# Minority carriers

Minority charge carrier is the name of the type of charge carrier in a doped semiconductor , which occurs less frequently than the majority charge carrier . With p-doping, the minority charge carriers are the electrons , with n-doping, they are the defect electrons (holes) .

## Calculation of the charge carrier density

 N A Acceptor concentration (doping) N D Donor concentration (doping) N A - ionized acceptor atoms N D + ionized donor atoms n i Intrinsic carrier density n n Majority charge carrier (with n-doping) p n Minority charge carrier (with n-doping) p p Majority charge carrier (with p-doping) n p Minority charge carriers (with p-doping) n Density of free charge carriers (electrons) p Density of free charge carriers (holes) m n effective mass of electrons m p effective mass of the holes W G Energy of the band gap in eV k Boltzmann constant in eV / K T absolute temperature H Planck's quantum of action

From the equations for the majority carrier concentration for single doping, the intrinsic conduction density of the semiconductor is significantly greater

p-area

${\ displaystyle p = p_ {p} \ approx N_ {A} ^ {\, -} \ approx N_ {A} = \ mathrm {const.}}$ (at room temperature)

or n-area

${\ displaystyle n = n_ {n} \ approx N_ {D} ^ {+} \ approx N_ {D} = \ mathrm {const.}}$ (at room temperature)

arises in thermodynamic equilibrium because of

{\ displaystyle {\ begin {aligned} n \ cdot p & = n_ {i} ^ {2} \\ & = 4 \ cdot \ left ({\ frac {2 \ cdot \ pi \ cdot k \ cdot T} {h ^ {2}}} \ right) ^ {3} \ cdot (m_ {n} \ cdot m_ {p}) ^ {3/2} \ cdot \ exp \ left (- {\ frac {W_ {G}} {k \ cdot T}} \ right) \ end {aligned}}}

the minority carrier concentration for

• p-area
${\ displaystyle n_ {p} \ approx {\ frac {n_ {i} ^ {2}} {N_ {A}}} = \ mathrm {const.} \ ll p_ {p}}$
• n area
${\ displaystyle p_ {n} \ approx {\ frac {n_ {i} ^ {2}} {N_ {D}}} = \ mathrm {const.} \ ll n_ {n}}$

## Individual evidence

1. a b Frank Thuselt: Physics of semiconductor components: an introductory textbook for engineers and physicists . Springer, Berlin / Heidelberg / New York 2005, ISBN 3-540-22316-9 , pp. 68 ff .