Gradient area-selective deposition for seamless gap-filling in 3D nanostructures through surface chemical reactivity control

The integration of bottom-up fabrication techniques and top-down methods can overcome current limits in nanofabrication. For such integration, we propose a gradient area-selective deposition using atomic layer deposition to overcome the inherent limitation of 3D nanofabrication and demonstrate the applicability of the proposed method toward large-scale production of materials. Cp(CH3)5Ti(OMe)3 is used as a molecular surface inhibitor to prevent the growth of TiO2 film in the next atomic layer deposition process. Cp(CH3)5Ti(OMe)3 adsorption was controlled gradually in a 3D nanoscale hole to achieve gradient TiO2 growth. This resulted in the formation of perfectly seamless TiO2 films with a high-aspect-ratio hole structure. The experimental results were consistent with theoretical calculations based on density functional theory, Monte Carlo simulation, and the Johnson-Mehl-Avrami-Kolmogorov model. Since the gradient area-selective deposition TiO2 film formation is based on the fundamentals of molecular chemical and physical behaviours, this approach can be applied to other material systems in atomic layer deposition.

Energy (eV) Adsorption of TDMAT precursor on the exposed TMPMCT inhibitor  Fig. 4: a, The saturated surface of TMPMCT still has unoccupied sites due to the steric interference. b, The unoccupied sites on exposed TMPMCT surface are potential sites for the next TDMAT precursor adsorption.  TMPMCT adsorption TDMAT on exposed TMPMCT surface

Supplementary
The model is composed of several equations: (1) growth initiation and film nucleation, (2) fraction of the growth surface covered with a film versus ALD cycles, (3) approximate calculated film thickness in the non-growth area, and (4) selectivity. Details for the JMAK model can be found in [3][4][5] .
In which, where, ̇( ) is the nucleation site generation rate for the non-growth area after n cycles (nm -2 cycle -1 ), ̇! is the nucleation site generation rate for the non-growth area (nm -2 cycle -1 ), " is the nucleation site generation delay cycles for the non-growth area (cycles), n is the number of ALD cycles (cycle), # is the area of the substrate covered by the film (nm 2 ), ! is the area of the substrate (nm 2 ), $ is the extended area (nm 2 ), ̇ is the growth rate for a material depositing on itself (nm cycle -1 ), 4 is the nucleation site density on a starting non-growth area (nm -2 ), v is the cycles when nucleus starts to grow (cycle), t' ( is the approximate calculated film thickness on the non-growth area (nm), and S is the selectivity (%). ̇ was obtained from experiments as 0.055 nm cycle -1 , as shown in Fig. 2c and Supplementary Fig. 1a-1d.
In this study, we considered cycle number n ranging from 0 to 1000, based on the experiments. Nucleation site density was defined based on the following assumptions: there is no growth site in the starting non-growth area and nucleation site density 4 = 0 when n = 0. No nuclei formation was observed in the first cycles. The calculations were repeated in cycle increments (1 cycle/step) until the selectivity dropped below 90% at a " cycle, which was recorded as a delay cycle. From this delay cycle ( " ) onwards, the nuclei were assumed to be randomly distributed with fixed positions on the surface, which were not covered by the inhibitor. In other words, nucleation sites were generated as a function of cycle number and nuclei site generation rate (!); the relation is shown in equation (1).
The nuclei size evolution was uniform in all directions with constant growth per cycle (̇), which was determined from the experimental results as 0.055 nm/cycle. After n cycles, each growth site would have grown into a circle with radius of ̇ × . The extended area, $ , due to the nuclei formation sites is the product of area of each nucleus and number of nuclei present, calculated using equation (3). As a result, the coverage of the initial substrate surface ( # / ! ) by the growing film varies with ALD growth cycles and is a function of ̇! , " , and ̇ (schematic in Supplementary Fig. 5). The coverage was calculated using equation (2).
The coverage of TMPMCT varied with the TMPMCT inhibitor exposure time, resulting in different nuclei site generation delay cycles ( " ) and ̇! . For instance, because the 20 s TMPMCT sample had the lowest coverage, it had a lower " and a higher ̇! than the 40 and 60 s samples.
After evaluating parameters ̇! , " , ̇, the approximate film thickness, t' ( ( ), on the non-growth area and the selectivity, ( ), for each ALD cycle can be estimated using equation (4)  The extracted parameters for the nucleation site generation rate, ̇! , were 68.0 × 10 -7 , 4.9 × 10 -7 , and 2.2 × 10 -7 nm -2 cycle -1 for 20, 40, and 60 s samples, respectively. ̇! of the 20 s sample was 31 times and 14 times larger than that of the 60 s sample and 40 s sample, respectively. Source data are provided as a Source Data file.
Supplementary Table 3: Parameters for the JMAK model shown in Fig. 3.  Based on the simple case (planar substrate) mentioned in the kinetic description about the number of molecules crossing a plane from one side per unit time and unit area in an ALD, we suggest the time t (s), which is required to cover the surface area of a 3D hole down to the depth l (nm). In an ideal ALD process, we assume that the sticking coefficient of TMPMCT on TiO2 surface is 100%, the time t (s) can be calculated by the following equation 6 : where P is the partial pressure of the precursor near the surface (Pa), Q is the number of molecules (saturation dose) that can be adsorbed on a square metre, m is the molecular mass (kg), k is the Boltzmann constant (1.38 × 10 -23 J/K), T is the temperature (K), p is the perimeter of the hole (nm), L is the depth of the hole (nm), and Ahole is the cross-sectional area (nm 2 ).