Why does the resistivity of a metal increases

In summary, the resistivity of a metal increases with an increase in temperature due to the vibrations of metal ions, which causes the conduction electrons to have a higher probability of being bumped into, creating extra resistance. On the other hand, in semiconductors, the resistivity decreases as temperature increases because the electrons in the valence band gain enough energy to jump to the conduction band, which has empty states for the electrons to conduct through. This trend is only valid within a certain range of temperatures.
  • #1
vptran84
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why does the resistivity of a metal increases while the resistivity of a semiconductor decreases with an increase in temperature? thanks in advance.
 
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  • #2
vptran84 said:
why does the resistivity of a metal increases while the resistivity of a semiconductor decreases with an increase in temperature? thanks in advance.

Metals and semiconductors have two different band structures. Metals have electrons occupying a partially filled conduction band. That is why those electrons can move about easily, since they have "empty" states to move into (Pauli exclusion principle). When you raise the temperature, the crude picture I can give you is that the ions of the metal vibrates with a larger amplitude. So these conduction electrons have a higher probability of being bumped into them. This creates extra resistance. So the higher the temperature, the larger the resistance.

In a semiconductor (intrinsic), there is an energy gap separating the valence band, and the conduction band. At T=0, the valence band is completely full, while the conduction band is completely empty. Because the valence band is full, electrons can't move about, since there are no empty states for the electrons to go into. However, if you raise the temperature of the semiconductor, some of the electrons at the top of the valence band may now gain sufficient energy to jump across the energy gap and get into the conduction band. Since the conduction band has empty states, these electrons then can conduct. The higher the temperature, the more the number of electrons that can occupy the conduction band. Thus, the resistivity drops as temperature increases.

As with any material, these trends are valid only within a certain range of temperatures.

Zz.
 
  • #3


The resistivity of a metal increases due to the scattering of free electrons by impurities and defects in the metal's crystal lattice. As the temperature increases, the atoms in the lattice vibrate more and create more obstacles for the free electrons to move through, resulting in an increase in resistivity.

On the other hand, the resistivity of a semiconductor decreases with an increase in temperature due to the increase in the number of charge carriers (electrons and holes) available for conduction. At low temperatures, most of the electrons are bound in the valence band and do not contribute to conduction. However, as the temperature increases, more electrons are excited to the conduction band, increasing the number of charge carriers and decreasing the resistivity.

This difference in behavior between metals and semiconductors can be explained by their respective band structures. In metals, the valence and conduction bands overlap, allowing for a large number of free electrons to move through the material at all temperatures. In semiconductors, there is a band gap between the valence and conduction bands, and at low temperatures, the electrons are not able to overcome this gap. However, as the temperature increases, more electrons are able to gain enough energy to move into the conduction band, leading to a decrease in resistivity.

In summary, the resistivity of a metal increases due to increased scattering of free electrons, while the resistivity of a semiconductor decreases due to an increase in the number of charge carriers available for conduction.
 

1. Why does the resistivity of a metal increase with temperature?

The resistivity of a metal increases with temperature because as the temperature rises, the atoms in the metal vibrate more and disrupt the flow of electrons. This increase in atomic vibrations creates more collisions between the electrons and atoms, making it more difficult for the electrons to move through the metal, resulting in a higher resistance.

2. What causes the resistivity of a metal to increase with impurities?

Impurities in a metal, such as other elements or defects in the crystal structure, can scatter the electrons as they move through the metal. This scattering increases the resistance and therefore the resistivity of the metal.

3. How does the structure of a metal affect its resistivity?

The structure of a metal, specifically the arrangement of its atoms and the presence of defects or impurities, can affect the resistivity of the metal. A more ordered and pure structure will have less resistance and therefore a lower resistivity, while a more disordered and impure structure will have higher resistance and a higher resistivity.

4. Why does the resistivity of a metal decrease with increasing cross-sectional area?

The resistivity of a metal is directly proportional to its length and inversely proportional to its cross-sectional area. This means that as the cross-sectional area of a metal increases, there is more space for the electrons to flow through, resulting in a lower resistance and a lower resistivity.

5. How does the type of metal affect its resistivity?

Each type of metal has a different atomic structure and composition, which can affect the movement of electrons and therefore the resistivity of the metal. Some metals, such as copper and silver, have a lower resistivity due to their high conductivity, while others, like iron and tungsten, have a higher resistivity due to their lower conductivity.

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