I am in doubt about which method i may use to calculate band gap of thin films, if the Kubelka-Munk method using diffuse reflectance spectra or the Tauc method using absorption spectra.
Here I repeat my answer regarding the question "How to obtain the energy band structure of the semiconductor".
Do you need to test the band gap experimentally ? In this case you can use both optical and photoelectric measurements. Optical studies include the measurements of the absorption, excitonic photoluminescence and reflection spectra. Excitons present the bound electron-hole pairs. Their excitation energy Eex is slightly less than the energy of the unbound electron and hole, i.e. than the electronic band gap energy Eg. The binding energy of excitons ∆Eex in semiconductor is usually about several tenths meV. The energy of exciton reflection spectrum, which present a dispersion curve, is acossiated with the formation of free exciton and determine the optical band gap of semiconductor. The measurement of photoluminescence spectra allows to observe the recombination of free and/or bound to acceptor(donor) excitons. The binding energy of bound excitons correspond about 10 meV (for exciton bound to acceptor this energy is about 0.1 Ea, where Ea - ionization energy of aceptor). In this case it is also possible to observe quantum-zise effect and its affect on the energy structure.
Usually, the traditional method of estimating of band gap of semiconductor materials is based on the results of absorption spectra measurements. However, in the case of polycrystalline films the light transmission depends not only on its absorption resulting from transitions between energy bands, as well as the light scattering by material and additional absorption resulting from the presence of different types of intrinsic defects. All these factors contribute to transmission of light. A evaluation of bandwidth is based only on the absorption measurements as a result of interband transitions. But it is not in the case of polycrystalline silicon. So, you can get any results that are not relevant to the evaluation of bandgap. Measurement of light transmission of polycrystalline films is valid only for the evaluation of their optical quality.
Effective method for the determination of semiconductor band gap is the measurements of the photodiffusion current spectra (see : J. Phys. : Condens. Matter, V.18, 5323 (2006)). This method allows to determine both the band gap energy and the energy of different defects in semiconductor. In this case, unlike photoconductivity, the measurements are made without an applied electric field. And so there is no bending of the energy bands. Usually we used both optical and photodiffusion current measurements. If you need to test of band gap of unknown semiconductor we must first all to carry out the measurements of absorption spectra. In this case you get approximate value of bandgap. Then, it is necessary to perform the photoluminescence and reflection as well as photodiffusion current measurementd described above.
For plasma thin films we use the Tauc method based on ultraviolet-visible infrared spectra as long as the Tauc plots can usefully be extrapolated to the x-axis (for amorphous thin films this is not always possible).
Steven F. Durrant
TO quantify the optical band gap of films, Tauc Model is employed in the high absorbance region of transmittance spectra, J.Tauc
Hi
Tauc method is used for calculating the Band gap in the absorption region of the transmittance spectra. . The energy band gap can be determined by extrapolating the straight line portion of the curve on to the energy axis (X-axis).
I once used this method for SeGe Alloy thin films: http://dx.doi.org/10.1088/0022-3727/23/4/012
I hope that you have access to it and it is usefull to you.
i did this process before for determinning the band gap, this is depend on the prepare a thin film, putting on glass, and you make this glass as a blank, then you did another measurment by UV-Vis spectophotometer..........and after this you will get your Transmission or your absorption as you like, then you will apply Munck relation, by converting the wavelength to energy in unit of electron Volts.
Why Steven Sir you are saying for amorphous material Tauc plot will not be possible.
Andre, If the material in question does not have a single phase, it will not likely have a single distinict absorbtion onset, thats why there is a correspondance to a more gradual sloped curve in the Tauc Plot....I think it is assumed that the absorption coefficient Alpha near the band gap edge shows an exponential dependance on photon energy for many materials. Ayad Alkaim said its dependant upon the think film prep, put on glass...make the glass a blank...then do another meausrment by UV-Vis Spectophotometer. The material is important because of the localized state associated with the amorphous state in the forbidden band....Hope this helps....Good luck...sounds like a very intresting project. Best wishes.
