Synthetic Atoms: High Energy Density and a Record Power Density Alfred Hubler, Department of Physics, University of Illinois at Urbana-Champaign CNLS Seminar, Los Alamos National Lab, July 30 th, 2013 Nano capacitor arrays with high energy density Measured Energy Density We study the dielectric strength of nanocapacitors experimentally. We designed theoretically a new type of nanocaps: Synthetic atoms are nanocapacitors which mimic the geometry of atoms and simple molecules, but are a factor 10 factor larger. Synthetic atoms are a potentially important new technology for storing energy: -In synthetic atoms energy is stored by moving electrons, instead of ions. Since electrons have much less mass, the power density of synthetic atoms is much higher than in Li-ion batteries. -In chemical batteries the energy density is limited by the energy density of the molecular bonds, which is typically around 1GJ/m 3. The theoretical limit for energy density in synthetic atoms is more than 100 times larger if the electrode material has a particularly high tensile strength, such as graphene, carbon nano tubes, or boron-nitrate nano-wires. -Arrays of synthetic atoms can be recharged, and discharged with minimal losses millions of times and operate in a large temperature range. -The combustion front in explosives propagates roughly with the speed of sound. Arrays synthetic atoms have a similar energy density, but the energy-release front propagates with the speed of light and creates an EMP. A second failure mode propagates roughly with the speed sound and creates a pressure wave.

Energy storage in capacitors vs. energy storage in chemical batteries, hydrogen fuel cells, and gasoline Energy stored in chemical systems is due to the interaction of positive and negative charges. Energy stored in capacitors is due to the interaction of positive and negative charges. => Energy storage in chemical systems and capacitors are the same, except for their dimensions. But, in chemicals such as hydrogen, the limiting electric fields are more than 10,000 times larger: Quantization phenomena on the nano-scale suppress charge recombination => Quantization suppresses sparks in nano-gaps Example: Atomic hydrogen w = 13.6eV / (volume of hydrogen atom) = 3.3 x J / m 3 (1.31 x J/kg) i.e. nine orders of magnitude above the maximum energy density in a conventional capacitor.

Energy storage in synthetic atoms: The geometry matters Synthetic Atoms are -spherical nanocapacitors -cylindrical nanocapacitors -planar double layer nanocapacitors Synthetic atoms have the geometry of an atom or a simple molecule, but are 10 times larger. In the gap is vacuum, or a low density gas, or a dielectric. Electrons are stored on the cathode surface and on quantum levels in the gap. Thin wires are attached to the electrodes to add/remove charges. The energy density of nanocapacitors with sharp anodes (nano vacuum tubes) can be 5-10 times higher than that for planar double layer capacitors. The energy density in Faradic systems and synthetic atoms is limited by the energy density in ionic bonds (about 1GJ/m 3 ). The energy density in nanocapacitors and synthetic atoms is limited by the energy density in covalent bonds (tensile strength of the electrodes, i.e. 1.5TJ/m 3 for doped boron nitrate). Faradic systems have a smaller power density, lower efficiency, and shorter life time. Cylindrical nano-capacitor, where a = 1nm and b = 10nm

Leak currents in nanocapacitors Fowler-Nordheim field emission current: where I is the tunnel current, A r is the effective field emitting area, a and b are the Fowler-Nordheim constants, v(f) is the Schottky barrier correction factor, E is the electric field at the cathode, φ is the work function of the cathode material, and β is the field enhancement factor.

The scaling of the field enhancement factor The field enhancement factor versus the gap size d. The circles indicate experimental values measured by Alpert, Lee, Lyman, and Tomaschke on tungsten electrodes. The squares indicate experimental values measured by Boyle, Kisliuk, and Germer on tungsten electrodes. The diamond indicates the theoretical value on an atomic scale. Break down occurs when the field emission current exceeds 10 5 A/cm 2.  Small β => Small field emission current => High electric fields at break down  Miniaturization increases the energy density

