Why is increasing the temperature the specific resistance of a conductor and a semiconductor?
2 Answers
The effect of temperature on the specific resistance (or resistivity) of conductors and semiconductors is fundamentally different due to their distinct electronic properties.
### Conductors
In conductors, such as metals, increasing the temperature generally leads to an increase in resistivity. This happens because:
1. **Increased Atomic Vibrations**: As temperature rises, the atoms in the metal lattice vibrate more vigorously. This increased motion causes more frequent collisions between conduction electrons and the vibrating atoms, which impedes the flow of electrons.
2. **Electron Scattering**: The increased lattice vibrations result in higher scattering rates for electrons, which raises the overall resistance.
### Semiconductors
In semiconductors, such as silicon or germanium, the behavior is quite different:
1. **Increased Charge Carriers**: At low temperatures, semiconductors have very few charge carriers (electrons and holes). As temperature increases, more electrons gain enough thermal energy to jump from the valence band to the conduction band, thus increasing the number of free charge carriers.
2. **Decreased Resistivity**: The increase in charge carriers outweighs the effect of any scattering that occurs, leading to a decrease in resistivity. This means that as temperature rises, semiconductors become better conductors.
### Summary
- **Conductors**: Resistivity increases with temperature due to enhanced atomic vibrations causing more scattering of electrons.
- **Semiconductors**: Resistivity decreases with temperature due to increased thermal energy enabling more charge carriers to participate in conduction.
This contrasting behavior is crucial for applications in electronics, where semiconductors can be engineered for specific responses to temperature changes.
### Conductors
In conductors, such as metals, increasing the temperature generally leads to an increase in resistivity. This happens because:
1. **Increased Atomic Vibrations**: As temperature rises, the atoms in the metal lattice vibrate more vigorously. This increased motion causes more frequent collisions between conduction electrons and the vibrating atoms, which impedes the flow of electrons.
2. **Electron Scattering**: The increased lattice vibrations result in higher scattering rates for electrons, which raises the overall resistance.
### Semiconductors
In semiconductors, such as silicon or germanium, the behavior is quite different:
1. **Increased Charge Carriers**: At low temperatures, semiconductors have very few charge carriers (electrons and holes). As temperature increases, more electrons gain enough thermal energy to jump from the valence band to the conduction band, thus increasing the number of free charge carriers.
2. **Decreased Resistivity**: The increase in charge carriers outweighs the effect of any scattering that occurs, leading to a decrease in resistivity. This means that as temperature rises, semiconductors become better conductors.
### Summary
- **Conductors**: Resistivity increases with temperature due to enhanced atomic vibrations causing more scattering of electrons.
- **Semiconductors**: Resistivity decreases with temperature due to increased thermal energy enabling more charge carriers to participate in conduction.
This contrasting behavior is crucial for applications in electronics, where semiconductors can be engineered for specific responses to temperature changes.
The relationship between temperature and the specific resistance (or resistivity) of a conductor and a semiconductor is governed by the behavior of electrons and the structure of the materials. Here's a detailed explanation of how and why this relationship differs for conductors and semiconductors:
### **1. Conductors:**
Conductors, like metals (e.g., copper, aluminum), have a structure that allows a large number of free electrons to move easily through the material. These free electrons are the primary carriers of electrical current. The specific resistance (resistivity) of a conductor typically **increases** with temperature. Here’s why:
#### **Behavior of Electrons in Conductors:**
- **At lower temperatures**, the atoms in a metal vibrate slowly, which means that free electrons can move through the material with fewer collisions with the vibrating atoms.
- **As temperature increases**, the thermal energy causes the atoms in the metal lattice to vibrate more vigorously. These vibrations increase the likelihood of collisions between the free electrons and the atoms.
- Each collision scatters the electrons, which makes it harder for them to flow in a consistent direction, thereby increasing the resistance of the material.
#### **Summary for Conductors:**
- **As temperature increases**, the increased atomic vibrations interfere with the flow of electrons.
- **More collisions** lead to **higher resistivity**, which means the material becomes less efficient at conducting electricity.
Mathematically, the relationship can be described as:
\[
\rho_T = \rho_0(1 + \alpha(T - T_0))
\]
Where:
- \(\rho_T\) is the resistivity at temperature \(T\),
- \(\rho_0\) is the resistivity at a reference temperature (typically room temperature),
- \(\alpha\) is the temperature coefficient of resistivity, which is positive for conductors,
- \(T_0\) is the reference temperature.
In conductors, \(\alpha\) is positive, meaning resistivity increases as temperature rises.
### **2. Semiconductors:**
Semiconductors (e.g., silicon, germanium) behave very differently from conductors. In a semiconductor, the specific resistance **decreases** as the temperature increases. The reason lies in the number of charge carriers available to conduct current.
#### **Behavior of Electrons in Semiconductors:**
- **At low temperatures**, semiconductors have very few free charge carriers (electrons and holes) because most of the electrons are bound to atoms and cannot move freely.
- **As temperature increases**, the thermal energy provided to the semiconductor is sufficient to excite more electrons from the **valence band** (where electrons are bound) into the **conduction band** (where electrons are free to move).
- This excitation creates more **electron-hole pairs**. The electrons in the conduction band and the holes in the valence band act as charge carriers. Since there are now more free carriers, the material's conductivity increases.
#### **Summary for Semiconductors:**
- **As temperature increases**, more electrons gain enough energy to jump into the conduction band, leading to an increase in the number of charge carriers.
