Is the Spencer-Attix Cavity Equation Applicable for Solid-State Detectors Irradiated in Megavoltage Electron Beams?

Abstract

The applicability of the Spencer-Attix cavity equation in determining absorbed doses in water using solid state detectors irradiated by megavoltage electron beams have been examined. The calculations were performed using the EGSnrc Monte Carlo code. This work is an extension of a recently published article examining the perturbation of dose by solid state detectors in megavoltage electron beams. The use of the Spencer-Attix cavity equation is based on the assumption that the charge particle fluence in the uniform medium and in the detector material are the same. Previous Monte Carlo simulation of the perturbation correction for common TLD materials in electron beams show that for solid state detectors having a density of at least double that of water, there is a significant difference at all depths between the energy spectra present in the water phantom and that in the solid state cavity. This means the assumption that the detector does not perturb the charged particle fluence is not valid. As the cavity size is increased, the difference between the energy spectra in the solid cavity and medium increases as expected. At depths beyond dmax not only is there a significant difference between energy spectra but there is also a significant difference in the number of low energy electrons which can not travel across the solid cavity (i.e. stopper electrons whose residual range is less than the cavity thickness). The number of these low energy electrons that are not able to cross the solid state cavity increases with depth. They also increase with the dimension of the cavity in the beam direction. These differences in the energy spectra and increasing percentage of the total dose in the cavity due to these stopper electrons means that the shape of the depth dose curve measured by a solid detector depends on its effective thickness and may differ from that measured with detectors of different effective thickness. The results show that for a 1 mm thick LiF solid cavity, the stopper to crosser ratio at a depth of 1 cm for a 5 MeV incident electron beam is about 0.2 but this ratio increases to 0.3 and 0.5 at a depth of 1.4 cm and 1.9 cm, respectively. For a 2.64 mm thick water cavity, the stopper to crosser ratio at a depth of 1 cm is 0.25 and this value rises to 0.38 and 0.95 at depths of 1.4 and 1.9 cm, respectively. The results show that even for a 1 mm thick LiF-cavity the response of the detectors is dominated by stoppers for depths equal or greater than R50.