The scaling of the field enhancement factor on the nano-scale UHV-STM with a tungsten tip of radius R=15nm is used at room temperature at 4 × 10 −11 Torr in constant current mode at I=10pA. The cathode is Au (111). => Miniaturization increases the energy density (electric fields ~ 1V/nm)

The scaling of the energy density at break down measured with a STM Measured Energy density, U, with a 15nm tungsten tip and flat gold cathode is found to scale with gap size d as: U=(26 GJ/m 3 )*(1nm / d) 1.5 (empirical power law) The experimental data deviate from the power law for d < 5nm, because electrons begin to tunnel directly from the cathode to the anode tip. The largest measured energy density is U=3.2 GJ/m 3 (25V/nm). => Miniaturization increases the energy density

The scaling of the self-discharge time due to field emission currents Charge stored in a vacuum nanocapacitor with gap size d and a pointed anode of radius R: Q = 2 πε 0 E (d + R) 2 Charge density in the center: q= 2 π E (d + R) 2 Field emission current density (β=1): j= a E 2 / φ exp(-b φ 3/2 /E) Self discharge time: τ self = q / j = 2 π (d + R) 2 φ exp(b φ 3/2 /E) / (a E ) Preliminary experimental results with dielectric nanocapacitors have self-discharge times greater than one day at 1V/nm (10MJ/m 3 ).  Field emission current is a potential problem = > Use electrode thickness, coatings, gases, and quantization phenomena to suppress leak current

Diagram of potential energy function. W c is the work function of the 2 cathodes. W a is the work function of the anode. The occupied levels of the conduction bands are shown in gray. The Fermi energy and occupied energy levels in the gap are shown in red. Thin red lines are un- occupied energy levels in the gap. We consider problem of a confined particle in this linear potential, U = F q ∣ x ∣ which is described by the following Schrodinger equation: Modeling quantized space charge in synthetic atoms => Leak currents are suppressed because electrons in the gap are governed by Fermi statistics and block field emission (Coulomb-blockade). No current Field Emission / STM style tunneling Field Emission, Coulomb blockade, Quantum cap.

Modeling quantized space charge in synthetic atoms => Leak currents are suppressed because electrons in the gap are governed by Fermi statistics and block field emission (Coulomb-blockade). The quantized energy levels are added into the potential energy function in a double layer capacitor with gap size 10 nm. The work function of the 2 tungsten cathodes is about W c = 4.55eV ≈7.29×10 −19 J. The work function of a graphene anode is about W a =4.56eV ≈7.31×10 −19 J. There are 69 bound states. 28 bound states are below the Fermi energy of the cathode. The largest energy spacing is between the ground and the first excited state, which is E 2 - E 1  7.12  J; the smallest energy spacing is between the highest two energy levels, which is E 69 - E 68  1.56  J. Thermal activation is rare at room temperature, because k b T ≈ 4.0  J is about a factor of 10 smaller.

Allowed energies E n for a confined particle with charge q and mass m in the potential U (x)=F q ∣ x ∣ : where and n=1,2,3…. For typical system parameters the energy difference between ground and first excited state is about 10 times larger than k b T at room temperature. We computed the corresponding wave functions numerically. The spontaneous transition rate from the n-th to the m-th state (n > m ) is: In this case, the spontaneous emission rate of the first excited state is about T= 470ns. Quantized space charge in the gap increases the capacity beyond the geometric capacity. The number of states per unit area and per eigenstate below the Fermi energy of the cathode is: Modeling quantized space charge in synthetic atoms => Leak currents are suppressed because electrons in the gap are governed by Fermi statistics and block field emission (Coulomb-blockade).

Modeling quantized space charge in synthetic atoms => Leak currents are suppressed because electrons in the gap are governed by Fermi statistics and block field emission (Coulomb-blockade). The quantized energy levels are added into the potential energy function in a double layer capacitor with gap size 4 nm. The work function of the 2 tungsten cathodes is about W c = 4.55eV ≈7.29×10 −19 J. The work function of a graphene anode is about W a =4.56eV ≈7.31×10 −19 J. There are 17 bound states. All bound states are above the Fermi energy of the cathode. The largest energy spacing is between the ground and the first excited state, which is E 2 - E 1  7.12  J; the smallest energy spacing is between the highest two energy levels, which is E 69 - E 68  1.56  J. Thermal activation is rare at room temperature, because k b T ≈ 4.0  J is about a factor of 10 smaller.

