impurities{ }

Calling sequence

impurities{ }

Properties

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • items: \(\mathrm{maximum\;1}\)

Functionality

Specifies properties of impurities (donors, acceptor and fixed charges)

Example
impurities{
    donor{...}
    donor{...}
    acceptor{...}
}

Nested keywords

donor{ }

Calling sequence

impurities{ donor{ } }

Properties

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • items: \(\mathrm{no\;constraints}\)

Functionality

Defines properties of donors.

Example
impurities{
    donor{...}
    donor{...}
}

donor{ name }

Calling sequence

impurities{ donor{ name } }

Properties

  • using: \(\mathrm{\textcolor{WildStrawberry}{required\;within\;the\;scope}}\)

  • type: \(\mathrm{character\;string}\)

Functionality

Name of the impurity for referencing during definition of the structure

Example
impurities{
    donor{
        name = "n-Si"
        ...
    }
}

donor{ degeneracy }

Calling sequence

impurities{ donor{ degeneracy } }

Properties

  • using: \(\mathrm{\textcolor{WildStrawberry}{required\;within\;the\;scope}}\)

  • type: \(\mathrm{integer}\)

  • values: {1, 2, 3, ..., 12}

  • unit: \(\mathrm{-}\)

Functionality

Degeneracy of the impurity. It affects the degree of ionization.

Note

The degeneracy of donors is usually assumed to be equal to 2 - degeneracy factor is 2. Outer s orbital is one-fold occupied (neutral state). There is one possibility to get rid of one electron, but there are two to incorporate one (spin up, spin down). More details on degenerate impurity levels can be found in e.g. [ChuangOpto1995].

Example
impurities{
    donor{
        name = "n-Si"
        degeneracy = 2
        ...
    }
}

donor{ energy }

Calling sequence

impurities{ donor{ energy } }

Properties

  • using: \(\mathrm{\textcolor{WildStrawberry}{required\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: no constraints

  • unit: \(\mathrm{eV}\)

Functionality

Ionization (activation) energy of the impurity, \(E_{ion}^{(0)}\). The positive value means that the donor level is located below the conduction band edge, while the negative value means that the level is located within the conduction band. See Doping for reference on typical activation energies.

Hint

The negative value can be used to force full ionization of donors despite the quasi-Fermi levels. The degeneracy factor effectively becomes irrelevant under the full ionization. This can be seen from eqs. \((1.4) - (1.7)\) in [BirnerPhD2011].

Example
impurities{
    donor{
        name = "n-Si"
        degeneracy = 2
        energy = 0.0058
    }
}

\(\mathrm{\textcolor{WildStrawberry}{Available\;in\;the\;next\;release.}}\)

donor{ N_ref }

Calling sequence

impurities{ donor{ N_ref } }

Properties

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: [1e10, ...)

  • default: \(\mathrm{infinity}\)

  • unit: \(\mathrm{cm^{-3}}\)

Functionality

Reference doping \(N_{ref}\) for doping-density-dependent activation energy

\[E_{ion} = E_{ion}^{(0)} \times \left[1-\left[\frac{N_{A,0} + N_{D,0}}{N_{ref}}\right]^c \right]\]

where \(N_{D,0}\) and \(N_{A,0}\) are donor and acceptor densities, and \(E_{ion}^{(0)}\) is ionization energy of a dopant at low doping concentrations.

\(\mathrm{\textcolor{WildStrawberry}{Available\;in\;the\;next\;release.}}\)

donor{ c }

Calling sequence

impurities{ donor{ c } }

Properties

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: [0.1, 1.0]

  • default: 1.0/3.0

  • unit: \(\mathrm{-}\)

Functionality

Exponent \(c\) for doping-density-dependent activation energy formula.

acceptor{ }

Calling sequence

impurities{ acceptor{ } }

Properties

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • items: \(\mathrm{no\;constraints}\)

Functionality

Defines properties of acceptors.

