**Kristinn Torfason**

Position: Research staff

# Research projects

- Molecular dynamics simulations of field emission from a planar nanodiode and prolate spheroidal tip.
- Perovskite solar cells.

# Publication

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." }

George Alexandru Nemnes, Cristina Besleaga, Andrei Gabriel Tomulescu, Ioana Pintilie, Lucian Pintilie, Kristinn Torfason and Andrei Manolescu.

**Dynamic electrical behavior of halide perovskite based solar cells**.*arXiv preprint arXiv:1606.00335*(2016).

Abstract A dynamic electrical model is introduced to investigate the hysteretic effects in the I-V characteristics of perovskite based solar cells. By making a simple ansatz for the polarization relaxation, our model is able to reproduce qualitatively and quantitatively detailed features of measured I-V characteristics. Pre-poling effects are discussed, pointing out the differences between initially over- and under-polarized samples. In particular, the presence of the current over-shoot observed in the reverse characteristics is correlated with the solar cell pre-conditioning. Furthermore, the dynamic hysteresis is analyzed with respect to changing the bias scan rate, the obtained results being consistent with experimentally reported data: the hysteresis amplitude is maximum at intermediate scan rates, while at very slow and very fast ones it becomes negligible. The effects induced by different relaxation time scales are assessed. The proposed dynamic electrical model offers a comprehensive view of the solar cell operation, being a practical tool for future calibration of tentative microscopic descriptions.

arXiv BibTeX@article{nemnes2016dynamic, title = "Dynamic electrical behavior of halide perovskite based solar cells", author = "Nemnes, George Alexandru and Besleaga, Cristina and Tomulescu, Andrei Gabriel and Pintilie, Ioana and Pintilie, Lucian and Torfason, Kristinn and Manolescu, Andrei", journal = "arXiv preprint arXiv:1606.00335", arxiv = "http://arxiv.org/abs/1606.00335", year = 2016, abstract = "A dynamic electrical model is introduced to investigate the hysteretic effects in the I-V characteristics of perovskite based solar cells. By making a simple ansatz for the polarization relaxation, our model is able to reproduce qualitatively and quantitatively detailed features of measured I-V characteristics. Pre-poling effects are discussed, pointing out the differences between initially over- and under-polarized samples. In particular, the presence of the current over-shoot observed in the reverse characteristics is correlated with the solar cell pre-conditioning. Furthermore, the dynamic hysteresis is analyzed with respect to changing the bias scan rate, the obtained results being consistent with experimentally reported data: the hysteresis amplitude is maximum at intermediate scan rates, while at very slow and very fast ones it becomes negligible. The effects induced by different relaxation time scales are assessed. The proposed dynamic electrical model offers a comprehensive view of the solar cell operation, being a practical tool for future calibration of tentative microscopic descriptions." }

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" }

Kristinn Torfason, Andrei Manolescu, Sigurdur I Erlingsson and Vidar Gudmundsson.

**Thermoelectric current and Coulomb-blockade plateaus in a quantum dot**.*Physica E: Low-dimensional Systems and Nanostructures*53, 178 - 185 (2013).

Abstract A Generalized Master Equation (GME) is used to study the thermoelectric currents through a quantum dot in both the transient and steady-state regime. The two semi-infinite leads are kept at the same chemical potential but at different temperatures to produce a thermoelectric current which has a varying sign depending on the chemical potential. The Coulomb interaction between the electrons in the sample is included via the exact diagonalization method. We observe a saw-teeth like profile of the current alternating with plateaus of almost zero current. Our calculations go beyond the linear response with respect to the temperature gradient, but are compatible with known results for the thermopower in the linear response regime.

URL arXiv, DOI BibTeX@article{Torfason2013178, title = "Thermoelectric current and Coulomb-blockade plateaus in a quantum dot", journal = "Physica E: Low-dimensional Systems and Nanostructures", volume = 53, number = 0, pages = "178 - 185", year = 2013, note = "", issn = "1386-9477", doi = "10.1016/j.physe.2013.05.005", url = "http://www.sciencedirect.com/science/article/pii/S1386947713001689", author = "Kristinn Torfason and Andrei Manolescu and Sigurdur I. Erlingsson and Vidar Gudmundsson", abstract = "A Generalized Master Equation (GME) is used to study the thermoelectric currents through a quantum dot in both the transient and steady-state regime. The two semi-infinite leads are kept at the same chemical potential but at different temperatures to produce a thermoelectric current which has a varying sign depending on the chemical potential. The Coulomb interaction between the electrons in the sample is included via the exact diagonalization method. We observe a saw-teeth like profile of the current alternating with plateaus of almost zero current. Our calculations go beyond the linear response with respect to the temperature gradient, but are compatible with known results for the thermopower in the linear response regime.", arxiv = "http://arxiv.org/abs/1303.3160" }

Kristinn Torfason.

