Recombination Generation: break-up of covalent bond to form

    electron and hole pairs In an intrinsic semiconductor, the number of holes is equal to the

    number of free electrons

    Generate new hole-electron pairs per unit volume per second requires energy from thermal or optical sources

    Generation rate: G = Gthermal + Goptical + …. [cm−3. s−1 ]

    Recombination: formation of covalent bond by bringing together electron and hole Releases energy in thermal or optical form

    Recombination rate R [cm−3. s−1 ]

    1 recombination event requires 1 electron + 1 hole

    On an average, a hole (an electron) will exist for ζp (ζ n) seconds before recombination. This time is called the mean lifetime of the hole (electron)

    Semiconductor Physics 1-12

  • Intrinsic Semiconductors Thermal Equilibrium

    Steady state plus absence of external energy sources

    With increasing temperature, the density of hole-electron pairs (free charge carriers) increases in an intrinsic semiconductor.

    where ni ≡ intrinsic carrier concentration [cm−3 ] EG0 is the energy gap (the energy required to break a covalent

    bond) at 0 K k is the Boltzmann constant in electron volts per degree

    kelvin (J/K) [k = 1.38x10-23 J/K] A is a material-dependent constant independent of T

    Semiconductor Physics 1-13







    pnni .2

  • Intrinsic Semiconductors

    In Si at 300 K (“room temperature”): ni ≈ 1x1010 cm-3

    In a sufficiently pure Si wafer at 300K (“intrinsic semiconductor):

    • Assume thermal equilibrium: n = p = ni ≈ 1 ×1010 cm−3

    ni is a very strong function of temperature T ↑ ⇒ ni ↑

    Why ?

    Semiconductor Physics 1-14

  • Effect of Temperature on Conductivity

    Conductor resistance increase with increase in heat (number of

    free charge carriers decreases)

    have a positive temperature coefficient

    Semiconductor resistance decrease (i.e., conductivity increase) with

    increase in heat (number of free charge carriers increases)

    have a negative temperature coefficient

    Semiconductor Physics 1-15

  • Controlling the properties of a Semiconductor

    Doping = engineered introduction of foreign atoms to modify semiconductor electrical properties

    Doping is the process of deliberately adding impurities to the crystal during manufacturing and increases the number of current carries (electrons or holes) Impurities (extraneous elements)

    Doping process create n-type and p-type of semiconductors

    A semiconductor material that has been subjected to the doping process is called an extrinsic material

    Semiconductor Physics 1-16

  • Doping

    Silicon: 4 valence electrons Each Si atom bonds to four

    others Replace some Si atoms with atoms

    that do not have four valence electrons

    These atoms will have: - an extra electron (group V) Donors

    - an extra hole (group III) Acceptors

    Doping increases the number of carriers

    Semiconductor Physics 1-17

  • Donors Introduce electrons to semiconductors (but not


    For Si, group V elements (dopants) with 5 valence electrons (Arsenic “As”, phosphorus “P”, antimony “Sb”)

    Semiconductor Physics 1-18

  • Donors 4 of five electrons participate in bonding

    The 5th electron easy to release at room temperature, each donor releases 1 electron that is available

    for conduction1 conduction

    Donor site become positively charged (fixed charge)


    Nd ≡ donor concentration [cm-3] If Nd > ni, doping controls carrier


    Extrinsic semiconductor ⇒

    n = Nd and p = ni2/ Nd

    Note: n >> p : n-type semiconductor

    In general: Nd ≈ 1015 1020 atom or electron m-3 Semiconductor Physics 1-19

  • Acceptors Introduce holes to semiconductors (but not


    For Si, group III elements with 3 valence electrons (usually Boron(B) , Gallium (Ga) and Indium (In))

    Semiconductor Physics 1-20

  • Acceptors 3 electrons participate in bonding

    one bonding site “unsatisfied” making it easy to “accept” neighboring bonding electron to complete all bonds at room temperature, each acceptor “releases”

    hole that is available for conduction

    Acceptor site become

    negatively charged

    (fixed charge)

    Semiconductor Physics 1-21

  • Acceptors

    Define: Na ≡ acceptor concentration [cm-3] If Na > ni, doping controls carrier concentration

    Extrinsic semiconductor ⇒ p = Na and n = ni2/ Na Note: p >> n : p-type semiconductor

    In general: Na ≈ 1015 1020 cm-3

    Semiconductor Physics 1-22

  • Energy levels of donors and acceptors.

    Semiconductor Physics 1-23

  • Summary of Charge Carriers

    Semiconductor Physics 1-24

  • Majority and Minority Carriers

    • n-type material, the electron is called majority carrier and hole the minority carrier

    • p-type material, the hole is called majority carrier and electron the minority carrier

    Semiconductor Physics 1-25

  • Charge Neutrality The semiconductor remains charge neutral even

    when it has been doped Overall charge neutrality must be satisfied

    In general: the net charge density ρ (C/cm3) in a semiconductor = ρ = q (p − n + Nd − Na) Where q: electric (elementary) charge = 1.6 Х 10-19 C

    Semiconductor Physics 1-26

    + −

  • Charge Neutrality

    Example Let us examine this for: Nd = 1017 cm-3, Na = 0

    Then, n = Nd = 1017 cm−3, p = ni2/Nd = 103 cm−3 Using the equation ρ = q (p − n + Nd − Na),

    we find that ρ ≠ 0 !!

    What is wrong??

    Semiconductor Physics 1-27

  • Charge Neutrality

    Nothing wrong!

    We just made the approximation when we assumed that n = Nd

    We should really solve the following system of equations (for Na=0):

    Semiconductor Physics 1-28

    p − n + Nd = 0 n.p = ni2

    n2 - n. Nd - ni2 = 0 n ≠ Nd


  • Charge Carrier Transport

    Any motion of free charge carriers in a semiconductor leads to a current

    Different causes for having motion Associated random motion due to the thermal

    energy (Thermal Motion)

    Motion can be caused by an electric field due to an externally applied voltage (Carrier Drift)

    Motion from regions where the carrier density is high to regions where the carrier density is low (Carrier Diffusion)

    Semiconductor Physics 1-29

  • Thermal Motion In thermal equilibrium, carriers are not

    sitting still: Undergo collisions with vibrating Si atoms

    (Brownian motion)

    Electrostatically interact with each other and with ionized (charged) dopants

    Semiconductor Physics 1-30

  • Thermal Motion (cont’d) Characteristic time constant of thermal motion

    mean free time between collisions • Tc ≡ Collison time (seconds)

    In between collisions, carriers acquire high velocity: • vth ≡ thermal velocity (cm/second)

    Characteristic length of thermal motion: • λ ≡ mean free path [cm] = vth Tc

    Example: Put numbers for Si at room temperature (27 oC or 300 oK): Tc ≈ 10−13 seconds, vth ≈ 107 cm/second ⇒ λ ≈ 0.01 μm

    Carriers undergo many collisions as they travel

    Semiconductor Physics 1-31

  • Semiconductor Physics 1-32

    Lecture Summary Covered material Continue Semiconductor Materials

    Types of semiconductors Two types of “carriers” (mobile charge particles):

    • electrons and holes

    Creation of electron-hole pairs Doping

    • Donors n-type semiconductor material • Acceptors p-type semiconductor material

    Important equations under thermal equilibrium conditions: (p − n + Nd − Na = 0) and (n.p = ni2)

    Material to be covered next lecture Continue Semiconductor Physics

    Carrier Transport (Carrier Drift and Carrier Diffusion)

    pn junctions (or diodes) Basics