The Impact of Electron Beam Heating during 3D Nanoprinting - ACS

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The Impact of Electron Beam Heating during 3D Nanoprinting Eva Mutunga, Robert Winkler, Jurgen Sattelkow, Philip D. Rack, Harald Plank, and Jason Davidson Fowlkes ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b09341 • Publication Date (Web): 15 Apr 2019 Downloaded from http://pubs.acs.org on April 15, 2019

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The Impact of Electron Beam Heating during 3D Nanoprinting Eva Mutungaa,b, Robert Winklerc, Jürgen Sattelkowc, Philip D. Racka,b,e, Harald Plankc,d and Jason D. Fowlkes a,b,e* Bredesen Center for Interdisciplinary Research, The University of Tennessee, Knoxville, Tennessee 37996, United States a

Nanofabrication Research Laboratory, Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States b

Christian Doppler Laboratory for Direct–Write Fabrication of 3D Nano–Probes, Institute of Electron Microscopy, Graz University of Technology, Steyrergasse 17, 8010 Graz, Austria

c

d

Graz Centre for Electron Microscopy, Steyrergasse 17, 8010 Graz, Austria

Materials Science and Engineering Department, The University of Tennessee, Knoxville, Tennessee 37996, United States

e

(*) [email protected]

This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). Keywords: 3D-nanoprinting, beam-induced heating, focused electron beam-induced deposition, direct-write, nanofabrication Abstract An artifact limiting the reproduction of 3D designs using nanoprinting has been quantified. Beam induced heating was determined, through complementary experiments, models and simulations, to affect the deposition rate during the 3D nanoprinting of mesh objects using focused electron beam induced deposition (FEBID). The mesh objects are constructed using interconnected nanowires. During nanowire growth, the beam interaction driving deposition also causes local heating. The temperature at the beam impact region (BIR) progressively rises as thermal resistance increases with nanowire growth. Heat dissipation resembles the classical mode of heat transfer from extended surfaces; heat must flow through the mesh object to reach the substrate sink. Simulations reveal that beam heating causes an increase in the rate of precursor desorption at the BIR causing a concomitant decrease in the deposition rate, overwhelming an increase in the deposition rate driven by thermally enhanced precursor surface diffusion. Temperature changes as small as 10 K produce noticeable changes in deposit geometry – nanowires appear to deflect/curve toward the substrate because the vertical growth rate (VGR) decreases. 3D FEBID naturally ensues from the substrate surface, upward, inducing a vertical temperature gradient along the deposit. Simulations, experiments, temperature–controlled studies, and process current monitoring all confirm the cause of nanowire distortion as beam

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induced heating while also revealing the rate determining physics governing the final deposit shape. 3D nanofabrication using focused electron beam induced deposition (FEBID) has emerged as an additive nanomanufacturing technique applicable over the micro– and nanometer scales.1 FEBID is a direct-write, bottom–up deposition method where an electron beam with a nanometer scale width locally dissociates surface bound precursor molecules.2 Low-energy (eV) secondary electrons (SE), liberated in the beam impact region, or BIR, during primary electron beam irradiation, are the most energetically favorable electron species to drive the precursor molecule dissociation required for FEBID. Regarding instrumentation, FEBID experiments require either a scanning or transmission electron microscope retrofitted with both a gas injection system (GIS) and beam scanning control hardware. Continuous electron exposure leads to deposit accumulation under steady precursor flow conditions although precursor–limited reaction conditions often develop3 due to pressure limitations imposed by the high vacuum environment required for stable SEM operation. 3D FEBID has recently been demonstrated over a welldefined range of beam patterning velocities, beam acceleration voltages and currents.4 Recent 3D FEBID demonstrations include simulation-guided FEBID,5 multi–precursor composition control,6 deposition using heteronuclear precursors,7 3D elements for scaffolding8 and optically active 3D nanostructures.9, 10 This makes 3D FEBID a promising technology for the fabrication of high-precision and high degrees of freedom 3D nano- and microstructures11 compared to other 3D techniques such as direct ink writing,12 electrohydrodynamic printing,13 laser-induced forward transfer,14 laser-assisted electrophoretic deposition15 and laser-induced photoreduction.16 Simulations provide a powerful means to identify proximity effects inherent to FEBID enabling compensation for complicating factors, especially considering the difficulties in achieving CAD– to–deposit replication under precursor–limited growth conditions typical of FEBID. 3D mesh style objects such as those reported in1,4,5,7,9,17 may exhibit a ‘compressed’ appearance toward the substrate surface, relative to CAD, due to the downward deflection of individual nanowires constituting the object. Recently, a 3D CAD program (3BID),17 specific to FEBID has been released making it possible to compensate for FEBID distortions yet complications remain. For example, downward bending is observed in overhanging 3D nanowires in certain cases when linear growth is specified. Nonetheless, corrections currently available in 3BID are only empirical in nature. However, an alternative pattern generating program has recently been released which provides proximity effect correction and the ability to compensate for vertical precursor coverage gradients.18 Simulations presented below reveal the distortion mechanism that causes this detrimental structural distortion providing a pathway to a more quantitative correction scheme. The current collected through the sample stage during FEBID contains information regarding deposition status.19-21 Time–dependent changes in the sample current magnitude (dis/dt) have been correlated with the loss of beam–deposit overlap which is critical for FEBID.19 Particularly relevant to the current study, previous work has shown that the time evolution of the sample current is strongly related to geometric changes taking place during 3D FEBID.21


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The research reported here is briefly overviewed. First, an unexplained feature of the simulated sample current profile, relative to complementary 3D FEBID experiments, is presented. Further, an analysis of the sample current collected during the sequential deposition of pillar and segment structures is provided. This deposition sequence is typically used for control/calibration experiments prior to 3D FEBID; vertical support nanowires, or ‘pillars’, followed by the growth of suspended nanowires, so–called ‘segments’. These combined elements will be referred to as ‘calibration structures’. Next, differences in the current signal collected during 3D FEBID simulations and experiments are explored using a 1D beam heating model in concert with a qualitative analysis of the impact that beam heating should have on precursor surface concentration during FEBID. 1D model predictions preempted the integration of a 3D beam heating simulation to our 3D FEBID solver.5 The effect of electron beam heating during FEBID has been previously recognized for various materials6, 22-27 and the 3D simulations reported here including the heating effect are consistent with previous observations. Simulations with the enhanced capability revealed the important role that heat transfer plays in dictating the final deposit geometry – a thermal gradient develops in the deposit which induces an opposing precursor concentration gradient. As a result, nonlinear, downward curving segments are produced where otherwise linear nanowires are expected. Ultimately, a thermal desorption activation energy and thermal conductivity are reported that (1) explain experimental observations and (2) reside within reasonable physical ranges reported in the literature. The thermal conductivity derived is that expected for amorphous carbon, which is the primary constituent in deposits derived from the volatile precursor MeCpPtIVMe3 (deposits of nominal composition PtC5– 28 while the activation energy used to describe temperature–dependent precursor desorption is 8, similar in magnitude to the value determined by density functional theory (DFT) calculations for MeCpPtIVMe3 absorbed on an SiO2 surface.29 Finally, the physical mechanisms governing 3D FEBID are revealed.

Background Simulations Confirm Past Observations Simulations of the sample current collected during 3D FEBID confirmed the basic physical mechanisms qualitatively rationalized previously by experiments.19-21 These mechanisms are briefly summarized below to provide the framework for the current study. The mechanisms are discussed in the context of a data set that exhibits the dependence of suspended segment angle on the electron beam digital patterning velocity (vb), a key parameter during 3D FEBID.4, 30, 31 Following the summary section, the influence of beam heating on sample current evolution is presented and discussed.


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Figure 1 (a) A 2D scheme of the pillar and segment calibration structure. The stages of deposition are ‘pillar’, ‘transition’ and ‘segment’. Pillar deposition occurs using stationary electron beam exposure. The electron beam moves at constant, digital beam velocity during ‘transition’ and ‘segment’ growth. 3D focused electron beam induced deposition simulations (FEBID) are shown for each stage. Beam scanning ensues in the (x,y), stationary focal plane (green). The pillar and segment are both 400 nm in length. Simulations were conducted using a beam acceleration voltage of (Eo) 30 keV and a beam current of (ib) 32 pA. The colormap represents the fractional monolayer coverage of the MeCpPtIVMe3 precursor on the PtC5 deposit surface. (b) The sample current (is) collected through the substrate during FEBID is sensitive to geometric changes during growth. The continuous black sample current profile was collected during an experiment that yielded a segment angle of  = 32.5o. Without electron beam heating in the FEBID simulation, dis/dt ~ 0 during the segment growth stage (see --). In real experiments dis/dt < 0 during segment deposition. (c) An electron micrograph of a real calibration structure (scale bar = 400 nm) acquired at an angle of 52o with respect to the substrate surface normal. The segment element is aligned with the tilt axis in the image. The discrepancy between the real and simulated sample current is realized as a downward deflection of the segment with respect to the linear design, i.e., the superimposed hatched white line.

