## 4 Discussion  
We designed a single pixel cold-electron bolometer with a maximum voltage responsivity 1.5 \(\times\) 10\({}^{10}\)-1 \(\times\) 10\({}^{9}\) V/W from an absorbed power of 0.2-16 fW and a bolometer NEP of about 7.3 \(\times\) 10\({}^{-19}\)-5.1 \(\times\) 10\({}^{-18}\) W Hz\({}^{-1/2}\). The photon noise of the signal will dominate over the noise of CEB for a signal power of 10 fW and higher at frequency 80 GHz and higher. In a recent paper [11], in which [PERSON] et al. fabricated and measured the NEP of 192 CEBs, extrapolation to a single CEB gave a bolometer NEP of about 3 \(\times\) 10\({}^{-18}\) W Hz\({}^{-1/2}\) at 300 mK, which is quite consistent with our experimental results.  
Figure 3: The total NEP, bolometer NEP and NEP due to the amplifier (open circles) compared to the theoretical predictions for varying modulation frequencies. The dashed line represents the value of the NEPs as predicted by theory.  
The obtained results agree reasonably well with the theoretical predictions. The CEB noise is limited by the noise due to a room temperature amplifier. A cold amplifier or an amplifier with lower voltage noise would reduce its thermal noise. In this work, we used an OPA111 amplifier with a voltage noise of 8 nV/Hz\({}^{-1/2}\). The AD743 or AD745 would be more suitable with a lower voltage noise and a lower impedance. Another method would be to improve the NEP by matching the dynamic resistance of CEB with the equivalent noise impedance of an amplifier. At the optimum bias current, the resistance of the CEB is in the order of 60 k\(\Omega\) and the source impedance for a typical amplifier (e.g., OPA111) would be around 15 M\(\Omega\). Thus, an array of CEBs would have good impedance matching with these low noise amplifiers [8,11]. Additionally, analyses by [PERSON] and [PERSON] of the CEB made [15] indicate that in order to achieve enhanced responsivity and NEP, the voltage-biased regime would be the optimal mode.  
The influence of the leakage resistance, \(\mathrm{R_{S}}\), was modelled by adding the Joule heating term, \(\mathrm{V^{2}/R_{S}}\), in the heat balance equation. This model theory agrees satisfactorily well with the current-voltage characteristics in the subgap region near zero-bias. On the other hand, the effect of this additional term is to compete with the other sources of heat. This is the dominant term up to 250 \(\mathrm{\SIUnitSymbolMicro eV}\). As the voltage increased above 250 \(\mathrm{\SIUnitSymbolMicro eV}\), the cooling term due to the tunnel junctions begins to dominate. The decreasing dependence of the NEP with increasing frequency is attributed to the attenuation due to the cryogenic filters. The attenuation due to the instrumentation amplifier was already taken into account.  
In general, this research shows that the CEB can be a competitive concept to TES and KID bolometers with some advantages in size, inherent electron cooling, immunity to cosmic rays, and avoiding saturation independently on small absorber size due to immediate removing heat from the absorber.  
Conceptualization, L.K.; Methodology, I.J.A. and L.K.; Validation, I.J.A.; Formal analysis, I.J.A. and L.K.; Investigation, I.J.A.; Resources, L.K.; Data curation, I.J.A.; Writing--original draft preparation, I.J.A.; Writing--review and editing, I.J.A. and L.K.; Visualization, I.J.A. and L.K.; Supervision, L.K.; Project administration, L.K.; Funding acquisition, L.K. All authors have read and agreed to the published version of the manuscript. This work was supported by Swedish National Space Board (SNSB) DNR 196/15 and Russian Science Foundation (Project No. 21-79-20227). Not Applicable.