Professor Dr. Khairul:

Best regards.

Although I am not as expert as you in device modeling and transport based analysis of FET devices, if your mx, my and mz values which generate anisotropy in effective masses are all at Gamma point, then proper syntax using in Silvaco AtLas may require aforethought and a little bit of programming intertwined to get the effective mass at gamma point. If you know the analytical equation involving mx, my and mz to get the isotropic effective mass at Gamma point, may be it can be directly put in equation form like we do for known materials. But may be the following syntax can be tried taking my from L point and mz fromt X point.

mx,y,z(NUM.DIRECT=1) = (mx (NUM.DIRECT=1) =?, my (NUM.DIRECT =3) =?, mz(NUM.DIRECT =4) = ?)

or

mx,y,z(NUM.DIRECT =1) = (mx(NUM.DIRECT =1,1) = ?, my (NUM.DIRECT = 1,2) =?, mz(NUM.DIRECT=1,3) =?

I believe you know the mx, my and mz values of this material at Gamma point. In the second equation I kept the NUM.DIRECT fixed at 1 Gamma point but made it an array to address mx, my and mz values at Gamma point. The first equation I proposed may not be accurate as it takes the my value from L point and mz value from X point but you have all these three values at Gamma point, so the syntax is really tricky here.

I do not have Silvaco Atlas, Sentaurus and MATLAB in my laptop because everyday I tussle with keeping my hardware safe and C drive virus free as spammers are everywhere and they are built-in in research softwares also.

It is nice to have some communication with you.

Sincerely,

Dr. Nabil Shovon Ashraf

Associate Professor

Department of ECE

North South University

Dhaka, Bangladesh.

Dr. Khairul: Best regards. In the first syntax I made an error in terms of indexing. NUM.DIRECT =3 should be for X valley point and I meant my may be taken from there and NUM.DIRECT = 4 should be L valley point and I meant mz can be taken from that valley point but the first syntax will be error prone as the mx, my and mz all are at Gamma point, so my second suggested syntax you may scrutinize if usable.

Sincerely,

Dr. Nabil Shovon Ashraf

Associate Professor

Department of ECE

North South University

Dhaka, Bangladesh.

Nabil Shovon Ashraf

Dear Nabil,

Thank you very much. It's really nice to hear from you. How you and your research are going on? Although I have been writing my own NEGF code and using it for a long time, I am a complete newbie in Silvaco. I have been learning Silvaco for the last two weeks.

Yes, I have the value of mx = 0.15, my = 0.706, and mz = 1.18 at the Gamma point, and these are extracted from the E-k dispersion.

Can you elaborate a little more? Your syntax looks like a function. Where in the silvaco atlas file should I write this? In the material statement, or as a separate function and point it in material statement? This question may sound stupid to you as a Silvaco expert, but I am a newbie here.

Also, with num.direct = 3 or 4, I believe that Silvaco automatically set the degeneracy factor. How can I set the degeneracy factor for a user-defined material?

Thanks a lot.

Khairul

Professor Dr. Khairul Alam: Best regards.

It is evident in your response how much depth you carry in device transport studies and assigning proper parametric values in Silvaco ATLAS. Your question and analogy most RG members will not be able to answer including myself. I just connotated a syntax that may be tried for Gamma value degeneracy case for your new material. You have many contacts through IEEE reviewing activities and being in EDS review committee members. May be personally contacting these Professors can help you even though I believe they will also feel the pressure and dilemma to solve your problem. I know you do detailed work Can Professor Dr. Roger Lake, who was your Doctoral supervisor, help? You may send him personal email and he will surely should show interest here as this is a top class work evident from your question. I am glad you replied to my answer and I cannot or do not know much cleanly or distinctly to assist you more with this question.

Sincerely,

Dr. Nabil Shovon Ashraf

Associate Professor

Department of ECE

North South University

Dhaka, Bangladesh.