I.

‘Pillar’

The pillar structural element was deposited under stationary electron exposure leading to vertical growth with respect to the primary electron beam impact trajectory (Figure 1a). Following pillar nucleation32, the vertical FEBID growth rate continuously decreases owing to the development of precursor–limited conditions at the growing pillar apex. The growth rate of the pillar scales with dis/dt (Figure 1b). The vertical growth rate continuously decreases (a decreasing slope with time) because (1) although the magnitude of emitted SE current increases as the surface area to volume ratio increases (SEs excited by back– and forward scattered electrons), which should


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increase the VGR, these additional SEs produce broadening while consuming precursor that would have contributed to vertical growth and (2) direct gas phase replenishment in the BIR is insufficient alone to fully replenish precursor there and must be aided by precursor surface diffusion. In part, the increase in the sample current (figure 1b, blue region) is simply a result of an increase in SE emission (an induced positive charge in the sample current) but the VGR is directly related to the convolution of the pillar tip shape, the electron–solid interaction and the precursor molecule surface coverage (). Eventually, the exponential decay of dis/dt tends to a plateau, depending on the height of the pillar (figure 1b, blue region at ~3 s), when the electron interaction volume–pillar convolution approaches quasi steady–state.21 II.

Transition

Segment growth requires lateral beam translation which begins following pillar growth. A period of significant beam/pillar overlap occurs during the segment growth phase because the pixel point pitch ( = 1 nm) is much less than the average pillar diameter of 2×rp~60nm where rp is the mean pillar base. Thus, when the beam advances to a lateral position coincident with rp, a distinct sample current peak (shaded orange in figure 1b) is observed indicating beam exposure of the larger pillar sidewall surface area. This is seen indirectly in figure 1a, labelled ‘transition’, as a reduction in  on the pillar flank caused by SE induced deposition. In the typical FEBID experiment it is assumed that the MeCpPtIVMe3 precursor is limited to a monolayer of coverage in the range  < 1. III.

‘Segment’

Bret et al. identified the thickness of the segment as a stage current determining factor during segment element deposition.19 Higher lateral beam speeds produce not only relatively smaller segment angles but also thinner segments measured parallel to the electron beam impact vector. The primary electron (PE) beam penetration range far exceeds the segment thickness in the FEBID voltage range (> 5 keV). PEs thus reenter the gas phase from the underside of the segment surface with only a slight redirection due to weak elastic scattering in the low Z, mostly carbonaceous deposit matrix. Additional SEs may be liberated by these PEs in three ways; (1) when the beam exits the segment underside and, either (2) during forward scattered impact with the pillar for PEs will a relatively larger scattering angle (lower probability) or (3) if weakly scattered PEs enter the substrate surface (higher probability). Experiments reveal that as the beam is scanned laterally during segment growth, a slight decay of the current is observed as the segment lengthens (green region, see arrows, figure 1b). Evidently, SE emission from the deposit to the vapor phase is decreasing during this phase of growth. This observation is the main topic of the current paper. More details regarding the sample current transient representative of 3D FEBID is provided in S1. Sample current data will be presented in multiple figures below. Regarding nomenclature, an ‘increase’ in (is) indicates a positive increase in (is) caused by the loss of electron species from the deposit/substrate surface which contributes a positive elemental charge to the sample current.


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Figure 2 Segment angle changes are resolved in time–dependent sample current profiles collected during FEBID. In each experiment, a 400 nm pillar was deposited followed by the deposition of a segment 400 nm long; the so–called ‘calibration structure’ using Eo = 30 keV and ib = 32 pA. Only the segment angle () was varied among the experiments. Each angle dependent profile has been shifted along the y–axis to create a separation of iS = 2 pA between each profile to avoid profile overlap and clarify trends. The sample current profile collected for the case of  = 12.5o was not shifted and provides a true sample current profile. The 3BID17 specified segment angle is shown for each curve followed by the measured value of () after deposition.

Results/Discussion Extension of FEBID Simulation to Include Thermal Effects I.

Sample Current Artifact

Figure 2 shows (is) profiles collected during the experimental deposition of calibration structures with a variable segment angle spanning 12.5° to 80°. The exposure files were created using the 3BID program.17 Recalibration17 was executed twice to achieve agreement of the segment angles observed in experiments with the design values, targeting an error of < 2o. Additional experimental conditions are provided in the figure caption and Methods. Experimental variation in calibration structure deposition is represented in figure 2 by including stage current traces from multiple experiments for the case of ( = 15o) and ( = 32.5o).


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Emphasis is placed on the relative differences observed in the sample current profile when () is changed. In order that relative comparisons between experiments can be made clearly, each current profile has been shifted vertically by is = 2 pA in figure 2 to avoid data overlap. However, the sample current trace representing ( = 12.5o) has not been shifted and thus represents the raw stage current profile expected at 30 keV and 32 pA for 3D FEBID. Segments with relatively higher () require a longer total processing time (figure 2) to deposit the same total segment length – as the digital beam speed (vb) is reduced, fewer pixels are exposed for a longer total beam dwell time favoring vertical growth. Quantitatively, this can be understood as follows. (vb) is a function of both pixel point pitch () and dwell time (d) via vb = /d. In the experiments and simulations reported here,  = 1 nm. Therefore, to increase () requires an increase in d. As a result, the electron dose per unit scan length (ibd/q) increases leading to more deposition per pixel (q = 1.6x10-19 C/e-). The total volume deposited per () increases with a concomitant increase in the surface area per unit length of segment. Consequently, more SEs are emitted driving the current signal more positive in the ‘segment’ stage of growth as () increases. For the same reasons, segment width increases with ().4 What has remained unexplained until now is the decay in (is) observed during segment FEBID (figure 2). However, considering the previous discussion, the net effect is clear – a decrease in the deposition rate per pixel due to a reduction in thickness in the z–dimension. This was confirmed by secondary electron imaging, which revealed a steady decrease in the segment angle and segment z–thickness with increasing segment length. Beam induced heating was investigated as the cause of the decrease in the growth rate. Now presented is an analytical model of FEBID-induced heating derived to estimate the range of temperatures expected to develop during FEBID, specifically, the maximum temperature at the BIR. The mean precursor surface residence time () on the deposit surface was found to be significantly impacted by changes in temperature suggested by the model due to the Arrhenius behavior of this parameter. This phenomenon was recognized in 200626 during FEBID studies using the precursor (hfac)CuVTMS where is was stated that; “The adsorbed amount of precursor per area decrease exponentially with increasing temperature due to increasing desorption”26 The derived 1D analytical model is now introduced because the assumptions and results provide an instructive guide to later interpret 3D beam heating results.


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Figure 3 Segment angle () is implicitly included in the 1D heating model by using a cross–sectional area function A(s) that varies over the pathlength (s) of the deposit. The influence of thermal resistance as a function of segment angle is thus included. The average cross–sectional area of the pillar element is Ap and As for the segment and are the critical parameters dictating the thermal resistance; Ap = 2830 nm2 while As exhibits a typical variation of As() = Ap(1 – e-/(30-0.2)), where the  unit is degrees, based on experiments.

II.

