**Dr. Ágúst Valfells**

Position: Professor

Website: http://www.ru.is/starfsfolk/av

# Research projects

- Vacuum microelectronics
- Space-charge effects in electronic beams

I am interested in nano- and microscale vacuum electronics. In devices of this magnitude the mean free path for electrons is greater than the length scale of the device even under atmospheric pressure. There are many similarites to the well known behaviour of macroscopic counterparts, but at the small scale many effects which are neglected in the macroscopic regime become quite important, e.g. Coulomb collisional effects, field emission, surface roughness and quantum effects to name a few. Lately I have been investigating space-charge effects in this regime. Recent discoveries include a new mechanism for generating oscillating current in a diode, with easily tunable frequency in the THz range; and also simple new scaling laws for space-charge limited emission from cylindrical and spherical emitters.

# Publication

Y Li, E Júlíusson, H Pálsson, H Stefánsson and Á Valfells.

**Machine learning for creation of generalized lumped parameter tank models of low temperature geothermal reservoir systems**.*Geothermics*70, 62 - 84 (2017).

Abstract Abstract Lumped parameter tank models have gained renewed interest in recent years as an alternative tool for geothermal reservoir analysis and production planning. The models can be structured in various ways regarding the number of tanks, connections between the tanks and the parameters representing the physical properties of the geothermal system. It usually requires a time consuming and difficult process of trials and errors to manually decide the optimal configuration of a tank model. Inspired by recent development in the use of machine learning methods, we propose a method for automatically generating accurate and computationally feasible generalized tank models for isothermal, single phase, reservoirs. This is an extension of earlier work on complexity reduction of generalized tank models (Li et al., 2016). Here, a recursive “switch-back” method is constructed to maximize prediction accuracy of the model. It is also shown how the K-means clustering algorithm can be used to aggregate production wells in generalized tank models. One synthetic example and one field application from t Reykir geothermal fields in Iceland are used to illustrate the effectiveness of these methods.

URL, DOI BibTeX@article{LI201762, title = "Machine learning for creation of generalized lumped parameter tank models of low temperature geothermal reservoir systems", journal = "Geothermics", volume = 70, pages = "62 - 84", year = 2017, issn = "0375-6505", doi = "doi.org/10.1016/j.geothermics.2017.05.009", url = "http://www.sciencedirect.com/science/article/pii/S0375650517300639", author = "Y. Li and E. Júlíusson and H. Pálsson and H. Stefánsson and Á. Valfells", keywords = "Geothermal reservoir modeling, Lumped-parameter models, Machine learning, Complexity analysis, Information criterion, Complexity reduction algorithm, Switch-back method, Model selection, -means clustering algorithm", abstract = "Abstract Lumped parameter tank models have gained renewed interest in recent years as an alternative tool for geothermal reservoir analysis and production planning. The models can be structured in various ways regarding the number of tanks, connections between the tanks and the parameters representing the physical properties of the geothermal system. It usually requires a time consuming and difficult process of trials and errors to manually decide the optimal configuration of a tank model. Inspired by recent development in the use of machine learning methods, we propose a method for automatically generating accurate and computationally feasible generalized tank models for isothermal, single phase, reservoirs. This is an extension of earlier work on complexity reduction of generalized tank models (Li et al., 2016). Here, a recursive “switch-back” method is constructed to maximize prediction accuracy of the model. It is also shown how the K-means clustering algorithm can be used to aggregate production wells in generalized tank models. One synthetic example and one field application from t Reykir geothermal fields in Iceland are used to illustrate the effectiveness of these methods." }

Kristinn Torfason, Agust Valfells and Andrei Manolescu.

**Molecular Dynamics Simulations of Field Emission From a Prolate Spheroidal Tip**.*arXiv preprint arXiv:1608.06789*(2016).

Abstract High resolution molecular dynamics simulations with full Coulomb interactions of electrons are used to investigate field emission from a prolate spheroidal tip. The space charge limited current is several times lower than the current calculated with the Fowler-Nordheim formula. The image-charge is taken into account with a spherical approximation, which is good around the top of the tip, i.e. region where the current is generated.

arXiv BibTeX@article{torfason2016molecular, title = "Molecular Dynamics Simulations of Field Emission From a Prolate Spheroidal Tip", author = "Torfason, Kristinn and Valfells, Agust and Manolescu, Andrei", journal = "arXiv preprint arXiv:1608.06789", arxiv = "http://arxiv.org/abs/1608.06789", year = 2016, abstract = "High resolution molecular dynamics simulations with full Coulomb interactions of electrons are used to investigate field emission from a prolate spheroidal tip. The space charge limited current is several times lower than the current calculated with the Fowler-Nordheim formula. The image-charge is taken into account with a spherical approximation, which is good around the top of the tip, i.e. region where the current is generated." }

Marjan Ilkov, Kristinn Torfason, Andrei Manolescu and Ágúst Valfells.