**Variations on Transport for a Quantum Flute**.

University of Iceland and Reykjavik University (2013).

Abstract A time-dependent Lippmann-Schwinger scattering model is used to study the transport of a time-modulated double quantum point contact system in the presence of perpendicular magnetic field. The conductance through the system is calculated using the Landauer-Büttiker framework. An observed magnetic field induced Fano resonance is seen in the conductance. A Generalized Master Equation (GME) is then used to describe the non-equilibrium time-dependent transport through a similar system, a short quantum wire connected to semi-infinite leads. A lattice model is used to described the leads and system, with the Coulomb interaction between the electrons in the sample included via the exact diagonalization method. The contact coupling strength between the leads and the wire is modulated by out-of-phase time-dependent potentials that simulate a turnstile device. The placement of one of the leads is fixed while the position of the other is varied. The propagation of both sinusoidal and rectangular pulses is examined. The current profiles in both leads are found to depend on not only the shape of the pulses, but also the position of the contacts. The current reflects standing waves created by the contact potentials, like in a wind musical instrument (for example, a flute). Finally thermoelectric currents through a quantum dot are studied in both the transient and steady-state regime using the GME. The two semi-infinite leads are kept at the same chemical potential but at different temperatures to produce a thermoelectric current, which has a varying sign depending on the chemical potential. A saw-tooth like profile is observed in the current along with plateaus of zero current.

URL BibTeX@phdthesis{torfason2013variations, title = "Variations on Transport for a Quantum Flute", author = "Torfason, Kristinn", year = 2013, school = "University of Iceland and Reykjavik University", url = "http://hdl.handle.net/1946/14320", abstract = "A time-dependent Lippmann-Schwinger scattering model is used to study the transport of a time-modulated double quantum point contact system in the presence of perpendicular magnetic field. The conductance through the system is calculated using the Landauer-Büttiker framework. An observed magnetic field induced Fano resonance is seen in the conductance. A Generalized Master Equation (GME) is then used to describe the non-equilibrium time-dependent transport through a similar system, a short quantum wire connected to semi-infinite leads. A lattice model is used to described the leads and system, with the Coulomb interaction between the electrons in the sample included via the exact diagonalization method. The contact coupling strength between the leads and the wire is modulated by out-of-phase time-dependent potentials that simulate a turnstile device. The placement of one of the leads is fixed while the position of the other is varied. The propagation of both sinusoidal and rectangular pulses is examined. The current profiles in both leads are found to depend on not only the shape of the pulses, but also the position of the contacts. The current reflects standing waves created by the contact potentials, like in a wind musical instrument (for example, a flute). Finally thermoelectric currents through a quantum dot are studied in both the transient and steady-state regime using the GME. The two semi-infinite leads are kept at the same chemical potential but at different temperatures to produce a thermoelectric current, which has a varying sign depending on the chemical potential. A saw-tooth like profile is observed in the current along with plateaus of zero current." }

Kristinn Torfason, Andrei Manolescu, Valeriu Molodoveanu and Vidar Gudmundsson.

**Excitation of collective modes in a quantum flute**.*Phys. Rev. B*85, 245114 (June 2012).

Abstract We use a generalized master equation (GME) formalism to describe the nonequilibrium time-dependent transport of Coulomb interacting electrons through a short quantum wire connected to semi-infinite biased leads. The contact strength between the leads and the wire is modulated by out-of-phase time-dependent potentials that simulate a turnstile device. We explore this setup by keeping the contact with one lead at a fixed location at one end of the wire, whereas the contact with the other lead is placed on various sites along the length of the wire. We study the propagation of sinusoidal and rectangular pulses. We find that the current profiles in both leads depend not only on the shape of the pulses, but also on the position of the second contact. The current reflects standing waves created by the contact potentials, like in a wind musical instrument (for example, a flute), but occurring on the background of the equilibrium charge distribution. The number of electrons in our quantum “flute” device varies between two and three. We find that for rectangular pulses the currents in the leads may flow against the bias for short time intervals, due to the higher harmonics of the charge response. The GME is solved numerically in small time steps without resorting to the traditional Markov and rotating wave approximations. The Coulomb interaction between the electrons in the sample is included via the exact diagonalization method. The system (leads plus sample wire) is described by a lattice model.