Modeling quantized space charge in synthetic atoms => Leak currents are suppressed because electrons in the gap are governed by Fermi statistics and block field emission (Coulomb-blockade). The quantized energy levels are added into the potential energy function in a double layer capacitor with gap size 4 nm. The work function of the 2 tungsten cathodes is about W c = 4.55eV ≈7.29×10 −19 J. The work function of a graphene anode is about W a =4.56eV ≈7.31×10 −19 J. There are 54 bound states. 45 bound states are below the Fermi energy of the cathode. The largest energy spacing is between the ground and the first excited state, which is E 2 - E 1  3.32  J; the smallest energy spacing is between the highest two energy levels, which is E 54 – E 53  7.88  J. Thermal activation is rare at room temperature, because k b T ≈ 4.0  J is more than a factor of 10 smaller.

Power density of synthetic atoms: We observed very bright flashes of light and sub-nano-second EMPs from a nm-sized spot. The power density is related to the energy density by a characteristic external discharge time τ e = sqrt(L C) of the system. For example, a 1 square cm capacitor discharging through 1cm long wires has τ e = s. Locally, is limited by the plasmon period of the metal, the time it takes for electrons oscillate in the atomic lattice. The plasmon period of silver, for example, is τ p = s. Formation of the plasma channel: τ c = (gap size) / (speed of light) = s Max. power density: From p = (1 GJ/m 3 ) / τ e = W/m 3 to p = (1 GJ/m 3 ) / τ p = W/m 3 Rocket engines have a power density of 10 5 W/m 3 Before break down Sub micron trench Trench with MWCNT After break down When an nano wire across a nano-scale trench is purposely charged to twice its operating voltage until it fails, the power density is high enough to melt the gold at each capacitor site, even though the melting point of gold is 1000C. => A record power density?

A simple method for fabricating synthetic atoms: Angled vapor deposition creates a Spindt ridge in a trench. In this experiment, the anode is a gold ridge with apex radius 30 nanometers sitting in a 300 nanometer trench. The cathode is placed to lie flat across the top of the trench. The gap size between electrodes is 75 nanometers

A simple method for fabricating synthetic atoms: Angled vapor deposition creates a Spindt ridge in a trench. Current-voltage curve of a 100 nm trench as shown in the top Figure, on a linear scale (left) and on a log-log scale (right). Even at 100V there is no arcing.

Easier to fabricate: Dielectric nanocapacitors. The dielectric strength of silicon oxide nanocapacitors. Figure. The leak current (left) and the resistance (right) versus the applied voltage of a 300 nm layer of SiO 2 with a thin gold electrode (1mm 2 ).

Easier to fabricate: Dielectric nanocapacitors. The dielectric strength of silicon oxide nanocapacitors. Figure. The break down voltage V b versus the thickness of the silicon oxide layer. The limiting dielectric strength of silicon oxide nanocapacitors is about 1 V/nm = 1GV/m. This is 3 orders of magnitude larger than the dielectric strength of macroscopic vacuum gaps and conventional capacitors (about 1 MV/m).

The dielectric strength household aluminum oxide layers Figure. The dielectric strength of aluminum foil (aluminum metal with a 4nm layer of aluminum oxide) is about 1V/nm. The Blue “Star” points are from the dull side and the other colors/shapes are from the shiny side. Aluminum oxide has a large dielectric constant of about 10 ε 0

The dielectric strength of household aluminum oxide layers at low temperatures The resistance of a two 4nm aluminum oxide layers versus the applied voltage at -10 degrees Celsius, after being treated with liquid nitrogen. A few samples appear to have a dielectric strength above 80V/nm. Other materials might have an even larger dielectric strength.

