Direct-Write Fabrication of Cellulose Nano-Structures via Focused Electron Beam Induced Nanosynthesis

In many areas of science and technology, patterned films and surfaces play a key role in engineering and development of advanced materials. Here, we introduce a new generic technique for the fabrication of polysaccharide nano-structures via focused electron beam induced conversion (FEBIC). For the proof of principle, organosoluble trimethylsilyl-cellulose (TMSC) thin films have been deposited by spin coating on SiO2 / Si and exposed to a nano-sized electron beam. It turns out that in the exposed areas an electron induced desilylation reaction takes place converting soluble TMSC to rather insoluble cellulose. After removal of the unexposed TMSC areas, structured cellulose patterns remain on the surface with FWHM line widths down to 70 nm. Systematic FEBIC parameter sweeps reveal a generally electron dose dependent behavior with three working regimes: incomplete conversion, ideal doses and over exposure. Direct (FT-IR) and indirect chemical analyses (enzymatic degradation) confirmed the cellulosic character of ideally converted areas. These investigations are complemented by a theoretical model which suggests a two-step reaction process by means of TMSC → cellulose and cellulose → non-cellulose material conversion in excellent agreement with experimental data. The extracted, individual reaction rates allowed the derivation of design rules for FEBIC parameters towards highest conversion efficiencies and highest lateral resolution.


Preliminary experiments (H2O dependence)
Geier and coworkers 1 demonstrated that the electrolysis of H2O is a key requirement for purification of carbon rich metal precipitates initially fabricated via Focused Electron Beam Induced Depostion (FEBID).
We therefore conducted preliminary experiments using QUANTA 200 ESEM (FEI, The Netherlands) in high-vacuum (2.10 -5 mbar chamber pressure) and low-vacuum mode with 10 Pa H2O partial pressure at room temperature. Prior to this exposure, we fabricated 100 nm thick TMSC films on SiO2 / Si (5 nm / bulk) substrates via spin-casting and immediately transferred them to the electron microscope. Results obtained by light microscopy are shown in Figure S 1. The left parts gives the patterned square regions after e-beam exposure while the right parts show same areas are 24h incubation to the highly specific enzyme cocktail Hypochrea jeronica (parental strain: RUT-C30). As evident, low-vacuum H2O conditions led to massive proximity effects which prevent high-resolution structuring as a consequence of the well-known skirt scattering effects in ESEMs. For high-vacuum conditions, however, no such proximity effects have been observed while the enzyme cocktail entirely removed the patterned areas. Based on the high specificity of the applied enzyme cocktail to pure cellulose and the fact that surrounding, pristine TMSC areas were entirely unaffected, we hypothesized that e-beam induced conversion is a pathway for defined highresolution cellulose structuring. Based on these preliminary experiments, we investigated the process in more detail which represents the main part of this manuscript. (left part) or LV mode with 10 Pa H2O partial pressure (right part). Acceleration voltage was 10 kV with a measured beam current of 778 pA, a frame size of 5 x 5 µm 2 at 3584 x 3094 pixels (which corresponds to a point pitch of approximately 1.6 nm) and a dwell time of 100 ns per pixel. In HV mode only the 1 frame pattern (1F, white dotted rectangle) shows a different layer height after cellulase treatment while in LV mode a change is seen up to 4 frames (4F, white dotted rectangles). The reason is simply, that skirt effects (schematic right site) lead to significant spreading of the particle beam which further leads also to degradation effects (see orange arrows).

FEBIC Patterning-parameters and -layout
In the following the applied structuring layout is specified in detail. For all experiments 100 nm TMSC films have been used which were spin-cast on SiO2 / Si (5 nm / bulk) substrates. For each pair of UBeam and IBeam (12 combinations in total, see Table S1), a systematic variation of dwell-time (DT) and frame-numbers (multiplicator) have been applied (see Figure S2). All pads were 1x1 µm 2 in size with 1 µm distance in between. The point-pitch (PP) was defined by a 50% beam overlap accounting for the fact that beam profiles change with voltage and current. This simplifies the dose calculation for further modeling.

S5
To clarify the experimental strategy used throughout this study, a work-flow chart can be found in Figure S3. As evident, the procedure starts with the (1) preparation of the TMSC films (as specified in the methods section of the main manuscript) followed by (2) the e-beam structuring (FEBIC) and (3) AFM height analysis after patterning (as prepared), then subjected to (4) the enzyme incubation with cellulases which removes transferred cellulose (conditions are again specified in the methods section of the main manuscript) and (5) finally analyzed via AFM height analysis after enzyme incubation. By using the calculation (hbe-hae)/hbe we are able to specify the non-degradable material in a relative fashion. The process is finished with a fitting routine as depicted in supplement 4.

