If the valence band maximum (VBM) and the conduction band minimum (CBM) are situated in same direction of first brillouin zone, you have a direct gap. Otherwise, when these points are situated in different symmetry directions, there are an indirect gap.
If the valence band maximum (VBM) and the conduction band minimum (CBM) are situated in same direction of first brillouin zone, you have a direct gap. Otherwise, when these points are situated in different symmetry directions, there are an indirect gap.
Indirect-band-gap are defined by the fact that the minimum energy in the conduction band and the maximum energy in the valence band occur at different values of the crystal momentum. This means that a direct transition from the valence (V.B.) to the conduction band (C.B.) of an electron requires a photon of energy higher than that of the band gap (here maybe a bit vage for you! but notice band gap means just the stright distance between V.B. maximume and C.B. minimum. To imagine that you need just to draw a tangential line from the C.B. minimum to the hypothetical arrow directed perpendicularly to C.B. see here: http://solarwiki.ucdavis.edu/The_Science_of_Solar/Solar_Basics/C._Semiconductors_and_Solar_Interactions/III._Absorption_of_Light_and_Generation/3._Indirect_Semiconductors). However, is it possible to make the transition at lower energies, but we require a new type of particle: the phonon. You can finde more in the mentioned address.
For any transition to take place, both energy conservation and the crystal momentum conservation has to be satisfied. Of course crystal momentum conservation can also have an addition of reciprocal lattice vector. Now photons have comparatively very low crystal momentum, so its value is often taken to be zero. Similarly phonons have very low energy but relatively higher value of crystal momentum. So again in simple calculations, their energy is taken to be negligible. Hence in a direct gap semiconductor (where conduction band minimum and the valance bad maximum occurs at the same value of crystal momentum), one needs only a photon to cause the transition. In case of an indirect gap semiconductor, one needs a phonon which can supply the crystal momentum equal to the difference between conduction band minimum and the valence band maximum .
Thanks for the question and Thanks for all valuable comments. I wish all of you a Happy New Year 2014.
Direct band gap : the diference between the wave vector is equal to zero and indirect band gap the differnce is not;
Dr A. Ouerdane
Direct band gap : the diference between the wave vector is equal to zero and indirect band gap the difference between the two wave vector of the two bands (valence and conduction) is not; for example the Silicon is with indirect band gap but the GaAs is with a direct one. For the semiconductor the one with direct band gap can give laser action but the one with indirect can not.
Dr A. Ouerda
In direct band gap when an electron wants to go to valence band from conduction band or in reverse, the momentum is constant, but in indirect band gap the momentum is not constant.
In the direct band semiconductors the minimum energy in the conduction band and the maximum energy in the valence band have the same momentum (K-vector) in the energy (E) momentum (K-vector) space. Otherwise semiconductor is referred to as indirect band gap. In the direct band semiconductors the electron makes a direct transition from conduction band to valence band emitting a photon. In an indirect semiconductors the electrons make transition from conduction band to valence band passing through intermediate states giving up its energy to the crystal lattice, causing rise in crystal temperature.
As has been clearly been mentioned by A.Ouerdane, for the indirect band gap, the difference between wave vector is not zero. So according the principle of conservation of energy, some energy must be supply to balance it and this energy come from phonon. As the band gap measures the photon energy, it in many times, the direct energy band gap should be higher that of the indirect energy band gap.
A materials has a direct band gap when the valence band maximum and the conduction band minimum are at the same point of the Brillouin zone (in general is the gamma-point, but in some materials are at a different k-point). In these materials, a photon can excite an electron from the valence to the conduction band if the energy is at or above the gap energy. When the valence band maximum and the conduction band minimun are at different points of the Brillouin Zone, the material becomes indirect. In order to absorb a phonon, a phonon is needed to conserve momentum. Silicon is the most common example of indirect band gap material. The indirect gap is around 1.1 eV, while the direct one (when the transition is produced at the same point of the Brillouin Zone) is around 3.85 eV..
In the band structure of a semiconductor material, bandgap is the forbidden region between the valence band (VB) and the conduction band (CB) that cannot occupy by the electrons. In a direct bandgap semiconductor, the electrons in the minimum of the CB and the maximum of the VB have the same wave vectors and consequently electron transition only need to the energy conversation. However, there is a difference in the momentum of electrons in the minimum of CB and the maximum of the VB in an indirect ban gap semiconductor that limits the electron energy transition from VB to CB to the presence of a phonon for momentum conservation .
