Important Formula of Electron Emission

 

( 1 ) Richardson Dushman equation relates for thermionic emission and emitter temperature

          J_S = AT²e ^{– b / T} Amp / meter²

          Where

          J_S = Current density in ampere per meter square

          T = Absolute temperature of emitter ( ^oK )

         A = Constant ( Amp / meter² / K² )

            = Depend upon type of emitter

         b = Constant for emitter

         e = Natural Logarithmic base

The value of b for metal is

                   b= φe / K

                  Where

                  e = Charge of electron

                     = 1.602 × 10 ^{– 19} Coulomb

                 φ = Emitter work function

                K = Boltzmann’s Constant

                   = 1.38 × 10 ^{– 23} J / K

( 2 ) If the temperature increases twice, the electron emission increases up to 10⁷ times.

( 3 ) Electron Mobility

The ability of electron moves through semiconductor or metal in the presence of applied electric field is called as electron mobility.

              µ_n = V_n / E

              Where

              µ_n = Mobility of electron

              V_n = Drift velocity of electron

              E = Applied electric field

( 4 ) Hole Mobility

The ability of holes moves through semiconductor or metal in the presence of applied electric field is called as electron mobility.

              µ_H = V_H / E

             Where

            µ_H = Mobility of electron

            V_H = Drift velocity of electron

              E = Applied electric field

( 5 ) Diffusion

The process by which electron / holes in the semiconductor moves from higher concentration region to lower concentration region is called as diffusion.

The concentration gradient for n type semiconductor is given by

             J_n α ( dn / dx )

             Where

             J_n = Current density of electrons

If both donors and acceptors are added to semiconductor, the semiconductor is called compensated.

• If N_d > N_a , the compensated semiconductor is N type.

       N_effective = N_d – N_a

• If N_a > N_d, the compensated semiconductor is P type.

       N_effective = N_a – N_d

( 6 ) The hole concentration in the valance band is given by

           P = N_V e ^{– ( EF – EV ) / KB * T}

           Where

           T = Absolute temperature of intrinsic semiconductor

           Nv = Effective current density in the valance band

           KB = Boltzmann’s Constant

           EF = Fermi level

           EV = Valance band

( 7 ) The electron carrier concentration is hole carrier concentration in the intrinsic semiconductor

                 P = n = n_i

                 Where

                 P = Hole carrier concentration

                n = Electron carrier concentration

                n_i = Intrinsic carrier concentration

( 8 ) Fermi level for intrinsic semiconductor

                    E_F = ( E_C + E_V ) / 2

                   Where

                   E_F = Fermi level

                   E_C = Conduction band

                   E_V = Valance band

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