The dielectric strength of household aluminum oxide layers at low temperatures The resistance of two 4nm aluminum oxide layers versus the applied voltage in liquid nitrogen. In a few samples the dielectric strength appeared to be above 80V/nm. Other materials might have an even larger dielectric strength.

Applications: General purpose rechargeable battery An array of four nanocapacitors (cross section, side view). The cathode (− − −) is planar. The anode (+ + +) is a nano tip on a flat electrode. The thin curved lines indicate the electric field lines. The cathode is a conducting solid with high work function, such as gold or platinum. The flat part of the anode needs to have a high tensile strength, such as steel. The nano tip is a conducting solid with extremely high tensile strength, such as a carbon nanotube clamped to the steel electrode, or a tungsten Spindt tip. The design of the electrodes is similar to a tunneling microscope, except that tunneling microscopes have one movable tip, whereas the vacuum tube arrays have many stationary tips. The insulating walls (dots) are solids with a high compressive strength, such as silicon oxides. The electrodes and the walls create a vacuum tube. The electric field is in the vacuum tube between the anode tip and the cathode. Potential failure modes: mechanical (speed of sound), thermal (speed of sound), electrical (speed of light) – very similar to stimulated emission in a LASER (70V EMP on open BNC connector 20cm from source)

Applications: General purpose rechargeable battery - Safety issues Propagating dielectric break down

Specific Energy [MJ/kg] Min. Energy Release Time [s] Peak Power-to-Weight Ratio [kW/kg] Typical electrostatic capacitor General Atomics high voltage capacitor  10 3 Saft VL 6Ah Li-ion battery  10 1 Nesccap Electric double-layer capacitor  nm SiO 2 nanocapacitor (0.8V/nm, soft  )   nm Al 2 O 3 nanocapacitor (1V/nm, soft  )   Typical Li-ion battery  nm synthetic atom (vac. gap., 25V/nm, soft  ) 1 3   TNT  10 8 Kerosene  nm Al 2 O 3 nanocapacitor (l N 2, 80V/nm, soft  ) 75? 1.2   Weapon grade Uranium (hard  ) 144,000, ? 1  Applications: Explosive work with synchronized energy release of synthetic atoms [1] 1 kWh = 3.6 MJ [2] [3] Alfred Hubler, Synthetic atoms: Large energy density and record power density, Complexity 18(4), (2013)

Applications: Explosive work with synchronized energy release of synthetic atoms Synthetic atoms have potentially a record power density, more than 20 orders of magnitude larger than Li-ion batteries and almost 1 million times larger than nuclear devices. This means 50 milligram (3 table spoon) of charged synthetic atoms can deliver the same power as a nuclear chain reaction of 50kg (100 pounds) of highly enriched nuclear material. Currently, 50 milligrams of synthetic atoms can store roughly the same as amount of energy as a digital camera battery, but can potentially store times more energy.

Application: Harvesting energy in particle radiation with synthetic atoms (stacks of graphene NCs) -Efficiency of conventional nuclear power plants (heat engines): 35 percent. Here: The kinetic energy of nuclear reaction products is directly converted into electric energy in a stack of charged capacitors with a gap size of 500 nm and graphene electrodes. -Graphene is expected to be chemically and mechanically stable in high radiation environments because it's tensile strength of 130 GPa is very large, about 100 times larger than most metals. -The dielectric strength of nanocapacitors is very large, above 1 GV/m. -In a 1 GV/m electric field charged nuclear reaction products, such as 5.6 MeV alpha particles, come to rest in of a stack with 5000 nanocapacitors. We show that during the deceleration more than 90 percent of kinetic energy of charged nuclear reaction products is stored as electric energy in the stack. Each stack is 2.5mm thick and produces a high voltage DC current. A device with a 1 Ci - 241Am source generates 22 mW of electric power. Similar reactors with a 200nm Am-242(m) foil and beryllium / beryllium oxide sheets to act as both neutron moderators and reflectors are critical [1]. 72 percent of kinetic energy of charged nuclear reaction products is stored as electric energy in a stack of 8000 sheets of graphene. [1] Y. Ronen, A. Hatav, N. Hazenshprung, Nucl. Instr. and Meth. A 531, 639 (2004). [2] E. Shinn, A. Hubler, D. Lyon, M. Grosse-Perdekamp, A. Bezryadin, A. Belkin, Complexity 18(3), 24–27(2013).