URL arXiv, DOI BibTeX@article{PhysRevB.85.245114, title = "Excitation of collective modes in a quantum flute", author = "Torfason, Kristinn and Manolescu, Andrei and Molodoveanu, Valeriu and Gudmundsson, Vidar", journal = "Phys. Rev. B", volume = 85, issue = 24, pages = 245114, numpages = 9, year = 2012, month = "Jun", doi = "10.1103/PhysRevB.85.245114", url = "http://link.aps.org/doi/10.1103/PhysRevB.85.245114", publisher = "American Physical Society", abstract = "We use a generalized master equation (GME) formalism to describe the nonequilibrium time-dependent transport of Coulomb interacting electrons through a short quantum wire connected to semi-infinite biased leads. The contact strength between the leads and the wire is modulated by out-of-phase time-dependent potentials that simulate a turnstile device. We explore this setup by keeping the contact with one lead at a fixed location at one end of the wire, whereas the contact with the other lead is placed on various sites along the length of the wire. We study the propagation of sinusoidal and rectangular pulses. We find that the current profiles in both leads depend not only on the shape of the pulses, but also on the position of the second contact. The current reflects standing waves created by the contact potentials, like in a wind musical instrument (for example, a flute), but occurring on the background of the equilibrium charge distribution. The number of electrons in our quantum “flute” device varies between two and three. We find that for rectangular pulses the currents in the leads may flow against the bias for short time intervals, due to the higher harmonics of the charge response. The GME is solved numerically in small time steps without resorting to the traditional Markov and rotating wave approximations. The Coulomb interaction between the electrons in the sample is included via the exact diagonalization method. The system (leads plus sample wire) is described by a lattice model.", arxiv = "http://arxiv.org/abs/1202.0566" }

Kristinn Torfason, Andrei Manolescu, Valeriu Molodoveanu and Vidar Gudmundsson.

**Generalized Master equation approach to mesoscopic time-dependent transport**.*Journal of Physics: Conference Series*338, 012017 (2012).

Abstract We use a generalized Master equation (GME) formalism to describe the non-equilibrium time-dependent transport through a short quantum wire connected to semi-infinite biased leads. The contact strength between the leads and the wire are modulated by out-of-phase time-dependent functions which simulate a turnstile device. One lead is fixed at one end of the sample whereas the other lead has a variable placement. The system is described by a lattice model. We find that the currents in both leads depend on the placement of the second lead. In the rather small bias regime we obtain transient currents flowing against the bias for short time intervals. The GME is solved numerically in small time steps without resorting to the traditional Markov and rotating wave approximations. The Coulomb interaction between the electrons in the sample is included via the exact diagonalization method.

arXiv, DOI BibTeX@article{1742-6596-338-1-012017, author = "Kristinn Torfason and Andrei Manolescu and Valeriu Molodoveanu and Vidar Gudmundsson", title = "Generalized Master equation approach to mesoscopic time-dependent transport", journal = "Journal of Physics: Conference Series", volume = 338, number = 1, pages = 012017, doi = "10.1088/1742-6596/338/1/012017", year = 2012, arxiv = "http://arxiv.org/abs/1109.2301", abstract = "We use a generalized Master equation (GME) formalism to describe the non-equilibrium time-dependent transport through a short quantum wire connected to semi-infinite biased leads. The contact strength between the leads and the wire are modulated by out-of-phase time-dependent functions which simulate a turnstile device. One lead is fixed at one end of the sample whereas the other lead has a variable placement. The system is described by a lattice model. We find that the currents in both leads depend on the placement of the second lead. In the rather small bias regime we obtain transient currents flowing against the bias for short time intervals. The GME is solved numerically in small time steps without resorting to the traditional Markov and rotating wave approximations. The Coulomb interaction between the electrons in the sample is included via the exact diagonalization method." }

Chi-Shung Tang, Kristinn Torfason and Vidar Gudmundsson.

**Magnetotransport in a time-modulated double quantum point contact system**.*Computer Physics Communications*182, 65 - 67 (2011).

Abstract We report on a time-dependent Lippmann-Schwinger scattering theory that allows us to study the transport spectroscopy in a time-modulated double quantum point contact system in the presence of a perpendicular magnetic field. Magnetotransport properties involving inter-subband and inter-sideband transitions are tunable by adjusting the time-modulated split-gates and the applied magnetic field. The observed magnetic field induced Fano resonance feature may be useful for the application of quantum switching.

arXiv, DOI BibTeX@article{Tang201165, title = "Magnetotransport in a time-modulated double quantum point contact system", journal = "Computer Physics Communications", volume = 182, number = 1, pages = "65 - 67", year = 2011, doi = "10.1016/j.cpc.2010.06.023", author = "Chi-Shung Tang and Kristinn Torfason and Vidar Gudmundsson", arxiv = "http://arxiv.org/abs/1002.1551", abstract = "We report on a time-dependent Lippmann-Schwinger scattering theory that allows us to study the transport spectroscopy in a time-modulated double quantum point contact system in the presence of a perpendicular magnetic field. Magnetotransport properties involving inter-subband and inter-sideband transitions are tunable by adjusting the time-modulated split-gates and the applied magnetic field. The observed magnetic field induced Fano resonance feature may be useful for the application of quantum switching." }