The question is not related to any specific material. It could be Si or Ge or any other material. Link to any published work regarding it would be much appreciated. Thank you in advance.
This question question is frequently asked on the reseachgate. I find the answers introduced are satisfactory. However i would like to stress some important point.
As the size of the material decreases its acoustical phonons will be reduced limiting the the possible values of momentum. Such that in the limit when the size is reduced to one atom one will have the the energy level diagram of one atom.
If the number of atoms is few then the material will tend to take the from of energy level diagram of molecules.
Such small size structure have direct transitions between the possible energy levels.
Best wishes
It depends on the micro structural property of the film. Like crystalline Si is indirect band gap semiconductor whereas amorphous Si is direct band gap, microcrystalline Si is quasi direct band gap semiconductor.
Hello,
The transition metal dichalcogenides (MoS2, for example) are indirect semiconducting materials in their bulk form and become direct gap semiconductors as you move to monolayers.
-Nick
I think not it depends on the structure propertie of semiconductor
It mainly depends on the structural properties of the materials. It will be varies from material to material
Size reduction of a given material can induce several different effects:
1. Dimensionality change e.g. change from 3D (bulk) to 2D (quantum well) or 1D (quantum wire) or even 0D (quantum dot) : here we are dealing with quantization effects (quantum confinement effects) i.e. change of properties from classical (or quasi-classical) to quantum. In this case there is not necessarily a change of the energy bandgap from indirect to direct. This holds as far as there is no structural change of the material, i.e. no change in crystal lattice and more particularly no phase transition induced. A 3D indirect bandgap material remains indirect bandgap at low dimensionality.
2. Size effects which behave as squeezing effects (or strain effects) inducing changes of the atomic distribution (structural changes) of the lattice inducing in turn crystal symmetry changes. In this case the energy band structure of the material may change as a whole and consequently, the energy band gap can turn from direct to indirect and vise-versa.
This the case of carbon nanotubes (CNT), graphene and fullerene which behave very differently from each other and from their 3D parents C-diamond and C-graphite.
e.g. 3D C-diamond is indirect bandgap along (100) direction with Eg=5.46eV, whereas CNT (1D-C) and graphene (2D-C) are characterized by direct energy bandgaps.
In the case of MoS2, both size and quantum confinement effects are active.
A.K.
The band gap character depends on the constraints placed by the available elastic vibrational modes in the material. Certain vibrations should be possible as the configuration of atoms change, since the acoustic or optical branch vibrations may become enhanced or inhibited in certainly direction. Remember, band gap is the energy difference between these two branches. In short, yes it is possible under specific symmetries.
Dear Mohd,
Yes reducing the dimentions of Si (at nano relem, i.e. below 5nm) it is demostrated that Si bandgap has been changed form indirect to direct bacdgap. Infact this has provided the oppurtunity of using Si to fabricate LEDs that illumates light in Visible spectrum.
1. Article Multicolor Silicon Light-Emitting Diodes (SiLEDs)
2. https://www.washington.edu/news/2013/06/12/silicon-based-nanoparticles-could-make-leds-cheaper-greener-to-produce/
3. https://www.frontiersin.org/articles/10.3389/fchem.2020.00191/full
Changing the dimensionality of a material also means to fundamentally change its band structure, as can be seen, e.g., by the density of states for the 3D/2D/1D/0D case. Note, however, that quantum dots and nanocrystallites only have energy levels (like atoms do). Since there are no wave vectors involved, for them the terms "direct / indirect bandgap" loose their meaning. Instead, the osicllator strength or the radiative lifetime can be discussed. Here are some related paper examples from former colleagues of mine (some of them can be found on ResearchGate):
"Structural relaxation in Si and Ge nanocrystallites: Influence on the electronic and optical properties" (Phys. Rev. B 67, 245304 [2003], https://journals.aps.org/prb/abstract/10.1103/PhysRevB.67.245304)
"Excitation Energies and Radiative Lifetimes of Ge1−xSix Nanocrystals: Alloying Versus Confinement Effects" (Phys. Rev. Lett. 90, 085501 [2003], https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.90.085501)
"Structure- and spin-dependent excitation energies and lifetimes of Si and Ge nanocrystals from ab initio calculations" (Phys. Rev. B 69, 115310 [2004], https://journals.aps.org/prb/abstract/10.1103/PhysRevB.69.115310)
"Optical properties of Si and Ge nanocrystals: Parameter‐free calculations" (Phys. Status Solidi B 242, 3053-3063 [2005], https://onlinelibrary.wiley.com/doi/abs/10.1002/pssb.200562229)
"Luminescence and absorption in germanium and silicon nanocrystals: The influence of compression, surface reconstruction, optical excitation, and spin-orbit splitting" (Phys. Rev. B 83, 125413 [2011], https://journals.aps.org/prb/abstract/10.1103/PhysRevB.83.125413)
Yes, it is possible. With reduction in size the broadening of uncertainty in k relaxes the k-selection rule as well as increases the probability of direct transition. Si in its bulk form is an indirect band gap material but in nano- crystalline form it behaves like a direct band gap material due to which it may be a potential material for electroluminescence.
