- Current Density Definition: Current density is defined as the electric current per unit area of a conductor’s cross-section, denoted by J.
- Formula for Current Density: The current density in a metal is calculated using J = I/A, where I is the current and A is the cross-sectional area.
- Semiconductor Current Flow: In semiconductors, current density is due to both electrons and holes, which move in opposite directions but contribute to the same direction of current.
- Current Density in Semiconductor: The total current density in a semiconductor is the sum of the current densities due to electrons and holes, each having different mobilities.
- Relation to Conductivity: Current density (J) is related to conductivity (σ) through the formula J = σE, where E is the electric field intensity.
Current density is the current through a unit area of a conductor. That quantity is used throughout electrical engineering.
Current Density in Metal
Imagine a conductor with a cross-section of 2.5 square mm. If an electric potential causes a current of 3 A, the current density is 1.2 A/mm² (3/2.5). This assumes the current is uniformly distributed. Thus, current density is defined as the electric current per unit cross-sectional area of the conductor.
Current density J is J = I/A, with I the current and A the cross-sectional area. If N electrons cross a section in time T, the charge transferred is Ne, where e is the electron charge in coulomb.
The charge passing the section per unit time is
If those N electrons occupy length L of the conductor, the electron concentration is
From equation (1),
Those N electrons occupy length L and all of them pass the section in time T, so their drift velocity is
Equation (2) then becomes
If the applied electric field is E, the electron drift speed at ordinary fields is proportional to E:
where μ is the mobility of electrons
Current Density of Semiconductors
Current density in a semiconductor has extra terms:
- Current in a semiconductor is carried by drifting electrons and by holes, not by electrons alone.
- Holes move opposite to the electrons that created them.
- Hole current is in the direction of hole motion. Electron current is opposite to electron motion. Both currents therefore point the same way.
- The electrons that carry current occupy the conduction band. The holes occupy the valence band, so mobility of electrons and holes differ in a semiconductor.
Current density in semiconductor is
Jn is the electron current density.
Jp is the hole current density,
so
n and p are the mobile electron and hole densities, e is the magnitude of the electron and hole charge and μn and μp are the electron and hole mobilities.
What is the Relation Between Current Density and Conductivity?
Current density can also be written
V is the applied voltage across the conductor,
R is the resistance of the conductor,
A is the cross-sectional area of the conductor,
L is the length of the conductor,
ρ is the resistivity of the conductor,
σ (= 1/ρ) is the conductivity of the conductor.
E is the electric field intensity, voltage divided by length for a uniform field. For an ohmic material this is J = σE.