- With more charge carriers available to conduct electricity, the resistivity **decreases** with increasing temperature.
Mathematically, the resistivity of a semiconductor typically decreases exponentially with temperature:
\[
\rho_T = \rho_0 e^{-\frac{E_g}{kT}}
\]
Where:
- \(\rho_T\) is the resistivity at temperature \(T\),
- \(\rho_0\) is a material-specific constant,
- \(E_g\) is the band gap energy (the energy difference between the conduction and valence bands),
- \(k\) is Boltzmann’s constant, and
- \(T\) is the temperature in kelvin.
Since the exponential factor decreases with increasing temperature, the resistivity of semiconductors decreases.
### **Key Differences Between Conductors and Semiconductors:**
- **Conductor:**
- The resistivity **increases** with temperature because the increased thermal vibrations of atoms lead to more collisions with free electrons, impeding their flow.
- **Fewer charge carriers (free electrons)** are affected by collisions, which reduces the current-carrying capacity.
- **Semiconductor:**
- The resistivity **decreases** with temperature because the thermal energy excites more electrons into the conduction band, increasing the number of charge carriers (electrons and holes).
- **More charge carriers** are available to carry current, improving conductivity.
### **Conclusion:**
The specific resistance of a conductor and a semiconductor reacts to temperature in opposite ways because of the different ways in which they conduct electricity. Conductors rely on free electrons, which face increasing resistance due to atomic vibrations as temperature rises. In contrast, semiconductors rely on temperature to create more charge carriers, which enhances their conductivity.
### **1. Conductors:**
Conductors, like metals (e.g., copper, aluminum), have a structure that allows a large number of free electrons to move easily through the material. These free electrons are the primary carriers of electrical current. The specific resistance (resistivity) of a conductor typically **increases** with temperature. Here’s why:
#### **Behavior of Electrons in Conductors:**
- **At lower temperatures**, the atoms in a metal vibrate slowly, which means that free electrons can move through the material with fewer collisions with the vibrating atoms.
- **As temperature increases**, the thermal energy causes the atoms in the metal lattice to vibrate more vigorously. These vibrations increase the likelihood of collisions between the free electrons and the atoms.
- Each collision scatters the electrons, which makes it harder for them to flow in a consistent direction, thereby increasing the resistance of the material.
#### **Summary for Conductors:**
- **As temperature increases**, the increased atomic vibrations interfere with the flow of electrons.
- **More collisions** lead to **higher resistivity**, which means the material becomes less efficient at conducting electricity.
Mathematically, the relationship can be described as:
\[
\rho_T = \rho_0(1 + \alpha(T - T_0))
\]
Where:
- \(\rho_T\) is the resistivity at temperature \(T\),
- \(\rho_0\) is the resistivity at a reference temperature (typically room temperature),
- \(\alpha\) is the temperature coefficient of resistivity, which is positive for conductors,
- \(T_0\) is the reference temperature.
In conductors, \(\alpha\) is positive, meaning resistivity increases as temperature rises.
### **2. Semiconductors:**
Semiconductors (e.g., silicon, germanium) behave very differently from conductors. In a semiconductor, the specific resistance **decreases** as the temperature increases. The reason lies in the number of charge carriers available to conduct current.
#### **Behavior of Electrons in Semiconductors:**
- **At low temperatures**, semiconductors have very few free charge carriers (electrons and holes) because most of the electrons are bound to atoms and cannot move freely.
- **As temperature increases**, the thermal energy provided to the semiconductor is sufficient to excite more electrons from the **valence band** (where electrons are bound) into the **conduction band** (where electrons are free to move).
- This excitation creates more **electron-hole pairs**. The electrons in the conduction band and the holes in the valence band act as charge carriers. Since there are now more free carriers, the material's conductivity increases.
#### **Summary for Semiconductors:**
- **As temperature increases**, more electrons gain enough energy to jump into the conduction band, leading to an increase in the number of charge carriers.
- With more charge carriers available to conduct electricity, the resistivity **decreases** with increasing temperature.
Mathematically, the resistivity of a semiconductor typically decreases exponentially with temperature:
\[
\rho_T = \rho_0 e^{-\frac{E_g}{kT}}
\]
Where:
- \(\rho_T\) is the resistivity at temperature \(T\),
- \(\rho_0\) is a material-specific constant,
- \(E_g\) is the band gap energy (the energy difference between the conduction and valence bands),
- \(k\) is Boltzmann’s constant, and
- \(T\) is the temperature in kelvin.
Since the exponential factor decreases with increasing temperature, the resistivity of semiconductors decreases.
### **Key Differences Between Conductors and Semiconductors:**
- **Conductor:**
- The resistivity **increases** with temperature because the increased thermal vibrations of atoms lead to more collisions with free electrons, impeding their flow.
- **Fewer charge carriers (free electrons)** are affected by collisions, which reduces the current-carrying capacity.
- **Semiconductor:**
- The resistivity **decreases** with temperature because the thermal energy excites more electrons into the conduction band, increasing the number of charge carriers (electrons and holes).
- **More charge carriers** are available to carry current, improving conductivity.
### **Conclusion:**
The specific resistance of a conductor and a semiconductor reacts to temperature in opposite ways because of the different ways in which they conduct electricity. Conductors rely on free electrons, which face increasing resistance due to atomic vibrations as temperature rises. In contrast, semiconductors rely on temperature to create more charge carriers, which enhances their conductivity.