The dust evolution models are performed using the Dustpy code**47**. The disk is assumed to be around a Solar-mass star, with a gas surface density that assumes a critical radius at 80AU and an initial disk mass of 5% of the Sun30. The model assumes a fragmentation velocity of νf = 10 m s-1, a gas viscous evolution parameter, radial diffusion, turbulent mixing, and vertical settling/stirring all set to 10− 4. All grains are initially small between 0.1-1 microns in size, with a power law distribution as \(\varvec{n}\left(\varvec{a}\right)\propto {\varvec{a}}^{-3.5}\). The models include the dust growth and dynamics of particles. The model output gives the density distribution of the dust grains (ρdust, Fig. 1.**A**) and of the gas (ρgas, Fig. 1.**B**) at 1 Myr of evolution. The data is portrait in a radial grid from 1 to 300 au (only 1 to 100 au shown in Fig. 1) with 300 logarithmically spaced cells. A logarithmically spaced grain size distribution between the minimum grain size of 0.5 micron to 10− 1 m in 127 steps is used. A gap centered at 40 AU is assumed in the disk30, which yields to a pressure bump at around 45 AU. Smaller and lighter dust grains are more easily stirred up in the disk and therefore dominate the particle sizes at greater disk heights, whereas larger particles concentrate around the disk midplane **[Fig. S1.]**.

From the dust density distribution, the grain surface area is calculated by assuming that all grains are spherical and have a density of \(\rho\)grain = 1.65 g cm-3. This allows us to calculate the particle mass for each grain size and convert the dust density (g cm-3) into a particle density (n cm-3). Next, the particle density is multiplied by the grain area to find the total grain area per volume, which gives:

$${A}_{grain}=\frac{\left(3 \cdot {\rho }_{dust}\right)}{\left({\rho }_{grain}\cdot {r}_{grain}\right)}$$

1

where rgrain is the grain size (that is, the radius). Using the grain area, the available amount of ice is calculated by assuming that each grain is covered with 100 monolayers (1 ML = 1015 molecules cm-2) of ice and by multiplying this value with the available grain surface area.

The thermal structure of the disk is modelled with RADMC-3D**48**, assuming a vertical grid of 180 cells over a semicircle following Z = R · cos(θ), were Z is the disk height and R the radius, and following the same procedure as30. The grain sizes that dominate the dust trap hotspot have sizes of 0.1 to several tens of µm and generally have temperatures greater than 50 K. However, only sub-µm grains are heated above 100 K, and only in specific regions of the hotspot **[Fig. S2.]**

The amount of photons throughout the disk is calculated with the Beer-Lambert law (**see main text**). The impinging photon flux is fixed to F0 = 1000 G0 (G0 = 108 photons cm-2 s-1), but we note the (grain) photon flux throughout the disk scales linearly with the value chosen for F0. Therefore, the dose rate can be scaled in the same way. The amount of photons absorbed by the mantle depends on its thickness and the UV photon absorption cross section. Assuming the mantle consist entirely of water-ice, then a film of 100 ML does not fully absorb the received flux**49**. The simplified division of the photon energy input by the column density to yield eV molecule-1 s-1 is therefore a rough assumption. However, since the photons that penetrate the ice mantle still hit the underlying grain, we assume that the energy is contributed to the overall system and therefore the simplified division holds.

Gravitational attraction causes grains to settle in the disk midplane, while turbulent stirring can move particles towards or away from the midplane. The velocities of these processes can be calculated**50** and in turn be used to assess how the dust is vertically distributed.

The equation to determine the velocity with which dust settles to midplane is given as:

$${\text{v}}_{\text{s}\text{e}\text{t}\text{t}}= \text{z} {{\Omega }}_{\text{k} }{c}_{S},$$

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where z is the vertical height in meter and \({{\Omega }}_{\text{k} }\) is the Keplerian frequency:

$${{\Omega }}_{\text{k}}= \sqrt{\frac{G {\text{M}}_{\text{☉}}}{{R}^{3}} },$$

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with G the gravitational constant, \({\text{M}}_{\text{☉}}\) the Solar mass in kg, and R the radius in m, and \({c}_{S}\) is the isothermal sound velocity:

$${\text{c}}_{\text{S}}= \sqrt{\frac{{k}_{B}{T}_{gas}}{{\mu }_{gas}{m}_{proton}}},$$

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with \({T}_{gas}\) the gas temperature (\({T}_{gas}\)= 50 K, the average dust temperature at the trap location and assuming Tgas = Tdust), \({\mu }_{gas}\) the mean molecular mass of the gas (\({\mu }_{gas}\) = 2), and \({m}_{proton}\)the proton mass in kg.

To calculate the vertical stirring velocity, the equation

$${\text{v}}_{stir} = \sqrt{3 {{\delta }}_{\text{t} }ST {c}_{S}}$$

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is used, where δt is a turbulent mixing parameter (δt = 10− 4) and *ST* the Stokes parameter, calculated following:

$$ST = \frac{{r}_{grain} {\rho }_{grain}}{{\varSigma }_{g}}\frac{\pi }{2}$$

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where \({\varSigma }_{g}\) the gas surface density.

For the model results used in this work, we find that vstir ≫ vsett for the µm-sized particles that reside at greater height in the dust trap. Therefore, stirring determines which direction material migrates. Since vertical stirring can point into two directions, namely away from the midplane (up) or towards the midplane (down), we assume that the likelihood of up- or downward motion is equal. This means that 50% of material in the dust trap hotspot goes to the disk atmosphere and 50% moves towards the midplane. We note that this situation holds for a static snapshot of the disk model, but in a dynamic and evolving environment the loss and settle fractions may be different.