Nabil Shovon Ashraf

Dear Nabil,

No problem. Maybe I can try to directly contact the Silvaco technical guy. Synopsys has that option. I saw it in their manual. Silvaco seems to be written that option with Si and Ge in mind.

Thank you and best regards

Khairul

Professor Dr. Khairul Alam:

Best regards.

I am very glad that you took time to address my comments to assist you someway with your research and replied to me which are very encouraging since I am very much cognizant about your research and publications. Here, I would like to share some important facts about effective masses of electrons and holes in all semiconductors. If you have in custody Professor Dr. R. F. Pierret's Advanced Semiconductor Fundamentals book, you will see he has provided equations to extract density of states effective mass and conductivity effective mass for Si, Ge and GaAs based on their E-K diagrams and these are closed form expressions. But all these values are derived from T = 4K. If you look into Professor Dr. Pierret's this book, he listed these masses for electron and hole for Si, Ge and GaAs at T = 4K and T = 300 K. How do you get an effective mass that is referenced at T = 4K to be at T = 300 K ? He has effective mass-versus temperature empirical equation in analytical form that gives for instance, Si effective mass for electron at T = 4K to be 1.06 mo and T = 300 K 1.18 mo. You see most books provide incorrect effective mass of Si for electron at T = 300 K and that is T = 4K value, i.e, 1.08 mo. I wrote a book on this that was to be published by Morgan & Claypool USA this year but was halted due to some misunderstanding with regard to copyeditor's suggested corrections. In this book, I wrote all strain based MOSFET modeling that Professor Dr. Scott Thompson's group did or other researchers did or even when they quote effective mass, strain effects on these mass and 2D confinement based alterations of these masses for Si at T = 300 K, these are actually T = 4K values. Professor Dr. Robert F. Pierret's book clearly shows this difference. So ideally, the E-K diagram of conduction band and valence band must be constructed for Si, Ge, GaAs and all other semiconductor devices we know at T = 300 K and then by fitting a parabola close to conduction band minima and valence band maxima, extraction of the effective mass at a stand alone temperature can be done. Otherwise, from T = 4K to T = 500 K as these are the general temperatures MOSFETs are operated, the modeling engineers needs to develop empirical analytical equation like given in Professor Dr. Pierret's book and use the right effective mass at right temperature, not the T = 4K reference value. These are the contents I discussed in my book that how illustrious researchers and Professors made this mistake to first quote electron and hole effective mass at T = 4K, assign these values at T = 300 K and then apply strain based analysis that we all know.

I had another question to you: For your new material for constructing the E-K diagram for conduction and valence band, did you use less cumbersome empirical pseudopotential method or more accurate k.p. method?

Sincerely,

Dr. Nabil Shovon Ashraf

Associate Professor

Department of ECE

North South University

Dhaka, Bangladesh.

Nabil Shovon Ashraf

I use the empirical tight-binding method for band structure calculation. The TB parameters are usually fitted against DFT band structures. However, in most cases people extract effective masses nowadays directly from DFT band structure, and theses are available in published literature.,

Tariful Azam

Mt and Ml are for X and L valley where Silvaco solves Schrodinger's equation 3 or 4 times depending on valley anisotropy and degeneracy. In my case, I want Silvaco to solve Schrodinger only once but not using isotropic mass but with anisotropic masses. The problem with silvaco is num.direct = 1 option only solves the isotropic band.

I saw in the Synopsis manual that users can provide quantization mass and transverse masses together with valley degeneracy. So the Schrodinger solver is under user control. I was wondering if such options are available in silvaco or not. Thanks.

Tariful Azam

Thank you very much. No, I am not trying to calculate different valleys. Only the Gamma valley. In Silvaco, for Gamma valley, mx = my = mz. This is set by num.direct = 1 command. But for my case mx, my, and mz have different values. That is, mx = 0.15, my = 0.706, and mz = 1.18. I do not know how to input these masses in Silvaco for Gamma valley.

Professor Dr. Khairul Alam:

Best regards.

