Compensation and Space Charge Neutrality

• Semiconductors can be doped with both donors ( N_d) and acceptors (N_A) simultaneously.
• Suppose a material doped with N_d >  N_A    predominantly n-type  E_F lies above acceptor level E_a completely full, although, with E_F above E_i, hole concentration cannot be equal to N_A.

• Mechanism:
  • The electrons are donated to conduction band from donor level E_d
  • An acceptor state gets filled by the valence band electron, hence creating a hole in thevalence band.
  • An electron from conduction band recombines with this hole.
  • Extending this logic, it is expected that resultant concentration of the electrons in the conduction band would be N_d, N_A in place of   N_d.
  • The process is called as compensation.

• By compensation, the n-type material can be made intrinsic (making  N_A =  N_d ) or even p-type (for  N_A >  N_d ).

Note that a semiconductor is neutral to begin with, and, after doping also, it remains neutral

(Since for all donated electrons, there are positively charged ions ( N_d⁺); and for all accepted electrons (or holes in the valence band), there are negatively charged ions ( N_a^-).

• Thus, the sum of positive charges should be equal the sum of negative charges, and this relation can be given by       P₀ + N_d  = n₀ +N_a  (2.17) 
• 
  is referred to as the equation for the space charge neutrality.
• This equation, solved simultaneously with law of mass action (given by  ) provides the information about the carrier concentrations. Note: for, 

Drift of Carriers in Electric and Magnetic Fields

• The collisions of the charge carriers with the lattice and with the impurity atoms under electric and/or magnetic fields must be accounted for, to compute the current flow through the device.
• These procedures will affect the ease (mobility) with which carriers move within the lattice.
• These collision and scattering processes rely on temperature, which affects the thermal motion of lattice atoms and velocity of the carriers.

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