Sensor Co-design for $\textit{smartpixels}$

Pixel tracking detectors at upcoming collider experiments will see unprecedented charged-particle densities. Real-time data reduction on the detector will enable higher granularity and faster readout, possibly enabling the use of the pixel detector in the first level of the trigger for a hadron collider. This data reduction can be accomplished with a neural network (NN) in the readout chip bonded with the sensor that recognizes and rejects tracks with low transverse momentum (p$_T$) based on the geometrical shape of the charge deposition (``cluster''). To design a viable detector for deployment at an experiment, the dependence of the NN as a function of the sensor geometry, external magnetic field, and irradiation must be understood. In this paper, we present first studies of the efficiency and data reduction for planar pixel sensors exploring these parameters. A smaller sensor pitch in the bending direction improves the p$_T$ discrimination, but a larger pitch can be partially compensated with detector depth. An external magnetic field parallel to the sensor plane induces Lorentz drift of the electron-hole pairs produced by the charged particle, broadening the cluster and improving the network performance. The absence of the external field diminishes the background rejection compared to the baseline by $\mathcal{O}$(10%). Any accumulated radiation damage also changes the cluster shape, reducing the signal efficiency compared to the baseline by $\sim$ 30 - 60%, but nearly all of the performance can be recovered through retraining of the network and updating the weights. Finally, the impact of noise was investigated, and retraining the network on noise-injected datasets was found to maintain performance within 6% of the baseline network trained and evaluated on noiseless data.