Application: Harvesting energy in particle radiation with synthetic atoms (stacks of dielectric NCs) Conclusion: Nuclear radiation (Co mCi gamma source, 8.51 mC Am 241 alpha source at a distance of 1cm from the NC) reduces the dielectric strength only by 25%.

Application: Synthetic atom as a nano scale particle accelerator If the polarization is reversed this design can be used as a nano-accelerator for propulsion, X-ray source for lithography, medical applications.

Application: Nuclear protection suits made of synthetic atoms - Fabric with 16mm thick, 1cm 2 -plates which reflect nuclear radiation Conclusion: Nuclear radiation suits are electrically neutral and can reflect charged particle radiation with energies up to 100MeV/charge, and efficiently scatter gamma radiation.

Synthetic atoms: High power density and a record power density A.Hubler, Physics, UIUC We study tunnel currents and electric break down in nanocapacitors and synthetic atoms (double layer capacitors). We find: (1)Miniaturization reduces the tunnel currents by several orders of magnitude. Dielectric nanocapacitors have a large dielectric strength and small leak currents. (2)In nanocapacitors the electric field at the cathode is limited by the work function of the cathode surface material (280 MJ/m 3 for platinum) and the tensile strength of the anode (150 GJ/m GJ/m 3 for MWNVTs, 1.5TG/m 3 for boron nitrate). Synthetic atoms with quantized space charges are not limited by the work function of the cathode and have an increased capacity. (3)In synthetic atoms leak currents are suppressed because the population of the electrons in the gap is governed by the Fermi statistics and because of Coulomb blockade. Recent Publications: [1] A. Hubler, Digital batteries. Complexity 14(3), 7-9 (2008). [2] A. Hubler and O. Osuagwu, Digital quantum batteries: Energy and information storage in nano vacuum tube arrays, Complexity 15(5), (2010). [3] A. Hubler and D. Lyon, Gap Size Dependence of the Dielectric Strength in Nano Vacuum Gaps, IEEE Transactions on Dielectrics and Electrical Insulation, 20(4), (2013). [4] E. Shinn, A. Hubler, D. Lyon, M. Grosse-Perdekamp, A. Bezryadin, and A. Belkin, Nuclear Energy Conversion with Stacks of Graphene Nano-capacitors, Complexity 18(3), 24–27(2013)E. Shinn, A. Hubler, D. Lyon, M. Grosse-Perdekamp, A. Bezryadin, and A. Belkin, Nuclear Energy Conversion with Stacks of Graphene Nano-capacitors, Complexity 18(3), 24–27(2013) This paper won a DOE innovation award. [5] Alfred Hubler, Synthetic Atoms: Large energy density and record power density, Complexity 18(4), (2013)Alfred Hubler, Synthetic Atoms: Large energy density and record power density, Complexity 18(4), (2013)

Synthetic Atoms: High energy density and a record power density A.Hubler, Physics, UIUC Synthetic Atoms are nano-capacitors which mimic the geometry of atoms and simple molecules. (1) In chemical batteries the energy density is limited by the energy density of ionic bonds, which is typically around 1GJ/m 3. The theoretical limit for energy density in synthetic atoms is more than 1000 times larger if the electrode material has a particularly strong covalent bonds and therefore high tensile strength, such as graphene, carbon nano tubes, or boron nitrate nano tubes. (2) In synthetic atoms electric energy is stored by moving electrons, instead of ions. Since electrons have much less mass, the power density arrays of synthetic atoms is much higher than in Li-ion batteries. Because the response times are extremely short ( s) and the electric fields more than 1000 times larger than in macroscopic capacitors power densities exceed W/kg. Arrays of synthetic atoms can be used as conventional capacitors. (3) Arrays of synthetic atoms require no maintenance, are low cost, and are fully operational in a large temperature range and under extreme conditions, such as strong nuclear radiation. Broader Impact: Potential applications include general purpose rechargeable batteries for advanced electronics (i.e. batteries integrated in CPUs & memory) power sources for electric cars and airplanes, temporary power storage for utilities, force actuators, robust and resilient power grids with digital wires, thin insulation for high-voltage power lines, propulsive and explosive work, EMP sources, nano- X-ray sources for nano lithography, medical micro accelerators, nuclear protection suits (alpha, beta, gamma) for people and equipment, harvesting energy from solar wind and nuclear chain reactions in very small distributed nuclear batteries (1 milligram and up, 90% efficient).