A 1D Analytical Model of FEBID-induced Beam Heating

Beam heating effects during FEBID were estimated using a 1D analytical approximation based on the classical heat transfer problem of the extended cylinder. The pillar and segment were modeled collectively as a linear nanowire, for all  spanning 0–90o. Therefore, it was required that the linear model implicitly account for the variation in the multidimensional segment angle. This aspect of the model is now described. Experiments revealed that segment cross–sectional area varies with . Thus, the effect of  was implicitly introduced into the model by measuring the segment cross–sectional area (As) from experiments for use as an input parameter in the 1D model (figure 3). The importance of (As) during heat flow can be understood considering the thermal resistance; 𝑅𝑇 =

𝑆 𝑘𝐴

[𝑊𝐾 ] [1]

where (S) is the total calibration structure pathlength and (k) is the thermal conductivity. Please note that (k) is assumed to be constant, independent of deposit length. A change in cross– sectional area versus the path length coordinate (s) along the nanowire A(s) also must be included in the model because the cross–sectional area of the pillar and segment are different under most deposition conditions. The details and functional form of A(s) are provided in (SI2). The model was derived starting with the integration of Fourier’s law (SI3) separated in temperature (T) and pathlength (s); 𝑞𝑏(𝑆)

∫

𝑆

𝑑𝑠 = ―𝑘 0𝐴(𝑠)

∫

𝑇𝐵𝐼𝑅

𝑑𝑇 [2] 𝑇𝑠

where qb(S) is the incident beam heating rate, (S) is the total deposit length and (Ts) is the substrate surface temperature. This method can be used when (1) heat transfer is steady–state, (2) energy is not generated in the volume of the object and (3) heat loss via transfer across the surface area 2rLT is negligible (SI4). Importantly, the beam heating rate induced in the solid qb(S) must be conserved at all points along the s–dimension, under steady–state conditions, and causes the temperature increase at (TBIR). The electron energy loss, or EEL, during primary electron transmission through the BIR provides the heating rate term qb(S); 𝑞𝑏(𝑆) = 𝑓𝑈𝑑𝐸′α(S)

𝑖𝑏 𝑞𝑒

[3]


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where (fU) is fraction of the inelastic energy transferred to the deposit as heat (SI5), (dE’) is the EEL per unit length of deposit5 and (S) is the primary electron path-length through the deposit. Inelastic EEL occurs continuously along the path-length as Joule heating and therefore (S) is an absorption thickness. Details regarding () and the integration of equation 2 are discussed in SI3. Each solution of equation 2 for TBIR in the range S = 0:L:LT, can be collectively viewed as the actual BIR temperature because the beam speed is extremely slow relative the thermal diffusion rate. As a result, steady–state conditions develop quickly after the beam is displaced. A non– dimensional analysis verifies this assumption;

𝑣𝐿 = 𝛼𝑇

() ( )

Λ 𝐿 𝜏𝑑 𝑇 𝑘 𝜌𝑐𝑝

[4]

where the numerator is an advection–like term that, in this instance, accounts for beam motion while the denominator is the thermal diffusivity (T). vL/T = 10-6 for LT = 103 nm and an electron beam speed of v = 102 nm/s. This very small value indicates that steady–state heat transfer is established along the length of deposit during 3D FEBID quickly after beam translation to a new dwell position on the deposit because the patterning velocity is very slow relative to the thermal diffusivity. The relevance of the Fourier number (Fo) with regards to the heat transfer rate will be discussed later after the presentation of results. Finally, the integration of equation 2, with the application of the boundary conditions, gives; 𝑇𝑚𝑎𝑥(𝑆) = 𝑇𝑠𝑢𝑏 +

𝑞𝑏(𝑆)ℎ𝑠 𝑞𝑏(𝑆) 𝐺(𝑆) + 𝐺(𝑆) [5] 𝑘𝑠 𝑆 𝑘

where (G) is a geometry dependent function and is provided in SI3 as well as additional information on the substrate boundary condition. (hs) is the SiO2 film thickness resting on the Si substrate at temperature (Tsub).


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Figure 4 The maximum temperature of the deposit as a function of the total deposit height along the z– coordinate as predicted by the 1D analytical mathematical model (solid lines) for Eo = 30 keV and ib = 32 pA. The maximum temperature always occurs at the beam–impact region, or BIR. The insets show virtual SEM images of 3D simulation results for  = 10o (●) and  = 90o (●). The scale bar is 200 nm. The images were acquired at 52o with respect to the substrate surface normal. The temperature trajectory has been correlated with the deposit image for the  = 10o case; (*) indicates the ‘transition’ stage between pillar and segment growth while (**) shows the completion of deposition. A 2D finite element simulation (FlexPDE®) of heating at  = 10o (□) and 50o (□) corroborated the 1D prediction.

The 1D beam heating model reveals several important characteristics of beam–induced heating. Figure 4 shows the predicted BIR temperature versus total deposit height in the z–coordinate for  = 10–50o in steps of 10o. The details regarding choice of (z) for the abscissa are provided in SI6. Briefly, (z) was used for two reasons. First, deposition time does not appear explicitly in the 1D model. Second, the bottom–up nature of 3D nanoprinting makes (z) the critical parameter for unraveling heat evolution as a 3D structure grows. For this reason, the spatial derivative (dT/dz) is an important quantity for discussing thermal effects in 3D FEBID nanostructures. The most significant results in figure 4 are now discussed. Pillar stage


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The 1D model predicts a linear rise of temperature during pillar deposition stage (figure 4). The beam heating rate (qb) is independent of pillar height due to the assumption of a constant beam absorption thickness. Thus, the increase in temperature is solely due to the increase in the thermal resistance caused by the increase in the pillar length. This simple prediction will later be shown to also agree with more detailed 3D simulations. This is surprising considering the dynamic 3D Joule heating caused by the convolution of the electron interaction volume and the deposit volume. Transition stage The transition stage is characterized by a significant reduction in temperature; a reduction which is more pronounced for smaller segment angles. The general temperature reduction observed for all segment angles is due to the abrupt change in adsorption thickness when the beam irradiation geometry switches from para–axial to trans–axial with respect to the deposit growth direction, i.e., the absorption thickness transitions from the relatively long pillar to the thin segment nuclei. The segment angle dependence of the temperature decrease is ultimately caused by the reduced VGR, a consequence of a relatively faster vb. The dose per unit length ib/(qevb) is thus lower yielding less deposition per unit length and a relatively low vertical growth rate (VGR). Thus, the initial segment nuclei are relatively small for large vb. As a result, the quantity of absorbed internal energy per incident electron is lower at lower (). This reduces the absorption thickness for the next pixel point propagating the effect via positive feedback. Segment stage The final BIR temperature and the change in BIR temperature with segment length (T/s) both vary with segment angle. These observations together characterize the heating situation in the segment stage. The final BIR temperature, measured at the final segment length of 400 nm, increases progressively with () due simply to the increase in absorption thickness. The source term (qb) magnitude increases with () as a result because more energy from the electron beam is deposited in the growing segment.


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Figure 5 (a) 1D beam heating model predictions of the BIR temperature versus pathlength along the deposit. The pathlength along the deposit is indicated by the variable (s). The slope of these curves (b, black line) in the segment growth stage, i.e., s > 400 nm, reveals the relative influence of the thermal resistance (RT) and the beam induced heating rate (qb). (b) 3D simulation results have been included (red line) for comparison purposes but are referenced to the right–most ordinate, also in red (same units). The color of each data point is referenced to each segment based on the segment angle ().

The impact of the thermal resistance (RT) on segment heating is revealed by plotting the BIR temperature as a function of segment path-length along the calibration element (s). Figure 5a shows (T) versus (s) trajectories ranging from 10o to 50o. (T/s) is the change in BIR maximum temperature per unit length of new deposit formed. (T/s) is derived from these plots and is shown in figure 5b. Please see SI7 for details in interpretation of ‘T/s’, not to be confused with dT/ds. The black line shows (T/s) derived from the 1D heat model and the magnitude is referenced to the left ordinate. (T/s) exhibits a minimum value at a  ~ 30o (figure 5b). At lower , RT increases due the smaller segment cross–sectional area. The increase in RT leads to an increase in the BIR temperature per unit segment path-length. As a result, below  ~ 30o an increase in (T/s) is observed with decreasing segment angle. Beyond 30o, the electron beam source term (qb) dominates heat transport, again, due to the increasing energy loss at higher segment thickness. The source term overwhelms the increase in thermal conductance, which increases with increasing thickness, as segment angle increases. Confirmation of model prediction The prediction of the BIR temperature suggested by the 1D model was confirmed using finite element modelling software (FlexPDE®) using a 2D simulation of the steady–state temperature profile in the coordinate (r,z) (see Methods and figure 4a, □)

III.

Temperature–Dependent Properties


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The BIR temperatures estimated for FEBID using the 1D analytical model suggests that a significant change in the mean precursor surface residence time (T) should be expected during FEBID, at least based on information available in the literature. This assessment was based on the activation energy29 and pre–exponential33 parameters reported for physical bonding between MeCpPtIVMe3 and an SiO2 surface.

Figure 6 The temperature–dependent MeCpPtIVMe3 surface residence time (T) on SiO2 reported in22 using ko = 1013 Hz and Ea = 669 meV (-). This parameter is revised anticipating that the MeCpPtIVMe3–PtCx interface is expected to control 3D FEBID, based on previous simulations.29 An updated value of Ea = 0.62 eV (--) produced simulation results that predicted 3D FEBID experiments and is taken as an estimate of the Ea for the MeCpPtIVMe3–PtCx interface. Surface diffusion D(T) is less sensitive to temperature changes () based on data provided in23 with Do = 42 m2/s and Ea(D) = 122 meV, at least when compared with (T).