Good definitions of direct and indirect band gap have already been given. In practice, semiconductors with direct energy gap have highest optical absorption coefficients than those with indirect gap. So they are more appropriate to make opto-electronic devices (light-emitting diodes and photovoltaic cells). Typical examples are silicon (indirect gap) and most III-V compounds (GaAS, AlAs…)
Thanks to all.
1) Is it possible to convert direct band gap semiconductor into indirect band gap semiconductor by doping metals or nonmetals?
2) Is phonon active in direct band gap materials ( even though phonon is not required to excite the electrons from VB to CB)?
The meanings of direct and indirect band gaps have been given nicely by many researchers in this discussion. The direct or indirect gap depends on the band structure, which in turn decides where are the positions of conduction band minimum and valence band maximum. Doping is however, a small percentage of the impurity atoms, which will not affect the band structure. Second question is whether phonon is active. Whenever temperature is non-zero phonon is very much there. Whether it is required for the optical transition or not is determined by the band structure
Dear Oleksiy Drachenko ,
How does GaAs become indirect under ultrahigh magnetic fields?
The electron mass in Gamma valley is much lighter than in L valley. As a result, under magnetic fields, the cyclotron energy of electrons in the Gamma valley rises more quickly than in L valley (cyclotron energy = hbar eB/m*). Finally, in the certain magnetic field (so far, above 200 Tesla) the crossover occurs, and the minimum of the conduction band energy is not any more in Gamma point, but rather in L point.
Dear Manjunatha Pattabi,
I think doing will affect the band gap energy of semiconductor and modify the position of the valance band of the semiconductor. Further you can refer this paper.
CVD Production of Doped Titanium Dioxide Thin Films,
Chem. Vap. Deposition 2012, 18, 89–101
Dear Oleksiy Drachenko,
I am having few questions to understand your point.
The band gap energies of GaAs for gamma, L and X valley are
Eg=1.42eV
EL=1.71eV
EX=1.90eV respectively.
1) To move an electron from gamma valley to L valley, an excess of energy 0.29 eV
is required. where it comes from?
2) To move an electron from gamma valley to L valley, additional momentum is required. This additional momentum is coming from magnetic field or phonon?
3) suppose it comes from phonon, what is the role of magnetic field?
1) the energy comes from the magnetic subbands. Google Landau Levels.
2) once the Eg>EL, transfer of electrons may occur via many processes, i.e. scattering on defects, emission of practically dispersion-less LO phonons (if Eg-EL>hbar wLO), two-acoustic phonons emission, Auger scattering,
3) the role of magnetic field is reconstruction of the bandstructure. The bandstructure of a semiconductor under magnetic field exhibits very important changes.
Those answers above are correct and detailed. I have also learned more from them.
The band gap represents the minimum energy difference between the top of the valence band and the bottom of the conduction band, However, the top of the valence band and the bottom of the conduction band are not generally at the same value of the electron momentum. In a direct band gap semiconductor, the top of the valence band and the bottom of the conduction band occur at the same value of momentum
In an indirect band gap semiconductor, the maximum energy of the valence band occurs at a different value of momentum to the minimum in the conduction band energy
The difference between the two is most important in optical devices. , A know In theory a photon can provide the energy to produce an electron-hole pair.
Each photon of energy E has momentum P/c, where c is the velocity of light. An optical photon has an energy of the order of 10–19 J, and, since c =3 × 108 ms–1, a typical photon has a very small amount of momentum.
A photon of energy Eg, where Eg is the band gap energy, can produce an electron-hole pair in a direct band gap semiconductor quite easily, because the electron does not need to be given very much momentum. However, an electron must also undergo a significant change in its momentum for a photon of energy Eg to produce an electron-hole pair in an indirect band gap semiconductor.
This figure can illustrate the difference between direct and indirect band gap which is extensively discussed in the previous comments (Ref: http://www.doitpoms.ac.uk/tlplib/semiconductors/direct.php). GaAs is an example of direct band gap and both Si and Ge have indirect band gap.
Another useful comment is that group 13 semiconductors are know to have direct band gaps that decrease as the atomic number of the group 13 element increases (B, Al, Ga, In).
