A p-n photodiode is fabricated from a semiconductor with band gap of \\(2.8\ eV\\). Can it detect a wavelength of \\(6000\ nm\\)?

Energy band gap \\(E=2.8\ eV\\)\\(E=\dfrac{hc}{\lambda}\\)\\(\Rightarrow\dfrac{6.6\times10^{-34}\times3\times10^8}{6000\times10^{-9}\times1.6\times10^{-19}}=0.207\ eV\\)The energy of a signal of wavelength \\(6000\ nm\\) is \\(0.207\ eV\\), which is less than \\(2.8\ eV\\), the energy band gap of a photodiode. Hence, the photodiode cannot detect the signal.

Write any two distinguishing features between conductors, semiconductors and insulators on the basis of energy band diagrams.

ConductorsInsulators Semiconductors 1. Valence band or conduction band are partially filled. Valence Band is completely filled with electrons and conduction band is empty. At 0K, electrons in valence band do not have sufficient energy to jump to conduction band.2. Valence and conduction bands overlap.Energy gap ~ 0 eV.Valence and conduction band have Energy gap ~ 6 eV. Forbidden gap in between conductors and insulators. Energy gap ~ 3 eV. 3. Conductivity is highest.Conductivity is very low. Conductivity is in between conductors and insulators.

Draw separate energy band diagrams for conductors, semi-conductors and insulators and label each of them.

Energy band diagrams for conductor, semiconductor and insulator are shown above.In conductors, both the valance band and conduction band overlap each other. So there is zero band gap in a conductor.In semiconductor, there is a small band gap approximately of \\(1 \ eV\\).In an insulator, there is a large band gap of nearly \\(5 \ eV\\).

Carbon, silicon and germanium have four valence electrons each. These are characterised by valence and conduction bands separated by energy band gap respectively equal to \\((E_g)_C,\, (E_g)_{Si}\\) and \\((E_g)_{Ge}\\).Which of the following statements is true?

For given elements, the energy band gap of carbon is the maximum and of germanium is the least.Hence option C is correct.

Explain the formation of energy bands in solids. On the basis of energy bands distinguish between a metal, a semiconductor and an insulator.

\\(\text{Formation of energy bands in solid:}\\)In a single isolated atom, the electrons in each orbit have definite energy associated with it. But in the case of solids all the atoms are close to each other, so the energy levels of outermost orbit electrons are affected by the neighbouring atoms.When two single or isolated atoms are brought close to each other than the outermost orbit. The electrons in the outermost orbit of one atom experience an attractive force from the nearest or neighbouring atomic nucleus. Due to this, the energies of the electrons will not be at the same level, the energy levels of electrons are changed to a value which is higher or lower than that of the original energy level of the electron.The electrons in the same orbit exhibit different energy levels.The grouping of this different energy levels is called energy band.However, the energy levels of inner orbit electrons are not much affected by the presence of neighbouring atoms. \\(\text{Insultaor:}\\) Insulator is material, in which there is a large energy gap between the conduction band and the valence band, A large amount of energy is required to shift the electron from valence band to conduction band.\\(\text{Semiconductor:}\\)Semiconductor is the material, in which there is a less energy gap required with respect to the insulator, When some amount of energy flow in the semiconductor, then it allows to flow the electron from valence band to conduction band.\\(\text{Conductior:}\\)Conductor is the material in which, there is no energy gap between the conduction band and valence band, so no extra energy is needed to flow the electron from valence band to conduction band.

Show on a graph, the variation of resistivity with temperature for a typical semiconductor.

The resistivity is given by:\\(\rho =\dfrac{m}{ne^{2}\tau }\\)where n = number density of electrons\\(\rho\\) = relaxation timeWith the rise in temperature, number density of electrons and holes (in case of semiconductors) increases, where \\(\tau\\) remains constant. So, \\(\rho\\) (resistivity) decreases.

The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than \\(2480\ nm\\) is incident on it. The band gap (in \\(eV\\)) for the semiconductor is

Band gap, \\(\displaystyle E_g = \dfrac{hc}{\lambda} = \dfrac{(6.63 \times 10^{-34})(3 \times 10^8)}{2480 \times 10^{-9} \times 1.6 \times 10^{-19}} eV = 0.5\ eV\\)

Fermi energy level for intrinsic semiconductors lies

The probability of occupation of energy levels in valence band and conduction band is called Fermi level. As the temperature increases free electrons and holes gets generated. In intrinsic semiconductor, the number of holes in valence band is equal to the number of electrons in the conduction band. Hence, the probability of occupation of energy levels in conduction band and valence band are equal. Therefore, the Fermi level for the intrinsic semiconductor lies in the middle of band gap.

A pn photo diode is fabricated from a semiconductor with a band gap of 2.5 eV. It can detect a signal of wavelength :

\\(\lambda_{max}=\frac{hc}{eV}\\) \\(=\frac{1242eVA^o}{2.5eV}=4960A^o\\)

In an insulator, the forbidden energy gap between the valence band and conduction band is of the order of

Forbidden energy gap, also known as band gap refers to the energy difference \\((eV)\\) between the top of valence band and the bottom of the conduction band in materials. Current flowing through the materials is due to the electron transfer from the valence band to the conduction band.Insulators do not conduct electricity because a large amount of energy is needed for the electrons to cross the forbidden energy gap. Moreover the forbidden energy gap is the widest \\((> 5 eV)\\) in case of insulators.Example: Forbidden energy gap in diamond is nearly \\(5.5 eV\\).

Electron Energies in Solids | Definition, Examples, Diagrams

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Semiconductor at absolute zero

Conductivity of semiconductors increases with increase in temperature. At absolute zero, electrons do not have any thermal energy and do not have the ability to conduct at all. Hence, at absolute zero, semiconductors behave like an ideal insulator.

definition

Energy Bands

Inside a solid crystal, each electron has a different energy level because of slightly different patterns of the surrounding charges. These electron energy levels form a continuous energy variation called as the Energy Bands. Energy bands of more tightly bound electrons have lower energy (more negative energy) as compared to that of loosely bound electrons.

definition

Band Gap

Energy band gap of a semiconductor is defined as:

E_{G} = E_{C} - E_{V}

where

E_{C} :

Lowest energy level in conduction band

E_{V} :

Highest energy level in valence band
Note:
1. Energy band gap is the lowest energy required for a material to conduct.
2. At

273 K

E_{g, S i} = 1.14 e V, E_{g, G e} = 0.67 e V

definition

Energy gaps in semiconductors

Semiconductors have a finite but small bandgap (

< 3 e V

). Because of this, at room temperature some electrons from valence band can acquire enough energy to to cross the energy gap and enter the conduction band. Hence, resistivity of semiconductors is not high as insulators.

Electron Energies in Solids

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Semiconductor at absolute zero

definition

Energy Bands

definition

Band Gap

definition

Energy gaps in semiconductors

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Metals, Conductors and semiconductors

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