Figure 6 (-) shows (T) predicted for the MeCpPtIVMe3–SiO2 interface using the reported activation energy of Ea = 669 meV29 and the estimated pre-exponential attempt frequency ko ~ 1x1013 Hz applicable in the limit of the large molecule approximation.33 Considering temperature changes predicted by the 1D heating model T ~ 10 K, a decrease in (T) exceeding 50% is expected. Please note, the Cullen/Toth22, 23 reports of the implications of the temperature–dependent behavior of this precursor and its participation in FEBID served as an extremely valuable resource in the development the current work ultimately leading to the exploration of the beam heating effect.22 Further, Utke26 identified importance of considering (T) while Randolph also identified the importance of (T) during TEOS deposition using FEBID.24


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The 1D model of beam heating predicted a significant impact of a BIR temperature rise on 3D FEBID. In response to this prediction, a 3D heat transport solver was integrated with our 3D FEBID simulation to include (T). Temperature–dependent precursor surface diffusion (figure 6, right hand ordinate) was also included in the precursor surface transport PDE. However, simulation results will later reveal that the weaker temperature dependence exhibited by this physical property causes minimal influences on 3D FEBID relative to (T). The introduction of 3D heating simulation into the current 3D FEBID simulation is described in the Methods. It is important to note that 3D FEBID simulations reported previously5, 34 have shown that the precursor coverage on the deposit surface primarily dictates the growth rate during MeCpPtIVMe3 FEBID through a surface diffusion enhanced mechanism; the so–called diffusion enhanced regime (DER). However, the data presented in figure 6, which serves as the basis for exploring the heat effect, pertain to the MeCpPtIVMe3–SiO2 interaction. This interface influences FEBID only in the initial stages of 3D FEBID when the deposit is in proximity to the substrate surface. Thus, this preliminary analysis served only as a starting point to explore the beam heating influence and Ea provided in the literature29 served as an initial condition to refine Ea for the MeCpPtIVMe3–PtCx interface that truly governs 3D FEBID. The thermal conductivity of the deposit (k), the activation energy for physical desorption of precursor from the deposit surface (Ea) and the fraction of inelastic energy deposited that contributes to Joule heating (fU) where modulated to match experimental results with simulations because these values are unknown for the PtC5 deposit. (k) was assumed to be dominated by the amorphous carbon phase and was restricted to the range of 0.1–1, reported in,35,36 when searching for simulations that reproduced experiments. The activation energy was varied over the range of 100 meV, centered on the value reported for the MeCpPtIVMe3–SiO2 interaction above (669 meV). (fU) was varied from 0.50–1 as it is well known that a significant amount of electron energy loss yields Joule heating.37


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Figure 7 3D FEBID simulations (●) of the BIR temperature as a function of calibration structure height. The segment angle for each case is indicated by color. Select 1D model results for  = 10o and 50o are again presented for direct comparison of 1D and 3D predictions. The pillar and segment elements are 400 nm in length. The total deposition time for each segment, in the order from  = 10o  90o, are 4.88, 4.95, 5.16, 5.16, 5.38, 5.46, 5.35 and 6.62 s. Finally, Eo = 30 keV and ib = 32 pA.

IV.

3D Simulation Results

Beam heating effects during the 3D FEBID of calibration structures First, the BIR temperature predicted using the full 3D simulation is compared with select results derived from the 1D heating model (figure 7). The complete 1D heating model data set is shown in figure 4. The maximum temperature is measured at the end of selected electron beam dwell periods and is naturally located in the BIR. Simulation predictions of the final segment geometry match experimental prediction within  < 2o which serves as the basis for comparing experiments and simulations. This convergence was found when the activation energy for (T) was reduced from the value of 0.669 eV,22 reported in the literature, to 0.62 eV and for k = 0.16 W/m/K. (T) is displayed over the temperature range 294–304 K in figure 6 (--) using Ea = 0.62 eV. The pre–exponential attempt frequency was kept constant. Figure 7 shows the simulation results for an array of calibration elements spanning  = 0  90o. The BIR temperature change along the z–coordinate (T/z) predicted by the 1D model and 3D


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simulation agree remarkably well considering the simplicity of the 1D model. For example, compare in figure 7 the magnitude of (T/z) at constant () and (z) for the cases of  = 10o and 50o. Conversely, the maximum BIR temperature predicted by the 1D model of heat transfer, at any given height (z), consistently predicts a larger maximum value relative to the 3D simulation of T~ 4 K. This discrepancy occurs because the 1D model ignores the complex 3D energy deposition profile in the deposit; the 1D model only considers a conserved heating rate qb (see equation 2). For example, during segment nucleation, EEL not only occurs in the thin segment predecessor but also in the pillar due to a grazing incidence along the pillar sidewall. The 1D model ignores the latter. Energy is thus lost in a complex profile extending along the pillar. In general, the 1D model tends to overestimate the temperature more as   0o because the 3D character of the geometry increases. Further, the T/s data for the full 3D simulation is provided in figure 5b (-) for direct comparison with the 1D model. In general, the 3D predicted BIR temperature change with segment length is reduced in magnitude by a factor of 2 which is discussed in detail in (SI8). Lastly, the segment stage heating rate tends to the pillar stage rate as   90o. Of course, at  = 90o (figure 7, ●) the calibration structure becomes simply an extended pillar and this convergence is expected.


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Figure 8 (a) 3D FEBID simulations of sample current evolution during the ‘transition’ and ‘segment’ growth stages for a calibration structure with a 400 nm tall pillar and a 800 nm long segment ( = 15o). The electron beam conditions of Eo = 30 keV and ib = 32 pA were used. FEBID parameters were artificially turned on and off to explore clearly the factors governing 3D FEBID. Artificial conditions including the electron–limited ‘ELR’, a precursor–limited ‘Refresh’ and diffusion–enhanced ‘DER’ regimes as well as a simulation with no surface diffusion ‘No Diffusion’. Until publication of this work, the most realistic simulation conditions were the ‘DER (No Heat)’ case reported in.5 Please note that the beam heating solver was only active during the ‘DER (Heat)’ simulation. The most realistic 3D FEBID simulation of the (is) includes electron beam heating ‘DER (Heat)’ (-). An experimental data set for a complementary calibration structure (●) is provided for reference. Measurements revealed  = 17o for the experiment and  = 15.6o for the simulation. (b) Surface temperature map for the ‘DER (Heat)’ case at the exact moment that the simulation is completed with electron beam heating applied at the BIR. (c) Surface precursor coverage for the ‘DER (Heat)’ under


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the same conditions as (b). The surface adsorbed precursor is limited to monolayer coverage  = 0–1 (see colormap).

Reaction Kinetics including Electron Beam Induced Heating The simulation makes it possible to selectively turn on and off physical parameters that influence 3D FEBID. This switching can help reveal the action of a single parameter involved in a complex multi-parameter interaction. This provides a powerful means to clarify an otherwise convoluted deposition process. In particular, the surface concentration of precursor C(x,y,z,t) on the deposit will be manipulated; ∂𝐶 𝛿Φ 𝐶 (𝑠𝑝 ― 𝐶) ― = 𝐷(𝑇)∇2𝐶 + ∇𝐷(𝑇)∇𝐶 + ― 𝜎𝐶𝑖𝑆𝐸 [6] ∂𝑡 𝑠𝑝 𝜏(𝑇) where () is the precursor sticking probability, () is the precursor vapor phase impingement flux, (sp) is the monolayer precursor surface concentration, () is mean electron impact precursor dissociation cross–section and (iSE) is the secondary electron current density 3D profile. Concerning the righthand side of equation 6, terms 1 and 2 govern precursor transport by surface diffusion. Term 3 is the precursor attachment flux and term 4 incorporates the precursor desorption flux while term 5 includes precursor dissociation by secondary electrons. The reaction regime for 3D FEBID was quantified using a calibration structure with a relatively low segment angle ( = 15o). This angle was chosen because Joule heating influences low angle segments strongly with the most pronounced segment deflection, thereby maximizing the influence of heating on reaction kinetics. The electron–limited regime (ELR) was first simulated as a reference point (figure 8a black trajectory). The simulated sample current is provided along with a virtual SEM of the final nanostructure in figure 8a. ELR conditions were obtained by artificially forcing the surface precursor coverage to the equilibrium value (Co=2 molecules/nm2), regardless of the rate of precursor consumption in the BIR. Co is a steady–state quantity established by the balance between the precursor attachment flux and the surface desorption flux. (Co) in terms of the equilibrium monolayer coverage is o ~ 0.7 = 2/2.8 where sp = 2.8 sites/nm2. Beam induced heating was not activated during this simulation. The ELR setting produces the largest sample current during segment growth producing the largest final deposit height and , (shown in the ‘ELR’ inset) when compared with the upcoming computer experiments. No segment deflection/bending is observed yet diS/dt < 0. A constant () should produce a constant (iS) according to facts stated in the Background. However, the finite simulation domain size restricts diS/dt < 0 affecting electron counting during the Monte Carlo simulation. The influence of precursor depletion during only the beam dwell period can be resolved by forcing o  0.7 at the end of each beam dwell (figure 8a grey line). During the dwell period the precursor surface coverage naturally evolves as dictated by equation 6, except that () is held constant at the room temperature (294 K) value of 4.22 ms. The label ‘Refresh’ is ascribed to this condition because the simulation emulates an infinitely long refresh period between beam displacements.