Example
impurities{
    acceptor{...}
    acceptor{...}
}

acceptor{ name }

Calling sequence

impurities{ acceptor{ name } }

Properties

  • using: \(\mathrm{\textcolor{WildStrawberry}{required\;within\;the\;scope}}\)

  • type: \(\mathrm{character\;string}\)

Functionality

Name of the impurity for referencing during definition of the structure

Example
impurities{
    acceptor{
        name = "p-C"
        ...
    }
}

acceptor{ degeneracy }

Calling sequence

impurities{ acceptor{ degeneracy } }

Properties

  • using: \(\mathrm{\textcolor{WildStrawberry}{required\;within\;the\;scope}}\)

  • type: \(\mathrm{integer}\)

  • values: {1, 2, 3, ..., 12}

  • unit: \(\mathrm{-}\)

Functionality

Degeneracy of the impurity. It affects the degree of ionization.

Note

The degeneracy of acceptors is usually assumed to be equal to 4 - degeneracy factor is 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].

The degeneracy factor may vary from 4 to 6 in nitride semiconductors crystallizing in the wurtzite structure because of a small valence band splitting.

Example
impurities{
    acceptor{
        name = "p-C"
        degeneracy = 4
        ...
    }
}

acceptor{ energy }

Calling sequence

impurities{ acceptor{ energy } }

Properties

  • using: \(\mathrm{\textcolor{WildStrawberry}{required\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: no constraints

  • unit: \(\mathrm{eV}\)

Functionality

Ionization (activation) energy of the impurity. The positive value means that the acceptor level is located above the valence band edge, while the negative value means that the level is located within the valence band. See Doping for reference on typical activation energies.

Hint

The negative value can be used to force full ionization of acceptors despite the quasi-Fermi levels. The degeneracy factor effectively becomes irrelevant under the full ionization. This can be seen from eqs. \((1.4) - (1.7)\) in [BirnerPhD2011].

Example
impurities{
    acceptor{
        name = "p-C"
        degeneracy = 4
        energy = 0.027
    }
}

\(\mathrm{\textcolor{WildStrawberry}{Available\;in\;the\;next\;release.}}\)

acceptor{ N_ref }

Calling sequence

impurities{ acceptor{ N_ref } }

Properties

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: [1e10, ...)

  • default: \(\mathrm{infinity}\)

  • unit: \(\mathrm{cm^{-3}}\)

Functionality

Reference doping \(N_{ref}\) for doping-density-dependent activation energy

\[E_{ion} = E_{ion}^{(0)} \times \left[1-\left[\frac{N_{A,0} + N_{D,0}}{N_{ref}}\right]^c \right]\]

where \(N_{D,0}\) and \(N_{A,0}\) are donor and acceptor densities, and \(E_{ion}^{(0)}\) is ionization energy of a dopant at low doping concentrations.

\(\mathrm{\textcolor{WildStrawberry}{Available\;in\;the\;next\;release.}}\)

acceptor{ c }

Calling sequence

impurities{ acceptor{ c } }

Properties

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • type: \(\mathrm{real\;number}\)

  • values: [0.1, 1.0]

  • default: 1.0/3.0

  • unit: \(\mathrm{-}\)

Functionality

Exponent \(c\) for doping-density-dependent activation energy formula.

charge{ }

Calling sequence

impurities{ charge{ } }

Properties

  • using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)

  • items: \(\mathrm{no\;constraints}\)

Functionality

Defines the type of charges which can be used to add positive or negative charges into the device, e.g., to describe interface charges.

Example
impurities{
    charge{...}
    charge{...}
}

charge{ name }

Calling sequence

impurities{ charge{ name } }

Properties

  • using: \(\mathrm{\textcolor{WildStrawberry}{required\;within\;the\;scope}}\)

  • type: \(\mathrm{character\;string}\)

Functionality

A reference name.

Example
impurities{
    charge{
        name = "positive_charges"
        ...
    }
}

charge{ type }

Calling sequence

impurities{ charge{ type } }

Properties

  • using: \(\mathrm{\textcolor{WildStrawberry}{required\;within\;the\;scope}}\)

  • type: \(\mathrm{choice}\)

  • choices: positive; negative

Functionality

Defines sign of the charge.

Example
impurities{
    charge{
        name = "positive_charges"
        type = positive
    }
}