Objective. Background noise experienced during extracellular neural recording limits the number of spikes that can be reliably detected, which ultimately limits the performance of next-generation neuroscientific work. In this study, we aim to utilize stochastic resonance (SR), a technique that can help identify weak signals in noisy environments, to enhance spike detectability. Approach. Previously, an SR-based pre-emphasis algorithm was proposed, where a particle inside a 1D potential well is exerted by a force defined by the extracellular recording, and the output is obtained as the displacement of the particle. In this study, we investigate how the well shape and damping status impact the output signal-to-noise ratio (SNR). We compare the overdamped and underdamped solutions of shallow- and steep-wall monostable wells and bistable wells in terms of SNR improvement using two synthetic datasets. Then, we assess the spike detection performance when thresholding is applied on the output of the well shape-damping status configuration giving the best SNR enhancement. Main results. The SNR depends on the well-shape and damping-status type as well as the input noise level. The underdamped solution of the shallow-wall monostable well can yield to more than four orders of magnitude greater SNR improvement compared to other configurations for low noise intensities. Using this configuration also results in better spike detection sensitivity and positive predictivity than the state-of-the-art spike detection algorithms for a public synthetic dataset. For larger noise intensities, the overdamped solution of the steep-wall monostable well provides better spike enhancement than the others. Significance. The dependence of SNR improvement on the input signal noise level can be used to design a detector with multiple outputs, each more sensitive to a certain distance from the electrode. Such a detector can potentially enhance the performance of a successive spike sorting stage.