Calculation of the electron dose
The applied electron dose (D) is calculated according to equation (1) and (2). Starting from the universal equation 1 the dose D can be re-written as shown in equation (2). In this special case we can substitute the current I with the beam current (IBeam) and the area A with the size of the beam spot (ABeam). The circular beam spot was treated as a squared profile (ABeam) with side length equal FWHM of the Gaussian beam to simplify the calculations without losing accuracy. As the beam overlap was constantly set to 50%, each quadrant of these squared areas (ABeam) is additionally irradiated during patterning by the surrounding 8 nearest neighboring patterning pixels. This finally leads to a factor of 4 for the total dose, explaining the multiplication term in equation (2). For the time t one can now set the pixel dwell time DT multiplied by the number of passes P. As alternative we may take the area spanned by the POP which is one fourth of the beam area. Note, we are aware that edge patterning points would require a different treatment with different multiplication factors. However, given the fact that a pattern with total area of 4 µm 2 yields between 5000 and 20000 points depending on the beam diameter, we treat edge patterning points as negligible.
The interaction of electrons with the TMSC and further its regenerated products may be described by chemical formalisms as depicted in equation (3). We have demonstrated that cellulose is an intermediate product by FTIR and indirect enzymatic degradation. However, we also observed the generation of nondegradable material with ongoing dwell-times (DTs) which most likely results from electron induced damage of the cellulose backbone. It is so far not clear, what products are generated precisely, but is feasible to assume that the main portion is carbon. We therefore may write the chemical reaction as follows: Here, − is representative for the accelerated electrons which contribute to such reactions. At first, it is feasible to neglect k1-and k2-as these reactions are rather unlikely. From here on k1+ and k2+ will be denoted as k1 and k2, respectively. Each partial reaction, first to cellulose and from cellulose to carbonized products follows by principle second order kinetics. Now, assuming a constant flow of electrons which is the case, at least for the dwell-time, we obtain a situation which is well known as pseudo first order chemical reactions (see equation (4) with B(t) = constant). In fact, our analysis to unravel the regeneration from TMSC to cellulose and further to carbonized and non-degradable material represents the corresponding reaction kinetics. By finding appropriate equations for this behavior, we may be able to fit the functions and derive important parameters in addition to the optimal dose. Further it would prove our hypothesis derived in equation (3). The following formalism is a concise summary of the theoretical background behind the used model. In the following, for simplicity variables summarized in Table S 2 will be used.  For the concentration of TMSC over time equation (4) is immanent: Reorganization and integration yields: As experimental curves denote the non-degradable material we must have a look at C(t) which is: If, we use the expression for C(t) as depicted in equation (6), we may write: This is an ordinary linear differential equation of γ(t) and thus of the concentration of non-degradable material. A solution to equation (7) may easily be found by using a variation of parameters ansatz. Here the homogenous part of the equation may be easily derived in similarity to equation (4).
A variation of constant ansatz now is: Straightforward differentiation and substitution to equation (7) yields:

S9
With homogenous and particular solution we can now find a general solution to equation (7): To solve for Cp+h we now have to find a boundary condition of equation (7). Needless to say, the equation must satisfy or The final solution to this problem is therefore as follows: By substitution of the general terms in equation (13) we then get the fitting function with parameters a1, a2,b1 and b2.
Furthermore a2 may be expressed by a1, b1 and b2, which yields the final fitting function: Data obtained by fitting equation (15) to experimental evaluated data is shown in Table 9 and Figure Figure S1. For the measurement height data before and after enzyme treatment is set into relation. Curves are fitted according to equation (14). S13 Figure S 6: Non-degradable material for 5 keV electrons evaluated from patterns as depicted in Figure S1. For the measurement height data before and after enzyme treatment is set into relation. Curves are fitted according to equation (14). S14 Figure S 7: Non-degradable material for 10 keV electrons evaluated from patterns as depicted in Figure S1. For the measurement height data before and after enzyme treatment is set into relation. Curves are fitted according to equation (14).

Figure S 5: Non-degradable material for 2 keV electrons evaluated from patterns as depicted in
A more detailed investigation concerning broadening effects reveals two different influences which, however, are essential to achieve highest lateral resolution. For lowest primary electron energies of 2 keV a structure broadening effect in the range of 20 -30 nm was found for ideal doses as representatively shown by AFM 3D height image in Figure S 8 (right image). For higher primary energies of 5 keV and 10 keV a stronger proximity broadening was found as evident from the AFM 3D height images at the center and at the right, respectively. According simulations concerning the BSE radius of the full TMSC / SiO2 / Si stack (100 nm / 5 nm / bulk) reveal histograms as representatively shown bottom right in Figure   To achieve successful application of FEBIC structuring on TMSC films, film thickness has to be considered. As shown in Figure 4 for a 100 nm thick film, energy distribution as an indicator for electron penetration depth is strongly shifted into the layer and substrate with increasing primary beam energy. In the case of thicker films, this has to be considered carefully as choosing the primary beam energy to low may result in incomplete curing due to insufficient penetration depth. We therefore applied additional simulations using the Monte Carlo method and the CASINO package (CASINO 2.48; Build 2.4.8.1).
Simulations were performed on 100, 250,500,750 and 1000 nm thick films with a 3 nm layer of SiO2 and an underlying Si Substrate. In order to give a guide for scientists according primary beam energy and film height we have chosen the following strategy: Instead of providing an optimal beam energy we decided to provide a minimal acceleration voltage based on the CASINO simulations. In detail, optimal primary beam energies are not clearly definable as special applications may require different beam energies. It is for instance well known that at very high primary beam energies, proximity effects may be reduced while the regeneration time may be strongly increased due to reduced secondary electron cross section. On the other hand lower beam energies may provide a faster regeneration time. However, there is a limit at lower beam energies when electrons do not fully penetrate the film. Therefore minimal beam energies where chosen to fulfil the following requirement: The minimal beam energy in Table S 5 is chosen when the maximum penetration depth is 30 % deeper as the TMSC film thickness. For instance 1000 nm would require an approximate penetration depth of 1333 nm or 333nm into the SiO2/Si substrate. It is, however, recommended to use higher beam energies as low beam energies show a stronger electron concentration gradient throughout the film.

FEBIC Structures
FEBIC structures may simply be generated by black and white bitmaps. Bitmaps are loaded into in-house written software (SIL-engine 3 ) which generates the corresponding stream files. Stream files are loaded into the patterning engine of a FIB Nova 200 (FEI, The Netherlands) and patterned into the film.