Nanotechnology/EBID

=Electron Beam Induced Deposition (EBID or EBD)=

EBID Background
It was apparent with the first electron microscopes in the 50's, that the presence of an electron beam slowly coated the sample with a carbonaceous substance.

Even earlier, it was observed that electron radiation decomposed organic vapors present in the vacuum chamber, such as oil vapors unavoidable in diffusion pumped vacuum systems or outgassing from the sample itself.

When the background gas is decomposed by irradiation through various ionization and dissociation processes, the gas turns partly into volatile compounds re-emitted into the chamber and partly into solid amorphous carbon. The material properties range from diamond-like-carbon (DLC) to polymers depending on the exact deposition conditions.

The reactions taking place during EBD are not well characterized. Both ionization and dissociation are expected to contribute. The cross-section for both dissociation and ionization are peaked at low electron energies (<50 eV), indicating that secondary electrons are likely to be the main cause of deposition rather than the primary electrons (PE).

By focusing the PE beam in a fixed spot, a thin needle-shaped deposit will grow up towards the electron beam. The tip width can be considerably wider than the PE beam diameter and typically of the order 100 nm. The width is determined by the scattering of the PE in the tip structure which in turn also creates SE escaping through the tip apex and sidewalls causing a wider deposit.

With many potential applications in micro- and nanotechnology, the EBD technique has received increasing attention since the 80's as a method for creating submicron structures. Comparing EBD to electron beam lithography (EBL), the EBD process must be considered "slow" while EBL is "fast" since the required irradiation dose is many orders of magnitude smaller for EBL.

The use of EBD in commercial production of nanostructures is today limited to "supertips" for AFM cantilevers with extreme aspect ratios that cannot readily be achieved by other methods.

For research purposes, where high throughput is not a requirement, the technique appears convenient in several applications. Apart from depositing structures, it has also been used to solder nanocomponents. Both single and multiwalled carbon nanotubes (SWNT and MWNT) have been soldered to AFM cantilevers for stress-strain measurements and to micromechanical actuators for electrical and mechanical tests

Metal deposition by EBID
A large fraction of the EBD publications have been focussing on the use of metal containing precursor gasses. Koops et al. and Matsui et al. pioneered the extensive use of metal containing source gasses to make deposits with high metal contents. They also began scanning the beam in patterns to make three-dimensional structures. Complex three-dimensional structures can be made by EBD with both carbonaceous and metal-containing EBD. Another intriguing possibility is to use EBD to make catalyst particles for subsequent growth of nanowires and tubes.

Compared to the planar and resist-based EBL, the EBD method is slow and difficult to scale to large productions, but on the other hand offers the possibility to create elaborate three-dimensional structures, which cannot readily be made by EBL. The EBD method appears to be a versatile tool capable of constructing nanodevies, contacting nanostructrues to create composite electronic nanostructures, and soldering nanostructures such as carbon nanotubes to microelectrodes.

For electronic applications one would like to achieve as high a conductivity as possible of the deposited material. Metal-containing EBD materials usually contain metallic nanocrystals in an amorphous carbon matrix with a conductance considerably lower than that of the pure metal. The metal content and conductivity of the EBD material can be increased to approach that of bulk metals by several methods:

1: Heating the substrate has been shown to increase the metal content of the deposit. Koops et al. have observed an increase from 40 wt. % at room temperature to 80 wt.% at 100°C. Others, for example Botman et al. have shown the link between deposit composition and conductivity as a function of post-treatment in heated gases.

2: Using a carbon free precursor gas, such as $$PF_{3}AuCl$$, Hoffman et al. made gold deposits with a resistivity of 22 µΩcm which is only 10 times the bulk value of Gold.

3: Introducing an additional gas such as water vapor while using an environmental scanning electron microscope (ESEM). It is even possible to create desposits with a solid gold core under controlled deposition conditions.

=Resources= (FEBIP)]
 * Review paper: Focused, Nanoscale Electron-Beam-Induced Deposition and Etching by Randolph et al.
 * [http://www.febip.info/ Focused Electron Beam Induced Processes

=A Simple Model of EBD=

To accurately model the EBD process, one has to resort to Monte Carlo simulations that can incorporate the different scattering effects taking place during the process. Extensive work has been done on models for the deposition of amorphous carbon tips. Generally there is very little available knowledge on:


 * The radiation induced chemistry of the metal containing precursor gas. A wealth of reactions are possible, but limited data is available for the conditions and substances used for EBD.


