# Hecht Equation Motivation: understanding the [[Mobility-Lifetime Product]] The Hecht Equation is an equation that characterizes the charge collection efficiency for semiconductor radiation detectors, like the [[CdZnTe (CZT) Detectors]] we use in our research. the Hecht equation is often used to calculate the [[Mobility-Lifetime Product]] of semiconductors by assuming a uniform electric field based on the [[Shockley-Ramo Theorem]] [^1]. For an applied bias $U$, the Hecht is Equation is as follows [^2] : $ CCE_{Hecht} (U) = \frac{\mu \tau U}{L^2} \left(1 - e^{-\frac{L^2}{\mu \tau U}} \right) $ where $L$ is the planar detector thickness. [^1]: [[@mengSimulationChargeCollection2022]] [^2]: [[@uxaEvaluationMobilitylifetimeProduct2013]] ## Limitations to the Hecht Equation As noted in the paper by [[@mengSimulationChargeCollection2022|Meng et. al]], there are some notable limitations in the Hecht Equation, which seem to mainly stem from the assumption of a uniform electric field in the detector bulk. Alternatives to the Hecht Equation are presently being developed. ## Other notes, - thank you visitor Gigabecquerel for catching an error in my equation!