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

Formula symbol
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

↑ ^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 .

[Thuselt-1] 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 .