Measure both absorption spectra and photoluminescence spectra to compliment both method to find the band gap.
Mostly the peoples use the Tauc plot to estimate the band gap (direct as well indirect band gap). For this method you need to calculate absorption coefficient alpha by UV-vis spectrophotometer as some of peoples mentioned above. You can see our paper "Optical properties of iron oxide (alpha-Fe 2 O 3 ) thin films deposited by the reactive evaporation of iron"
Dear Andre and colleagues. Concerning films: the Tauc's method is based on the assumption of disorder in the electronic functions and on parabolic bands. If I am not wrong it also assumes that the transition matrix element is constant, so the transition probability is assumed constant in the energy range studied. It is widely used for amorphous materials, even though there is some questioning in the literature about the validity of the mentioned assumptions. Another concern is the correct calculation of the absorption coefficient. For an accurate calculation one has to take in account the interference fringes, and use the correct thickness.
Concerning powder: it is important to take into account the light scattering. I don´t know what is a good procedure... I became interested in your question to check for this answer. If someone has a reply please post.
Hi colleagues!
Thanks for the answers!
Well, I always applied theTAUC method for my powder samples, but starting to work with thin films I've heard that the Kubelka MUNK is better. So, I was in doubt about which method I must use for calculating the band gap of my powders and thin films samples. I would like to compare all the results because my samples are based on the same material, so i would like to use only one method for that.
In respect to amorphous samples, I know it's possible but sometimes is hard to apply TAUC method because the band gap values are so small, negative sometimes as expected for these kind of samples due to the highest degree of disorder. Additionally, as suggested by Rajneesh Mohan, I do also photoluminescence spectra for all the samples and i agree that is a very nice tecnique to characterize the optical properties of the samples and complement the band gap results.
If there is a strong exciton feature at the band edge, like ZnO or GaN, those features should be taken into account. The band edge will shift with the broadening of the exciton from disorder as the exciton can be broadened also Franz Keldysh. Also as your films get thicker, Defects and band tailing become more important. Band gap is really a kind of fuzzy concept, if you are really trying get a very precise number. Different methods will give slightly different results. Especially with alloys. For materials development, a combination of experimental methods is probably best, but practically speaking often people just choose something simple like the slope of the band edge or PL FWHM.
For a thin film sample one can use Tauc's plot for band gap estimation (valid for all direct/indirect materials and crystalline/amorphous) by extrapolating the linear portion of the curve on to X-axis i.e (ahv)^m = A(hv-Eg) with (ahv)^m --> 0 where m = 2 for direct transition and m=1/2 for indirect transition.
For a powder sample one can use Kubelka-Munk method (f(r) = (1-R)^2/2R and extrapolating the linear portion of the curve on to X-axis using diffuse reflectance spectra
For thin films, either Kubelka–Munk function F(R) = (1-R)2/2R or the procedure described by Pankove J (1971 Optical Processes in Semiconductors, New Jersey: Prentice-Hall Inc) can be applied using spectrophotometer data.
Use Photo Acoustic Spectroscopic method to get the band edge position. PAS would be more accurate for powder samples than reflectance spectroscopic methods.
My problem is that I can't do both method in my lab because we don't have an accessory for diffuse reflectance. I tryed to use Tauc's method for both materials, but in the case of thin films my substrates are not transparent (one only polished face) and it makes difficult to mesure the band gap of my thin films using Tauc method because the absorbance of the UV beam.
As J. Silva said it is important to take into account the light scattering for powders. But it applies also for thin film because you are also scattering the light by the thin film surface and in this case the material reflects light diffusely with great efficiency than in powder.
I will make a correlation with other techniques like PL or try doing Kulbelba Munk to compare my results obtained by Tauc's method.
Thanks everybody!
you can do it theoretically, by applying DFT. You will extract the bandstructure and also the optical spectra. I can collaborate with you. Best
Why not! Is it possible to calculate band gap for thin films, simulating the materials deposed on different substrates (amorphous and single crystal substrates)?
