The state-of-the-art quantum infrared photodetectors have high performance, but obtaining high sensitivity in mid- and long-wavelength infrared (MWIR and LWIR) requires cooling and exotic materials. Whereas thermal detectors offer lower cost without the need for cooling but are typically slower and less sensitive than cooled quantum infrared detectors. Nanothermoelectrics and nanomembranes offer opportunities for enhancing the performance of uncooled MWIR and LWIR imaging and sensing. Similar to thermoelectric detectors, the infrared sensitive signal in those is generated by the thermoelectric effect, providing advantages over resistive bolometers, i.e. less noise sources and zero power consumption in the detector itself. We have recently demonstrated that nano-thermoelectrics provides a route towards high-sensitivity and cost-effective LWIR detection. When the thickness of the thermoelectric polysilicon membrane is reduced, increased phonon scattering leads to reduced thermal conductivity. This gives rise to the high thermoelectric figures of merit determining the detector sensitivity. The speed stems from the low-thermal-mass device design with an integrated metal nanomembrane absorber and the lack of separate support structures. We report integrated circuit concept for the readout of these detectors, and study how the absorber grid geometry determines the device performance. The fabricated devices have thermal time constants, responsivities and specific detectivities D* in the ranges of 190 – 208 μs, 334 – 494 V/W, and (7.9 – 8.7)·107 cmHz1/2/W, respectively. The differences in the device performance originate from the differences in the thermal mass, total resistance, and impedance matching of the absorber grid. By optimization, we expect that D* = 8.3·108 cmHz1/2/W can be reached.