I do not know how long it takes for you to extract the effective masses for electrons and holes by the tight binding method fitted against density functional theorem (DFT) simulation to extract E-k plot for a particular semiconductor material at T = 300 K. But since now a days you will notice more FETs are operating at cryogenic temperatures and temperatures being much lower than 300 K, where according to Drude's mobility model, mean time between scattering extends multifold and effective mass for electron and hole reduce at lower temperature and since mobility is reciprocally related to effective mass and directly related to mean time between scattering, mobility enhances very higher degree and saturated drift velocity can increase as phonon scattering related velocity saturation is less due to temperature related phonon scattering reduction at lower temperature ( I am giving here simpler explanation for mobility increase at lower temperature of the substrate) . Now let' say we need effective masses of electrons and holes for every semiconductor material between T = 4K and T = 300 K. Depending on the simulation time requiring for each DFT run to extract one E-K plot at one temperature, for good accuracy how should we proceed to extract effective mass versus temperature curve for electron and hole for a semiconductor? Should we go with DFT run with T = 4k, increase the range to be 2K and go up to 300 K and then getting the dispersion relationship and fitting an empirical equation based curve as closely as possible and quote them as analytical equations for calculation of effective mass for electron and hole as a function of temperature from T = 4K to T = 300 K of a particular semiconductor material. I guess we need these effective mass versus temperature curve for almost all semiconductors so that the benefits of low temperature operation and mobility increase, drift velocity increase and drive current increase can be realized. Do we have enough papers on this requirement for Si, Ge, III-V, II-VI and 2D materials with precision accuracy since E-K diagrams at every temperature need to be really perfect to extract the effective mass at that temperature?

Sincerely,

Dr. Nabil Shovon Ashraf

Associate Professor

Department of ECE

North South University

Dhaka, Bangladesh.

Professor Dr. Khairul Alam:

Best regards.

If Synopsis or Sentaurus gives you the option to put anisotorpic effective mass at any valley point, be it Gamma, X or L , the manual can help and I had one if you need it but you need to purchase or download the Synopsis TCAD software and most of the time, these softwares have bugs in-built. I witnessed it once while taking a course at the PH.D. study at ECE department of Arizona State University where for a problem, I defined a material at Silvaco ATLAS, wrote the syntax for simulating it with proper meshing. It gave the plot I wanted for my first run and after some time, when I did another run with the same syntax, the plot was error prone. Then in an internship project where Professor Dr. Dieter Schroder was my university level supervisor, I had no problem showing the industry various plots using ISE-TCAD (Switzerland based) and Synopsis is the most updated version of ISE-TCAD. So these bugs are problematic.

Anyway, you may also try like this : mx(NUM.DIRECT=1(1)) = ?, my(NUM.DIRECT = 1(2)) = ? , mz (NUM.DIRECT = 1(3)) = ?

Then how these mx, my and mz values are combined to give one value of effective mass for electron and hole, the TCAD should handle in fact if Synopsis can do that. 1(1), (1(2) and 1(3) I just wrote so that three indexes of the effective masses mx, my and mz can be differentiated.

I will be very glad if you give your points to my previous answer just before this one as it was very long elaborated comment and the picture I put there is very much needed to accomplish so that low temperature operation of today's FET devices give precise values for drive current. Since you are expert in these, I really elaborated my comment just before this one.

Sincerely,

Dr. Nabil Shovon Ashraf

Associate Professor

Department of ECE

North South University

Dhaka, Bangladesh.

Professor Dr. Khairul Alam:

Best regards.

Since band parameters and band diagrams of III-V materials are more of concern for high speed electronics, I kept a pdf whose citation count today is 8150. I used this pdf to write a chapter of device physics based assessment of III-V semiconductor based MOSFETs in my third book to be published by Morgan & Claypool USA I told you earlier but being on hold now because I really did not distinctly understand the scope of copyeditor's corrections of author written draft. Anyway, you might have this copy in your reserve. But I am attaching it again in case the paper is useful for your research and data collection. Probably we need a review paper today exactly like the content arrangement in this paper with DFT based band diagrams of listed III-V materials and their alloys in this attached paper. The paper is published in 2001.

