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In a semiconducting material the mobilities of electrons and holes are $\mu_{e}$ and $\mu_{h}$ respectively. Which of the following is true?
a) $\mu_{e} > \mu_{h}$
b) $\mu_{e} < \mu_{h}$
c) $\mu_{e} = \mu_{h}$
d) $\mu_{e} =0, \mu_{h}>0$

Last updated date: 24th Jul 2024
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Hint: The mobility is proportionate to the transmitter relaxation time and inversely proportional to the transmitter effective mass. The electron mobility is frequently greater than hole mobility because the electron-effective mass is minor than the hole's adequate size.

Complete step-by-step solution:
The relaxation times are usually of the same order of magnitude for electrons and holes, and hence, they do not produce too much difference. In order to enhance the speed of a device, one has to keep materials with little electron and effective hole masses and significant relaxation times, i.e., where the holes and electrons do not have to feel too many collisions on crystal defects, impurities, i.e., one has to take materials with high crystal feature.
In crystalline materials, the mobility is inversely proportional to the effective mass of the drifting charge, both electrons or holes.
The electrons flow in the conduction band, a partly-filled band, while the holes run on the roof of the valence band, which is a partly empty band. The electrons and holes travel under the effect of the electric field, including an effective mass $m*$ because of the periodic cooperation with lattice atoms. The idea of effective mass is submitted to consider these periodic physical forces on the movement of electrons and holes. The effective mass is defined from the energy band composition determined by answering the mechanical wave equalizations where one understands $E = f (p)$, the energy E as a purpose of momentum p. The simplest way to get the effective mass is to provide the conduction band least and the valence band height by a parabola:
$E = \dfrac{p^{2}}{2 m*}$
Typically, the effective mass of electrons is less than the effective mass of holes—thus the hole mobility usually is smaller than the electron mobility in crystalline materials.
The mobility depends on crystallographic errors, with the most effective in decreasing the mobility is the grain boundaries.
In semiconductors, the mobility of electrons is greater than that of a-holes (indirectly referring to 'valence electrons') different band structure and scattering mechanisms of these two carrier types.
Conduction electrons travel in the conduction band, and holes travel in the valence band. Valence electrons cannot flow freely as the free electrons in an implemented electric field because their motion is restricted. The particle mobility in a semiconductor is more significant if its effective mass is less and the time between scattering events is more significant.
Option (a) is correct.

Note:Holes are generated by elevating electrons from inner shells to higher shells or shells with greater energy levels. Since holes are constrained to the more vital atomic force attracted by the nucleus than the electrons remaining in the higher shells or more faraway shells, holes have weaker mobility.