2.1

Metal selection

The wide spectral range in which the coating must guarantee high reflectivity suggests the use of a coating based on a metal layer covered by one or more protective dielectric layers. Three are the typical metals used as reflective layer for the bandpass from the near UV to the FIR: silver, gold and aluminum.

Silver, Ag, although having a high reflectance in the visible and infrared bands, is extremely reactive and prone to surface oxidation/passivation. Moreover, silver shows low UV reflectance due to the absorption edge at 310 nm; in the bandpass centered at 280 nm the reflectance is always below 0.25 [3].

Gold, Au, has no chemical instabilities. Gold is extremely stable on the long term and it could be used without any protective layer, being prone only to mechanical damages. However, gold has low reflectance for wavelengths shorter than 550 nm, resulting in poor reflectance performance in the visible and UV band. In particular, gold reflectivity is 0.37 at 280 nm [4].

Aluminum, Al, has the best behavior, with a high reflectance in the whole spectrum of interest. Its absorption edge is placed well below the 150 nm, so the reflectance in the bandpass centered at 280 nm is extremely high (around 0.9) as well in the visible (>0.9) and IR (>0.95). However, aluminum is reactive and prone to oxidation, so it has to be protected with a dielectric capping-layer [4],[5].

Considering the requirements previously described, we can observe that silver and gold cannot be considered suitable for this specific application, especially since both of them show low UV reflectance and particularly in the wavelength bandpass centered at 280 nm. Therefore silver and gold are not considered valid option to produce an optical coating with the requested characteristics. Aluminum is the metal layer that we consider in the proposed optical coatings.

2.2

Protective layer material selection

Once the metal layer has been chosen, we analyze several different types of dielectric materials which could be used to create one or more protective layers over the metallic layer. We considered six different oxides:

The first two types of materials, SiO₂ and MgF₂, are commonly used in mirror coating applications. For these two materials we analyze also a single layer protective coating, in order to obtain a baseline and simple solution to be compared to other more complex structures.

We considered the other four materials in the definition of a multilayer structure, in combination with layers of SiO₂ due to its greater stability than MgF₂. The multilayer structures (e.g. number of layers, thickness) has been calculated using a suitable algorithm, as described in the following section.

2.3

Thickness and multilayer structure optimization

The analysis of the proposed single layer and multilayer protective coating has been performed considering the foreseen solar input at the Slit Assembly and then optimizing the structure with respect to the absorbed heat, since the thermal load seems to be the most critical issue for the slit substrate.

The solar input at the slit assembly level is dependent on the characteristics of the primary mirror of EUVST, which focuses the solar radiation on the slit. Multiple different primary mirror coatings have been proposed, and we have considered two different scenarios: a primary mirror with the baseline Mo/Si multilayer coating (P3157), and a primary mirror with a Mo/Al multilayer coating which has a significantly higher reflectivity (N7422). Coating P3157, being the baseline solution, allows a thermal analysis considering rather standard conditions, while coating N7422 allows the analysis at the highest power incident on the slit assembly. The solar input data on slit for the two cases have been collected from [6] and they are summarized in Fig. 2. During the optimization, we have considered the spectrum band between 250 and 1700 nm, that is the band where almost 90% of the total solar energy is concentrated; in this way, the optimization is focused on the most critical portion of the incident spectrum.

Figure 2.

Solar flux input at the Slit Assembly. On the left, for P3157 primary mirror coating; on the right, for N7422 primary mirror coating [6].

The analysis to calculate the thickness of the coating layers has been performed using a genetic algorithm; then the comparison between the different structures has been performed considering the heat absorbed by the analyzed structure. The genetic algorithm, similar to those described in [7], randomly creates a set of initial structures (the first group of “parents”) of the optical coating and then the algorithm modifies each individual using processes that are mimicking the natural evolution of a biological being. In particular, we impose an initial population of some tens of randomly generated individuals. Then, we randomly choose two of them to perform a crossover in which a portion of the first parent is combined with a portion of the second parent and vice versa, in order to create two new individuals with the same dimension of the parents but a complete new structure (the same event happens in the genetic crossover). We take these individuals and we perform a mutation of their characteristics, finding finally the new generation. At each step of the process, an evaluation of the individual fitness is performed by comparing the calculated absorbed heat with the best value ever found. So, the calculated absorbed heat works as a “cost function” at each passage of the algorithm, allowing to discard the individuals that are not suitable for our purposes. In order to restrain the calculation time, a maximum number of generations has been imposed, setting it at 2500 with a population of 50 individuals. We have also integrate some boundary conditions considering the maximum thickness value of each single layer, in order to satisfy the maximum thickness constraint, but especially the minimum thickness value, set at 10 nm due to the typical deposition precision of the standard facility used to produce such types of optical coating.

