## 4 Discussion
For an array of NP agglomerates, the processes of backscattering and absorption on individual NPs limit the radiation penetration into the array to a certain thickness, at which NPs acquire energy through direct radiation heating. Further, the energy from the zone of radiation direct heating is transmitted deeper via thermal conductivity process. And then we may assume that the thickness of the zone directly heating by radiation is close to the experimentally observed thickness of the sintered pore-free layer in the range 0.5-1 \(\upmu\)m. Previously the idea of two mechanisms of laser radiation energy input to silver NPs at different depths of the array was discussed in the literature. In particular, in [11] authors use significantly different optical penetration depth for radiation with wavelengths 532 and 1064 nm for sintering processes modeling. Since the radiation absorption by NP as a function of incident radiation wavelength is resonant due to plasmon oscillations, the sintering processes of NP arrays should significantly depend on the wavelength of laser radiation. It was previously established [35; 36] that silver NP of spherical shape with an average size of 15 nm effectively absorb radiation with a wavelength 400 nm, and when the wavelength increases, for example, to 527 nm, the absorption efficiency of such particles sharply decreases. However, with the particles enlargement, the resonance wavelength of the absorbed radiation redshifts. In particular, at a particle diameter of around 100 nm, the radiation absorption with a wavelength 527 nm reaches its maximum, but for a wavelength 980 nm, the absorption is still small. It is this resonant effect that explains the need to use more energy for laser sintering with increasing the wavelength of the radiation in order to obtain close results of the average conductivity of microstructures. Thus, from the comparison of the optimal regimes for laser sintering of silver NP arrays by pulsed radiation at wavelengths 527 and 1054 nm and by CW radiation at wavelengths 527 and 980 nm, we see (Figure 4) that in both cases the energy used is almost of an order of magnitude greater for longwave radiation. This effect may be explained by the significantly different absorption efficiency of laser radiation with different wavelengths as follows. In the laser sintering processes, crystallites increase in the average sizes from 15 to 70-120 nm and at the final stage combine into a solid body. It means the energy of laser radiation enters the NP array through absorption by increasing in size individual NP and at the final stage the radiation interacts with a monolithic polycrystalline metal. We may expect a significant increase in the efficiency of the laser radiation energy absorption and sintering if the particle size, corresponding to the resonant absorption of the radiation used, gets in the range of particle size caused by growth during sintering process. It occurred in our experiments with laser sintering of silver NP arrays with a wavelength 527 nm. Previously this effect of strong absorption of laser radiation with a close wavelength (532 nm) by silver NPs was discussed and demonstrated,in particular, in the articles [11; 12] contributed to laser sintering of silver NP ink with initial particle sizes of 30-50 nm. The natural result is that the values of the average specific conductivity of silver lines obtained by pulsed laser sintering with wavelengths 527 and 1054 nm in optimal regimes on silicon substrates (Figure 4a,b) were about three times less than for similar values of the lines conductivity on polyamide substrates (Table 3). Since the radiation energy transmitted to the NP array at a given wavelength was the same for both types of substrates, we assume that the energy supplied to the sample is more efficiently spent on NPs sintering on polyamide substrates than on silicon substrates. A similar effect was previously observed in [10] where authors compared the laser sintering processes of NP inks on glass and PET substrates at radiation wavelength 532 nm.