Field emission (FE) electron sources are made close to atomic-scale to reach the highest spatial resolution as well as stable emission for electron microscopy, electron beam inspection and lithography. At present, no single agreed method exists of using FE current-voltage data to extract the apparent emission area, which is needed for predicting some beam properties. The 1956 theory of Murphy and Good (MG) is better physics than the 1920s theory of Fowler and Nordheim (FN) and colleagues, but many researchers use simplified FN theory to analyse experimental data. The present paper reports an experimental method of finding apparent emission area, based on using field ion and field electron microscopes (FIM-FEM). The discrepancy of emission area between the FIM-FEM method and MG-based analysis is a factor of 7.4, while that with simplified FN-based analysis is about 25, confirming MG theory is better for FE data analysis. The result allows deduction of key indicators, including source energy spread, reduced brightness and emission efficiency. A downloadable program is made available to help analysis. Our work provides a new experimental method of characterizing FE electron sources, especially the atomic-scale cold cathode, for which existing plot-based data-analysis methods are not suitable.
Comments
41 pages (including Electronic Supplementary Material), 4 combination figures in main paper
Field emission (FE) electron sources are made close to atomic-scale to reach the highest spatial resolution as well as stable emission for electron microscopy, electron beam inspection and lithography. At present, no single agreed method exists of using FE current-voltage data to extract the apparent emission area, which is needed for predicting some beam properties. The 1956 theory of Murphy and Good (MG) is better physics than the 1920s theory of Fowler and Nordheim (FN) and colleagues, but many researchers use simplified FN theory to analyse experimental data. The present paper reports an experimental method of finding apparent emission area, based on using field ion and field electron microscopes (FIM-FEM). The discrepancy of emission area between the FIM-FEM method and MG-based analysis is a factor of 7.4, while that with simplified FN-based analysis is about 25, confirming MG theory is better for FE data analysis. The result allows deduction of key indicators, including source energy spread, reduced brightness and emission efficiency. A downloadable program is made available to help analysis. Our work provides a new experimental method of characterizing FE electron sources, especially the atomic-scale cold cathode, for which existing plot-based data-analysis methods are not suitable.
This technical note provides a high-level overview of the present state of basic field electron emission (FE) theory, as suitable for use in the context of technological applications of FE theory. At present there is much theoretical confusion in FE literature, and a partial breakdown of the peer review system. Even in sensitive technological contexts, many papers have stated and used out-of-date theory that makes current-density predictions that are several hundred times less than those of modern FE theory. A primary aim of this note is to help reduce the confusion and error in future published FE literature. It is not intended as a detailed review of FE theory.
Field electron emission (FE) and electrostatic field ionization (ESFI) are quantum-mechanical tunnelling processes that provide basic theory for important technologies. However, the basic theories of FE and ESF1 are not yet completely understood. This paper attempts to identify related fundamental quantum mechanical issues, problems and relevances. The following topics have been identified as deserving closer investigation or discussion. (a) The implication that if a "real electron" cannot have negative kinetic energy, then this necessarily implies that a "real electron" is a distributed object rather than a point object. (b) The implication that the language we use to discuss quantum mechanics needs to be changed in order to avoid referring to the "position of a (point) electron". (c) The idea that "quantum mathematics" (i.e., the mathematics of quantum mechanics) has different utilisations, namely the "matter distribution" and "pathway choice" utilisations, with "measurement" being observed pathway choice. (d) Difficulties with the present formulations of the uncertainty principle and wave-particle duality. (e) Fundamental difficulties in the exact calculation of exchange-and-correlation effects in both FE and ESFI theory. (f) Conceptual problems associated with "seeing electrons" in the field electron (emission) microscope. (g) Field emission tunnelling and the arrow of time. (h) The choice between tunnelling-integral and overlap-integral formulations of tunnelling theory, and the apparent incompleteness of both types of formulation.
Electrons emitted from single-atom tips are analysed in a model with the tip as a round tubelike constriction. The source creates two-dimensional minimum wavepackets whose temporal evolution agrees well with observed beam divergences. With few-atom tips interference effects may arise due to the electron's non localized emission from several atoms. The phase space density of emitted electrons is around 10 −2 h −3 , and electron-electron correlation experiments become feasible. In ion field emission mode observed beam divergences are dominated by thermal broadening and other effects rather than quantum mechanical principles. Applications include electron interferometers of lower energy and wider beam separation than hitherto in use, as well as proton and possibly other ion interferometers. Highly focused low energy beams could also be produced.
We study the excitation and ionization of cesium Rydberg states in an electric field ($\ensuremath{\approx}\phantom{\rule{0.16em}{0ex}}2200\phantom{\rule{4pt}{0ex}}\mathrm{V}/\mathrm{cm}$) near the classical field-ionization threshold ($\ensuremath{\approx}\ensuremath{-}280\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ binding energy) by three-dimensional (3D) ion-electron coincidence spectroscopy. Cesium atoms are produced by an effusive oven and excited with lasers to Stark-shifted Rydberg states or directly ionized. Using a double time-of-flight setup we record 3D (X,Y, time of flight) coincidence imaging of electrons and ions. Above-threshold photoionization creates broad images with poor electron-ion spatial correlation. Fast ionizing states produce very good correlations and the images reveal the electric-field map of the ionization region. Slow ionizing states show that the relatively high atomic velocity is detrimental to the correlations. Experimental data are accurately reproduced by detailed Monte Carlo excitation and ionization simulations based on Stark maps obtained with local-frame transformation (LFT) theory. Agreement between our spectroscopic experiment and LFT theory is very good, with better that hundreds of megahertz accuracy. But, on rare particular states, several gigahertz discrepancy is found. This study can be used to select appropriate states for the creation of ion and electron beams with high brightness, good correlation, and low energy dispersion.
