(05) extrinsic semiconductors

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  • 7/28/2019 (05) Extrinsic Semiconductors


    2 July 2013 Extrinsic Semiconductors 1

    Types of Extrinsic Semiconductors

    Donor or N -typeIf a pentavalent atom(e.g., As, Sb, P)replaces the

    tetravalent Ge or Siatoms in the crystallattice, donor or N -type Extrinsic type

    Semiconductor isformed.

    Acceptor or P -typeIf a trivalent atom(e.g. B, Ga, In)replaces tetravalentGe or Si atoms in thecrystal lattice,acceptor or P -type Extrinsic type

    Semiconductor isformed.

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    Donor or N -type Semiconductors

    Four of the five electrons make the covalent

    bonds.The fifth is unbound and available as carrier of current.

    The energy required to detach this fifthelectron from the atom is of the order of only0.01 eV for Ge and 0.05 eV for Si.Not only the number of electrons increasesin the n-type semiconductor, but the number of holes decreases below the intrinsic value.

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    EC-E F = k T ln (N C/ND)WhereNC = effective density of statefunction in conduction band

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    Charge Equation

    N D + p = n(+ve ions) (holes) (electrons)


    n >> p

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    Representation of N -type Semiconductor

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    Acceptor or P -type Semiconductors

    Only three of the covalent bonds can be

    filled.There remains a vacancy in the fourth bond. Is this vacancy a hole ?Ans. No. The single electron in the incomplete bondhas a great tendency to snatch an electronfrom a neighbouring bond.

    Only a little energy ( 0.01 eV) is needed for the electron from a neighbouring bond to jump to this vacancy.

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    When this happens a hole is created.

    Not only the number of holes increasesin the P -type semiconductor, but thenumber of electrons decreases below

    the intrinsic value.

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    EF-E V = k T ln (N C/ND)WhereNV = effective density of statefunction in valance band

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    Charge Equation

    N A + n = p(-ve ions) (electrons) (holes)


    p >> n

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    Representation of P -type Semiconductor

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    Charge Densities In SemiconductorsSuppose,

    Concentration of electrons in N -type material = n n Concentration of electrons in P -type material = n pConcentration of holes in N -type material = p nConcentration of holes in P -type material = p

    pConcentration of donor atoms = Positive chargecontributed by donor ion = N D

    Concentration of acceptor atoms = Negative chargecontributed by acceptor ion = N A

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    In general,

    The electron and hole concentrations inthe relation np = n i 2 can further beinterrelated by the law of electricalneutrality.

    Total positive charge density = N D+ p Total negative charge density = N A+ n

    According to electrical neutrality,

    N D+ p = N A+ n

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    In case of N -type material having N A= 0and n n>>p n,

    The equation for electrical neutrality becomes,N D+ p n= N A+ n n

    i.e. n n N D In an N -type material the free electron

    concentration is approximately equal to thedensity of donor atoms.Concentration of holes in N -type semiconductor is given by


    in N

    n p


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    In case of P -type material having N D= 0and p p >> n p ,

    The equation for electrical neutrality becomes,N D+ p p = N A+ n p

    i.e. p p N A

    In an P -type material, the hole concentrationis approximately equal to the density of acceptor atoms.Concentration of holes in semi-conductor isgiven by


    i p N



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    It is possible to add donors to P -typecrystal, or conversely, to add acceptors toN -type crystal.

    What happens if equal concentration of donors and acceptors are added to anintrinsic semiconductor ?

    Ans. It remains intrinsic.N D = N A and n = p

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    2 July 2013 Diffusion 20

    What is Diffusion ? Suppose that there is a concentration

    gradient in space in an ensemble of particles.

    The particles tend to move from a regionof higher concentration to a region of lower concentration.

    This is done so as to destroy the non-uniformity of the concentration.

    This phenomenon is known as Diffusion .

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    Diffusion Current Density It is possible to obtain non-uniform

    concentration of electrons (or holes) insemiconductors (as we shall see in a PN -Junction).

    Let the concentration of holes p vary withthe distance x in semiconductor.

    Let the concentration gradient be dp/dx . If dp/dx is negative, obviously the hole

    concentration decreases with increase in x .

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    Although the holes move in a randomfashion due to their thermal energy, adiffusive flow of holes exist in the positive

    x -direction. This flow of holes results in a diffusion

    current in the positive x -direction. Note that the diffusion does not arise from

    the mutual repulsion among charged

    particles of like sign, but it is the result of astatistical phenomenon.

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    Diffusion Current Density

    Diffusion hole-current density J p is proportionalto the concentration gradient dp/dx and isexpressed as

    This is sometimes referred to as Ficks Law .Here q is the magnitude of the electronic charge

    and DP is called the Diffus ion Cons tan t or Diffusio n Coeff ic ient or Diffusivi ty .


    qD J p p

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    Since dp/dx is negative , J p is positive inthe positive x -direction.In SI units, q is in coulomb, dp/dx is in m -4 and J p is in A/m 2.What are the units of diffusivity D p ?

    Ans. m 2/s.

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    Similarly, the electron-current density J n can be written by replacing p by n , D p by

    Dn and the minus sign by the plus sign, as

    It is possible for both a potential gradient and concentration gradient to existsimultaneously along the positive x -direction within a semiconductor.


    dnqD J nn

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    In such a situation, the total current is the

    sum of the drift current and the diffusioncurrent.Thus,


    qD E pq J p p p

    dxdnqD E nq J nnn

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    Einstein RelationshipSince both diffusion and mobility are statisticalthermodynamic phenomena, D and are notindependent. The relationship between them isgiven by the Einstein equation:

    where V T is the voltage equivalent of temperature , defined by,


    T qT k

    V T

    T n



    p V D D

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    Here is the Boltzman Constant in J/K. (k is theBoltzman Constant in eV/K).

    =1.60X10 -19 k

    At room temperature (300 K), V T = 0.026 V= 26 mV