How does band theory helps in explaining semiconductor and insulator in metallic bond?
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Answer:
Conductors vs. Insulators
A conductor is a material which contains movable electric charges. In metallic conductors such as copper or aluminum, the movable charged particles are electrons. Positive charges may also be mobile, such as the cationic electrolyte(s) of a battery or the mobile protons of the proton conductor of a fuel cell. Insulators are non-conducting materials with few mobile charges; they carry only insignificant electric currents.
In describing conductors using the concept of band theory, it is best to focus on conductors that conduct electricity using mobile electrons. According to band theory, a conductor is simply a material that has its valence band and conduction band overlapping, allowing electrons to flow through the material with minimal applied voltage.
Band Theory
In solid-state physics, the band structure of a solid describes those ranges of energy, called energy bands, that an electron within the solid may have (“allowed bands”) and ranges of energy called band gaps (“forbidden bands”), which it may not have. Band theory models the behavior of electrons in solids by postulating the existence of energy bands. It successfully uses a material’s band structure to explain many physical properties of solids. Bands may also be viewed as the large-scale limit of molecular orbital theory.
The electrons of a single isolated atom occupy atomic orbitals, which form a discrete set of energy levels. If several atoms are brought together into a molecule, their atomic orbitals split into separate molecular orbitals, each with a different energy. This produces a number of molecular orbitals proportional to the number of valence electrons. When a large number of atoms (1020 or more) are brought together to form a solid, the number of orbitals becomes exceedingly large. Consequently, the difference in energy between them becomes very small. Thus, in solids the levels form continuous bands of energy rather than the discrete energy levels of the atoms in isolation. However, some intervals of energy contain no orbitals, forming band gaps. This concept becomes more important in the context of semi-conductors and insulators.
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Conductors, Semiconductors and Insulators: On the left, a conductor (described as a metal here) has its empty bands and filled bands overlapping, allowing excited electrons to flow through the empty band with little push (voltage). Semiconductors and insulators have a greater and greater energetic difference between the valence band and the conduction bands, requiring a larger applied voltage in order for electrons to flow.
Within an energy band, energy levels can be regarded as a near continuum for two reasons:
The separation between energy levels in a solid is comparable with the energy that electrons constantly exchange with phonons (atomic vibrations).
This separation is comparable with the energy uncertainty due to the Heisenberg uncertainty principle for reasonably long intervals of time. As a result, the separation between energy levels is of no consequence.
Conductors
All conductors contain electrical charges, which will move when an electric potential difference (measured in volts) is applied across separate points on the material. This flow of charge (measured in amperes) is what is referred to as electric current. In most materials, the direct current is proportional to the voltage (as determined by Ohm’s law), provided the temperature remains constant and the material remains in the same shape and state.
Most familiar conductors are metallic. Copper is the most common material used for electrical wiring. Silver is the best conductor, but it is expensive. Because gold does not corrode, it is used for high-quality surface-to-surface contacts. However, there are also many non-metallic conductors, including graphite, solutions of salts, and all plasmas. There are even conductive polymers.
Thermal and electrical conductivity often go together. For instance, the sea of electrons causes most metals to act both as electrical and thermal conductors. However, some non-metallic materials are practical electrical conductors without being good thermal conductors.
Answer:
The metallic bands corresponds to a large no. of separate quantum states of the electrons.
In the semiconductor the band is small which allows the electrons to populate the conduction band.
In insulators it is large which makes it difficult for the electrons to flow through the conduction band.