Internal cooling efficiency of a junction diode

The three thermal rate equations were built newly up at both ends and at the junction of a p–n diode, in order to derive analytically the temperature difference ΔT (between a junction and both ends) and the internal cooling efficiency η defined newly for a homojunction diode. The maxima ΔT and η of a diode were derived analytically as a function of Vj within the short-length approximation and calculated numerically as a function of Vj or Vbi, where Vj is a voltage across the junction and Vbi is a built-in voltage at the junction. As a result, ΔT increases abruptly with an increase of Vj below Vj=0.050 V or of Vbi below Vbi=0.10 V, while above their values, it increases slowly with an increase of Vj or Vbi to saturate a certain value. For example, ΔT was estimated as 14.6 K for Hg0.8Cd0.2Te diode with Vbi=0.36 V. η has a local maximum of 63% at Vj≈0.01 V or at Vbi≈0.03 V, while above their respective values, it decreases abruptly with an increase of Vj or Vbi and falls to 4.4% at Vbi=0.80 V which is equivalent to that of a diode emitting a laser for fiber optical communication. However, the greater enhancements in ΔT and η of a diode are required to apply the internal cooling system to a laser-emitting diode which needs the exact control of temperature. These results should be useful for the application of the internal cooling system to the double heterojunction diode used in the optical communication.