2.6.8. impurities{} (optional)

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

donor{ } / acceptor{ }

name

Name of the impurity for referencing during definition of the structure

type:

String

energy

Ionization energy of the impurity

type:

Real number

degeneracy

Degeneracy of the impurity

type:

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 impurity 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 }
}

Activation Energies

Table 2.6.8.1 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_nn3.in or at this link

Table 2.6.8.2 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_nn3.in or at this link