Yes, it possible to calculate the Bandstrucure of a thin film, usually we use Slab model. If you want to consider the substrates effect :amorphous is somehow difficult than a single crystal one .Thin-film and substrate will be considered as interfaces.
people once suggested me that UPS measurements can be a way to derive band gap values. You may have a try.
Yujing Liu, Does it mesure the band gap of the compound or give information about isolate orbitals energy of the elements which compose the compounds? Sorry but I've never heard about this techinique mesure the band gap? I am wrong, maybe!
Hi André, Ultraviolet photoelectron spectroscopy aka UPS will give you only half the information you need, you can determine the valence band edge (of your electronic band gap) using UPS. You will need another technique to get the conduction band position (such as measurement of photo voltage). But if you can get a "standard" thin film (possibly single crystalline) of the same material then comparing the UPS and XPS core spectra you may be able to determine the shift in the band gap. This is assuming "certain behavior" of your material and you know the band gap of the standard. I have not really gone through all your responses here to see if you have mentioned the material. Fact is determining band gap values of powder samples, particularly if it is absorbing, remain a challenge. DFT values will be close to the ordered thin film value but will give you a ballpark number. In most semiconductor type material powders (and porous ones) the band gap shifts significantly compared to their crystalline counterparts.
Andre, concerning the effect of light scattering, the problem is generally much bigger on powders and composite materials because there are many scattering layers as light goes though as compared to films (just air film interface and film/substrate interface) of homogeneous materials. If the interfaces of your films have roughness comparable with the wavelength of the radiation the scattering can be very high, and you will need an integrating sphere for both transmittance and reflectance measurments.. Polished substrates will help to improve the accuracy of T measurements. I am curious about your materials and the thickness and powder grain size range you use. I believe these parameters will be very important in solving your question.
It was good to know about the use of Kubelka-Munk method. I will check the literature concerning this. Would somebody suggest references?
An interesting issue concerns also the exciton effects mentioned by J. Muth. Will the excitons and the Frank-Keldish affect somehow the compounds bandgap determination (absorption edge behavior) based on the T and R data at room temperature?
@J. Silva, Kubelka-Munk works very well on powder sample if you have diffused reflectance accessory (which André doesn't). You will find many examples if you look for band gap measurements in photocatalysts. Applied Optics, 1973, vol 12, page 573 has very detailed treatment on using diffused reflectance spectra and Kubelka-Munk.
Cyclic Voltammetry (CV) is a great tool to measure the oxidation/reduction potentials of a material. Therefore, you determine the bandgap and its position relative to vacuum. Works for films and powders.
Dear Cory Cress, could you please be kind enough and explain in deatails on CV method. Thanks in advance
Thanks for helping me!
I am glad to know different techniques to mesure the band gap values of powders and thin films that were suggested by the colleagues. But, unfortunately I don't have acess to many of those techniques, including UPS, XPS and specially Cyclic Voltammetry suggested by Cory Cress. It would be nice if I could use some of these tecniques, but I am very happy to know about them.
I am interested to know more about CV method.
Thanks again!
Roberta DiLeo's Master's thesis (https://ritdml.rit.edu/handle/1850/7367) has a good background on the topic and a number of good papers referenced. CV essentially consists of taking current voltage measurements of your sample in a solution, with the voltage scanned at a specific rate (i.e., 10 mV/s). Your sample is the working electrode, current flows between it and a counter electrode (Pt wire) and the potential different is determined precisely using standard electrode like SCE. In a typical forward sweep (biasing the working electrode more positive in reference to the counter) the working electrode attracts electrons, which are injected into your material when the voltage offset is sufficiently high to inject them into the conduction band (i.e, the electron affinity). Continued sweeping provides some data regarding the density of states, or in something like C-60, will reveal many discrete levels. Sweeping back the current will go back to ~0 A until the working electrode is at large reverse bias (with respect to the counter electrode) at which point electrons are extracted from your sample (i.e., holes injected) indicating the energy of your valence band or your ionization potential. The technique is relatively inexpensive and only needs a power supply that can be swept at a precise rate and the reference electrode.
