  A novel methodology, named the diffusion profile method, is proposed in this
research to measure the electric field of a low gain avalanche detector
(LGAD).The proposed methodology utilizes the maximum of the time derivative of
the edge transient current technique (edge-TCT) test waveform to quantify the
dispersion of the light-induced carriers. This method introduces the estimation
of the elongation of the carrier cluster caused by diffusion and the divergence
of the electric field force during its drift along the detector. The
effectiveness of the diffusion profile method is demonstrated through the
analysis of both simulated and measured edge-TCT waveforms. Experimental data
was collected from a laser scan performed on an LGAD detector along its
thickness direction.A simulation procedure has been developed in RASER
(RAdiation SEmiconductoR) to generate signals from LGAD.An assumption of
immediate one-step carrier multiplication is introduced to simplify the
avalanche process.Simulation results were compared with transient current data
at the waveform level and showed a favorable match. Both simulation and
experimental results have shown that the diffusion profile method could be
applied to certain edge-TCT facilities as an alternative of electric field
measurement.