This thesis presents details of a new type of cold atom electron source (CAES) that uses an alternating current magneto-optical trap (AC-MOT). Cold atom electron sources produce electron bunches by threshold photoionisation from a population of laser-cooled atoms. The electrons extracted from the atoms are made into a beam which has an ultra-low transverse velocity distribution. The low velocity distribution increases the brightness and reduces the energy spread of the beam, making CAESs potential sources for future electron diffraction and electron spectroscopy studies.
The newly commissioned source detailed here produces focused electron bunches with characteristic temperatures as low as 12.6 ± 0.8 K, at a rate of up to 10 Hz, and with a bunch charge of 2.2±0.2fC, comparable to other state-of-the-art cold atom electron sources. The AC-MOT CAES can also produce cold bunches with energies <200 eV, which is lower than has previously been reported for this type of source.
The electrons originate from a population of laser-cooled 85Rb atoms held in an AC- MOT. The AC-MOT CAES design allows the magnetic trapping fields to be switched to zero in 32 μs, more than ��175 times faster than is possible using a comparable DC-MOT source. This means that electron bunches can be created and extracted in a magnetic field-free environment without any reduction in trap density and hence bunch charge, as occurs in conventional DC-MOT sources.
The design, development, characterisation, and operation of the systems needed for the new AC-MOT CAES are detailed in this thesis. This includes details of the atom trapping system, the photoionisation system, the electron extraction system and the various timing systems for creation and characterisation of the resultant cold electron bunches.
Finally, the characterisation of the AC-MOT CAES itself is presented, and the measured beam metrics are used to compare the new AC-MOT CAES with other CAES designs which are under development.
UltraCold Ion Beam Source. Focused ion beam (FIB) machines are largely used in the semiconductor industry mainly for imaging, milling and deposition of material, at the nanometer scale. To keep up with the trend of making smaller and smaller components, FIBs need to be continuously improved. A FIB is mainly made of an ion source and a focusing column. In this thesis, two concepts of ion sources are presented, modeled and discussed. The ultra-cold ion source (UCIS) is based on creating very cold ion beams (T <1 mK) by near-threshold photo-ionization of a laser-cooled and trapped atomic gas. In our experiment, 85Rb atoms are confined in a magneto optical trap built directly inside an accelerator structure. A spherical portion of the atom cloud is ionized with a 2-step ionization process and the bunched ions are accelerated by either a DC or a pulsed electric field. The liquid-metal ion source (LMIS) is the current state-of-art for focused ion beam technology, having a reduced brightness of 106 A/m2 sr eV. The reduced brightness characterizes the source and is proportional to the ion current and inversely proportional to the beam emittance (closely related with the source temperature). A high brightness is of importance as much as a low energy spread of the ion beam, since the latter is related with the focus ability of the beam. We have already shown that the UCIS can provide much lower energy spread (20 meV) than LMIS (˜ 4.5 eV), see Reijnders et al. (PRL, 2009), but not yet in combination with a high brightness as well. The energy spread is the limiting factor for the final achievable spot size in a FIB based on a LMIS. Chapter 3 and 4 present measurements of the source temperature and of the extracted current to complete the characterization of the UCIS. The ultra low temperature of the source permits collimated bunches to be created at low kinetic energy (down to few eV), which allows using time-dependent fields for accelerating and focusing. With this lens, a transversal ion temperature of (3±2) mK has been measured, as shown in chapter 3. This temperature is an upper limit since it is ten times higher than the expected value. The novel technique of focusing with time-dependent electric field is successfully applied to an ultra cold ion beam. In chapter 4, a dynamic model of the source describing its properties under pulsed operation has been developed and experiments validated it. A maximum average ion current of (13 ± 1) pA has been extracted from the UCIS and this is enough for imaging (1-100 pA are used). Those results correspond to a source reduced brightness of (8 ± 1) × 104 A/m2 sr eV with 0.9 eV energy spread. This result is 12.5 times lower than the brightness of a LMIS. An interesting "pushing effect", due to the laser used to excite the atoms in the cloud, is described as well. Particle tracking simulations show that disorder induced heating has an important effect on the brightness, lowering its value by 1-2 orders of magnitude depending on the extracted current. Calculations and simulations of a different ion source, the atomic beam laser-cooled ion source (ABLIS), are presented in chapter 6. The follow-up project is based on a similar idea as an UCIS but aims for production of ion beams from a much higher initial atomic flux. The atoms originate from a Knudsen cell and, after being cooled and compressed transversally with laser cooling and trapping techniques, are photo-ionized and accelerated. The source size is reduced as well with respect to the UCIS. Realistic particle tracking simulations with 87Rb show that disorder induced heating is still very important, but in certain conditions, the so-called "pencil-beam" regime is reached and the disorder-induced heating does not deteriorate the brightness anymore. Depending on the extracted current, it is possible to reach a reduced brightness of 2 × 107 A/m2 sr eV with an ion current of 22 pA (corresponding to a final aperture diameter df = 1.6 µm) and an energy spread of 0.7 eV can be achieved. This source is likely capable of provide a high brightness and a low energy spread at the same time. The calculations are done assuming a purified 87Rb source. Eventually, it is possible to reach very high current (1 nA), making the ABLIS ideal also for milling applications with FIBs.