AlGaAs Examples

Technical Issues - Dispersion in Alloys (e.g. AlGaAs) and Mixed Materials

With the ability to calculate n&k in alloys such as Al(x)Ga(1-x)As vs. x, we should be able to optimize the Al fraction. In this page, we show how to compute n&k from analytical formulas and dispersive tables. Please note that {curly brackets} indicate files required by the various methods.

1. UV-Visible (n,k tables)...Index Formulator: AlGaAsVis-FM.itw, Excel: AlGaAsVis-XL.itw {AlGaAsVis.xlxs}, FS Workbook: AlGaAsVis-WB.itw {AlGaAsVis.vts}

2. Infrared (n func, k=0)...BASIC: AlGaAsIR-BAS.itw, Workbook: AlGaAsIR-WB.itw {AlGaAs.vts}, Excel DDE: AlGaAsIR-XL.itw {AlGaAs.xlsx}, Excel DDE+VBA: AlGaAsIR-XL+VBA.itw {AlGaAs.xlsm}

With AlGaAs as example, we implement User-Defined Index Functions for complex materials. Methods apply as well to temperature variation, etc. FilmStar BASIC, the Workbook and/or Excel is required in order to modify examples. To get started...

Download and extract AlGaAs.zip. This includes *.itw and *.faw examples plus supporting files. Excel workbooks AlGaAs.xlsx, AlGaAs.xlsm, AlGaAsVis.xlsx do not require FilmStar.

Option A: Save all in a new directory, e.g. ..\Winfilm\AlGaAs and edit paths in File.. Configuration.. Directories (recommended).

Option B: Copy *.itw to ..\Winfilm\Index, *.bas to ..\Winfilm\Basic32, AlGaAs.itf to ..\Winfilm\Config, AlGaAs.xlsx to ..\Winfilm\Excel 2007, and AlGaAs.vts to ..\Winfilm\Workbook.

After verifying results in INDEX, try a design, say a QWOT stack in DESIGN. Vary coefficient A in Film Indices to test different fractional x. Please contact FTG Software with any errors, issues, suggestions, or need for further explanation. Click here for our 2021 SVC PowerPoint narrated presentation Specifying n&k in Optical Thin Film Calculations.

IMPORTANT: After opening a design (.faw) or index file (.itw) using the Workbook or Excel DDE, be sure that the corresponding worksheet {file} is open before doing anything else. Should you forget and find yourself in an error message loop, EndFTGprocs.exe is handy to have on your desktop. (You can also press <Shift+Ctrl+Esc> to get to the Task Manager.

1. UV-Visible (Formulator) AlGaAsVis-FM.itw: FilmStar BASIC program RefractiveIndexInfo.bas converted Aspnes .csv n,k files to INDEX .itw format. We then implemented an interpolation function with coefficient 'A' (Al fraction x) ranging from 0 to 80.4% (relative speed: 1). While the linear interpolation formula is simple algebra, it is rather messy and should be thoroughly verified.

After opening AlGaAsVis*.itw or AlGaAsIR*.itw, the User Index Function dialog should contain 8 functions: (1) ALXGAAS (BASIC, IR), (2) ALYGAAS (Formula, Vis), (3) ALZGAAS (Workbook, IR), (4) ALEGAAS (DDE Excel, IR), (5) ALVGAAS (DDE Excel+VBA, IR), (6) ALWGAAS (DDE Excel, Vis), (7) ALTGAAS(Workbook, Vis), (8) ALUGAAS (DDE EXE, IR)

If missing, click File.. Open Collection and open ..\Winfilm\Config\AlGaAs.itf.

The Index Formulator lets you edit and test lengthy interpolation equations. In the screen image below the wavelength is 495.9 nm and Al fraction = 20%.

To prevent errors, we found it useful to list differences as shown at the right and to arrange the Formulator equation in a way that makes it easier to verify. As illustrated below, a pattern becomes obvious. Test by comparing to original data; set A to 19.8 and compare with Aspnes_19.8.itw, etc.

Minus signs are required because the FilmStar equation editor returns -1 for True and 0 for False (why?). Test this with a simple expression like (4>3). Note the use of '&' as AND operator, not to be confused with the same symbol in Excel or BASIC (concatenate strings).

Calculation speed depends on the complexity of the Index Formulator function. This is especially an issue in Stack Mode where n,k must be recomputed for each layer.

NOTE (26 Apr 2024) This section based on Aspnes 1986 data range 207 to 827 nm.

Papatryfornos 2021 data range 260 to 1880 nm. Click to download INDEX files (*.itw).

The THK variable (not used here) is utilized in Double Dispersion
which is similarly programmed in the Index Formulator.