For semiconductors, the most common method in my business (solar cells) is to measure the transmission curve. Obviously, the film will transmit for light energies less than the bandgap, and be highly absorbing of light energies greater than the bandgap. This really only works for thin films (less than ~ 1 micron) on substrates. Self-supporting films will probably need to be so thick that they won't pass enough light to be detected by the detectors in conventional optical spectrophotometers. A good reference is "Optical Processes in Semiconductors" by J. Pankove. Nearly every lab or academic organization has at least one optical spectrophotometer. This was the first way I measured the bandgap of CdS in graduate school over 25 years ago.
How can AFM mesure the Bang Gap of the materials, Xuemei Kang? Could you explain me?
Optical methods such as transmittance versus wavelength or spectroscopic ellipsometry are commonly used to measure the band gap of materials.. However, there is some confusion in the published literature about the type of curves to fit.. in amorphous materials, the contribution of the band tails states to the absorption can be important and needs to be analyzed properly...There is a good review on the subject in the following reference..Klingshirn Phys. Status Solidi B 247, No. 6, 1424–1447 (2010).
Read ''Optical Processes in Semiconductors" by J. Pankove from pg34-95 for a full understanding.
Most of optical methods are good for meauring the energy of band gap only. For a complete band structure measurement, angular resolved photo-emission spectroscopy (ARXPS) is a way to determine the band structure. However, this method can only be applied for a few nm of the surface of a signle crystal.
DRS measurement by fitting the reflectance results in Kubelka-Munk equation is a trustworthy method to determination of band-gap energy.
Measurement of diffuse reflectance with a UV-visible
spectrophotometer is a standard technique in the determination
of the absorption properties of materials.
Tauc Plot band gap versus (absorbance*hv)2 is easy method to find bandgap vaues of materials.
Spectroscopic study using both visible and invisible radiations is the best method one has to follow for such measurements.
For relatively smooth thin films the Tauc method, using absorption spectra, is generally used and gives acceptable results. But for powders and samples with a large diffusely reflecting component you can see the thesis of Joshua A. Russell available online in this link:
http://ir.library.oregonstate.edu/xmlui/bitstream/handle/1957/20605/ThesisFormated.pdf?sequence=1
Tauc plot may help you better for solid samples as well as liquids/dispersed powders in respective solvents using absorbance/transmittance spectra.
Spectroscopic technique is the best option for the measurement.
I usually use Hamberg et al equation, ref I. Hamberg et al Phys.Rev.B30
(1984) 3240
Tauc-lorentz model give good results for organic films produced by dusty plasma. If you Know the chemical composition of your film this can help also.
Both should give the same result. Kubelka-Munk method transformed the reflectance signal into absorbance signal. Therefore I do believe both Kubelka-Munk and Tauc method should provide same result for band gap.
Hi André, Have you been able to determine band gap of your material / film? I do not see anything new being posted here -- but would appreciate if you share your solution, if you have found any. Thanks, Palash
If you want to avoid quantum mechanical methods, DFT calculation methods can be a promising method.
As far as I know, Kubelka-Munk is suitable for powder materials using the diffuse reflectance spectra. For thin film, you can get the transmitance spectra then calculate the absorption spectra [abs=log(1/tran)]. regarding the Tauc method easily you can find the band gap.
In the other way if your sample has direct band gap and PL emission, you can find it using PL peak, by exciting with an appropriate wavelength.
If your films are with wider band gap (> 1.5 < ~4.5 eV) deposited/grown on quartz substrate the Tauc plots from UV-Vis-NIR spectroscopy is a best one method. However for the powder the Kubelka-Munk (Physica Status Solidi 38, 1970, 363) is suitable method, you have to perform reflection spectra but the thickness of powder/film should be more than cutt of wavelength. For thin films with a lower band gap the Cyclic Voltammetry is suitable for the band gap measurements.