Dear Sudipta Chakrabarty, do you have any paper in mind that shows the potential application of Si nanocrystals for electroluminescence? This would surprise me, since (as far as I know) silicon remains a poorly luminescent material even in nanocrystalline form. The only exception might be the lonsdaleite variant of silicon (hexagonal diamond structure) mixed with germanium; this was realized just recently (cf. https://www.tue.nl/en/news/news-overview/08-04-2020-eindhoven-researchers-present-revolutionary-light-emitting-silicon/).
Yes, indirect band gap to direct band gap can be changed by reducing the size of material
Yes it is possible, the indirect band gap to direct band gap can be changed by reducing the size of material.
Dear Jan-Martin Wagner, I have taken the example of bulk Si as it is the most well-known indirect band gap material though it shows electroluminescence from nanocrystalline Si based systems. You are right that efficiency as well as intensity of electroluminescence from Si nanocrystal based devices is low but the visible luminescence may support the fact of conversion of an indirect band gap material to direct band gap material in nano dimension as asked in the question.
Well, the emission of visible light only confirms the quantum confinement effect leading to an increase of the bandgap (as mentioned above already by Abderrahmane Kadri). However, this effect is independent of a possible change from an indirect bandgap to a direct one. Remember that even standard bulk silicon emits (infrared) light – only weakly, but measurable; such emission is used, e.g., in the investigation of silicon solar cells.
Hello Mohd,
if the dimension is reduced, the density of states changes in that manner that the lowest occupied energy level shifts to higher energies (or lower energies in the case of holes). Therefore, the gap increases. The shift depends on the effective mass. So lower the mass, so stronger the shift. If the mass of the "indirect band" is smaller than the mass of the direct band, the energy states can cross. Otherwise the character of the semiconductor remains.
Another interesting possibility is the changeover from halfmetal to a semiconductor like in bismuth. The hole (T-band) and electron (L-band) overlapp in the 3-dim. case and you have a half-metal. Due to dimension reduction both band shift and a gap opens. Then you have a semiconductor.
With Regard
R. Mitdank
To say it explicitly: Since the notion of a direct or indirect gap is only valid in a k-vector dependent band structure, and since the k vector is related to periodicity, the material under consideration needs to extend at least in one spatial dimension. Hence, the concept of a direct or indirect gap exists only for quantum wires, quantum wells, or bulk material, but not for quantum dots or nanocrystallites – because the latter only have levels, not bands.
Dear Abdu Saeed, many thanks for the paper you provided; what a nice approach!
I think the example of Si/Ge superlattices shows that DFT can suggest such a transition from indicret to direct bang-gap but it has never really worked in experiments, as far as I know.
I would like to add few remarks to this very exciting discussion thanks to all contributions:
1. A nanosystem is not necessarily quantized because it is nanosized. To be quantizied, a nanosystem needs to have at least one characteristic length (e.g. thickness, wavelength, ...) of order or smaller than the De Broglie wavelength (DBW) of the particles involved in this system. And this inequality depends (roughly) on particle's effective mass: the larger the effective mass the smaller is DBW and the smaller must be the size of the nanosystem to be quantizied. A nanosystem with very small effective mass particles can be quantizied at roughly large size e.g. some 100nm wide while other nanosytems with large effective mass particles need nanosize lower than 10nm to be quantizied.
2. In this same spirit, a dot is not necessarily quantum unless it obeys the rules above. More particularly, sometimes reported large size ''quantum'' dots are not so quantum, but they are interesting dots with 3D confinement.
3. A quantum dot is not really an atom. Indeed the smallest QD's are of order 2nm wide which corresponds to some hundreds of atoms since 2nm corresponds roughly to 4 conventional lattice cells for InAs QD for example and their total spatial number is 4x4x4=64 which corresponds to 64x8 atomes roughly 500 atoms. It is really not a single atom.
In fact it is a kind of ''artificial atom made of several atoms averaged through the mean field approximation'' which can be better defined as ''a finite fermionic system with controlled manybody interactions through size control'''.
In addition to the highly attracting QD's potential or real applications in various fields (ultrafast electronics, optoelectronics, photonics, plasmonics, spintronics...) the QD's are very attracting objects from the fundamental point of view, for they give the possibility just by changing their size to explore the borderline between real discrete atomic like bound states and the manybody less bound states, and the underlying formation of macromolecular and/or solid state energy bands.
They also give the opportunity to explore some very specific electron interactions exchange and correlations unique to QD systems as Coulomb blockade under controlled strain effects at the nanosize.
4. Unlike strain or hydrostatic pressure effects, quantum confinement is not strong enough to induce direct to indirect change of the energy bandgap.
In the practical scholar case of the well known GaAs/AlxGa1-xAs (x
Mos2 has this behavior. According to the First principles studies, we see such transition. At bulk, it is in-direct band gap - while at 2ML thick - it is direct band gap.
This question question is frequently asked on the reseachgate. I find the answers introduced are satisfactory. However i would like to stress some important point.
As the size of the material decreases its acoustical phonons will be reduced limiting the the possible values of momentum. Such that in the limit when the size is reduced to one atom one will have the the energy level diagram of one atom.
If the number of atoms is few then the material will tend to take the from of energy level diagram of molecules.
Such small size structure have direct transitions between the possible energy levels.
Best wishes
WS2 shows this behaviour.
In bulk the band is indirect and the value is 1.29eV, while at monolayer the band gap becomes direct with value 2.21 eV.
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