CAUTION/LIMITATION

It is assumed that the interpolated dispersion curve for %Al = 40
lies halfway between dispersion curves for %Al =35 and %Al=45.
That is, nothing 'strange' happens at interpolated Al fractions.
Interpolation accuracy requires close %Al spacing.

2. VIS (DDE Excel) AlGaAsVis-XL.itw {AlGaAsVis.xlsx}: n&k computed from Aspnes tables using bilinear interpolation.

3. VIS (Workbook) AlGaAsVis-WB.itw {AlGaAsVis.xlsm}: In comparison to DDE Excel, calculation is very fast (see below), especially if the Workbook is minimized or hidden (BASIC WbOpenHidden). An Excel worksheet (no VBA) saved in 5.0/95 .xls format can be opened in the Workbook. We found it necessary, however, to copy and paste array formulas manually. Not every Excel function is available in the Workbook (PDF available). Minimize for maximum speed which, in this case is faster than the Formulator.

4. IR (FilmStar BASIC) AlGaAsIR-BAS.itw {AlGaAs.bas}: INDEX BASIC program AlGaAs.bas directly computes n from 900 to 2000 nm (k = 0) based on the work of Sadao Adachi presented here. Bug fixes in BASIC n,k algorithm: INDEX 2.51.0693 & DESIGN 2.61.4760 (21 Nov 2022). Contact FTG Software if you have difficulty reproducing the graphs shown on this page.

5. IR (FilmStar Workbook) AlGaAsIR-WB.itw {AlGaAs.vts}: BASIC is somewhat slow. A faster alternative is the FilmStar Workbook. Opening Workbook AlGaAs.vts before INDEX file AlGaAsIR-WB.itw is recommended (relative speed: ~4).

6. IR (DDE Excel) AlGaAsIR-XL.itw {AlGaAs.xlsx}: Excel can be used as DDE (dynamic data exchange) server. While slower than the Workbook, it supports complex models functions requiring VBA. Opening AlGaAs.xlsx before INDEX file AlGaAsIR-XL.itw is recommended (relative speed: ~0.025).

7. IR (DDE Excel+VBA) AlGaAsIR-XL+VBA.itw {AlGaAs.xslm}: In the previous case, calculations are performed in the worksheet. We now add VBA code. In addition to Coefficients and Indices, we require an Execute Topic and Command. Here Sub Main is triggered in each iteration (relative speed: ~0.02).

Opening AlGaAs.xlsm before INDEX file AlGaAsIR-XL+VBA.itw is recommended. In contrast to Method 4, the worksheet has no formulas. Manually updating cells $B$1 and $B$2 triggers the VBA calculation. Compare the VBA code to FilmStar BASIC program AlGaAs.bas (Method 1). You will want to verify that different methods give the same values as shown below.

8. IR (DDE EXE) AlGaAsIR-EXE.itw {AlGaAs.exe}:

Should the Workbook or Excel not suffice, complex n&k models can be implemented in MATLAB or any language supporting DDE (Dynamic Data Exchange). Example: AlGaAs.exe.

Communicating with AlGaAs.exe IR Server

Alternate methods must be equivalent. Here we superimpose traces calculated with Methods 1, 6, and 7 (31 layer Al(.5)Ga(.5)As-SiO2 stack, 250-800 x 0.1 nm).

Workbook time reduced to 1.6 sec if Workbook minimized!

9. GaInAsP (aka InGaAsP) (added 11.14.22)

A user inquired about GaInAsP, more properly expressed as Ga_xIn_1-xAs_yP_1-y.

https://en.wikipedia.org/wiki/Indium_gallium_arsenide_phosphide

https://aip.scitation.org/doi/10.1063/1.343580

http://www.ioffe.ru/SVA/NSM/Semicond/GaInAsP/

For x=0.48 and y=0.24:

https://refractiveindex.info/?shelf=other&book=GaAs-InAs-GaP-InP&page=Adachi

converted to FilmStar INDEX file InGaAsP.itw. Interpolation over wavelength, x and y fractions will require trilinear interpolation. If utilizing the INDEX Formulator, be sure to develop an alternative verification algorithm (say in Excel).

In general, the Formulator and Workbook should be implemented whenever possible. While the above material might seem complex, it's really an extension of the much simpler My TiO2 example. Another example is given in a discussion of temperature variation.

Stack Mode calculations can be slow as n,k is recomputed for each layer. Be sure to group repeated layers. In the Al example below, expanding to 31 layers slows calculations by a factor of 6.

FTG Software cannot certify the accuracy of n,k values. Users should verify values, noting that n,k depends on fabrication methods, temperature, etc.

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