**Terahertz pulsed photogenerated current in microdiodes at room temperature**.*Applied Physics Letters*107, (2015).

Abstract Space-charge modulation of the current in a vacuum diode under photoemission leads to the formation of beamlets with time periodicity corresponding to THz frequencies. We investigate the effect of the emitter temperature and internal space-charge forces on the formation and persistence of the beamlets. We find that temperature effects are most important for beam degradation at low values of the applied electric field, whereas at higher fields, intra-beamlet space-charge forces are dominant. The current modulation is most robust when there is only one beamlet present in the diode gap at a time, corresponding to a macroscopic version of the Coulomb blockade. It is shown that a vacuum microdiode can operate quite well as a tunable THz oscillator at room temperature with an applied electric field above 10 MV/m and a diode gap of the order of 100 nm.

URL arXiv, DOI BibTeX@article{ilkov2015terahertz, author = "Ilkov, Marjan and Torfason, Kristinn and Manolescu, Andrei and Valfells, Ágúst", title = "Terahertz pulsed photogenerated current in microdiodes at room temperature", journal = "Applied Physics Letters", year = 2015, volume = 107, number = 20, eid = 203508, pages = "", url = "http://scitation.aip.org/content/aip/journal/apl/107/20/10.1063/1.4936176", doi = "10.1063/1.4936176", abstract = "Space-charge modulation of the current in a vacuum diode under photoemission leads to the formation of beamlets with time periodicity corresponding to THz frequencies. We investigate the effect of the emitter temperature and internal space-charge forces on the formation and persistence of the beamlets. We find that temperature effects are most important for beam degradation at low values of the applied electric field, whereas at higher fields, intra-beamlet space-charge forces are dominant. The current modulation is most robust when there is only one beamlet present in the diode gap at a time, corresponding to a macroscopic version of the Coulomb blockade. It is shown that a vacuum microdiode can operate quite well as a tunable THz oscillator at room temperature with an applied electric field above 10 MV/m and a diode gap of the order of 100 nm.", arxiv = "http://arxiv.org/abs/1508.06308" }

Kristinn Torfason, Agust Valfells and Andrei Manolescu.

**Molecular dynamics simulations of field emission from a planar nanodiode**.*Physics of Plasmas (1994-present)*22, - (2015).

Abstract High resolution molecular dynamics simulations with full Coulomb interactions of electrons are used to investigate field emission in planar nanodiodes. The effects of space-charge and emitter radius are examined and compared to previous results concerning transition from Fowler-Nordheim to Child-Langmuir current [Y. Y. Lau, Y. Liu, and R. K. Parker, Phys. Plasmas 1, 2082 (1994) and Y. Feng and J. P. Verboncoeur, Phys. Plasmas 13, 073105 (2006)]. The Fowler-Nordheim law is used to determine the current density injected into the system and the Metropolis-Hastings algorithm to find a favourable point of emission on the emitter surface. A simple fluid like model is also developed and its results are in qualitative agreement with the simulations.

URL arXiv, DOI BibTeX@article{4914855, author = "Torfason, Kristinn and Valfells, Agust and Manolescu, Andrei", title = "Molecular dynamics simulations of field emission from a planar nanodiode", journal = "Physics of Plasmas (1994-present)", year = 2015, volume = 22, number = 3, eid = 033109, pages = "-", url = "http://scitation.aip.org/content/aip/journal/pop/22/3/10.1063/1.4914855", doi = "http://dx.doi.org/10.1063/1.4914855", arxiv = "http://arxiv.org/abs/1412.4537", abstract = "High resolution molecular dynamics simulations with full Coulomb interactions of electrons are used to investigate field emission in planar nanodiodes. The effects of space-charge and emitter radius are examined and compared to previous results concerning transition from Fowler-Nordheim to Child-Langmuir current [Y. Y. Lau, Y. Liu, and R. K. Parker, Phys. Plasmas 1, 2082 (1994) and Y. Feng and J. P. Verboncoeur, Phys. Plasmas 13, 073105 (2006)]. The Fowler-Nordheim law is used to determine the current density injected into the system and the Metropolis-Hastings algorithm to find a favourable point of emission on the emitter surface. A simple fluid like model is also developed and its results are in qualitative agreement with the simulations." }

M Ilkov, K Torfason, A Manolescu and A Valfells.

