Define mass Action Law and it's operations and working

ENGINEERS DARPAN February 07, 2022
• Mass Action Law

In a semiconductor ( intrinsic and extrinsic ) under thermal equilibrium the product of electrons &  holes is always a constant and is equal to the the square of intrinsic concentration.
And independent of amount of doping by the donor and acceptor impurities.

=) Thermal equilibrium = stable temperature = temperature =constant
n.p = constant
T = constant

At  constant temperature the concentration of minority charge carrier is inversly proportional to the doping concentration.
Note - mass action law is used to determine concentration of minority charge carrier

* Concentration/ density of charge carrier --

      n.p = ni^2
         Where  n = concentration of electron
                     P = concentration of holes
                ni = intrinsic concentration
              ND = concentration of donar atom cm^3
             NA = concentration of accepter atoms / cm^3               
 In a semiconductor,
         electrically neutrality ,
Total +ve charge = total - ve cahrge
              ND + p = NA + n

(a) For N- type semiconductor,

For n-type materials concentrations of electrons is almost equal to the donor concentration.

    NA = 0
ND + p = 0 + n
ND = n - p   ( n>>p)
ND ≈ n 
According Mass action law,
          n.p = ni^2
    =)   ND.p = ni^2
    =)   p = ni^2 / ND

(b) for p - type semiconductor,
    
For n - type materials concentration of electron is almost equal to the acceper concentration

    ND =0
=) 0 + p = NA + n
=) NA = p - n.   ( P >>n )
=) NA ≈ p

According Mass action law,
          n.p = ni^2
    =) n.NA = ni^2
   =)  n = ni^2/NA.






     
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