 * The chemical content of the produced amorphous carbon in the deposit.


 * The current density in the electron beam is rarely well characterized.

Not knowing the chemical details of the deposition process, the exact product of the deposition, or the electron beam, a simple analytical model will also provide insight to the essential parameters. A simple model is reviewed below to provide an understanding of the basic requirements and limitations for the EBD process.

The Rate Equation Model
Electron beam deposition of planar layers on surfaces can be reasonably described by a simple rate equation model.

The model shows the fundamental limitations for growth rate and its dependence on beam current and precursor gas flow. The model calculations and most experiments in this thesis, are based on the precursor gas dimethyl gold acetylacetonate, here abbreviated to DGAA. The vapor pressure of the precursor gas determines the flux of precursor molecules to the surface. The flux rate of molecules F [m²s¹] of an ideal gas at rest is


 * $$F=\frac{P}{\sqrt{2\pi mk_{B}T}}$$

with pressure P, atomic weight m, Boltzmann's constant $$k_{B}$$ and temperature T. For DGAA which has a vapor pressure of 1.3 Pa at 25 °C, this gives a flux rate $$F=10^{18} cm^{2}s^{-1}$$

The cross-sections for electron beam induced ionization and dissociation of the precursor gas to form the deposits are generally not known. Cross-sections are usually of the order Å² and peak at low energies, corresponding the low energy of the secondary electrons which are probably the main cause of the deposition.



The adsorption of molecules on the target surface and highest density of SE near the surface make it reasonable to assume that the deposition rate dN_{dep}/dt depends on the surface density of adsorbed precursor molecules N_{pre}, the beam current density J, and the effective cross section s_0 as


 * $$\frac{dN_{dep}}{dt}=N_{pre}\sigma_0 \frac{J}{q_{e}}$$

The surface density $$N_{pre}$$ of the adsorbed precursor molecules in Eq. is the source for the deposited material and depends on both the deposition, ad- and desorption processes as sketched in the figure.

With maximum surface density $$N_0$$ (e.g. one monolayer, since generally more than one monolayer cannot be expected unless the target is cooled compared to the source, to give condensation of the source gas. Then adsorption probability a and lifetime t (s), a rate equation can be written for the precursor surface density as


 * $$\frac{dN_{dep}}{dt} = aF(1-(N_{pre}/N_0))-\sigma_0 JN_{pre}/t-N_{pre}/q_{e}$$

The steady state adsorbate density, $$N_{pre}$$, is then


 * $$N_{pre}=\frac{aF}{aF/N_0+1/\tau+\sigma_0J/q_{e}}$$

If each deposition event on average results in a cubic unit cell of deposited material with volume V, the vertical growth rate R [nm/s] is


 * $$R = N_{pre}V\sigma_0J/q_{e}$$
 * $$= V\frac{aF}{q_{e}\frac{\tau aF/N_0+1}{\sigma_0Jt}+1}$$

The dependence on precursor flux falls into two cases:


 * $$\tau aF>N_0$$ when a monolayer is always present and increasing the flux rate F has little effect on the growth rate R, since the surface is saturated


 * $$\tau aF<N_0$$ when less than a monolayer is present, and increasing F will increase the growth rate R.

Increasing the electron beam current will in this model always increase the deposition rate. The rate increases relatively linearly with the electron flux, until it begins to saturate when the source gas flux becomes the limiting factor for the growth rate.

Scheuer et al. have measured the EBD deposition cross section of $$Ru_{3}(CO)_12$$ to be of the order $$\sigma_0$$ =0.2 Å² and $$\tau=1$$ s. Using these values, a rough estimate of the growth rate can be calculated. For the estimate, we assume a monolayer is present $$(\tau aF=N_0)$$; a sticking efficiency of a=100%; the vapor pressure flux of DGAA; an electron beam diameter of 20 nm; a total beam current of 0.2 nA; and finally that the unit cell volume V for deposition is that of gold. With this set of values, the deposition rate becomes R= 100 nm/s.