**Synchronization in Arrays of Vacuum Microdiodes**.*Electron Devices, IEEE Transactions on*PP, 1-1 (2014).

Abstract Simulations have shown that space-charge effects can lead to regular modulation of photoemitted beams in vacuum diodes with gap sizes on the order of 1 μm and accelerating voltage on the order of $1$ V. These modulations are in the terahertz regime and can be tuned by simply changing the emitter area or accelerating vacuum field. The average current in the diode corresponds to the Child–Langmuir current, but the amplitude of the oscillations is affected by various factors. Given the small size and voltage of the system, the maximum radiated ac power is expected to be small. In this paper, we show that an array of small emitters produces higher frequency signals than a single large emitter of the same area and how these emitters may be synchronized to produce higher power signals.

arXiv, DOI BibTeX@article{6979259, author = "Ilkov, M. and Torfason, K. and Manolescu, A. and Valfells, A.", journal = "Electron Devices, IEEE Transactions on", title = "Synchronization in Arrays of Vacuum Microdiodes", year = 2014, month = "", volume = "PP", number = 99, pages = "1-1", abstract = "Simulations have shown that space-charge effects can lead to regular modulation of photoemitted beams in vacuum diodes with gap sizes on the order of 1 μm and accelerating voltage on the order of $1$ V. These modulations are in the terahertz regime and can be tuned by simply changing the emitter area or accelerating vacuum field. The average current in the diode corresponds to the Child--Langmuir current, but the amplitude of the oscillations is affected by various factors. Given the small size and voltage of the system, the maximum radiated ac power is expected to be small. In this paper, we show that an array of small emitters produces higher frequency signals than a single large emitter of the same area and how these emitters may be synchronized to produce higher power signals.", keywords = "Cathodes;Couplings;Frequency synchronization;Oscillators;Quantum cascade lasers;Space charge;Synchronization;Synchronization;terahertz;vacuum microelectronics.", doi = "10.1109/TED.2014.2370680", issn = "0018-9383", arxiv = "http://arxiv.org/abs/1409.0516" }

Y B Zhu, P Zhang, A Valfells, L K Ang and Y Y Lau.

**Novel Scaling Laws for the Langmuir-Blodgett Solutions in Cylindrical and Spherical Diodes**.*Phys. Rev. Lett.*110, 265007 (June 2013).

Abstract It is found that the Langmuir-Blodgett solutions for the space charge limited current density, for both cylindrical and spherical diodes, may be approximated by J = 4/9\epsilon_0\sqrt(2e/m)(E_c^(3/2)/D) over a wide range of parameters, where $E_c$ is the surface electric field on the cathode of the vacuum diode and D is the anode-cathode spacing. This dependence is valid whether \(R_a/R_c\) is greater than or less than unity, where \(R_a\) and \(R_c\) are, respectively, the anode and cathode radius. Minor empirical corrections to the above scaling yield fitting formulas that are accurate to within 5% for 310E-5<\(R_c/R_a\)<500. An explanation of this scaling is given. An accurate transit time model yields the Langmuir-Blodgett solutions even in the Coulomb blockade regime for a nanogap, where the electron number may be in the single digits, and the transit time frequency is in the THz range.

URL, DOI BibTeX@article{PhysRevLett.110.265007, title = "Novel Scaling Laws for the Langmuir-Blodgett Solutions in Cylindrical and Spherical Diodes", author = "Zhu, Y. B. and Zhang, P. and Valfells, A. and Ang, L. K. and Lau, Y. Y.", journal = "Phys. Rev. Lett.", volume = 110, issue = 26, pages = 265007, numpages = 5, year = 2013, month = "Jun", doi = "10.1103/PhysRevLett.110.265007", url = "http://link.aps.org/doi/10.1103/PhysRevLett.110.265007", abstract = "It is found that the Langmuir-Blodgett solutions for the space charge limited current density, for both cylindrical and spherical diodes, may be approximated by J = 4/9\epsilon_0\sqrt(2e/m)(E_c^(3/2)/D) over a wide range of parameters, where $E_c$ is the surface electric field on the cathode of the vacuum diode and D is the anode-cathode spacing. This dependence is valid whether \(R_a/R_c\) is greater than or less than unity, where \(R_a\) and \(R_c\) are, respectively, the anode and cathode radius. Minor empirical corrections to the above scaling yield fitting formulas that are accurate to within 5% for 310E-5<\(R_c/R_a\)<500. An explanation of this scaling is given. An accurate transit time model yields the Langmuir-Blodgett solutions even in the Coulomb blockade regime for a nanogap, where the electron number may be in the single digits, and the transit time frequency is in the THz range.", publisher = "American Physical Society" }

P Jonsson, Marjan Ilkov, A Manolescu, A Pedersen and A Valfells.