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The absolute value of (iS) decreases relative to the ‘ELR’ trace during segment growth which indicates that the deposit volume is decreasing which is consistent with precursor depletion. Therefore, the kinetic regime has been artificially switched from ELR to a precursor limited condition. Again, a linear segment is produced as confirmed by the virtual SEM image and the fact that diS/dt ~ 0. Next, we allow the surface coverage to evolve naturally at all processing times based on realistic physics (figure 8a green line). As a result, DER conditions develop where continuous segment growth requires the diffusion of surface bound precursor to the BIR along the growing segment.17 Beam heating was again switched off during this simulation. The FEBID simulation better emulates reality and captures all aspects of the stage current profile, relative to experiments (figure 8a, ●), except the segment deflection and the concomitant decay in sample current observed during real segment deposition (diS/dt < 0). The most realistic (iS) simulation is shown using a solid blue line in figure 8a. Beam heating was active during this simulation. Segment deflection is captured by the decay in sample current in the segment growth stage. The 3D temperature profile for the surface voxels of the deposit is presented in figure 8b. In the Discussion section it will be shown that the temperature gradient (dT/ds) reduces the reservoir of precursor along the segment that feeds the diffusion flux to the BIR, directly through the term C/(T) in equation 6. As a result, (C) is reduced along the calibration element axis, approaching the BIR. The diffusion–enhanced regime has been reported to be the reaction regime dictating 3D FEBID based on both experiments and simulations.4, 17 Now, with the inclusion of the beam–induced heating, the DER condition is seen to still dictate shape evolution. This is revealed using a computer experiment where the magnitude of the diffusion coefficient is artificially reduced by a factor of 5. The computer experiment is labelled as ‘No Diffusion’ in figure 8a. 3D FEBID is impossible under this condition, and FEBID is relegated to the deposition of a substrate bound nanowire.


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Figure 9 Temperature–dependent, real FEBID experiments conducted at a fixed electron dose for several cases (■ 5 keV, 98 pA, 1 second stationary beam exposure and ● 30 keV, 44 pA, 2 s and 4 s). Each data point represents an individual pillar growth experiment. Complementary 3D FEBID simulations (□ 5 keV, ○ 30 keV) are included along with exponential fits (data lines) for clarity. Virtual SEM images are included for select computer experiments. The images were collected at 52o with respect to the substrate surface normal. Pillar height decreases as the substrate temperature increases due to a concomitant reduction in precursor surface residence time with temperature. Conversely, surface diffusion coefficient (D) increases with temperature exerting a positive influence on pillar height.

Lastly, temperature–controlled FEBID experiments were conducted to corroborate the influence of beam heating suggested by 3D FEBID simulations (figure 9). Further, the experiments widen the range of absolute temperatures explored. For example, the table inset shows the temperature range and affected properties. Figure 9a shows the results of constant dose, stationary electron beam exposures executed for nine different substrate temperatures at two distinct beam acceleration voltages of 5 and 30 keV. The final pillar height is plotted versus temperature in figure 9a as a relative measure of the change in deposition rate caused by a change in bulk substrate temperature. The results presented thus far suggest that elevated temperatures should lead to significant changes in the


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VGR because the mean precursor residence time on the deposit surface decreases significantly with increasing temperature. The experimental results are consistent with this prediction. It was encouraging that the simulation predicted experiments reasonably well at the distinctly different beam voltage of 5 keV where the inelastic energy loss profile is concentrated in the segment. This suggests a robust simulation of the beam heating effect. However, the agreement between experiments and simulations diverge at larger temperatures as indicated by ‘!’ in the figure. The following discussion begins (Section V) with a non–dimensional analysis comparing the rates of heat transfer, precursor surface diffusion and net precursor vapor attachment using the calibration deposit length (~ 1m) as the characteristic length. The heating and attachment rates are predicted to control the precursor coverage along the deposit surface. The 3D beam heating simulation confirms the prediction (Section VI) and reveals that the heat transfer rate is extremely fast relative to precursor transfer rates, so much so, that steady–state heating conditions may be assumed even considering digital beam displacement. The constant T–profile impacts the absolute precursor concentration through the T–dependent desorption rate. In (Section VII), 3D FEBID simulations with beam heating reveal that the precursor surface diffusion rate clearly affects the deposition rate on the reduced length scale of the BIR/beam size (< 100 nm) – precursor dissociation induces a steep, local precursor gradient sustaining precursor diffusion to the BIR. Also, the elevated temperature at the BIR increases the diffusion coefficient. Simultaneously, at the BIR boundary, vapor absorption/desorption maintains the precursor reservoir to feed the precursor gradient and the absolute precursor surface concentration is dictated by the T– dependent, precursor desorption rate. These physical mechanisms are best characterized during intermittent FEBID where beam on/beam off cycling reveals precursor consumption and precursor recovery dynamics. V.

3D Nanoprinting under Continuous Electron Beam Exposure

Calibration structures (pillar + segment) are deposited using continuous electron beam exposure conditions. During continuous exposure conditions, sequential electron beam patterning occurs along adjacent, overlapping pixels with the beam tracing a single continuous path – the electron beam/deposit intersection is maintained without disruption. This mode of exposure has been used for all simulations/experiments presented thus far.


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Figure 10 (a) Virtual SEM images of single, binary and tertiary branch nanostructures. The image was acquired at 52o with respect to the substrate surface normal. The CAD characteristics included a pillar height of 400 nm,  = 20o and a segment length of 800 nm. (b) Complementary real experiments using Eo = 30 keV and ib = 32 pA. The scale bar in (a) and (b) measures 500 nm. (c)  increases as the number of segments increases on the 2nd exposure level. Image processing consisted of false coloring followed by image registration overly. (d) A 3D temperature map for solid voxels located on the surface of the deposit. The image was acquired at the end of the beam dwell period (4.64 ms) during left hand segment exposure. The temperature quickly reaches the steady–state condition shown here.


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Experiments and simulations have shown that a thermal gradient develops along the deposit length (figure 8c) causing a diminishing VGR and nanowire deflection. In an extreme example of deflection, induced by the combination of a relatively long segment (L = 800 nm) and low segment angle ( = 20o), deflection tends to   0o followed by loss of beam/deposit intersection (figure 10a-b, top image). It has been shown in figure 2 that the sample current is sensitive to this phenomenon. The following discussion will reveal that electron beam induced heating is transient for a brief time only, after digital beam displacement, momentarily perturbing a mostly quasi steady–state temperature profile along the nanowire length. Interestingly, the reservoir of surface bound precursor available on the nanowire is immediately impacted (via the precursor desorption) relative to surface precursor diffusion, which is effectively stationary in the heat transport time frame, at least on the length scale of the total deposit length.

