$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
Specify here the properties of the impurities used for doping.
- impurity-number
- type:
integer
- presence:
required
- example:
1
1, 2, 3, … are unique impurity numbers labeled in $doping-function.
Optionally, a name for the impurity can be provided.
- impurity-name
- type:
character
- presence:
optional
- example:
n-As-in-Si
- example:
0.010*x+0.050*(1-x)
(unit: eV)- example:
0.010*x+0.050*(1-x)-0.020*x*(1-x)
(unit: eV) Here, a bowing factor of 0.020 eV is included.Specify an arbitrary name. The name will be part of some output files. (for later use; it is planned to read in impurity parameters from the database.)
Special feature: If
impurity-name
contains the characterx
, this string is then interpreted as an equation wherex
is the alloy content. This way, a position dependent impurity level can be simulated, e.g. for graded Al(x)Ga(1-x)N layers. In this example, the impurity level would be 10 meV for AlN (x=1) and 50 meV vor GaN (x=0). Note that this has influence on CPU time, i.e. the calculation will take longer because the result of the equation has to be evaluated during the calculation.(For later use: It is planned to read in impurity parameters from the database.)
Several types of impurities are supported.
- impurity-type
- type:
character
- presence:
required
- options:
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. Optiontrap
is not supported so far.
Each impurity can have several different energy levels.
- number-of-energy-levels
- type:
integer
- presence:
required
- example:
1
- example:
1 2
Number of different energy levels for this impurity. Each energy level is specified in
energy-levels-relative
.
Energy levels
- energy-levels-relative
- type:
double array
- presence:
required
- unit:
eV
- example:
0.005
- example:
0.005 0.015
- example:
1000.0
A large negative value, e.g. -1000.0 eV implies full ionization.
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 kBT at room temperature, incomplete ionization must be considered.
Note
‘Cheat’ parameter:
energy-levels-relative = -1000.0
, 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-1000.0
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 the specified energy levels
- degeneracy-of-energy-levels
- type:
integer array
- presence:
required
- example:
2
- example:
4 4
Shallow donors have 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 have 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. [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.
If full ionization is assumed, i.e.
energy-levels-relative = -1000.0
, then the degeneracy factor effectively becomes irrelevant. This can be seen from eqs. (1.4) - (1.7) in [BirnerPhD2011].
- transition-times-cb-to-levels
- type:
double array
- presence:
optional
- unit:
?
Transition times tau1, tau2, tau3, … from conduction band(s) to energy levels; required in case of
trap
: times from conduction band to discrete levels.
- transition-times-levels-to-vb
- type:
double array
- presence:
optional
- unit:
?
Transition times tau1, tau2, tau3, … from energy levels to valence bands 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.
Example
$impurity-parameters !-------------------------------- ! n-type in GaAs !-------------------------------- impurity-number = 1 impurity-name = n-Si-in-GaAs impurity-type = n-type number-of-energy-levels = 1 energy-levels-relative = 0.0058 degeneracy-of-energy-levels = 2 ! 2 for n-type !-------------------------------- ! n-type in GaAs (fully ionized) !-------------------------------- impurity-number = 2 impurity-name = n-fully-ionized impurity-type = n-type number-of-energy-levels = 1 energy-levels-relative = -1000.0 ! fully ionized degeneracy-of-energy-levels = 2 ! 2 for n-type !-------------------------------- ! p-type in GaAs !-------------------------------- impurity-number = 3 impurity-name = p-C-in-GaAs impurity-type = p-type number-of-energy-levels = 1 energy-levels-relative = 0.027 degeneracy-of-energy-levels = 4 ! 4 for p-type !-------------------------------- ! p-type in GaAs (fully ionized) !-------------------------------- impurity-number = 2 impurity-name = p-fully-ionized impurity-type = p-type number-of-energy-levels = 1 energy-levels-relative = -1000.0 ! fully ionized degeneracy-of-energy-levels = 4 ! 4 for n-type $end_impurity-parameters
Database values
energy-levels-relative = ... ! energy in units of [eV] = -1000.0 ! a large negative value implies full ionization = 0.054 ! n-As-in-Si = 0.045 ! n-P -in-Si = 0.039 ! n-Sb-in-Si = 0.045 ! n-N -in-Si = 0.006 ! n-Si-in-Al0.27Ga0.73As = 0.0058 ! n-Si-in-GaAs = 0.007 ! n-Si-in-AlAs = 0.10 ! n-N -in-SiC = 0.20 ! p-Al-in-SiC = 0.045 ! p-B -in-Si = 0.16 ! p-In-in-Si = 0.027 ! 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/