In this unit, we will go through material properties available for semiconductor materials
used by the CHARGE solver.
Material properties are accessible in two ways.
First, directly through material database and second through the objects tree after
being added to the simulation from material database.
Since the material added to the objects tree is a copy of the material existing in material
database, it is always recommended to make changes to material properties from the objects
tree rather than from material database.
This way, the original material properties will remain unchanged and also the changes
made to the material properties will be considered by the solver immediately.
Otherwise, the material has to be added to the objects tree again after the changes have
been made in the material database.
Every semiconductor material defined in a charge transport simulation should have a
series of electronic properties specified.
The first property is “DC permittivity” which is the permittivity of the material
under DC or zero frequency condition.
In a semiconductor, the work function describes the energy cost of removing an electron from
the intrinsic energy level (the Fermi energy of the undoped semiconductor) and placing
it at vacuum energy level.
The conduction band of semiconductors can have several valleys and by default the lowest
valley is enabled for each semiconductor in the material database.
For each valley, a different set of semiconductor properties can be specified and by default
only those from the lowest valley are used.
The user can choose to change this by picking between the L, X or Gamma valleys.
To account for the influence of the crystal lattice potential of the semiconductor, electrons
and holes can be approximated as free charges with an effective mass (relative to the electron
rest mass) that can depend on the electronic band-structure of the material.
In DEVICE, the effective mass is treated as a parameter of the material model.
In addition, the variation in the effective mass as a function of temperature can be accounted
for with a quadratic model.
A key physical property of the material is the band gap, which describes the energy difference
between the top of the valence band and the bottom of the conduction band.
In DEVICE, the band gap energy is treated as a parameter of the material model.
The temperature-dependent variation in the band gap is accounted for with a "universal"
The intrinsic carrier concentration is calculated from the effective mass and band gap, and
is only displayed in the Material Database for reference.
When impurities are added to the intrinsic (or pure) semiconductor, localized allowed
energy states may be introduced at energies that lie within the band-gap.
In the case of dopants, these impurity states will exist with energies near the conduction
or valence band edges (such that the dopants readily ionize at moderate temperatures).
When the concentration of dopants is large, these discrete states will begin to merge
and form a thin "band" of allowed states within the band gap, effectively narrowing the band
This can be viewed as a narrowing of the band gap or an increase in the effective density
The Slotboom model for band gap narrowing is provided in DEVICE to account for this
The mobility parameter is the physical link between the motion of carriers (electrons
and holes) and the semiconductor material.
The mobility can be viewed as a measure of how easily electrons and holes can move through
the crystal lattice of the semiconductor.
In the absence of any interactions with the lattice, impurities, or other carriers, electrons
and holes would move freely in the periodic potential of the lattice; interactions that
change the momentum of the carriers are termed scattering events.
Different types of scattering events contribute to the variation in mobility of the electrons
and holes, including lattice scattering, ionized and neutral impurity scattering, and carrier-carrier
In addition, the velocity of the carriers is observed to saturate at high-fields.
Each of these scattering mechanisms can be modeled in DEVICE by applying the appropriate
The fundamental process that impedes the free motion of the carriers in the lattice is thermal
scattering off of the lattice itself.
The mobility due to lattice scattering is treated as a basic input into the DEVICE semiconductor
model, and may be entered as a constant value or with a temperature dependence described
by the "universal" temperature model.
Many models exist to account for the influence of impurities on the carrier mobility.
DEVICE provides support for three common models with wide-range of applications: the Caughey-Thomas
model , the Masetti model , and the Klaassen model.
Each model requires a variety of coefficients and their default values are provided in material
database for most common semiconductors.
For general modeling purposes, the Caughey-Thomas or Masetti models are often sufficient, and
coefficients are available for multiple semiconductor materials.
The Klaassen model is primarily tuned for silicon at room temperature, and coefficients
for other materials are not available.
At moderate doping densities, the mobility predicted by all models reduces to that of
the Caughey-Thomas model.
To account for extremely large doping concentrations, the Masetti model can be selected, which adds
a correction to the Caughey-Thomas model for large doping values.
The mobility model proposed by Klaassen can be used to account for the aforementioned
doping effects (at moderate and high concentrations), as well as the influence of carrier-carrier
As the electric field within the semiconductor increases, the drift velocity of the carriers
is commonly observed to saturate, reducing the mobility accordingly.
To account for this effect, DEVICE includes high-field mobility models that describe the
monotonic (silicon-like) or overshoot (GaAs-like) velocity saturation behaviour.
The driving field can be defined as the magnitude of the quasi-Fermi level gradient (grad phi)
or the component of the electric field in the direction of the current density (E dot
The grad phi method is only valid when the charge transport within the material is close
If the charge transport is 2D or 3D or the device contains heterojunctions, the E dot
J option should be used.
The saturation velocity of the carriers in the material is also needed as an input for
the models and can be temperature dependent.
While the electrical material database contains models for many common semiconductors, it
may be necessary to add new semiconductor materials for different systems.
Here we describe how to set the parameters necessary for a minimal semiconductor model.
A new semiconductor can be added to the material database by opening the material database
and choosing the "Semiconductor" option from the "Add" button menu.
The newly defined semiconductor can be named and a color can be chosen to represent the
material in the layout.
The basic properties that define the electronic behaviour of a semiconductor, include the
relative dielectric permittivity, work function, conduction band valley, effective mass, and
Each of these values may be entered as constants.
Often times the effective density of states is known, while the effective mass is not:
to convert from effective density of states to effective mass, please refer to the related
The minimum definition for a semiconductor material must also include a constant lattice
scattering mobility for both the electrons and holes.
These values can be entered as constants.
A basic semiconductor model does not require recombination and generation models defined.
These models will be the subject of the next video in this unit.