Quaternary alloys can be created by using a compound semiconductor and a ternary alloy as base materials. The compound semiconductor in most cases will be available in the material database (defined as a 'semiconductor' type material). The ternary alloy is however, an 'Alloy' type material created by mixing two compound semiconductors. Being as 'Alloy' type material, the ternary alloy cannot be directly used as a base material for the quarternary alloy. We therefore have to create a new 'semiconductor' type material for the ternary alloy before it can be used as a base material for the quaternary alloy. The semiconductor material properties for the ternary alloy can be calculated from its 'Alloy' type material version. An example of how AlxGayIn1-x-ySb can be created in CHARGE is shown below:
The AlxGayIn1-x-ySb quarternary alloy can be created by mixing AlSb, GaSb, and InSb. The first step would be to mix InSb and AlSb together to create In1-xAlxSb. Next, the semiconductor properties of In1-xAlxSb are extracted from the alloy material model and are used to create a 'semiconductor' material model for it. Finally, the semiconductor model of In1-xAlxSb is mixed with GaSb to get AlxGayIn1-x-ySb.
Step 1: create alloy model for In1-xAlxSb
Create a new alloy using the 'Binary Alloy' option under the 'new material' button. Choose InSb as the first base material and AlSb as the second base material. Choose the interpolation option to be 'multi valley.'
Set the name to be In(1-x)Al(x)Sb.
Since InSb is the first and AlSb is the second base material, the alloy mole fraction will be (InSb)1-x(AlSb)x or In1-xAlxSb.
NOTE: The default electrical material database in CHARGE comes populated with the common ternary alloys. If the database already contains the desired ternary alloy then it is recommended to use the existing model rather than creating one from scratch.
Step 2: get semiconductor material properties for In1-xAlxSb
Use the 'Visualize' button on the material properties window of In(1-x)Al(x)Sb to display the semiconductor material properties as a function of alloy mole fraction 'x'.
The minimum semiconductor material properties that are necessary to create the 'semiconductor' material model of In1-xAlxSb are permittivity (epsr), work function (W), bandgap (Eg), electron and hole effective mass (mn, mp), electron and hole mobility (mun, mup), and the carrier lifetimes for SRH recombination (taun, taup).
A fixed value for alloy mole fraction 'x' needs to be chosen. In this example, we have chosen x = 0.45.
Note: Although the work function is not available for visualization, it can be calculated easily using a linear interpolation for the given alloy mole fraction.
Step 3: create semiconductor material model for In1-xAlxSb
Use the parameter values from the ternary alloy model In(1-x)Al(x)Sb for an alloy mole fraction of x = 0.45 to create a new semiconductor material. Name the material In(0.55)Al(0.45)Sb.
Note: Note that a conduction valley needs to be selected for the new semiconductor material. Since the interpolation used the minimum valleys from the constituent binary alloys to generate the parameters, we can just select any conduction valley (e.g. Gamma) and enable it to input the parameters.
Step 4: create the quaternary alloy AlxGayIn1-x-ySb
Finally, use the new semiconductor material model for In1-xAlxSb [In(0.55)Al(0.45)Sb] and GaSb to create a 'Binary Alloy' material model for AlxGayIn1-x-ySb. Name the material Al(0.45)Ga(y)In(1-0.45-y)Sb.
Note: The actual alloy mole fraction for the new alloy should be In(1-x)(1-y)Alx(1-y)GaySb. However, for the case where x and y are both small enough so xy << x or y, we can rewrite the alloy mole fractions as AlxGayIn1-x-ySb.