3D Nanoprinting via laser-assisted electron beam induced deposition: growth kinetics, enhanced purity, and electrical resistivity

We investigate the growth, purity, grain structure/morphology, and electrical resistivity of 3D platinum nanowires synthesized via electron beam induced deposition with and without an in situ pulsed laser assist process which photothermally couples to the growing Pt–C deposits. Notably, we demonstrate: 1) higher platinum concentration and a coalescence of the otherwise Pt–C nanogranular material, 2) a slight enhancement in the deposit resolution and 3) a 100-fold improvement in the conductivity of suspended nanowires grown with the in situ photothermal assist process, while retaining a high degree of shape fidelity.

: Cross-sectional SEM images demonstrating the utility of in situ laser purification compared to ex situ laser purification. a) shows a complex 10-sided polygon as-deposited without any laser annealing. b) shows the same polygon purified with laser annealing ex situ and c) shows the same polygon purified in situ. The insets show the top down SEM images corresponding to each cross-sectional image. This illustrates the importance of in situ purification strategies when dealing with complex 3D structures. The deformation is much larger with ex situ annealing than the in situ annealing. The scale bar is 100 nm.

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Bridge Patterning 1 4 Figure S2: Schematic illustrating the alternating pattern of the nanobridges spanning the gap in the two-point probe contact pads. The arrow represents the electron beam location and the silver circles represent a deposit created during the beam dwell at the particular point. The patterning of the beam progresses from 1 to 4 and beyond bridging the gap by an alternating patterning strategy [1].

Temperature Simulations
Pt-C Figure S3: a) Time-Temperature simulation results of a nanopillar segment with constant length (600 nm) and various segment thicknesses (δ) as denoted in the legend. The pillar is placed at the edge of a solid silicon block directly horizontal from the substrate and perpendicular to the direction of the laser. The peak temperature slightly decreases as the thickness of the pillar grows due to enhanced coupling with the substrate. The temperature profiles are taken from the top of the pillar; the farthest point away from the substrate, illustrated by an orange dot in the schematic. b) A schematic illustrating the simulation geometry.
COMSOL™ Multiphysics 5.0, a commercial finite element method software package, was used to simulate the thermal profile of a single laser pulse on the different geometries. The expression for heat delivered to the substrate from the laser is derived from the Beer-Lambert law: ; where Q 0 is the optical power of the laser, R c is the reflectivity, A c is the absorption coefficient, G(x,y) is the 2-dimensional Gaussian laser profile, σ x nd σ y are the 1/e radii of the Gaussian laser profile, f(t) is the laser on time, and z is the depth from the surface. The reflectivity and absorption coefficient are given by: where the values for n, k, and lambda are given in Table S1 for both silicon and EBID platinum. The laser on time, f(t), was approximated as a rectangular pulse with a 10 ns ramp time and a pulse width of 10 µs. The following time dependent heat equation was used to simulate the heat transfer throughout the silicon substrate: where ρ is the mteril density, C p is the heat capacity at constant pressure, u is the velocity vector for thermal transport (which for a stationary system such as this is equal to 0), nd κ is the therml conductivity. Convective heat transfer to the surrounding atmosphere was neglected since irradiation conditions were under high vacuum. T 0 was defined as 293.15 K. A backward differentiation formula time-stepping method with strict time steps of 10 ns was used to generate the temporal temperature evolution for system during laser irradiation. The asymmetry of the Gaussian beam profile accounts for the angle of the laser with respect to the substrate during pillar growth (52 o ). For more information concerning the EBID platinum material values consult [2].
The material values used in Table S1 including the optical constants, density, heat capacity, and thermal conductivity are held constant for the sake of simplicity in this model. In reality, these values change throughout the course of the laser pulse as a function of both temperature and morphological evolution.
In reference to the silicon substrate, the absorption coefficient will change with temperature because the extinction coefficient is temperature dependent. In general, k increases slightly with temperature whereas n stays relatively stable [3] leading to a larger absorption coefficient and therefore a hotter substrate temperature. The heat capacity at constant pressure will also change with temperature increasing slightly (~14%) from room temperature to 600 K [4]. This increase will effectively decrease the temperature of the irradiated silicon. The thermal conductivity of silicon scales as T -1.2 [5] meaning that over the simulated temperature ranges, the thermal conductivity will decrease by roughly a factor of 2. In our described system this decrease in thermal conductivity would lead to an increase in overall temperature of the silicon substrate.
With regards to the platinum deposit, the dominant mechanism for change is the granular Ptamorphous carbon composite to metallic transition. As carbonaceous material is removed, the density and thermal conductivity will increase and the n and k values will increase as well. The thermal conductivity of the as-deposited PtC x is largely dominated by the thermal conductivity of the amorphous carbon, which is very low. As carbon is removed and graphitized, the thermal conductivity of the wire is expected to increase which will decrease the temperature of the wire moderately self-limiting the heating from the laser pulse. As the wire becomes more metallic, the corresponding increase in n and k values will increase both the reflectivity and absorption coefficient. It is expected that the temperature of the wire would experience a relative increase. This prediction arises from the observation that PtC x has a penetration depth longer than the dimensions of the wire itself (~234 nm). Platinum, on the other hand, has an absorption depth of ~8 nm at room temperature. This means that the absorption depth will shrink as the carbon is removed leading to more of the incident laser irradiation being absorbed.