**Tunability of the terahertz space-charge modulation in a vacuum microdiode**.*Physics of Plasmas*20, 023107 (2013).

Abstract Under certain conditions, space-charge limited emission in vacuum microdiodes manifests as clearly defined bunches of charge with a regular size and interval. The frequency corresponding to this interval is in the terahertz range. In this computational study, it is demonstrated that, for a range of parameters, conducive to generating THz frequency oscillations, the frequency is dependant only on the cold cathode electric field and on the emitter area. For a planar micro-diode of given dimension, the modulation frequency can be easily tuned simply by varying the applied potential. Simulations of the microdiode are done for 84 different combinations of emitter area, applied voltage, and gap spacing, using a molecular dynamics based code with exact Coulomb interaction between all electrons in the vacuum gap, which is of the order 100. It is found, for a fixed emitter area, that the frequency of the pulse train is solely dependant on the vacuum electric field in the diode, described by a simple power law. It is also found that, for a fixed value of the electric field, the frequency increases with diminishing size of the emitting spot on the cathode. Some observations are made on the spectral quality, and how it is affected by the gap spacing in the diode and the initial velocity of the electrons.

URL arXiv, DOI BibTeX@article{jonsson:023107, author = "P. Jonsson and Marjan Ilkov and A. Manolescu and A. Pedersen and A. Valfells", collaboration = "", title = "Tunability of the terahertz space-charge modulation in a vacuum microdiode", publisher = "AIP", year = 2013, journal = "Physics of Plasmas", volume = 20, number = 2, eid = 023107, numpages = 7, pages = 023107, keywords = "molecular dynamics method; plasma diodes; plasma oscillations; plasma simulation; plasma transport processes; space charge", url = "http://link.aip.org/link/?PHP/20/023107/1", doi = "10.1063/1.4793451", abstract = "Under certain conditions, space-charge limited emission in vacuum microdiodes manifests as clearly defined bunches of charge with a regular size and interval. The frequency corresponding to this interval is in the terahertz range. In this computational study, it is demonstrated that, for a range of parameters, conducive to generating THz frequency oscillations, the frequency is dependant only on the cold cathode electric field and on the emitter area. For a planar micro-diode of given dimension, the modulation frequency can be easily tuned simply by varying the applied potential. Simulations of the microdiode are done for 84 different combinations of emitter area, applied voltage, and gap spacing, using a molecular dynamics based code with exact Coulomb interaction between all electrons in the vacuum gap, which is of the order 100. It is found, for a fixed emitter area, that the frequency of the pulse train is solely dependant on the vacuum electric field in the diode, described by a simple power law. It is also found that, for a fixed value of the electric field, the frequency increases with diminishing size of the emitting spot on the cathode. Some observations are made on the spectral quality, and how it is affected by the gap spacing in the diode and the initial velocity of the electrons.", arxiv = "http://arxiv.org/abs/1301.6533" }

Andreas Pedersen, Andrei Manolescu and Ágúst Valfells.

**Space-Charge Modulation in Vacuum Microdiodes at THz Frequencies**.*Phys. Rev. Lett.*104, 175002 (April 2010).

Abstract We investigate the dynamics of a space-charge limited, photoinjected, electron beam in a microscopic vacuum diode. Because of the small nature of the system it is possible to conduct high-resolution simulations where the number of simulated particles is equal to the number of electrons within the system. In a series of simulations of molecular dynamics type, where electrons are treated as point charges, we address and analyze space-charge effects in a micrometer-scale vacuum diode. We have been able to reproduce breakup of a single pulse injected with a current density beyond the Child-Langmuir limit, and we find that continuous injection of current into the diode gap results in a well-defined train of electron bunches corresponding to THz frequency. A simple analytical explanation of this behavior is given.

URL PDF, DOI BibTeX@article{PhysRevLett.104.175002, title = "Space-Charge Modulation in Vacuum Microdiodes at THz Frequencies", author = "Pedersen, Andreas and Manolescu, Andrei and Valfells, \'Ag\'ust", journal = "Phys. Rev. Lett.", volume = 104, issue = 17, pages = 175002, numpages = 4, year = 2010, month = "Apr", doi = "10.1103/PhysRevLett.104.175002", url = "http://link.aps.org/doi/10.1103/PhysRevLett.104.175002", publisher = "American Physical Society", abstract = "We investigate the dynamics of a space-charge limited, photoinjected, electron beam in a microscopic vacuum diode. Because of the small nature of the system it is possible to conduct high-resolution simulations where the number of simulated particles is equal to the number of electrons within the system. In a series of simulations of molecular dynamics type, where electrons are treated as point charges, we address and analyze space-charge effects in a micrometer-scale vacuum diode. We have been able to reproduce breakup of a single pulse injected with a current density beyond the Child-Langmuir limit, and we find that continuous injection of current into the diode gap results in a well-defined train of electron bunches corresponding to THz frequency. A simple analytical explanation of this behavior is given.", pdf = "http://www.researchgate.net/publication/44610968_Space-charge_modulation_in_vacuum_microdiodes_at_THz_frequencies/file/9fcfd5138362adda55.pdf" }