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We report on the spectral peak-shift behavior of a Si-drift detector with integrated JFET operated in a source follower configuration. The experimental results are based on the measurements of the JFET's source voltage in the time domain and the analysis of the corresponding multiline X-ray fluorescence spectra. The transient measurements confirm a slew-rate limited decay of the source voltage pulses, which is attributed to the I-V characteristic of the JFET's gate-to-channel junction. We found that the slew rate depends linearly on the product of the center of energy and the count rate. Transient analysis of SDD/JFET circuit model and a new BiCMOS readout chip show a baseline shift, which is directly proportional to the slew rate and responsible for the peak shift. Considering the offset and gain of the subsequent spectroscopy system, the simulated peak positions agreed very closely with the results obtained from the measurements.