InP/InGaAs separate absorption, grading, charge, and multiplication avalanche photodiodes (SAGCM APDs) have been widely applied in optics communication systems [
1]. Moreover, there continues to be a strong interest in the application of the APD in the fields of quantum key distribution (QKD), national defense, and astrosurveillance, as so-called single photon avalanche diodes (SPADs) used in Geiger mode [
2–
6]. It is fascinating to notice that the design philosophy of APDs for the optical communication systems and that of SPADs for the quantum information applications, especially the QKD systems, are quite different [
7]. Nevertheless, there is no doubt that the temperature dependence characteristics are crucial for APDs applied in the field of traditional optical communication, as well as SPADs in quantum communication systems. From the point of view of application, APDs immune to the change of temperature, i.e., APDs with low temperature coefficient is strongly designed, which has been drawn a lot of attention in recent years [
8–
11]. An empirical equation for temperature coefficient of APD was first reported in 1997 [
8], but without considering the dead space effect. A simplified approach to time-domain modeling of avalanche photodiodes considering the dead space effect was reported in 1998 [
9]. And then an improved empirical formula was proposed in 2010 [
11].