Once the best stack sequence is found, another optimization algorithm is used to analyze the possible impact of a non-perfect deposition of the layers (i.e., an error in the thickness of the layer during the deposition process). This analysis is crucial to understand if a deviation from the theoretical model can produce a significant variation of the coating performance. A gaussian distribution for the thickness random error is imposed with a sigma of 0.5 nm, according to the errors obtained in standard deposition facilities. This random error is added to each layer and the algorithm calculates the amount of absorbed heat, repeating the process for a thousand of cycles.

4.1

Single-layer protected Al coating

Two typical materials for protecting aluminum have been considered: SiO₂ and MgF₂. Both materials are commonly used in mirror coating applications; they are transparent for the spectrum portion of interest, stable and the deposition procedure is well known [8],[9].

Using the optimization algorithm, the results of the optimization of the two types of single layer protected Al coatings are shown in the following table.

Table 2.

Data for single-layer protected aluminum coating considering P3157 primary mirror coating

Table 3.

Data for single-layer protected aluminum coating considering N7422 primary mirror coating

The single-layer protected Al coatings have relatively worse performance with respect to the bare Al, since the absorbed heat increases by roughly 30%. However, this type of coating is a simple and robust solution, since it gives high reflectance in the bandpass centered at 280 nm and it has a simple deposition process. SiO₂ has slightly better performance than MgF₂ in terms of higher reflectivity at 280 nm and lower absorbed heat.

Figure 2.

Reflectance of the two single-layer protected Al coatings with P3157 solar input (left) and N7422 solar input (right) [8], [9].

4.2

Multilayer protected al coating

The analysis of the multilayer type of structures is based on the idea of “boosting” the aluminum layer reflection. The coating will be a fully dielectric multilayer in order to improve as much as possible the aluminum reflection to enhance the heat rejection. Usually, multilayer coatings have tens of different layers, in order reach the maximum efficiency. However, one of the main requirements of the Slit Assembly is on the upper limit of the total thickness of the coating: 600 nm. Considering that each coating would have a 90 nm thick layer of Al and a 10 nm thick layer of Cr, the total amount of thickness for the protective multilayer would be at maximum 500 nm. This fact leads to a multilayer stack in which the number of different layers is small. Also the precision of the deposition process has to be considered, because it depends on the thickness of the deposited layer: the thinner is the layer, the higher is the uncertainty in the deposition process.

Four different types of multilayer stacks have been analyzed; each of these multilayer types considers two different materials, one of these being always SiO₂ for its stable and well-known behavior. The second material is a metallic oxide, chosen from the group of transparent oxide commonly used for mirror coatings. The four types of multilayer stack analyzed are:

The resulting multilayer has been analyzed using the IMD software [10].

4.2.1

[MgF₂/SiO₂]/Al, 6 layers

The first type of multilayer structure is simply the combination of the two materials used in the single layer baseline coatings. The multilayer has indeed roughly the same absorbed heat of the single layer, therefore it is not considered as a suitable solution since it simply increases the complexity of the coating.

Table 4.

Data for the 6-layers [MgF2/SiO2]/Al coating, considering P3157 primary mirror coating

P3157 primary mirror coating
Label	Structure	Total thickness	Absorbed heat (250-1700 nm)	Reflectivity at 280 nm
[MgF2/SiO2]/Al	MgF2 (22 nm)	352 nm	0.14 W	0.86
6 layers_P3157	SiO2 (71 nm)
	MgF2 (23 nm)
	SiO2 (70 nm)
	MgF2 (46 nm)
	SiO2 (20 nm)
	Al (90 nm)
	Cr (10 nm)

Table 5.