Sincerely,

Dr. Nabil Shovon Ashraf

Associate Professor

Department of ECE

North South University

Dhaka, Bangladesh.

Tariful Azam

me*DOS = (ml·mt·mt)^1/3 = silvaco parameter, mc

This is DOS effective mass and it is used in carrier density calculation. If I use this as mc of silvaco then I will not get the correct eigen energy levels in the quantization direction. But that might be a good approximation.

Nabil Shovon Ashraf

Regarding effective mass vs temperature, the DFT and analytical approach that you described is the best process that I can think of. Because empirical method such as k.p or TB, the methods depends on the parameters. So, the effective mass will be corresponding to the temperature at which the parameters were fitted.

Regarding synopsis and silvaco, we do not have a synopsis license. That is why I am looking a way in silvaco.

Thanks.

Thank you Professor Dr. Khairul Alam.

Expert comments like this inspire a fellow colleague to assess his research management. Your comments and your computational works are always beneficial and in Bangladesh we all know how reputed a faculty you are. Now it is up to the established researchers to derive these equations for effective masses of electron and hole for Si and almost all alternative materials to silicon between T = 4K and T = 300 K, since low temperature or cryogenics operation of MOSFET or other FETs seem to extremely required to be in line with International Roadmap for Semiconductor and Devices where the maximum drive current of FET seems to be bottleneck for all present day device architectures at T = 300 K.

Sincerely,

Dr. Nabil Shovon Ashraf

Associate Professor

Department of ECE

North South University

Dhaka, Bangladesh.

Professor Dr. Khairul Alam:

Best regards.

In SILVACO ATLAS there is a provision for defining and adding a C-interpreter file that will contain special parameters which will be linked with the modeling syntax of Silvaco ATLAS for that material. I just can think like this what you may try in a C-interpreter file:

mx = NUM.DIRECT = 1 (1),

my = NUM.DIRECT = 1 (2),

mz = NUM. DIRECT = 1(3),

mx = ?,

my = ?,

mz = ?,

Now you may save this file by assigning a name as per C-interpreter file indexing requirement and then in the syntax under material section where you define your modeling part, add this C-interpreter file with other parameters as usual. What I just wrote here is just an example. But C-interpreter files are used to define parameters that can be linked to modeling in Silvaco ATLAS.

Now, I have some other important concepts to discuss with you As you confirmed 3D DFT based extraction of E-K diagrams for conduction band and valence band of a semiconductor is the best approach to compute effective mass from conduction band minima and valence band maxima, does DFT method give density of states effective mass and conductivity effective mass both? Conductivity effective mass is used to calculate channel mobility which is also dependent on scattering time from scattering events whereas density of states effective mass for electron and hole are used in effective density of states determination for electrons and holes at a reference T = 300K and probably bulk mobility which is usually higher than channel mobility due to the reason that although the density of states effective masses for electron and holes are generally higher than conductivity effective masses of these carriers, but the scattering events are less in bulk than at channel interface and scattering time is therefore larger in bulk than in channel. This conductivity effective mass of electron and hole separately is important for channel mobility calculation in presence of strain and 2D confinement effects from quantization. So I believe if you make it clear to me that DFT analysis can be tailored to extract both density of states effective mass and conductivity effective mass of any semiconductor material, it will be important information to me.

Sincerely,

Dr. Nabil Shovon Ashraf

Associate Professor

Department of ECE

North South University

Dhaka, Bangladesh.

Nabil Shovon Ashraf

Once you got the mx, my, and mz, you can calculate DOS effective mass and conductivity effective mass. The following link has a good description. See the bottom part of the following link.

https://www.nextnano.de/nextnano3/input_parser/database/docu/effective_masses.htm