Rapid Heat Flow during Nanoprinting 3D Nanoprinting requires electron beam exposure dwell times per pixel on the order of; 𝜏𝑑≅10 ―2 ― 10

―3

(𝑠) [7]

to construct mesh style objects as verified for a multitude of precursors including, but not limited to, MeCpPtIVMe3, Me2(AuIII)(acac), 4, 31, 38 W(CO)6,4, 5 HCo3Fe(CO)12,39 Co2(CO)8,40,41 and Si(OC2H5)4.4, 30 Interest around 3D nanomagnetic structures42 has bloomed recently1,39 in part due to the relatively high purity of as–deposited elements derived from HCo3Fe(CO)12. The (d) timescale is 3–4 orders of magnitude larger than the heat transport time scale based on the experiments and simulations reported here. As an estimate, consider that the Fourier number (Foheat) for heat transport makes it possible to estimate the characteristic time required (theat) for thermal penetration to an arbitrary depth (L); 𝐹𝑜ℎ𝑒𝑎𝑡 =

𝛼𝑇𝑡ℎ𝑒𝑎𝑡 𝐿2

[8]

The thermal diffusivity (T) dictates the rate of heat flow, in response to the development of a temperature gradient, based on several physical properties of the material. 𝛼𝑇 =

𝑘 [9] 𝑐𝑝𝜌

Relevant to the nanowire geometry, the Fourier number equals 1/2 for thermal penetration under quasi 1D thermal transport conditions and can be derived simply from the mean squared displacement L2 = 2dTtheat, by algebraic rearrangement to 1/2 = dTtheat/ L2, where (d) is the dimensionality of the problem; d = 1 for 1D transport. An estimate of the characteristic time for thermal transport then becomes; 𝑐𝑝𝜌𝐿2 𝑡ℎ𝑒𝑎𝑡 = ≅10 ―6 (𝑠) [10] 2𝑘


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assuming L = 10-6 m as a representative length for a practical calibration structure with k = 0.16 W/m/K,  = 1250 kg/m3 and cp = 700 J/kg/K. An important guideline for 3D nanoprinting is revealed; (1) In response to beam translation to a new exposure pixel during 3D nanoprinting, a quasi–steady state temperature profile is quickly achieved, relative to the total beam dwell time. Stated mathematically, this condition is met when; 𝑐𝑝𝜌𝐿2 2𝑘𝜏𝑑

≪ 1 [11]

Calibration structures recover to the equilibrium substrate temperature at a rate of MHz when the beam is turned off following deposition, or when moved to a new surface position on the deposit.

Sluggish Precursor Surface Diffusion during Nanoprinting Contrary to heat transport, the surface mass flow rate by diffusion is sluggish relative to the 3D nanoprinting timescale. Consider that an estimate of the characteristic time for surface diffusion is the mass Fourier number (Fomass); 𝐹𝑜𝑚𝑎𝑠𝑠 =

𝐷𝑡𝑚𝑎𝑠𝑠 𝐿2

[12]

where the (D) governs the surface diffusion (mass flow) rate in the presence of a precursor surface gradient along the deposit. The characteristic time for precursor surface diffusion (tmass) is 6– orders of magnitude larger than (theat); 𝐿2 𝑡𝑚𝑎𝑠𝑠 = ≅1 (𝑠) [13] 2𝐷 and 2–3 orders of magnitude larger than the 3D nanoprinting beam dwell time per pixel. Thus, a second, equally important maxim emerges upon consideration of the surface diffusion timescale; (2) Precursor surface diffusion is effectively frozen in the brief time it takes for the steady– state 3D temperature profile, associated with the beam impact at the nth pixel, to change to a new steady–state following beam translation to the (n+1)th pixel. The precursor desorption rate (1/) is measured in kHz while diffusive replenishment is sluggish, on the scale of Hz. The precursor attachment rate is also measured in kHz. Thus, the mean precursor surface residence time adjusts to the new temperature profile at the surface with negligible time for surface diffusion effectively ejecting precursor molecules relatively quickly. A third and final maxim is revealed; (3) The precursor surface concentration gradient (dC/ds) is dictated by (dT/ds) via physisorption dynamics outside the BIR, before surface diffusion has a chance to contribute.


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Unfortunately, the temperature gradient (dT/ds) along the nanowire is small in magnitude. This imposes a relatively small (dC/ds). The mass flux is driven by; 𝐽′′𝑚𝑎𝑠𝑠 = ―𝐷

𝑑𝐶 [14] 𝑑𝑠

Thus, a decrease in magnitude of dC/ds hampers mass flow along the segment to the BIR. Importantly, the impact of the electron beam has been neglected from this non–dimensional analysis. It will be shown below that beam–induced precursor dissociation introduces a relatively steep precursor concentration gradient which drives precursor flow to the BIR. This explains the diffusion dependence seen in figure 8a ‘No Diffusion’ case. Consider this example: in our previous simulations, the absence of beam heating facilitated the formation of a relatively ‘steeper’ surface coverage gradient along the segment element which counteracted rapid precursor consumption there (see ‘DER (No Heat)’, figure 8). As a result, the VGR was relatively large and produced a large segment angle. Now, this situation is revised with heating causing non–linear segment deflection that must be included in design. Fortunately, recently released software ‘3BID’4, 17 provides a capability to correct for segment deflection during nanowire growth, at least empirically. The more complex situation of simultaneous intermittent exposure is now examined with focus on the deposition of multiple segments grown from a common starting node. The deposit geometry is introduced first in the limit of fully developed segments, i.e., when beam exposures on different segments do not overlap. The analysis concludes with the case of interacting, time adjacent beam exposures. VI.

3D Nanoprinting under Intermittent Electron Beam Exposure

An intermittent electron beam exposure is carried out when it is desired to simultaneously deposit multiple elements/nanowires on a common exposure level. In this mode, time adjacent beam exposures having relatively large displacements move back and forth between pixels on different deposition elements.17 This beam translation sequence introduces a natural precursor refresh period (SI9) for un-irradiated elements on the shared exposure level. Concomitantly, surface coverage increases on unexposed elements because these elements decrease in temperature and new precursor attaches from the vapor supply. Precursor refresh at the Last Irradiated Pixel, or LIP, is particularly important. Figure 10 provides two examples where the 2nd FEBID exposure level is defined by intermittent exposure between two and three segment elements. Simulations (figure 10a) and complementary experiments (figure 10b) are presented. Closer inspection by multi–image registration and overlay (figure 10c) reveals that the  increases with the number of segments included on the 2nd exposure level. The increase in FEBID VGR with increasing segment number is understood, at least in part, with the aid of a 3D surface temperature map (figure 10d). Figure 10d shows the surface temperature of the binary segment deposit at the final moment of beam dwell (2.32 ms, SI9) on the righthand segment. The temperature of the unirradiated segment has equilibrated to a significantly lower temperature (~295.5 K) relative to the BIR. As suggested by the Foheat calculated in the previous section, the quasi–steady state temperature


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profile develops quickly ~30 s after the beam dwell begins – 98.7% of the 2.32 ms dwell period is spent under quasi steady–state irradiation! SI10. Thus, in the 3D FEBID simulation, the steady– state heat transfer is solved; ∇2𝑇 = ―

𝑞′′′𝑏 𝑘

[15]

in place of the time–dependent problem and requires recalculation under only two conditions; (1) when the beam is displaced or (2) after a fixed time period, to account for changes incurred by additional FEBID (SI11). Further validation for the steady–state condition stems from an estimate of the VGR during the brief transient phase of heat transport; the growth rate during transient heat flow yield 130nm/s×(1–0.987)×2.32x10-3s ~ 4x10-3nm demonstrating negligible FEBID during this brief period. Rapid cooling following beam displacement allows the surface precursor concentration at the LIP to increase in preparation for the next intermittent beam exposure. The FEBID rate scales with (C) and thus we arrive at the conclusion that temperature controlled, vapor phase replenishment plays at least some role in dictating the observed increase in  with the number of joined segments. Now, the refresh time by vapor impingement is calculated and compared with precursor recovery by surface diffusion to quantify the exact mechanism by which the segment VGR increases.


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Figure 11 (a) The precursor surface diffusion rate (Jdiff) to the segment tip as function of the concentration gradient span (L). A deposit tip concentration of C = 0.8 molecules/nm2 is assumed which is a typical depletion surface concentration during steady beam irradiation. Jdiff is significantly larger during the ‘beam on’ condition as compared with the negligible contribution during the surface concentration recovery in the Last Irradiation Pixel, or LIP. The average vapor phase precursor attachment rate to the surface (Jvapor) does not depend on (L) and appears as a constant in the plot. (b) The 3D precursor surface concentration map shows the concentration gradient located at the termination of the beam dwell period in the BIR and LIP. Jvapor is strongly influenced by the steady–state temperature profile along the irradiated segment due to the temperature dependence of the mean precursor surface residence time, or (T). This precursor flow feeds the surface adsorbed reservoir outside the BIR which maintains the diffusion flux required to sustain 3D FEBID.


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VII.

