Question

Why does Hall voltage decrease with temperature?

Answer 1

Hall voltage decreases with temperature primarily due to the following reasons:

1. Increase in Carrier Scattering: As the temperature increases, the number of lattice vibrations (phonons) in a material also increases. These vibrations cause more frequent collisions between the charge carriers (like electrons) and the atoms in the material, increasing the scattering rate. This increased scattering reduces the mobility of the charge carriers, which in turn decreases the Hall voltage.
   

1. Carrier Concentration: In some materials, particularly semiconductors, an increase in temperature can lead to an increase in the number of charge carriers (because more electrons are excited to the conduction band). However, this increase in carrier concentration often results in a decrease in the overall Hall voltage because the Hall voltage depends on the carrier concentration and the mobility. A higher concentration of charge carriers can lead to a decrease in the effective voltage because the carriers become "spread out" over a larger number, and the deflection caused by the magnetic field becomes less significant.
   

1. Reduced Resistivity: With increasing temperature, the resistivity of metals generally increases (though for semiconductors it may decrease). This can change the relationship between the current and the applied voltage, leading to a change in the Hall voltage.
   

In summary, the decrease in Hall voltage with temperature is due to a combination of reduced carrier mobility, changes in carrier concentration, and the general effects of temperature on material properties.