It is possible use direct method by using the photodiffusion current (PDC) method, if your films have high resistance. .
Actually you can use both. Let me explain what we did : We use an spectrometer with a D2/halogen light source and reflection probe to investigate the optical reflectance and absorbance of semiconductor photocatalysts, YBCO precursor sols and Cu-Ni alloys. The reflection probe measures the diffuse reflectance (light scattered to all angles) as a function of wavelength in a close approximation to the signal obtained from an Integrating Sphere system. The Kubelka-Munk function, F(R), allows the optical absorbance of a sample to be approximated from its reflectance: F(R) = (1-R)^2/2R. For a semiconductor sample this allows the construction of a Tauc Plot - (F(R).hv)^n vs hv. For a direct band gap semiconductor the plot n = 1/2 will show a linear Tauc Region just above the optical absorption edge. Extrapolation of this line to the photon energy axis yields the semiconductor band gap- a key indicator of its light harvesting efficiency under solar illumination. Indirect band gap materials show a Tauc Region on the n = 2 plot.
The determination of semiconductors band gap by approximation of the absorption edge is the bar and widespread. However, the accuracy this method, even in the case of single crystals, is insufficient. It due to the fact that the slope of the absorption edge is strongly dependent on the presence of intrinsic defects in the crystal: the more defects, the slope is less. Therefore, the presence of defects can lead to deformation of the energy bands, as well as to an additional absorption besides the intrinsic absorption. Therefore, for the same semiconductor compound can be obtained different values of the band gap. In the case of nanostructured semiconductor films there is a significant amount of their intrinsic defects. Therefore, to obtain the relative change in the band gap for diiferent samples, it is nesessary to have the samples of same optical and crystalline quality. Besides, it is very desirable to carry out the structural measurements of those samples. Method for the determination of the band gap by measuring the absorption edge should be considered as an express method. If you want to get the exact value of the band gap, it is necessary to carry out the low-temperature measurements of photoluminescence spectra. Observation of exciton lines allow to determine not only the band gap, as well as to obtain information about the crystalline and optical quality of the investigated films, which may be correlated with the structural measurements (see, for example, Journal of Luminescence V. 132, 2855 (2012); Journal of Crystal Growth V. 312, 1726 (2010 ) ).
In the paper, which attached, an efficient method for determining the bandgap and the energy levels of impurity centers and intrinsic defects is proposed. Simultaneously, different types of centers (donors or acceptors) are also determined. This method can successfully be used for both bulk crystals and films as well as for the pressed powders, containing polycrystalline grains.
Ander, Why not you follow the methods described to ascertain the view of the scientists?
Thank you for pointing out. I am sorry, we cannot measure the bandgap with XRD. I have worked with quantum dots where I measure the bandgap with UV and used XRD to compute the size. I somehow mixed the two - I was calculating the size both from UV and XRD to show bandgap increases as size decreases. Thanks again for correcting me.
Palash,
Thanking you pointed out the mistake that Sonal did and that will carry an impression of expressing her views only after realizing what she wants.
@Sonal -- Thanks, I just wanted to clarify.
@Dillip -- everyone makes mistakes, accepting it is what makes us good students of science. Kudos to Sonal that she did it.
Palas,
We should discourage for the mistakes, otherwise they will repeat in future and that will make their life miserable.
Soumitro,
Can you justify for your comments. If yes please justify. I don't belief it's not and never the best option.
The most efficient method is determination of the bandgap and the energy levels of impurity centers and intrinsic defects. This method can successfully be used for both bulk crystals and films as well as for the pressed powders, containing polycrystalline grains.
@ Hi, Oday. I am very glad that you fully share the method proposed by me.
Following techniques can use
1. diffuse reflectance spectroscopic technique for the compacted POWDER sample and use Kubelka-Munk function as suggested by Md Hossain
2. UV-Vis spectroscopic technique in transmission (for transparent thin films) or in reflection (sample should be reflecting) mode
3. cathodoluminescence method by which you can reach as high as 4.5 eV
For details on KM method, please following book will be helpful
Reflectance Spectroscopy, G. Kortüm, Springer, Berlin (1969).
