In this unit, we will describe the way alloy materials are created and modeled in CHARGE
DEVICE supports simulation with alloy materials, which combine two or more base materials (either
unary or compound) to create a new alloy.
Physically, this is accomplished by depositing a material where a fraction of its constituent
atoms are substituted with those of another species.
An example is the alloy of silicon and germanium: replacing some of the Si atoms in the crystal
lattice with Ge atoms creating the alloy SiGe where x is the mole fraction of Ge.
Some of the most commonly used alloy materials already exist in the materials database but
you can create your own alloy materials as well.
In order to form an alloy, the first step is to pick two base materials that the alloy
is consist of.
The first material will assume a mole fraction of (1-x) and the second one, x.
To determine the properties of the alloy material, the properties and behavior of the base materials
are interpolated according to the formula shown here.
Here x is the mole fraction of species B, and “c” is the bowing parameter with the
same unit as the interpolated parameter.
The mole fraction x may vary as a function of position (as in a graded heterojunction).
The bowing parameter “c” can be used to specify quadratic behavior for the interpolation
For example, this is how the band gap energy of SiGe would be calculated.
Often the bowing parameter is zero, but may be modified in the alloy material property
The only exception is mobility which is interpolated by a reciprocal equation as shown here.
In this case, the term with bowing parameter will be ignored if the bowing parameter is
set to zero.
There are two interpolation methods available for creating an alloy from two specified base
Single valley and multi-valley.
In a single valley interpolation, the lowest valley from semiconductor A and the lowest
valley from semiconductor B are considered and by interpolating between the two, the
new valley for the alloy is calculated.
On the other hand, for a multi valley interpolation, all valleys from both semiconductors are considered.
For example, as shown here, we interpolate first between the two L valleys of semiconductor
A and B and then we interpolate between the two gamma valleys of semiconductor A and B
and then we take the lower valley of the two interpolation results.
This is a more accurate interpolation method.
If we choose to use the multi-valley method, we should have available data for all valleys
of both semiconductors in the material database.
Typically, multi-valley interpolation is the most physically realistic; however, single-valley
interpolation is useful for strained materials (e.g. SiGe) and materials where information
about the higher energy conduction band valleys is not available.
After choosing the base materials and interpolation method, the bowing parameter for all the properties
in electronic and recombination properties can be specified under their corresponding
It is important to remember that in these tabs, we are setting the bowing parameter
for the corresponding property in the same units as the property not the values of the
Each alloy can take four sets of bowing parameters (one for single-valley interpolation, and
one each for Ec valley gamma, L, or X when using multi-valley interpolation).
The alloy mole fraction (x) can be adjusted through the Material tab in the property editor
window of any geometric structure object.
Geometric objects will be covered in the “simulation objects” section of this course.
This feature is only available when a material of type alloy is selected for the object.
There are a variety of functions available for the x value.
The fixed option means that x will be a constant value between 0 and 1.
The LINEAR option can be used to make x variable as a function of position x or y or z.
In this case, user can specify the min and max fraction values for the min and max spatial
points and the fraction will be interpolated linearly in between.
The user can also enter a customized equation for the fraction that varies with respect
Some users might need to define ternary alloys which consist of three species.
The steps involved in creating a ternary alloy is similar to that of a binary alloy.
However, there is one key difference.
The base semiconductors for a ternary alloy are compound semiconductors.
The default material database in DEVICE contains models for many common compound semiconductors
used in ternary alloys.
For example, the GaAs and InAs material models can be used as base materials to create InGaAs.
The alloy mole fraction will be (InAs)x(GaAs)1-x, or equivalently InxGa1-xAs.
Quaternary alloys formed of four species can also be created in a similar manner by using
a compound semiconductor and a ternary alloy as base materials.
However, the material database allows only 'semiconductor' type materials to be used
as base materials for alloys.
This means that in order to create a quaternary alloy, we have to first create 'semiconductor'
material models for the constituent alloys and then use them as base materials to create
the desired quaternary alloy.
For an example of how to create quaternary alloys, please visit the related links below.