Advanced Materials Engineering - Electrical Properties

Ohm's Law

Ohm's Law is a fundamental principle in electrical engineering and physics that describes the relationship between voltage (V), current (I), and resistance (R). It is essential for understanding how electric circuits operate and can be utilized to calculate the parameters involved. The law is expressed mathematically as:

V = I \times R

Resistance (R)

Resistance is a measure of the opposition that a circuit presents to the flow of electric current. It depends on several factors:

• Material Properties (Resistivity \rho): Different materials have different resistivities, which is a measure of how strongly a material opposes the flow of electric current. Metals like copper and silver have low resistivity and hence low resistance, while insulators like rubber have high resistivity.

• Geometric Factors:

  • Length (L): Resistance increases with the length of the conductor; longer wires have more resistance because electrons collide with more atoms along the path.

  • Cross-Sectional Area (A): Resistance decreases with an increase in cross-sectional area; wider wires allow more electrons to flow and reduce resistance.

Electrical Conduction

The flow of electric charge is described by current density (J) and electric field (\epsilon). The relationship between these two quantities is given by:

J = \sigma \times \epsilon where \sigma is the conductivity of the material, a measure of how easily electrons can move through it.

Furthermore, the resistance can also be expressed as:

R = \frac{\rho \times L}{A}

Conductivity and Resistivity

Conductivity (\sigma) is the reciprocal of resistivity (\rho):

\sigma = \frac{1}{\rho}

• Dependent Factors Include:

  • Temperature: As temperature rises, resistivity in conductors typically increases due to greater atomic vibration, hindering electron movement.

  • Material Impurities: Contact with various impurities can drastically alter conductivity; for example, the addition of certain elements can improve or hinder conductivity.

Room temperature conductivity values for common materials are:

• Silver: 6.8 \times 10^{7} \, (\Omega \cdot m)^{-1}

• Copper: 6.0 \times 10^{7} \, (\Omega \cdot m)^{-1}

• Aluminum: 3.8 \times 10^{7} \, (\Omega \cdot m)^{-1}

Energy Bands in Solids

Understanding electrical conductivity in materials is aided by Band Theory:

• Valence Band: The band that is filled with electrons and where they reside.

• Conduction Band: The empty band where electrons can move freely and contribute to conductivity.

• Band Gap (E_g): The energy difference between the conduction band and the valence band.

  • Conductors: Exhibit no band gap as the bands overlap, allowing free movement of electrons.

  • Semiconductors: Have a small band gap (typically < 2 eV), allowing for controlled conductivity dependent on external factors (like temperature and doping).

  • Insulators: Exhibit a large band gap (> 2 eV), preventing electron movement and conductivity under normal conditions.

Charge Carriers

Charge carriers are the particles responsible for the flow of electricity:

• In metals, conduction primarily occurs through electrons, while ionic charge carriers play a significant role in ionic liquids.

• Holes: Represent the absence of an electron in the valence band and facilitate conduction by allowing other electrons to jump into the vacancy.

Factors Affecting Electrical Properties

Several factors can influence the electrical properties of materials:

• Temperature: Increased temperature generally raises the resistivity of conductors due to increased atomic vibrations.

• Impurities: Impurities disrupt the path of conduction by scattering electrons, leading to increased resistance and reduced conductivity.

Semi-conductivity

The conductivity of semiconductors can be controlled through the process of doping:

• Extrinsic Semiconductors: Impurities are intentionally added to influence conductivity.

  • n-Type: Doping with donor atoms (e.g., Phosphorus) adds extra electrons, enhancing conductivity.

  • p-Type: Doping with acceptor atoms (e.g., Boron) creates holes by removing electrons, also increasing conductivity.

Applications of Conductors and Semiconductors

Conductors and semiconductors are essential components in various applications:

• Used in electrical wiring, electronics, and numerous device frameworks such as transistors and diodes.

• Piezoelectric Effects: Certain materials can generate an electrical voltage when subjected to mechanical stress, which has applications in sensors and actuators.

Summary

Understanding the electrical properties of materials involves examining the effects of temperature, impurities, and material defects on conductivity and resistivity. Essential concepts include Ohm's law, band theory, charge carriers, and the distinctions between metals, semiconductors, and insulators. By grasping these foundational principles, one gains better insight into the behavior of electrical components in various applications, ultimately enhancing the design and functionality of electronic devices.