impurity-parameters

To specify the properties of impurities used in the simulation.

!-------------------------------------------------------------------!
$impurity-parameters                                     optional   !
 impurity-number                         integer         required   !
 impurity-name                           character       optional   !
 impurity-type                           character       required   !
 number-of-energy-levels                 integer         required   !
 energy-levels-relative                  double_array    required   !
 degeneracy-of-energy-levels             integer_array   required   !
 transition-times-cb-to-levels           double_array    optional   !
 transition-times-levels-to-vb           double_array    optional   !
$end_impurity-parameters                                 optional   !
!-------------------------------------------------------------------!

impurity-number = integer
number, 1 or 2 ... (impurity numbers labeled in doping-function)
A unique integer number as usual.

impurity-name = character
a name (for later use - planned to read parameters from database)
An arbitrary name - currently not in use.

impurity-type = n-type
              = p-type
              = trap
Specifies the type of an impurity. n-type means, that the impurity is treated as a donor, p-type as an acceptor.
Option trap is not supported so far.

number-of-energy-levels = integer
number of different energy levels of this impurity

energy-levels-relative = energy1 ... ! in units of [eV]
                       = -1000d0     ! a large negative value implies full ionization
                       = 0.054d0     ! n-As-in-Si
                       = 0.045d0     ! n-P -in-Si
                       = 0.039d0     ! n-Sb-in-Si
                       = 0.045d0     ! n-N -in-Si
                       = 0.006d0     ! n-Si-in-Al0.27Ga0.73As
                       = 0.0058d0    ! n-Si-in-GaAs
                       = 0.007d0     ! n-Si-in-AlAs
                       = 0.10d0      ! n-N -in-SiC
                       = 0.20d0      ! p-Al-in-SiC
                       = 0.045d0     ! p-B -in-Si
                       = 0.16d0      ! p-In-in-Si
                       = 0.027d0     ! p-C -in-GaAs

More parameters can be found in the database file database_nn3.in or at this website: http://www.ioffe.ru/SVA/NSM/Semicond/

Energy levels relative to 'nearest' band edge (n-type -> conduction band, else valence band) in units of [eV].
As many energies as energy levels. 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.

When impurity levels are relatively deep compared to the thermal energy k_BT/e at room temperature, incomplete ionization must be considered.
('Cheat' parameter: energy-levels-relative = -1000d0 (e.g.), 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 -1000d0 one can force them to be completely ionized.)

The energy levels of the donors and acceptors relative to the lowest conduction band edge and highest valence band edge can be output using dopant-energy-levels = yes (see $output-densities).

See also our tutorial on Doped semiconductors to learn more about partial ionization.

degeneracy-of-energy-levels = deg1 deg2 ...
                            = 2   ! n-type
                            = 4   ! p-type
Degeneracy of the specified energy levels
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 sp³ 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. "Physics of Optoelectronic Devices" by Shun L. Chuang.
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.

If full ionization is assumed, i.e. energy-levels-relative = -1000d0, then the degeneracy factor effectively becomes irrelevant. This can be seen from eqs. (1.4) - (1.7) in PhD thesis of S. Birner.

transition-times-cb-to-levels = tau1 tau2 ...
Transition times from conduction band(s) to  energy levels
required in case of trap: times from conduction band to discrete levels

transition-times-levels-to-vb = tau1 tau2 ...
Transition times from energy levels to valence band(s)
required in case of trap: times from discrete levels to valence bands

Note: Currently no interlevel transition times implemented. Can be added provided there are also models which can handle such things.