The used values make $$\sigma_0 J/q_{e}>>\tau aF/N_0$$ so the deposition is not limited by the electron beam current but by the gas flux which would have to be 10 times higher to reach saturation. The beam radius will have to be increased to r= 0.5 µm to reach the electron flux limited region and this radius is much larger than the observed resolution in most experiments. Its is important to secure as high as possible flux of precursor gas in the experiments, since this is the main limiting factor in the model whereas the focus of the electron beam is expected to be less important due to the high current density.

Limitations to the model
The rate model is suited for describing deposition of planar layers, but for the case of deposition of tip structures in a real system, several other effects influence the deposition rate:

Scattering of primary electrons in the deposited structure. BSE and SE are emitted through the sidewalls and apex of the structure in a non-uniform way, and the PE/BSE scattering make SE generation take place in a larger region than the PE beam radius, which considerably limits the minimal radius for tip structures.

The figure above illustrate these effects. Simulations are needed to make proper estimates of the influence of scattering, but qualitatively it should cause a lower vertical growth rate as less electrons must be expected to emerge through the upper surface of the structure.

The PE beam is not uniform as considered in the model. In an ESEM, a Gaussian distribution of the PE beam can be expected, and the scattering of the electron beam in the environmental gas creates an low current density "electron skirt" around the PE beam. This should be considered both for the possible contamination in the larger region irradiated with low current density, but also for reducing the current in the primary beam and thus the growth rate.

It was assumed that the source supply precursor gas with the vapor pressure gas flux rate. The rate could be considerably lower if the source material does not have enough surface area to sustain the gas flow or the distance to the source is too large. The fact that many organometallic compounds decompose in contact with water in the case of EEBD could also reduce the source gas flow.

Not all irradiation induced events will result in deposition of material. Substantial amounts of material could be volatile or negatively ionized and carried away, especially in an the ESEM environment. Electron attachment is also taking place in the ESEM and is known to influence the detection of secondary electrons. This could reduce the supply of precursor gas and hence the deposition rate.

Surface diffusion of the precursor gas will influence the supply rate. When depositing in only a small area, surface diffusion of adsorbed molecules from the surrounding area can considerably increase the supply of precursor molecules. This is usually the explanation given why many EBD experiments observe that the tip deposition is faster in the beginning; for then to decrease to a steady state growth rate, when a tip structure is formed which limits the supply by surface diffusion. This could increase the rate at the very beginning of the deposition.

The predicted vertical growth rate from the model must be an upper estimate on the achievable rate, since most unaccounted effects will work to reduce the steady state growth rate.

Summary
Little data is available on the precursor gasses for EBD. A simple rate equation model gives an estimated deposition vertical growth rate of 100 nm/s for the typical precursor gasses. This estimated growth rate is expected to be an upper limit. Especially the flow rate of precursor gas should be as high as possible in the experiment since this is the limiting factor for the deposition rate.

=Environmental Electron Beam Deposition (EEBD)=



The ESEM makes it possible to use various gasses in the sample chamber of the microscope since there are narrow apertures between the sample chamber and the gun column, and a region in between that is connected to a differential pumping system. Pressures up to about 10 Torr are normally possible in the sample chamber.

The standard Everly-Thornhart SE detector would not work under such conditions since it would create a discharge in the low pressure gas. Instead a "gaseous secondary electron detector (GSD)" is used, as shown in the figure below. The GSD measures the current of a weak cascade discharge in the gas, which is seeded by the emission of electrons from the sample.



In the ESEM one can work with, for instance, water vapour or argon as the environmental gas, and is is possible to have liquid samples in the chamber if the sample stage is cooled sufficiently to condense water.

Without precursor gas present in the chamber, the EBD deposition rate is normally negligible in the high vacuum mode as well as in the gas mode of the ESEM.

In environmental electron beam deposition (EEBD), the deposited tips have a shell structure and consist of different material layers each characterized by a certain range of gold/carbon content ratio. Above a certain threshold of water vapor pressure and a certain threshold of electron beam current, the deposited tips contain a solid polycrystalline gold core.

=Acknowledgement= This page was started based on the material in:
 * Kristian Mølhave's PhD thesis chapter 4 and accompanying papers and.
 * Please add material here if you add to the page content!

=References=

See also notes on editing this book about how to add references Nanotechnology/About.