Data for the 6-layers [MgF2/SiO2]/Al coating, considering N7422 primary mirror coating

N7422 primary mirror coating
Label	Structure	Total thickness	Absorbed heat (250-1700 nm)	Reflectivity at 280 nm
[MgF2/SiO2]/Al	MgF2 (22 nm)	316 nm	0.47 W	0.85
6 layers_N7422	SiO2 (71 nm)
	MgF2 (21 nm)
	SiO2 (51 nm)
	MgF2 (68 nm)
	SiO2 (15 nm)
	Al (90 nm)
	Cr (10 nm)

[Al₂O₃/SiO₂]/Al, 6 layers

The second type of multilayer has a common metal oxide, alumina Al₂O₃, as second type of material to be combined with SiO₂. Al₂O₃ is a stable well-known material [11]. This multilayer has an absorbed heat respectively of 0.12 W considering P3157 primary mirror coating and 0.39 W considering N7422 primary mirror coating, much closer to bare aluminum than the single layer coating.

Table 6.

Data for the 6-layers [Al2O3/SiO2]/Al coating, considering P3157 primary mirror coating

P3157 primary mirror coating
Label	Structure	Total thickness	Absorbed heat (250-1700 nm)	Reflectivity at 280 nm
[Al2O3/SiO2]/Al, 6 layers	Al2O3 (113 nm)	562 nm	0.12 W	0.81
	SiO2 (105 nm)
	Al2O3 (34 nm)
	SiO2 (24 nm)
	Al2O3 (99 nm)
	SiO2 (87 nm)
	Al (90 nm)
	Cr (10 nm)

Table 7.

Data for the 6-layers [Al2O3/SiO2]/Al coating, considering N7422 primary mirror coating

N7422 primary mirror coating
Label	Structure	Total thickness	Absorbed heat (250-1700 nm)	Reflectivity at 280 nm
[Al2O3/SiO2]/Al, 6 layers	Al2O3 (94 nm)	406 nm	0.39 W	0.90
	SiO2 (34 nm)
	Al2O3 (34 nm)
	SiO2 (81 nm)
	Al2O3 (28 nm)
	SiO2 (35 nm)
	Al (90 nm)
	Cr (10 nm)

Figure 3.

Reflectance of the 6-layers [Al₂O₃/SiO₂]/Al coatings with P3157 solar input (left) and N7422 solar input (right)

[TiO₂/SiO₂]/Al, 6 layers

The third type of analyzed multilayer uses a classical coating material, the titanium dioxide TiO₂. TiO₂/SiO₂ multilayer is widely used in mirror coating manufacturing because it shows extremely good characteristics: very stable behavior with high durability and a low mechanical stress [12]. Also, the TiO₂ has one of the highest index of refraction in the visible band, so it is extremely useful to generate low reflecting film in combination with other materials like SiO₂. Indeed, the multilayer [TiO₂/SiO₂]/Al has a calculated absorbed heat of 0.16 W and 0.36 W considering the two types of primary mirror coating, close to that of the bare aluminum. However, a drop of the reflectance curve occurs in the UV region because of the absorption edge of the TiO₂ at 350 nm. This gives a low reflectance at 280 nm, that is considered as a major limitation for such a coating.

Table 8.

Data for the 6-layers [TiO2/SiO2]/Al coating, considering P3157 primary mirror coating

P3157 primary mirror coating
Label	Structure	Total thickness	Absorbed heat (250-1700 nm)	Reflectivity at 280 nm
[TiO2/SiO2]/Al, 6 layers	TiO2 (23 nm)	476 nm	0.16 W	0.56
	SiO2 (67 nm)
	TiO2 (20 nm)
	SiO2 (81 nm)
	TiO2 (97 nm)
	SiO2 (88 nm)
	Al (90 nm)
	Cr (10 nm)

Table 9.

Data for the 6-layers [TiO2/SiO2]/Al coating, considering N7422 primary mirror coating

N7422 primary mirror coating
Label	Structure	Total thickness	Absorbed heat (250-1700 nm)	Reflectivity at 280 nm
[TiO2/SiO2]/Al, 6 layers	TiO2 (86 nm)	468 nm	0.36 W	0.35
	SiO2 (100 nm)
	TiO2 (74 nm)
	SiO2 (22 nm)
	TiO2 (64 nm)
	SiO2 (22 nm)
	Al (90 nm)
	Cr (10 nm)

Figure 4.