Hi Sonal Mazumder,
I know I am deviating the discussion a bit. But please excuse me. Can U tell more about how to find partcle size from UV data.
Photoluminescence (PL) measurements are effective method to determine the nanoparticle sizes. In this case it is possible to observe quantum-zise effect and its affect on the energy structure. Using the energy position of PL bands it is possible to determine nanoparticle size. I see that you study Bi2Te3 nanoparticles where band gap is very small (about 0.15 eV). If the nanoparticles, investigated by you, are very small you can observe PL in more short-wavelength region.
Very good discussion. I have calculated band gaps of nanostructured thin films with Tauc equation. But the results are very strange.
Here I repeat my answer regarding the question "How to obtain the energy band structure of the semiconductor".
Do you need to test the band gap experimentally ? In this case you can use both optical and photoelectric measurements. Optical studies include the measurements of the absorption, excitonic photoluminescence and reflection spectra. Excitons present the bound electron-hole pairs. Their excitation energy Eex is slightly less than the energy of the unbound electron and hole, i.e. than the electronic band gap energy Eg. The binding energy of excitons ∆Eex in semiconductor is usually about several tenths meV. The energy of exciton reflection spectrum, which present a dispersion curve, is acossiated with the formation of free exciton and determine the optical band gap of semiconductor. The measurement of photoluminescence spectra allows to observe the recombination of free and/or bound to acceptor(donor) excitons. The binding energy of bound excitons correspond about 10 meV (for exciton bound to acceptor this energy is about 0.1 Ea, where Ea - ionization energy of aceptor). In this case it is also possible to observe quantum-zise effect and its affect on the energy structure.
Usually, the traditional method of estimating of band gap of semiconductor materials is based on the results of absorption spectra measurements. However, in the case of polycrystalline films the light transmission depends not only on its absorption resulting from transitions between energy bands, as well as the light scattering by material and additional absorption resulting from the presence of different types of intrinsic defects. All these factors contribute to transmission of light. A evaluation of bandwidth is based only on the absorption measurements as a result of interband transitions. But it is not in the case of polycrystalline silicon. So, you can get any results that are not relevant to the evaluation of bandgap. Measurement of light transmission of polycrystalline films is valid only for the evaluation of their optical quality.
Effective method for the determination of semiconductor band gap is the measurements of the photodiffusion current spectra (see : J. Phys. : Condens. Matter, V.18, 5323 (2006)). This method allows to determine both the band gap energy and the energy of different defects in semiconductor. In this case, unlike photoconductivity, the measurements are made without an applied electric field. And so there is no bending of the energy bands. Usually we used both optical and photodiffusion current measurements. If you need to test of band gap of unknown semiconductor we must first all to carry out the measurements of absorption spectra. In this case you get approximate value of bandgap. Then, it is necessary to perform the photoluminescence and reflection as well as photodiffusion current measurementd described above.
UV-vis in reflectance mode or transmission mode/ luminescence spectra can be used to measure the band gap. XPS analysis will definitely tell about the band position.
Arindum,
You are correct and many techniques are there to solve one problem.
Hi Crishnan,
Here is our paper, where we determine the sizes of layered PbI2 nanoparticles.
Here is theoretical paper, where the relation for the determination of nanoparticles sizes are presented for cubic or wurtzite crystals. Use these relation and the energy of photoluminescence lines it is possible the sizes of nanoparticles.
I personally used DRUV for bandgap measurement through Kubelka-Munk method for semiconductors
If you have access to an EELS apparatus you can measure the ionozation potential and obtain a gap value for thin films deposited on a conducting substrate. See for instance, the reference herein and others contained in this paper: Electronic excitation and secondary electron emission studies by low energy electrons backscattered from thin polystyrene film surfaces" - A. M. Botelho do Rego, M. Rei Vilar, J. Lopes da Silva, M. Heyman, M. Schott - Surface Science 1986, 178, 367.
Good luck.
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