Synthetic Atoms: High energy density and a record power density A.Hubler, Physics, UIUC IP Protection: [1] H. Higuraskh, A. Toriumi, F. Yamaguchi, K. Kawamura, and A. Hübler. Correlation tunnel device. Unites States Patent # 5,679,961 (1997). [2] A. Hubler and O. Osuagwu, Digital Quantum Batteries, provisional patent filed by the University of Illinois (2009) [3] A. Hubler, D. Lyon, M. Grosse-Perdekamp, A. Bezryadin, A. Belkin, A. Friedl, Nanocapacitor Arrays for Energy Storage using Native Aluminum Oxide Layers and Other Ultra-Thin Dielectrics, provisional patent filed by the University of Illinois, TF12200 (2013) [4] A. Hubler, E. Shinn, D. Lyon, M. Grosse-Perdekamp, A. Bezryadin, A. Belkin, A. Friedl, Energy Conversion with Stacks of Nanocapacitors, provisional patent filed by the University of Illinois, TF12206 (2013) Trend lines for the energy density of commercial energy storage devices by Chris Magee, “Towards qualifications of the role of materials innovation in overall technological development “, Complexity 18(1), 10–25 (2012) Thank you.

References [1] J. Schindall. The Charge of the Ultracapacitors Spectrum IEEE, 44(11):42-46, [2] A. Hubler and O.Osuagwu. Digital quantum batteries: Energy and information storage in nano vacuum tube arrays. Complexity, 15(5):48- 55, [3] H. El Brouji and J.-M. Vinassa and O. Briat and N. Bertrand and E.Woirgard. Ultracapacitors self discharge modelling using a physical description of porous electrode impedance. Vehicle Power and Propulsion Conference, VPPC '08. IEEE, 1-6, [4] R. H. Fowler and L. Nordheim. Electron Emission in Intense Electric Fields. Proceedings of the Royal Society of London. Series A, 119(781): , [5] R.G. Forbes and J.H.B. Deane. Reformulation of the standard theory of Fowler-Nordheim tunneling and cold electron emission. Proceedings of the Royal Society A, 463(2087): , [6] S.I. Shkuratov and S.A. Barengolts and E.A. Litvinov. Heating and failure of niobium tip cathodes due to a high-density pulsed field electron emission current. J. Vac. Sci. Technol. B, 13(5): , [7] W.P. Dyke and J.K. Trolan. Field emission: Large current densities, space charge, and the vacuum arc. Physical Review, 89(4): , [8] J.C. Sherman and R. Webster and J.E. Jenkins and R. Holmes. Cathode spot motion in high-current vacuum arcs on copper electrodes. J. Phys. D, 8: , [9] D. Alpert, D.A. Lee, E.M. Lyman, and H.E. Tomaschke. Initiation of electrical breakdown in ultrahigh vacuum. Journal of Vacuum Science and Technology, 1:35-50, [10] CRC Handbook of Chemistry and Physics, , [11] Yun Qi and Xucun Ma and Peng Jiang and Shuaihua Ji and Yingshuang Fu and Jin-Feng Jia and Qi-Kun Xue and S. B. Zhang. Atomic- layer-resolved local work functions of Pb thin films and their dependence on quantum well states. Applied Physics Letters, 90(1):013109, [12] A.J. McAlister and E. A. Stern Plasma Resonance Absorption in Thin Metal Films. Phys. Rev. 132(4): , 1963.