electronic-band-theory
I want to know why the bands like valence or conduction splits up into two parts as shown in this diagram. why the energy gaps exist with in these bands? As you can see in this diagram that their is an energy gap with in conduction as well as valence band. what are their physical significance?
One could write a novel about those questions... I'll try to nail down the most important facts.
Regarding what you figured out so far:
Basically correct. I would say: Every system of atoms has a quantum mechanical ground state. You can approximately assign an energy to each of the electrons (depending on the approximation you are using, e.g. Hartree-Fock or density-functional theory).
Bands are a fancy way of plotting those levels in case of a periodic crystal lattice. The k-axis, called crystal momentum, should only be understood as a quantum number or an index. It is NOT the momentum.
The forbidden band is not an actual band - it marks the absence of bands. That's why you call it band gap. The band gap/forbidden band is between the valence bands (=lower, filled bands) and the conduction bands (=upper, not filled bands). The band gap may also be nonexistent (metals).
It's not "closest to the atom", and there are no electrons there because there are no states that they can occupy (it's a gap).
The valence band is essentially fully occupied. This implies (nontrivially) that for every electron moving in one direction, there is an electron moving in the exact other direction. Therefore, there is no conduction. If an electron jumps (for whatever reason) into the conduction band, it doesn't have the aforementioned partner there - thus, it conducts. The same goes for the hole it leaves behind. One can show that a single "absent electron" behaves like a positive charge governed by the same equations as the electron. That's what you call a hole.
It's below the band gap (if the latter one even exists).
Essentially, all electrons of the atom can move throughout the material. The probability that this happens is not equal for all electrons though. So, doesn't really take them any energy.
That's correct. I'm not aware of a temperature dependence of the band gap. Temperature makes it easier to jump over the gap, though. (Edit by @lemon: the band gap actually decreases almost linearly with increasing temperature (at least for silicon and germanium))
Concerning the questions:
Like I mentioned before, if you remove an electron from a band, it leaves behind a quasiparticle that acts like an electron with the opposite charge. This is what you call a hole.
One band can always hold 2 electrons per crystal unit cell. If a crystal has 8 atoms per unit cell, there will be four filled bands. This comes from the Pauli principle which states that a quantum mechanical state can only be occupied by 1 electron, or 2, if you count spin degeneracy. When a state in the band structure is occupied by 2 electrons, there can't be another one there. The states will be filled from bottom to top (concerning energy). The energy of the topmost filled state is called Fermi energy.
All the electrons in the system are free to move, in principal. The problem is, as I explained in 3), that a full band does not conduct. Only if an electron "jumps" into the valence band, it can conduct (and the hole it leaves behind will also conduct).
Every electron can move. Holes can move as well as electrons. Mind though, that a hole is only a missing electron which behaves equally to an electron with opposite charge (imagine that you have 100 people in a room, and everyone has a ball. Nothing will ever change. If you take away one ball, the person without a ball can be given a ball from the person next to him, and it will be as if the "hole" moved).
The picture illustrates the concept of a band structure quite nicely:
Mind that "band" can mean "one solid line" as well and "a bunch of solid lines". The conduction band and the valence band are actually a bunch of bands (=a bunch of solid lines).
Semiconductors can be split into two groups. Intrinsic semiconductors have a band gap that is around thermal energies, so a few electrons can be promoted from the valence to conduction band at room temperature. This corresponds to the third picture from the left in your post.
Extrinsic semiconductors have had a dopand added, and this creates new states in the band gap. These extra states can either accept electrons from the valence band or donate electrons to the conduction band. In the former case you get conduction due to holes in the valence band (p type) and in the latter you get conduction due to electrons in the conduction band (n type). This corresponds to the rightmost picture in your post, though whether the dopant states form a band is debatable, though maybe this is just terminology. Note that conduction is movement on holes or electrons in the semiconductor valence or condustion bands, and not due to transport in the dopant states.
Now to your questions:
I suppose all semiconductors have some intrinsic semiconduction, but for an extrinsic semiconductor this is usually negligable. The conductivity is dominated by the doping.
I think this is covered by the into above. An extrinsic semiconductor has either holes in the valance band and an empty conduction band, or electrons in the conduction band and a full valence band, but not both.
In a p type semiconductor I suppose you could excite electrons from lower bands into the holes in the valence band, but the energies required are far greater than thermal energy so this doesn't happen at room temperature. In n type or intrinsic semiconductors you can excite electrons from inner bands into the valence band because the valence band is full.
Extrinsic semiconductivity isn't based on electrons jumping between the valence and conduction bands.
Best Answer
The shape of the bands depends on how the atomic orbitals interact with their neighbors in the crystal as a function of wavevector $k$ - where $k$ represents a phase shift from atom to atom. When the orbitals of nearest neighbors overlap a small change of phase will change the nature of the overlap and, thus, of the energy level. In many familiar semiconductors the lowest conduction and highest valence bands correspond to the anti-bonding and bonding levels of $sp^3$ hybridized orbitals in the diamond or zinc-blende structure. In such cases the gap between bonding and anti-bonding is the band gap which makes the crystal a semiconductor. Orbitals involved in bonding tend to have large overlap and a strong dependence of energy on $k$.
Now, the answer to your question:
However, there are other atomic orbitals as well. For example, in silicon there are unfilled $3d$ levels which lie higher up in energy. The $d$ orbitals do not overlap with neighbors as much as $s$ and $p$ orbitals tend to, and they result in very flat bands. Flat bands are less likely to overlap with other bands in energy and can create additional gaps in the band structure.
Deeper levels that are lower in energy and filled also tend to have lower principal quantum number, $n$, and are thus more deeply bound in the atoms and thus less liklely to overlap with one another and also result in flat bands lying deep in the valence structure - possibly also creating additional gaps there.
Most semiconductors physicists study just the lowest few conduction bands and the highest few valence bands because it is the filling and unfilling of these levels near the main band gap that determine the properties of fabricated devices like transistors. Studying the more distant bands is less common.