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Short Answer:
Electrons are waves and waves in a confined geometry can exist only with specific allowed wavelengths. This is true for sound waves in Musical Instruments, water waves in a ripple tank, light waves and electron waves in solids. Bad gaps and allowed wave regimes exist for all waves and are the consequence of simple reflection, refraction and interference.
Long Answer:
Electrons in crystals (not all solids, but only regular periodic arrays of atoms) have energies that restricted to certain allowed values or ranges of values called "bands" or "energy bands" and not other values called "gaps" or "band gaps" for a simple reason. Electrons are waves and electron dynamics is described by a wave equation, specifically the Schroeding equation. Quantum waves must respect the same dynamics as all waves and that includes the processes of reflection, refraction, and interference. It is these processes that create the bands and band gaps.
If you are asked to explain why a musical instrument gives out specific notes and not all possible sounds, you explain it as a condition of wave dynamics. A guitar string, for instance, vibrates with waves that can exist with whole wavelengths that fit within the length of the string. That is completely analogous to the phenomena that forces the existence of bands and band gaps for electrons in solids.
In fact, if you scale things up to wavelengths appropriate to sound (Sound wave are about a trillion time larger than electron waves.) you will get bands of allowed sound and band gaps where sound is not allowed. You can create a volume of space with a regular array of objects that reflect and refract sound and in that space only certain bands of wavelengths of sound will be allowed. The phenomena is the same. The equations are the same. The cause is the same.
Though quantum mechanics is strange and complicated, the reason energy bands in crystals exist is simple and completely faithful to the analogy of notes from a musical instrument.
Caveat: Though the existence of bands follows from this simple explanation, the prediction of the behavior of electrons in particular solids requires a sophisticated description of the particular atomic and electronic interactions. One can spend a career as a physicist making such descriptions and explaining the properties of the various kinds of solids.
More Answers:
Electrons may only possess specific energies. Another way of saying this is that they can only occupy certain energy levels. A band gap is a continuous spectrum of energies where no such energy levels exist. The band gap is simply a range of energies that the electron cannot have.
If you want to know why there are energies the electron can have and why there is a gap in between these energy ranges then that's quite a bit more complicated. A short answer would be that there are gaps because there are asymmetries in the basic repeating unit of the crystal structure but I appreciate that that probably prompts a bunch of other questions.
What else can I help you with?
Why effective mass is infinite at the middle of the band gap?
It sounds like a math trick because the electron cannot exist in the middle of the band gap. The trick would be that it would take an infinite amount of energy to excite the electron to the middle of the band gap.
What is the energy band gap of barium titanate?
The energy band gap of barium titanate is approximately 3.2 electron volts (eV). This wide band gap makes barium titanate a good candidate for various applications in electronics and optoelectronics.
What is the forbidden energy gap?
The forbidden energy gap refers to the energy range within a material where electron states are not allowed to exist. This gap prevents electrons from moving freely and conducting electricity. Materials with larger forbidden energy gaps are typically insulators, while materials with smaller gaps or none are conductors or semiconductors.
Energy Band gap value for calcium carbonate and barium carbonate?
The energy band gap value for calcium carbonate (CaCO3) is around 5.6 eV, while for barium carbonate (BaCO3) it is approximately 6.3 eV. These values indicate the amount of energy required to promote an electron from the valence band to the conduction band in the respective materials.
Valence electron conductor also can be called?
A valence electron conductor can also be called a semiconductor. Semiconductors have a small but nonzero energy gap between the valence band and the conduction band, allowing them to conduct electricity under certain conditions.
What are the difference between direct and indirect band gap materials?
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
Why effective mass is infinite at the middle of the band gap?
It sounds like a math trick because the electron cannot exist in the middle of the band gap. The trick would be that it would take an infinite amount of energy to excite the electron to the middle of the band gap.
What is the energy band gap of germanium?
The energy band gap of germanium is approximately 0.67 electronvolts (eV). This means that it requires this amount of energy to move an electron from the valence band to the conduction band in germanium.
What is the energy band gap of barium titanate?
The energy band gap of barium titanate is approximately 3.2 electron volts (eV). This wide band gap makes barium titanate a good candidate for various applications in electronics and optoelectronics.
What is the value of band gap of zinc selenide?
The band gap of zinc selenide is approximately 2.7 electron volts (eV). This value indicates the energy difference between the valence band and the conduction band in the material. Zinc selenide is a semiconductor commonly used in optoelectronic applications due to its wide band gap.
What is the energy band gap for germanium?
The energy band gap for germanium is around 0.67 electron volts (eV) at room temperature. This makes germanium a semiconductor with properties in between those of conductors and insulators.
What are applications of direct and indirect band gap?
direct band gap means in e-k diagram valance bands are exactly below covalance band,in this band electron falls from the conduction band to valance band directly without going to metastable state and in indirect band gap the band electron falls from the conduction band to valance band by first going through the metastable state
What is the forbidden energy gap?
The forbidden energy gap refers to the energy range within a material where electron states are not allowed to exist. This gap prevents electrons from moving freely and conducting electricity. Materials with larger forbidden energy gaps are typically insulators, while materials with smaller gaps or none are conductors or semiconductors.
Do you find electrons in forbidden energy gap?
No, electrons cannot exist in the forbidden energy gap of a material. The forbidden energy gap is the energy range where no electron states can exist in a crystalline solid. Electrons can only occupy energy levels within the allowed energy bands of a material.
Can extrinsic semiconductor conduct at 0 k?
Normally, no electron energy states exist in the band gap, the gap between the valence band and conduction band in a semiconductor. However, if we dope the semiconductor, i.e. add donor (n type) or acceptor (p type) atoms to it, we introduce new electron energy states in the band gap! Take for example silicon, in which we introduce phosphorus, which is a group V element and thus a donor atom. This will introduce extra filled electron states just below the conduction band. Now, this all happens at 0K, so no current can flow (this is logical as electrons don't move at this temperature, even with an electric field applied). But if we raise the temperature e.g. until room temperature at 300K, the electrons gain energy and can jump into the free energy states in the conduction band. These electrons in the conduction band can now conduct electricity.
When was The Gap Band created?
The Gap Band was created in 1967.
Energy Band gap value for calcium carbonate and barium carbonate?
The energy band gap value for calcium carbonate (CaCO3) is around 5.6 eV, while for barium carbonate (BaCO3) it is approximately 6.3 eV. These values indicate the amount of energy required to promote an electron from the valence band to the conduction band in the respective materials.
