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1.5 Reliability Science and Engineering
An electronic device in operation is an open system because electrical charges flow in and out of the device. While the number of charges in transport is conserved, entropy production is not. The waste heat in entropy production is Joule heating on the basis of irreversible processes. [4, 5] For electrical conduction, Onsager’s Eq. (ssss1) below shows that entropy production is the product of the conjugated flux of j (current density = coulomb/cm2‐sec) and the conjugated driving force of E (electric field E = jρ, where ρ is resistivity). Derivation of the Onsager equation will be given in ssss1.
where T is the temperature, V is the volume of sample, dS/dt is the entropy production rate, and j2ρ is the Joule heating per unit volume per unit time. Typically, the power from Joule heating is written as P = I2R = j2ρV, where I is the applied current and R is the resistance of the sample. Thus, j2ρ is power density or Joule heating per unit volume per unit time of the sample, in units of Watt/cm3, and I2R is Joule heating per unit time for the entire sample, in units of Watt. Clearly, this is the reason why we need low‐power devices or low entropy production devices.