Reflectance of the 6-layers [TiO₂/SiO₂]/Al coatings with P3157 solar input (left) and N7422 solar input (right) [12]

[ZrO₂/SiO₂]/Al, 7 layers

The fourth type of multilayer analyzed uses another material often used in mirror coatings application, the zirconia or zirconium dioxide ZrO₂; the optical characteristics of this material has been extrapolated with Sellmeier dispersion formula from previous transmittance measurements. In combination with SiO₂, it is used to create multilayer coatings with high durability and low mechanical stress. The multilayer stack consists of 7 layers, and not 6 like the others multilayer coatings here described, because the long exposition to UV can damage an exposed ZrO₂ layer. In order to protect the coating in a long-term mission, the layer facing directly the space is assumed to be SiO₂, more durable and stable. [ZrO₂/SiO₂]/Al multilayer has a calculated absorbed heat of 0.12 W and 0.36 W, with a performance very close to bare aluminum. The zirconium dioxide has a reflection drop in the UV centered at 230 nm, therefore the reflectance of the multilayer in the region around 280 nm is higher than those of the titanium dioxide multilayer.

Table 10.

Data for the 7-layers [ZrO2/SiO2]/Al coating, considering P3157 primary mirror coating

P3157 primary mirror coating
Label	Structure	Total thickness	Absorbed heat (250-1700 nm)	Reflectivity at 280 nm
[ZrO2/SiO2]/Al, 7 layers	SiO2 (22 nm)	514 nm	0.12 W	0.80
	ZrO2 (75 nm)
	SiO2 (83 nm)
	ZrO2 (20 nm)
	SiO2 (43 nm)
	ZrO2 (90 nm)
	SiO2 (81 nm)
	Al (90 nm)
	Cr (10 nm)

Table 11.

Data for the 7-layers [ZrO2/SiO2]/Al coating, considering N7422 primary mirror coating

N7422 primary mirror coating
Label	Structure	Total thickness	Absorbed heat (250-1700 nm)	Reflectivity at 280 nm
[ZrO2/SiO2]/Al, 7 layers	SiO2 (40 nm)	523 nm	0.36 W	0.72
	ZrO2 (74 nm)
	SiO2 (82 nm)
	ZrO2 (25 nm)
	SiO2 (32 nm)
	ZrO2 (90 nm)
	SiO2 (80 nm)
	Al (90 nm)
	Cr (10 nm)

Figure 5.

Reflectance of the 7-layers [ZrO₂/SiO₂]/Al coatings with P3157 solar input (left) and N7422 solar input (right)

4.3

Coating thickness random error

The thickness error analysis has been performed adding a random (gaussian) error with a sigma of 0.5 nm at the single layer of the single layer protected Al coating or at each layer of the multilayer protected Al coating. An optimization algorithm has been created to analyze the absorbed heat, then the mean value of absorbed heat and the standard deviation have been calculated. The analysis shows that the deposition error expected in a standard deposition facility has a negligible impact on the absorbed heat, with an extremely low standard deviation. It can be concluded that, once the stack has been optimized, the effect of a random error in the thickness of the layers is negligible.

5.1

Reflected and absorbed heat

The analysis shows that the [MgF₂/SiO₂]/Al multilayer has no advantages with respect to the single layer coatings and simply increases the complexity of the optical coating. The [TiO₂/SiO₂]/Al multilayer, on the other hand, has performance slightly worse than those of the [ZrO₂/SiO₂]/Al multilayer, especially from the point of view of the reflectivity in the bandpass centered at 280 nm. Due to these reasons, both [MgF₂/SiO₂]/Al and [TiO₂/SiO₂]/Al multilayers are not considered as suitable. In the following analysis we will concentrate on the other types of proposed multilayer coatings.

The following tables summarize the reflected and absorbed heat.

Table 12.

Reflected and absorbed heat for all the proposed configurations, considering P3157 primary mirror coating

Table 13.

Reflected and absorbed heat for all the proposed configurations, considering N7422 primary mirror coating

Considering both the absorbed heat and the reflectivity at 280 nm, two multilayer coatings could be considered as the most interesting types of slit substrate coatings: the 6 layers coating [AL₂O₃/SiO₂]/Al and the 7 layers coating [ZrO₂/SiO₂]/Al. The former has a higher reflectivity in the band centered at 280 nm and it has a relatively known behavior, while the latter has a slightly better heat rejection performance.

Concerning the total heat reflected toward the Slit-Jaw Imager (mainly in the visible and near IR bands), this varies by almost a factor 2 with the coating on the primary mirror, but is almost independent of the coating that is used on the slit assembly.

Further analysis must be performed to address the mechanical behavior and the lifetime of the coating, in order to obtain a complete characterization of the optical coating and to collect the data necessary to choose the best solution for the Slit Assembly of Solar-C EUVST.