Photodiode Arrays Do Not Violate the Second Law of Thermodynamics: Photocurrent Bandwidth Trade-Off

Photodiode (PD) arrays do not violate the second law of thermodynamics. In this paper, we explore the trade-off between PD array photo current and PD size when arrays with the same geometrical fill factor are considered. For this study, we assume a square matrix arrangement of PD. We apply the principles of energy conservation and, by extension, the second law of thermodynamics to demonstrate that reducing the size of individual PD in the array results in a decrease in photocurrent. This decrease is anticipated even when the geometrical fill factor of the array remains constant, i.e., even if the number of PDs in the array is increased. The photocurrent and size trade-off leads to the photocurrent bandwidth trade-off. The trade-off indicates that the PD array photocurrent is inversely proportional to its bandwidth. The derivation of this trade-off relation assumes a uniform irradiance distribution across the photodetector array. However, our findings show that this trade-off holds true for nearly uniform irradiance distributions and even for non-uniform distributions, such as those encountered with a compound parabolic concentrator (CPC). Our simulation results align closely with theoretical predictions. The implications of this study highlight the importance of considering the trade-off when designing optical wireless communication (OWC) or visible light communication (VLC) links for high data throughput.