In semiconductor physics, the band gap of a semiconductor is always one of two types, a direct band gap or an indirect band gap. The minimal-energy state in the conduction band and the maximal-energy state in the valence band are each characterized by a certain crystal momentum (k-vector) in the Brillouin zone. If the k-vectors are the same, it is called a "direct gap". If they are different, it is called an "indirect gap". The band gap is called "direct" if the momentum of electrons and holes is the same in both the conduction band and the valence band; an electron can directly emit a photon. In an "indirect" gap, a photon cannot be emitted because the electron must pass through an intermediate state and transfer momentum to the crystal lattice.
It is sometimes said that a semiconductor possesses both direct and indirect band gap. The above mentioned descriptions don't consider this point. It is very trivial at first, because the definition is very clear. As an instance, cadmium oxide is often mentiond as a semiconductor with direct and indirect band gap (the pertinent values can be found in literatures).
Your answer:
http://www.youtube.com/watch?v=EZQrVFWPnj4
Regards,
Michele Romeo
Dirct gap is obtained when the valence band maximum and the conduction band minimum are situated in the same direction of first zone.
Indirect gap is when the valence band maximum and the conduction band minimum are situated in different symmetry directions.
Direct gap: the max of energy in valance band and min of energy in conduction band have same momentum.
Indirect gap: the max of energy in valance band and min of energy in conduction band don't have same momentum.
Therefore in indirect gap instead of electron and photon, we need electron and photon and phonon to momentum and energy's conservation be established.
In an direct band gap the electron only needs energy to jump to the conduction band(c.b).In an indirect band an electron needs energy and momentum to jump to the conduction band(c.v)
Direct band gap: electron fall's c.b to v.b directly without giong to metastable state ,but in indirect band gap the same electron have to pass by a metastble state before reaching the v.b.
In a direct band gap the electron only needs energy to jump to the conduction band. In an indirect band an electron needs energy and momentum to jump to the conduction band
I found that video, I hope it is useful
http://www.youtube.com/watch?v=EZQrVFWPnj4
I am so happy that this question has all this interest from researchers.Indeed the semiconductor are deeply studied but they stay the best materials that benefical secret are to be developped. and published.
In a direct band gap semiconductor, the top of the valence band and the bottom of the conduction band occur at the same value of momentum.
In an indirect band gap semiconductor, the maximum energy of the valence band occurs at a different value of momentum to the minimum in the conduction band energy
In direct bangap semiconductor electrons transition from Conduction band to Valence band take place directly without change in their momentum. The transition accompanies photon emission with energy E= Eg = hf where h is the Plank's constant and the f is the frequency, and Eg is the bangap energy. In indirect semiconductor transition involves change in momentum. The energy in general is given up as to heat the lattice.
When we talk about a direct band gap energy, we can say that the electron only needs energy to jump to the conduction band. On the other hand, when we talk about an indirect band gap energy, we can say that the electron needs energy and momentum to jump to the conduction band.
Ok it's right and simplified way to explain the direct and indirect band gap
We can add:
In direct band gap: electron fall's c.b to v.b directly without going to metastable state ,but in indirect band gap the same electron have to pass by a metastable state before reaching the v.b.That is the difference between the two band gap in semiconductor.
Another deduction is that the semiconductors with direct band gap as III-V can light easily and give laser emission but the one with indirect band can not.
In a direct band gap the electron only needs energy to jump to the conduction band. In an indirect band an electron needs energy and momentum to jump to the conduction band
For indirect band gap, the electron need energy normally phonon(heat) to assist it jump from valence band to conduction band. One of the example of indirect band gap material is silicon.
Band gap refers to a gap between the conductance and the valance bands of energy. In a direct one, the photon spectrum peaks are well aligned that make it easier for electron to jump up to the conductance band with given condition.
Dear Sridhar
see book(optical process in semiconductor by pankove) this is important book to understand the direct and in direct bad gap
Dear All,
How can I calculate the value of Eg from Uv-Vis spectra? If we do not known the band structure thus can we detect Eg from fitting equation (hfa)~(hf-Eg)^(n)?
Fit the data (optical absorption data) to the equation, with different values of n (text books will tell you what those values mean). Depending on which value of n gives best fit, you can conclude, if it is direct or indirect ( allowed or forbidden transitions too)
Thanks for your comment. But what is the mean of "best fit", I have tried to plot for all n value as 1/2, 2, 3 and 3/2 but it is hard to conclude and hard to determine the band gap of this sample.
Here I add the original file below. Please, find down and give me the comment.
Thanks you.
