Why mobility of holes is less than electrons and relationship between conductivity and temperature in semiconductors?
Lower Mobility of Holes:
The mobility of holes in semiconductors is indeed less than the mobility of electrons for two main reasons:
1. Effective Mass: In solids, electrons and holes behave like particles with an effective mass, which can be different from their actual mass. The effective mass often depends on the material's band structure and how electrons interact with the lattice. Generally, the effective mass of holes in semiconductors is greater than the effective mass of electrons. This larger mass makes it harder for holes to accelerate under an electric field, leading to lower mobility.
2. Scattering Mechanisms: Semiconductors have imperfections like dopant atoms and lattice vibrations that can scatter both electrons and holes as they move. However, the way these imperfections interact with each particle can differ. Holes often experience stronger scattering due to their interaction with the surrounding positive ions and the fixed atomic positions they "hop" between. This additional scattering further hinders their mobility compared to electrons.
Conductivity and Temperature in Semiconductors:
The conductivity of a semiconductor, which measures its ability to conduct electricity, is related to temperature in a non-linear way:
- As temperature increases:Thermal excitation: More electrons gain enough thermal energy to jump from the valence band to the conduction band, increasing the number of free electrons and holes contributing to conduction. This increases conductivity. Increased scattering: However, the higher temperature also intensifies the thermal vibrations in the lattice, leading to more frequent collisions between electrons, holes, and other imperfections. This decreases mobility and partially counteracts the conductivity increase.
Therefore, the overall effect of temperature on conductivity depends on which factor dominates: the increase in carrier concentration or the decrease in mobility. In some cases, the conductivity might initially increase with temperature but then decrease at extremely high temperatures due to the dominance of scattering.
In summary, the lower effective mass and less favorable scattering environment contribute to the lower mobility of holes compared to electrons in semiconductors. Additionally, conductivity in semiconductors exhibits a complex relationship with temperature due to the interplay between carrier concentration and mobility.
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