Why the resistivity of semiconductor and insulator decreases with temperature?
2 Answers
The resistivity of materials depends on their ability to conduct electric current, which in turn is influenced by their charge carriers (electrons and holes) and how easily these carriers can move through the material. Here's why resistivity changes with temperature for semiconductors and insulators:
### **1. Semiconductors**
In semiconductors, resistivity decreases with temperature due to increased charge carrier generation:
- **Intrinsic Semiconductors**: At low temperatures, the number of charge carriers (electrons and holes) in an intrinsic semiconductor is low because the energy gap between the valence band and the conduction band is significant. As temperature increases, more thermal energy is available to excite electrons from the valence band to the conduction band. This results in more electron-hole pairs being generated. The increased number of charge carriers enhances the material's ability to conduct electricity, thus reducing its resistivity.
- **Extrinsic Semiconductors**: In extrinsic semiconductors (doped materials), the effect is somewhat different. For n-type semiconductors (which have excess electrons), resistivity decreases with temperature up to a certain point because the increased thermal energy can release more electrons from donor levels into the conduction band. For p-type semiconductors (which have excess holes), resistivity also decreases with temperature as thermal energy helps release more holes from acceptor levels into the valence band.
### **2. Insulators**
In insulators, resistivity decreases with temperature due to the activation of charge carriers:
- At low temperatures, insulators have very few charge carriers because the energy gap between the valence band and the conduction band is large. Thermal excitation at higher temperatures provides sufficient energy to excite some electrons into the conduction band, creating electron-hole pairs. This process is similar to what happens in semiconductors, but it usually requires much higher temperatures for insulators because of the larger band gap. As more charge carriers become available, the resistivity of the insulator decreases.
### **Summary**
- **Semiconductors**: Resistivity decreases with temperature due to increased generation of charge carriers as thermal energy helps electrons jump to the conduction band.
- **Insulators**: Resistivity decreases with temperature as thermal excitation creates more charge carriers by overcoming the large band gap.
In both cases, the key factor is the generation and movement of charge carriers, which enhances conductivity and reduces resistivity as temperature rises.
### **1. Semiconductors**
In semiconductors, resistivity decreases with temperature due to increased charge carrier generation:
- **Intrinsic Semiconductors**: At low temperatures, the number of charge carriers (electrons and holes) in an intrinsic semiconductor is low because the energy gap between the valence band and the conduction band is significant. As temperature increases, more thermal energy is available to excite electrons from the valence band to the conduction band. This results in more electron-hole pairs being generated. The increased number of charge carriers enhances the material's ability to conduct electricity, thus reducing its resistivity.
- **Extrinsic Semiconductors**: In extrinsic semiconductors (doped materials), the effect is somewhat different. For n-type semiconductors (which have excess electrons), resistivity decreases with temperature up to a certain point because the increased thermal energy can release more electrons from donor levels into the conduction band. For p-type semiconductors (which have excess holes), resistivity also decreases with temperature as thermal energy helps release more holes from acceptor levels into the valence band.
### **2. Insulators**
In insulators, resistivity decreases with temperature due to the activation of charge carriers:
- At low temperatures, insulators have very few charge carriers because the energy gap between the valence band and the conduction band is large. Thermal excitation at higher temperatures provides sufficient energy to excite some electrons into the conduction band, creating electron-hole pairs. This process is similar to what happens in semiconductors, but it usually requires much higher temperatures for insulators because of the larger band gap. As more charge carriers become available, the resistivity of the insulator decreases.
### **Summary**
- **Semiconductors**: Resistivity decreases with temperature due to increased generation of charge carriers as thermal energy helps electrons jump to the conduction band.
- **Insulators**: Resistivity decreases with temperature as thermal excitation creates more charge carriers by overcoming the large band gap.
In both cases, the key factor is the generation and movement of charge carriers, which enhances conductivity and reduces resistivity as temperature rises.
The resistivity of materials, including semiconductors and insulators, is influenced by how easily electric charges (electrons or holes) can move through them. Let's break down why the resistivity of **semiconductors** and **insulators** decreases with temperature.
### 1. **Semiconductors:**
Semiconductors are materials whose electrical conductivity lies between that of conductors (like metals) and insulators. Their resistivity is relatively high at low temperatures but decreases significantly as temperature increases. This is due to the **behavior of charge carriers** (electrons and holes) and the **energy band structure** of the material.
#### Energy Band Model in Semiconductors:
- Semiconductors have two key energy bands:
- **Valence band**: Where electrons are bound to atoms.
- **Conduction band**: Where electrons are free to move and conduct electricity.
- Between these two bands is an **energy gap** (or band gap), which is the amount of energy required to excite an electron from the valence band to the conduction band.
#### Impact of Temperature:
- **At low temperatures**, most electrons are stuck in the valence band because they don't have enough energy to jump over the band gap into the conduction band.
- **As temperature increases**, thermal energy is supplied to the semiconductor. This energy excites more electrons to jump from the valence band to the conduction band, creating more free electrons (in the conduction band) and more holes (in the valence band).
- These **free electrons** and **holes** act as charge carriers, contributing to electrical conductivity.
Because the number of charge carriers increases with temperature, the **resistivity** (which opposes the flow of charge) decreases. More charge carriers mean more pathways for current to flow, leading to better conductivity and lower resistivity.
