impurities{}

Specifications that define imputities (donors, acceptor and fixed charges)

donor{ } / acceptor{ }

name
value

<String> from the database.

energy
value

<Float>

degeneracy
value

<Integer>

The energy separation from the conduction or valence band edge is given in units of electron-volts, \(eV\). These energies are meant as ionization energies, e.g. a donor with an energy level right below the conduction band edge would be specified by a small positive energy level. Degeneracy of impuritiy levels affects their degree of ionization. The degeneracy of donors is usually assumed to be equal to 2, for acceptors it is equal to 4.

  • shallow donors: degeneracy factor 2

    Outer s orbital is onefold occupied (neutral state). There is one possibility to get rid of one electron but there are two to incorporate one (spin up, spin down).

  • shallow acceptors: degeneracy factor 4

    The \(sp^3\) orbital is threefold occupied. Thus, one possibility to incorporate an electron, four possibilities to get rid of one.

More details on degenerate impurity levels can be found in e.g. [ChuangOpto1995]. Note that in nitride semiconductors crystallizing in the wurtzite structure the degeneracy factor may vary from 4 to 6 because of a small valence band splitting.

Example:

impurities{
    donor{    name = "n-P-in-Si"       energy = 0.045   degeneracy = 2 }
    donor{    name = "n-As-in-Si"      energy = 0.054   degeneracy = 2 }
    acceptor{ name = "p-B-in-Si"       energy = 0.045   degeneracy = 4 }
}

Cheat parameter: energy = -1000 (for instance), that means, all electrons are fully ionized from the donors (similar for holes/acceptors). This might be useful for low temperatures like 4 K where usually the degree of ionization is very small. By using -1000 one can force them to be completely ionized. If full ionization is assumed, i.e. energy = -1000, then the degeneracy factor effectively becomes irrelevant. This can be seen from eqs. \((1.4) - (1.7)\) in PhD thesis of Stefan Birner.

impurities{
    donor{    name = "fully-ionized"   energy = -1000   degeneracy = 2 }
    acceptor{    name = "fully-ionized"   energy = -1000   degeneracy = 4 }
}

charge{ }

name
value

<String>

type
value

positive, negative

default

It can be used to put positive or negative charges into the device (e.g. to describe interface charges)

Example:

impurities{
    charge{ name = "positive-charge"   type = positive }
    charge{ name = "negative-charge"   type = negative }
}
Donor levels (n-type) in units of \(eV\) relative to conduction band edge

Donor Name

Energy

Source

n-As-in-Si

0.054

DESSIS

n-As-in-Si

0.049

American Institute of Physics Handbook, 3rd ed., McGraw-Hill, New York (1972)

n-P-in-Si

0.045

DESSIS, American Institute of Physics Handbook, 3rd ed., McGraw-Hill, New York (1972)

n-Sb-in-Si

0.039

DESSIS

n-N-in-Si

0.045

DESSIS

n-As-in-Ge

0.013

American Institute of Physics Handbook, 3rd ed., McGraw-Hill, New York (1972)

n-P-in-Ge

0.012

American Institute of Physics Handbook, 3rd ed., McGraw-Hill, New York (1972)

n-N-in-SiC

0.10

DESSIS

n-Si-in-GaAs

0.0058

n-Si-in-AlAs

0.007

300 K, Landolt-Boernstein

n-Si-in-Al0.27Ga0.73As

0.006

Landolt-Boernstein

More parameters can be found in the nextnano³ database file database.in or at this link

Acceptor levels (p-type) in units of \(eV\) relative to valence band edge

Acceptor Name

Energy

Source

p-In-in-Si

0.16

DESSIS

p-B-in-Si

0.045

DESSIS, American Institute of Physics Handbook, 3rd ed., McGraw-Hill, New York (1972)

p-Al-in-Si

0.057

American Institute of Physics Handbook, 3rd ed., McGraw-Hill, New York (1972)

p-B-in-Ge

0.010

American Institute of Physics Handbook, 3rd ed., McGraw-Hill, New York (1972)

p-Al-in-Ge

0.010

American Institute of Physics Handbook, 3rd ed., McGraw-Hill, New York (1972)

p-Al-in-SiC

0.20

DESSIS

p-C-in-GaAs

0.027

Landolt-Boernstein 1982

More parameters can be found in the nextnano³ database file database.in or at this link