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Temperature influenced Diffusion–Enhanced Refresh during FEBID

Consider the precursor flow rate into the BIR by two pathways; replenishment directly from the vapor phase (Jvapor [molecules/s]) and precursor surface diffusion along the segment (Jdiff [molecules/s]). Jvapor includes precursor adsorption and desorption. These mass flow rates are provided in logarithm form as the ordinate in figure 11a. The abscissa in figure 11a is the characteristic length scale (L) over which the precursor surface concentration changes along the segment axis. Analysis is first focused on the precursor refresh rate taking place at the LIP – this mass attachment rate does not depend on L and is therefore constant in figure 11a (--). The details of the vapor replenishment calculation are summarized in SI11. At t = 0, we take the depleted surface concentration as C = 0.8 molecules/nm2 ( ~ 0.30, or 30% coverage). The color map referenced to the 3D FEBID simulation confirms this as a representative depletion value (see deep blue color in figure 11b). The depleted region at the LIP exists at t = 0 because the electron beam has just departed. SI11 shows the surface concentration of precursor in the LIP as a function of refresh time showing that the vapor attachment rate partially replenishes the depleted segment apex during the un-irradiated period of 2.32 ms. The term ‘partially’ refers to the slight depletion remaining on the un-irradiated segment apex (yellow spot at LIP, figure 11b) compared with the orange–red hue representative of equilibrium precursor coverage, e.g., on the substrate. This recovery status is also consistent with the plot shown in SI11 where the coverage (-) has not recovered to the equilibrium coverage line (--). Jdiff is now compared with Jvapor. Jdiff depends strongly on the concentration gradient oriented along the segment axis (equation 15). This concentration gradient spans significantly different lengths scales during (1) ‘beam on’ and (2) ‘beam off’ periods. The concentration gradient extends over a length scale comparable to the beam size during ‘beam on’, in the BIR, while the characteristic length increases to the segment length scale during ‘beam off’ in the LIP. Please note, the concentration change for the (Jdiff) estimate in figure 11a was taken as the difference between equilibrium coverage and a depleted state during dwell, or (1.98 – 0.8) molecules/nm2. In fact, during FEBID ‘beam on’ at the segment apex, it is the steep surface concentration gradient, induced by precursor dissociation, that activates surface diffusion to maintain FEBID – figure 8 has already demonstrated the importance of surface diffusion during FEBID. The red, vertical ‘beam on’ line in figure 11a shows that Jdiff > Jvapor at L = 10 nm, a typical BIR length scale. 3D FEBID at the BIR is summarized with the aid of the following simplified equation; 𝐽𝑑𝑖𝑓𝑓 ∝ 𝐷

𝐶𝑒[Φ,𝜏(𝑇)] ― 𝐶𝐵𝐼𝑅[𝜎𝑖𝑆𝐸] Δ𝐿[𝜎𝑖𝑆𝐸]

> 𝐽𝑣𝑎𝑝𝑜𝑟 [∆𝐿≅𝑟𝑏] [16]

where the key parameter(s) which strongly influence each term is/are provided in square brackets. (Ce) is the precursor surface concentration at the edge of the BIR. The SE current density (iSE) simultaneously drives the decrease in both (CBIR) and (L) needed to maintain large dC/ds promoting 3D FEBID. The rich physics of the 3D FEBID problem emerges in the (Ce) term where


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the beam dwell time, vapor replenishment, and diffusion time scales are roughly equal and thus simultaneously control (Ce). (Ce) must be large to maximize the numerator in equation 16. However, (Ce) is controlled by opposing factors, the incoming vapor flux acts to increase the concentration at the BIR boundary but is resisted by the lower () caused by heat escaping the BIR. A 3D FEBID simulation reveals that () strongly influences (Ce) during intermittent exposure of multiple segments. This is revealed in figure 12 where the ( map is shown during multi–segment nucleation for the tertiary branch deposit. ( is shown at the final moment of deposition in the indicated BIR. ( varies at each branch apex and ( increases with increasing of fresh time (r). Both trends confirm the importance of the vapor phase attachment rate as a governing mechanism during intermittent FEBID to refresh (Ce) at the BIR edge. In fact, this mechanism overwhelms the influence of temperature on segment angle during intermittent exposure (SI12).

Figure 12 Precursor surface coverage on the tertiary branch deposit during segment nucleation as viewed from several imaging angles (a–c) at the same instant in time. The ball and stick model provided by the 3BID CAD program is shown superimposed for clarity. The order of exposure introduces a natural refresh time (r) for each segment nuclei and these values are provided in (b). The precursor coverage replenishment during beam off periods is driven by vapor phase replenishment flux. Notice in (c) that the precursor surface coverage is different (compare the red ovals) on the two unirradiated segments because the implicit refresh times, defined inherently by intermittent exposure, are different.

Conclusions Precision in 3D nanoprinting using focused electron beam induced deposition (FEBID) is dictated by how well a deposited structure replicates the original digital design. Currently, empirical corrections are required to compensate for nanowire distortion/bending during deposition which limits the nanoscale precision. Here, we have identified beam induced heating as the mechanism that causes these artifacts. Experiments, mathematical models and simulations corroborate this finding. Multidimensional models and simulations of heat flow predicted that a 10 K temperature increase at the beam impact region (BIR) reduces the precursor surface residence time by more than 50%. This produces a steady decrease of the nanowire vertical growth rate over process time. An


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observed increase in the temperature–dependent surface diffusion rate is not enough to compensate for the overwhelming loss of precursor by enhanced surface desorption causing the steady decrease in the vertical growth rate. Linear nanowire deposition requires a steady growth rate so, unfortunately, nanowire bending is observed. Specifically, it was found that the temperature at the BIR gradually increases as the nanowire lengthens due to a combination of thermal resistance and Joule heating, the latter produced by the spatial convolution of the electron scattering beam interaction volume with the deposit. A thermal gradient rapidly develops along the nanowire axis following beam displacement to a new exposure pixel and quickly reaches a new steady state (s). The total beam exposure time per pixel is on the (ms) timescale so steady– state heating prevails during 3D FEBID. FEBID is sustained by precursor surface diffusion from a precursor reservoir adjacent to the BIR. A steep concentration gradient develops as the nanoscale electron beam dissociates precursor in the BIR leading to monolayer growth on the scale of (ms). However, the precursor reservoir adjacent to the BIR is maintained by physisorption, also on the (ms) timescale, and the steady decrease in precursor surface residence time caused by beam heating reduces the reservoir precursor concentration over time causing the observed vertical growth rate reduction. Intermittent beam exposure, a simultaneous exposure of multiple nanowires, introduces a natural precursor refresh time at the last irradiated pixel, which is replenished directly from the vapor phase and not surface diffusion – in the absence of a beam induced precursor concentration gradient during beam off periods, surface diffusion is sluggish with a characteristic time of seconds. In light of the proposed 3D FEBID growth mechanism, a compensation tactic is in development to prevent the heat related degradation of 3D mesh objects. The compensation tactic is being derived directly from the governing surface mass balance at the BIR interface (see equation 16) and will replace an empirical strategy reported in.17 In the meantime, those pursuing the high– quality reproduction of mesh object nanostructure designs for functional mechanical, optoelectronic or magnetic nanomaterials can engineer solutions via trial and error using beam speed modulation. Research work is currently underway to quantify heating effects in solid object models in order to extend the range of 3D objects that may be accurately printed using FEBID, beyond the current mesh object model. Lastly, the limits of the 3D FEBID simulation are presented. Certain precursors exhibit an autocatalytic decomposition during FEBID.43 The 3D FEBID simulation reported here is not applicable to this case. The precision of the 3D FEBID simulation temperature predictions are probably most limited by the assumption of constant materials properties, i.e., thermal conductivity, heat capacity and density, for the platinum–carbon composite deposit, which are known to vary in real deposits.6,44 Further, the partial fragmentation of the MeCpPtIVMe3 precursor molecule28,45 is ignored in favor of a mean precursor dissociation cross–section. Methods/Experimental Experiments