It seems you have a film thin enough to see both direct and indirect gaps. A theory tells us about films thick enough to see only one kind of absorption, in your case an absorption in red region seems to be saturated and the another one taking its place in blue. Try direct absorption for red region and indirect for blue and look into Net for papers with both terms to find. I have seen the papers with such result, but can not quote any of them at moment.
When the energy minimum ( the bottom) of the conduction band lies directly above the energy maximum (the bottom) of the valance band is direct band gap otherwise indirect band gap.
the band gap is said to be direct when the maximum of valance band (MVB) and minimum of conduction band of a material exist along the same "K" vector, therefore, during transition of carriers change of momentum is zero, whereas the band gap is indirect, MVB and MCB exist in different “K”, hence, when carrier move from MVB to MCB/vis versa the change of momentum is different from zero.
For the same value of K vector, the difference between minimum conduction band and maximum valence band is direct band gap and for others it is indiect band gap.
A direct band gap occurs when the valence band maximum (VBM) and the conduction band minimum (CBM) are at the same k point., generally at the Gamma point.
We have an indirect band gap when the VBM and the CBM are at two different k points.
The above definitions are for the optical band gaps, They are sometimes called fundamental (smallest) gaps, even though there exists another definition of the "fundamental" gap that involves difference of energies for the system with (N-1), N, and (N+1) particle (electrons).
Generally, the VBM is at the Gamma point. Depending on the materials (i.e., crystal symmetry), the CBM can be found at the X, L or other high symmetry points.
As the lattice constant INCREASES (i.e., effect of increasing temperature), the direct band gaps of semiconductors generally DECREASES (at the gamma point).
However, as the lattice constant INCREASES, some indirect gaps are found to INCREASE (a bit) in many materials [even though the direct gap at Gamma, that is not the optical gap for indirect gap materials [as it is larger than the indirect gap] DECREASES as the lattice constant increases.
As per my knowledge is concerned..the question is what is the difference between OPTICAL direct and indirect band gap which we study in the UV data? how does the concept of election comes????
In addition to the above points the Energy and momentum conservation laws applied directly for emission of a radiation on direct band gap materials while for indirect bandgap materials the momentum/energy first transferred to the lattice and then only, transition takes place. hence apart from the photon contribution some phonon need to be added for conservation of energy and momentum...
In the direct band gap, the maximum of the valence band and the minimum of the conduction band are at the same point of the Brillouin Zone (BZ). In most semiconductors this happens at the Gamma point but, for instance, in InSe the direct band gap is at the Z-point of the BZ. In an indirect band gap, they are in different points in the BZ. From the optical point of view, in a direct band gap the optical absorption or emission takes place through the absorption or emission of one photon. For this reason, since the wave number k of the photon is very small compare with the size of the BZ, we can assume k=0. If the parity of the valence iband s different from that of the conduction band, the transition is dipole allowed. If the parity is different, the transition is dipole-forbidden (we cannot reach the conduction band from the valence band with only one photon, we need two photons).
In the case of an indirect band gap, the absorption of the light is acompanied by the absorption or emission of one phonon, giving the necessary wave number to reach the minimum of the conduction band. It is thus, a second order process, where the electron goes, in a first step, from the maximum of the valence band to a conduction band at the same point of the BZ (virtually, actually we have to some over all the possible virtual states), the virtual electron emits a phonon and goes to the minimum of the conduction band, i.e. it goes to the final state in two steps. This is what happens, for instance, in Si or Ge. Since we have an intermediate virtual state, if the conduction band is far away from the gap at the maximum of the valence band, the energy difference between the electronic transition to the virtual state is very different from the gap, the indirect transition is very weak.
Neglecting excitonic effects, the absorption in a direct band gap is proportional to the square root of (E-E_c), while in the case of an indirect band gap is proportional to the (E-E_c+-E_p) to the square, where E_p is the energy of all possible phonons (- for phonon absorption and + for phonon emission). For this reason, there is already absorption below the band gap, the energy of the gap minus the energy of a phonon.
If the minimum energy state of the conduction band and the maximum energy state of the valence band are the same crystal momentum (K vector) in the same Brillouin zone is said to be direct band gap.( Brillouin zone is a primitive cell in a reciprocal space). However, the indirect band gap is when the conduction is shifted to another K-vector different from that of the valence band.
