Joule Heating

Joule heating is the conversion of electrical energy into thermal energy when current passes through a material with resistance. In a semiconductor, the electric field gives energy to mobile electrons and holes; repeated scattering transfers this energy to the crystal lattice as vibrations, thereby raising its temperature.

Microscopic mechanism

Charge carriers acquire a net drift velocity under an electric field. They are scattered by lattice vibrations, impurities, defects and interfaces, so the ordered energy supplied by the field is continually converted into random lattice motion, which appears as heat.

• Resistance measures the opposition created by these scattering processes to carrier drift.
• The local rate of energy conversion per unit volume is J·E, where J is current density and E is electric field.

Governing relations

For a steady current through an ohmic element, heat generated in time t is given by H = I²Rt. The corresponding power is P = VI = I²R = V²/R, with the equivalent forms applying when Ohm's law and the stated current or voltage conditions hold.

• At a given resistance, a larger current produces disproportionately more heat because power varies as I².
• Electrical energy is conserved: the energy lost by carriers is gained mainly by the lattice and subsequently transferred to the surroundings.

Significance in semiconductor circuits

Transistor channels, doped regions, contacts and metallic interconnects all possess finite resistance. Regions carrying high current density can therefore become local hot spots, especially where current paths are narrow or resistance is concentrated.

• Semiconductor devices are often non-ohmic, so the general expressions P = VI or J·E are safer than assuming a constant resistance.
• The resulting rise in junction temperature changes device characteristics and can reduce performance and reliability, making heat sinks, cooling systems and low-resistance interconnects important.
• Charging and discharging circuit capacitances also draws energy, which is ultimately dissipated through resistive paths.