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Experiments were conducted in a NOVA 600 (FEI Company, The Netherlands) dual beam instrument equipped with a gas injection system (GIS). A platinum carbon composite was deposited from the precursor MeCpPtIVMe3, injected via a nozzle at 52° relative to a silicon substrate. The base of the tilted nozzle was located at a vertical distance of 100 μm above the substrate. The GIS nozzle position was located at 25 µm in the x-direction and 28 µm in the ydirection relative to the beam center. The precursor pressure at the substrate surface was simulated for the GIS nozzle position. The simulated pressure was P = 0.60 mTorr with a precursor impingement flux of  = 1.81x103 /nm2/s. The sticking probability () is assumed to be equal to 1 so the impingement flux equals the attachment flux. The equilibrium precursor surface coverage (eq) was calculated to be  ~ 0.7 for a substrate temperature of 294 K and a surface adsorption site density of sp = 2.8 /nm2. 3D FEBID simulations predicted a reduction in the steady–state precursor coverage to  ~ 0.3 in the BIR during experiments. Please note that this value varies based on the deposit geometry. More details regarding precursor delivery can be found in3, 46 The Pt-based precursor was heated to 45°C for at least 30 min prior to any deposition. Beam focusing was carefully done at high magnification (300kX) by depositing small pillars near the region of interest until pillar diameters below 50 nm were achieved in top view electron imaging. Prior to any deposition, the GIS valve was opened for at least 1 minute to allow equilibrium precursor coverage to establish on the substrate surface. Electron exposure of the region of interest was reduced to a minimum to prevent contamination. The dual beam base pressure was 1 × 10−6 mbar, and the background pressure increased to 2 × 10−5 mbar after opening the GIS valve. Temperature–controlled FEBID experiments were performed on the metal paths of calibrated MEMS heater chips (Wildfire S3, DENSsolutions, Delft, The Netherlands) using the software Digiheater (v.3.2,DENSsolutions). A FEBID CAD program (3BID)17 was used to generate an exposure file for each experiment in the form of a list of exposure coordinates. Each exposure coordinate consists of (1) an x and (2) y beam position plus (3) a dwell time (d) per pixel. The displacement between exposure points, called the ‘pixel point pitch’, or , was constant for all exposures at 1 nm. The patterning velocity was set using the dwell time via vb = /d. First, 3BID4, 17 CAD calibration files were created for FEBID an exposure setting of 30 keV and 32 pA. Calibration is required at each distinct voltage setting and is explained thoroughly in.4 The acceleration voltage controls the electron–solid scattering convolution which drastically impacts FEBID growth rate, segment element cross–section and unwanted deposition due to stray electron scattering, a proximity effect. Therefore, calibration is required at each distinct voltage setting. The primary electron beam probe currents (ib) were measured using a faraday cup. The in situ substrate currents were collected during FEBID using a Keithley Model 6485 Picoammeter that was externally connected to the microscope stage. The data acquisition time of the picoammeter was ~50 ms. In most cases, subsequent electron imaging for characterizing deposition results was conducted at 7.5 keV, 0.11 nA and a 52° stage tilt position after a waiting period of more than 30 min to evacuate the chamber of residual precursor molecules which minimizes unwanted FEBID during imaging.


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The incident beam current (ib) was measured using a Faraday cap (Table I). Multiple measurements were collected to determine both the average beam current and the variation as 32.0 ± 0.3 pA. The variation of the current measurement captures the fluctuations in both in emission current and the detection electronics. This variation served as the reference variation for comparison with sample current collected during 3D FEBID. The mean and variation of sample current (is) was also measured for the underlying Si wafer substrate, prior to FEBID as 25.5 ± 0.4 pA. The backscattered electron yield from the Si substrate was derived from simulations ( = 0.17±0.05). Simulations Steady–State 2D Numerical Simulation of the Temperature Profile The prediction of the BIR temperature suggested by the 1D model was confirmed using finite element modelling software (FlexPDE®). A 2D simulation of the steady–state temperature profile in the coordinate (r,z); 𝑘 ∂ ∂𝑇 ∂2𝑇 𝑟 + 𝑘 2 = 0 [17] 𝑟 ∂𝑟 ∂𝑟 ∂𝑧

( )

yielded a solution (figure 4a, □) which shows very good agreement between the 1D temperature prediction at  = 10o (□) and 50o (□). Beam heating was introduced into the 2D problem as a flux boundary condition at the BIR and therefore does not appear as a source term in equation 17. The remaining boundary conditions and treatment of the calibration structure cross–sectional area applied to the 1D model were duplicated for the 2D numerical simulation. 3D FEBID Simulation with Beam Heating The 3D heat diffusion equation; 𝑐𝑝𝜌

∂𝑇 = 𝑘∇2𝑇 + 𝑞′′′𝑏 [18] ∂𝑡

was solved in parallel with the 3D FEBID simulation; (cp) is the heat capacity of the deposit, () is the density of the deposit, (k) is the thermal conductivity and (q’’’b) is the Joule heating induced per unit volume. cp and  are estimated from the volume fractions of the two phases constituting the deposit composite. The values for cp and  were derived from47 assuming amorphous carbon using k = 0.16 W/m/K. The composite consists of Pt nanoparticles embedded in a C–based continuous phase assuming PtC5. The temperature–dependence of (k) is not considered due to a lack of information regarding this parameter. Further, (k) was assumed to be dominated by the amorphous carbon phase and was restricted to the range of 0.1–1, reported in, 35, 36 when searching for simulations that reproduced experiments. In summary, it was found that k = 0.16 W/m/K, Ea = 0.62 eV and fU = 0.86 reproduced a broad range of experiments when (k), (Ea) and (fU) were floating variables used to reproduce experimental results. Temperature is coupled into the transport equation governing precursor surface coverage through;


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∂𝐶 𝛿Φ 𝐶 (𝑠𝑝 ― 𝐶) ― = 𝐷∇2𝐶 + ∇𝐷∇𝐶 + ― 𝜎𝐶𝑖𝑆𝐸 [19] ∂𝑡 𝑠𝑝 𝜏(𝑇) where (C) is the surface concentration of precursor, () is the precursor sticking probability, () is the precursor vapor phase impingement flux, (sp) is the monolayer precursor surface concentration, () is mean electron impact precursor dissociation cross–section and (iSE) is the secondary electron current density 3D profile. The temperature dependence of D(T) produces an associated variation in space.

Table 1 Key simulation/experimental parameters.

Table 1 presents key simulation variables. Finally, the volumetric deposition rate (dVd/dt) of PtC5 is; ∂𝑉𝑑 ∂𝑡

=

Ω𝑑 𝜎𝐶𝑖𝑆𝐸 [20] 𝑠𝑑

The variables T, C, iSE, qe, , D and Vd are all dependent on x, y and z. (d) is the molecular volume of PtC5. Discretization of the simulation domain is required to solve equations 18–20. However, q’’’b and iSE are derived using a Monte Carlo simulation of elastic and inelastic electron scattering which treats the electron–solid interaction using a trajectory of absolute coordinates.5,48 To discretize energy deposited into the solid, each primary electron trajectory pathlength is sliced into increments by the faces defining each voxel to exactly allocate EEL to each voxel. The inelastic energy loss is divided amongst Joule heating and SE production; the former induces volumetric heating while the latter induces deposition (see again SI5).


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A thermal insulating boundary condition is applied to the surface of the deposit considering that convection heat transfer via the 0.60 mTorr MeCpPtIVMe3 vapor phase is negligible. Radiation heat transfer was also ignored due to the relatively small change in temperature induced by FEBID relative to the RT surroundings. Deposit voxels in contact with the hs = 5 nm SiO2 layer on the substrate surface are subjected to a conduction flux boundary condition;

|

𝑑𝑇 ― 𝑘𝑠 𝑑𝑠

𝑆𝑖𝑂2

|

𝑑𝑇 = ―𝑘 𝑑𝑠

[21] 𝑃𝑡𝐶5

where (ks) is the thermal conductivity of SiO2. The Si substrate, located below the SiO2 5nm thin film, is assumed to have a constant temperature of 294 K based on measurements of the temperature acquired during experiments. Acknowledgements HP, RW, JS thank Prof. Ferdinand Hofer for scientific discussions and for financial support concerning instrumentation. The financial support by the Austrian Federal Ministry of Science, Research and Economy and the National Foundation for Research, Technology and Development is gratefully acknowledged. Financial support is also received from the FFG Austria in the frame of the “Beyond Europe” initiative (Project AIM, Nr. 11056459). JDF, PDR, HP, RW, EM acknowledge that the simulation was developed and executed, as well as select experiments, at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility. Supporting Information Available: This material is available free of charge via the Internet at http://pubs.acs.org. As the presented work has been done in very much detail, we provide supplements on 1) Sample current equation for 3D FEBID; 2) Mathematical model of the area function used in the 1D heating model; 3) Detailed description of the 1D beam heating model; 4) relevant heat transfer modes for 3D FEBID; 5) Description of Joule heating by inelastic electron energy loss; 6) Transformation between the pathlength coordinate (s) and height coordinate (z); 7) Interpretation the y–axis (T/s) used in figure 5, 8) A description of the beam heating mechanism as a function of segment angle, 9) Implicit refresh times introduced by the beam pattern sequence chosen during multi– nanowire/segment growth, 10) Rationalization of the use of steady–state heat transfer in the 3D FEBID simulation, 11) Precursor surface concentration as a function of the net precursor attachment refresh time and 12) The role of vapor phase precursor refresh during simultaneous segment exposure. Table of Contents Graphic


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