The band gap represents the minimum energy difference between the top of the valence band and the bottom of the conduction band, However, the top of the valence band and the bottom of the conduction band are not generally at the same value of the electron momentum. In a direct band gap semiconductor, the top of the valence band and the bottom of the conduction band occur at the same value of momentum,
In an indirect band gap semiconductor, the maximum energy of the valence band occurs at a different value of momentum to the minimum in the conduction band energy:
The difference between the two is most important in optical devices. As has been mentioned in the section charge carriers in semiconductors, a photon can provide the energy to produce an electron-hole pair.
Each photon of energy E has momentum p = E / c, where c is the velocity of light. An optical photon has an energy of the order of 10–19 J, and, since c = 3 × 108 ms–1, a typical photon has a very small amount of momentum.
A photon of energy Eg, where Eg is the band gap energy, can produce an electron-hole pair in a direct band gap semiconductor quite easily, because the electron does not need to be given very much momentum. However, an electron must also undergo a significant change in its momentum for a photon of energy Eg to produce an electron-hole pair in an indirect band gap semiconductor. This is possible, but it requires such an electron to interact not only with the photon to gain energy, but also with a lattice vibration called a phonon in order to either gain or lose momentum.
The indirect process proceeds at a much slower rate, as it requires three entities to intersect in order to proceed: an electron, a photon and a phonon. This is analogous to chemical reactions, where, in a particular reaction step, a reaction between two molecules will proceed at a much greater rate than a process which involves three molecules.
The same principle applies to recombination of electrons and holes to produce photons. The recombination process is much more efficient for a direct band gap semiconductor than for an indirect band gap semiconductor, where the process must be mediated by a phonon.
As a result of such considerations, gallium arsenide and other direct band gap semiconductors are used to make optical devices such as LEDs and semiconductor lasers, whereas silicon, which is an indirect band gap semiconductor, is not. The table in the next section lists a number of different semiconducting compounds and their band gaps, and it also specifies whether their band gaps are direct or indirect.
So the reflection increase from 500nm wavelenght is caused by direct interband transitions ? Si band gap is ~1,1 eV (IR region), but the transitions are seen at UV region. Is this result of the indirect band gap ?
Direct band energy only involves electromagnetic radiations (Photon) emitted when electron jump from conduction band to valence band while indirect band energy involves Photon plus Phonon (thermal energy carrying particles produced due to vibration or loss of momentum) emitted when electron jumps to valence band from minima of conduction band which lies in momentum and energy region (1st Quadrant).
Unlike direct transition, no phonon is involved in the case of in-direct optical transition. Quantum efficiency is more in case of direct optical transition.
In direct band gap the diffrence between the wave vectors Delta k is zero but in the indirect band gap Delta k is diffrent of zeo
Direct and indirect band gaps
https://en.wikipedia.org/wiki/Direct_and_indirect_band_gaps
Direct and indirect band gaps:
In semiconductor physics, the band gap of a semiconductor is always one of two types, a direct band gap or an indirect band gap.
The minimal-energy state in the conduction band and the maximal-energy state in the valence band are each characterized by a certain crystal momentum (k-vector) in the Brillouin zone. If the k-vectors are the same, it is called a "direct gap".
If they are different, it is called an "indirect gap".
The band gap is called "direct" if the momentum of electrons and holes is the same in both the conduction band and the valence band; an electron can directly emit a photon. In an "indirect" gap, a photon cannot be emitted because the electron must pass through an intermediate state and transfer momentum to the crystal lattice.
From the free encyclopedia
In semiconductor physics, the band gapof a semiconductor is always one of two types, a direct band gap or an indirect band gap. The minimal-energy state in the conduction band and the maximal-energy state in the valence band are each characterized by a certain crystal momentum (k-vector) in the Brillouin zone. If the k-vectors are the same, it is called a "direct gap". If they are different, it is called an "indirect gap". The band gap is called "direct" if the momentumof electrons and holes is the same in both the conduction band and thevalence band; an electron can directly emit a photon. In an "indirect" gap, a photon cannot be emitted because the electron must pass through an intermediate state and transfer momentum to the crystal lattice.
Examples of direct bandgap material includes some III-V materials such asInAs, GaAs. Indirect bandgap materials include Si, Ge. Some III-V materials are indirect bandgap as well, for exampleAlSb.
how can we understand a material is direct or indirect band gap? the shape of abs-wavelength or k/m-energy can say us if the material has a direct or indirect band-gap?
See the attached figures. I think these will helpful for understanding the direct and indirect band gap semiconductors.
In addition to the above, for indirect transition phonons are involved in the energy and momentum conversation rules. Unlike direct transition, indirect transition does not occur vertically at the same value of k in the BZ.
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