In short, in semiconductors:
- **Higher temperature → More charge carriers (electrons and holes) → Lower resistivity**.
### 2. **Insulators:**
Insulators also follow a similar principle, but their **band gap** is much larger than that of semiconductors. The reason their resistivity decreases with temperature is also due to the creation of charge carriers, but it happens at a much slower rate compared to semiconductors.
#### Energy Band Model in Insulators:
- In insulators, the **band gap** between the valence band and the conduction band is very large (greater than 3-5 eV), meaning that under normal conditions (room temperature), almost no electrons have enough energy to jump to the conduction band.
- As a result, at low temperatures, insulators have **very few free electrons** or holes, making their resistivity extremely high.
#### Impact of Temperature:
- **At very high temperatures**, thermal energy becomes sufficient to excite a small number of electrons from the valence band to the conduction band. This results in a few charge carriers being created.
- Though the number of these charge carriers is still very small compared to a semiconductor, it is enough to decrease the resistivity of the insulator slightly.
In insulators:
- **Higher temperature → A few more charge carriers → Slight decrease in resistivity**.
### 3. **Why Doesn't This Happen in Metals?**
The situation in **metals** is different because they already have plenty of free electrons available for conduction even at low temperatures (i.e., they have no band gap). In metals, increasing temperature actually **increases resistivity**. This is because the atoms in the metal lattice vibrate more at higher temperatures (increased thermal motion), which scatters the free electrons more often, hindering their flow and increasing resistivity.
### Summary:
- **Semiconductors**: At higher temperatures, more electrons are excited across the band gap into the conduction band, increasing the number of charge carriers and thus decreasing resistivity.
- **Insulators**: At very high temperatures, a small number of electrons are excited across a large band gap, leading to a slight decrease in resistivity.
- In both cases, the **increased availability of charge carriers** (electrons and holes) at higher temperatures is the main reason for the reduction in resistivity.
This is in contrast to metals, where resistivity increases with temperature due to the scattering of charge carriers by atomic vibrations.
### 1. **Semiconductors:**
Semiconductors are materials whose electrical conductivity lies between that of conductors (like metals) and insulators. Their resistivity is relatively high at low temperatures but decreases significantly as temperature increases. This is due to the **behavior of charge carriers** (electrons and holes) and the **energy band structure** of the material.
#### Energy Band Model in Semiconductors:
- Semiconductors have two key energy bands:
- **Valence band**: Where electrons are bound to atoms.
- **Conduction band**: Where electrons are free to move and conduct electricity.
- Between these two bands is an **energy gap** (or band gap), which is the amount of energy required to excite an electron from the valence band to the conduction band.
#### Impact of Temperature:
- **At low temperatures**, most electrons are stuck in the valence band because they don't have enough energy to jump over the band gap into the conduction band.
- **As temperature increases**, thermal energy is supplied to the semiconductor. This energy excites more electrons to jump from the valence band to the conduction band, creating more free electrons (in the conduction band) and more holes (in the valence band).
- These **free electrons** and **holes** act as charge carriers, contributing to electrical conductivity.
Because the number of charge carriers increases with temperature, the **resistivity** (which opposes the flow of charge) decreases. More charge carriers mean more pathways for current to flow, leading to better conductivity and lower resistivity.
In short, in semiconductors:
- **Higher temperature → More charge carriers (electrons and holes) → Lower resistivity**.
### 2. **Insulators:**
Insulators also follow a similar principle, but their **band gap** is much larger than that of semiconductors. The reason their resistivity decreases with temperature is also due to the creation of charge carriers, but it happens at a much slower rate compared to semiconductors.
#### Energy Band Model in Insulators:
- In insulators, the **band gap** between the valence band and the conduction band is very large (greater than 3-5 eV), meaning that under normal conditions (room temperature), almost no electrons have enough energy to jump to the conduction band.
- As a result, at low temperatures, insulators have **very few free electrons** or holes, making their resistivity extremely high.
#### Impact of Temperature:
- **At very high temperatures**, thermal energy becomes sufficient to excite a small number of electrons from the valence band to the conduction band. This results in a few charge carriers being created.
- Though the number of these charge carriers is still very small compared to a semiconductor, it is enough to decrease the resistivity of the insulator slightly.
In insulators:
- **Higher temperature → A few more charge carriers → Slight decrease in resistivity**.
### 3. **Why Doesn't This Happen in Metals?**
The situation in **metals** is different because they already have plenty of free electrons available for conduction even at low temperatures (i.e., they have no band gap). In metals, increasing temperature actually **increases resistivity**. This is because the atoms in the metal lattice vibrate more at higher temperatures (increased thermal motion), which scatters the free electrons more often, hindering their flow and increasing resistivity.
### Summary:
- **Semiconductors**: At higher temperatures, more electrons are excited across the band gap into the conduction band, increasing the number of charge carriers and thus decreasing resistivity.
- **Insulators**: At very high temperatures, a small number of electrons are excited across a large band gap, leading to a slight decrease in resistivity.
- In both cases, the **increased availability of charge carriers** (electrons and holes) at higher temperatures is the main reason for the reduction in resistivity.
This is in contrast to metals, where resistivity increases with temperature due to the scattering of charge carriers by atomic vibrations.