The number of electrons generated through inelastic scattering could be calculated using the following formula. The number of electrons generated is equal to the energy of the β-decay electron divided by the amount of energy required to generate a charge in a diamond.
During each scattering event. Energy from the β-decay electron is deposited to the surrounding diamond. This then requires a set amount of energy (13.6eV) to free a charge. As a rule of thumb, the energy required to generate a charge is three times the bandgap of the semiconductor (diamond).
The additional energy requirement is from the phonon generation due to the conservation of momentum. Therefore the number of charges generated by a single β-decay electron. Is equal to the number of scattering events a β-decay electron could go through before it runs out of energy.
is the number of charge generated by the β-decay electron.
is the energy of the β-decay electron released from carbon-14.
is the energy required to generate a charge in diamond (13.6 eV).
Since the maximum energy of a β-decay electron released from carbon-14 (Emax) is 156.18keV and the mean energy of the β-decay electron (Emean) is 49.16 keV. One could calculate the max and mean number of charge generated per β-decay to be:
Therefore, an ideal device could produce up to 11,484 electrons per decay with an average of 3,610 electrons. In addition, the diamond will have multiple electrons decaying simultaneously. Resulting in a sizable number of electrons, thus electric current.
The exact amount of current NDB nano battery could yield depends heavily on variables such as device design, diamond purity/crystallinity, and size.
The production of multiple electrons through inelastic scattering with diamond by an energetic electron is known as the secondary electron effect.
It is important to note here that electron generation is not a linear process. The majority of the electron generation happens at the terminal depth of the β-decay electron. One of the more accepted explanations of this phenomenon is that this is due to the increased interaction time between the β-decay electron and diamond as it loses momentum towards the end of its scattering track.
The relationship between the number of electrons produced by the energetic electron and the depth at they are generated where R is the terminal range. This graph shows that at its terminal distance. The energetic electrons generate the greatest number of electrons.
The above highlights the importance of geometry to this device.
Namely, the smaller the distance the charge has to travel, the greater the collection efficiency will be. This is due to the reduced chance of the generated charge being lost to recombination.
– Be cheap, as large surface area growth is an established area of nanotechnology.
– Be easy to produce as semiconductor film fabrication through Chemical Vapor Deposition (CVD) has been rapidly developed over the last couple of decades due to the economic interest in the production of cheaper and more powerful computer chips.
– Have a large surface area to extract the current from.
– Easily control one of the most important variables, film thickness.
– Have high charge collection efficiency. By fine-tuning the thickness of the diamond layer such that the β-decay electron will generate most of its electrons near the charge collector’s surface. One could optimize the device output.
– Maximize radiation capture, by confining the C-14 into a near 2D thin film, most of the β-decay from the C-14 will partake in the generation of collectible electrons. For example, if the NDB was to be a cube much of the radiation generated near its center will be lost before collection. Therefore by using a thin film structure, one could gain access to a greater number of the electron in the NDB maximizing its generated charge utilization.
– Easily contain the radiation by encapsulating the radiation-emitting C-14 layer with a non-radioactive C-12 layer using CVD growth.
NDB is an emerging nano battery technology. This is due to the challenges in its execution of the design. Nano battery is a direct product of cutting-edge nanotechnology where atomic material manipulation is crucial. As such, NDB requires experts to design and build it.
Some examples are the thickness of the diamond layer, crystallinity, and doping concentration:
– Have too thick a layer of diamond and the electrons released will recombine (become lost) in the diamond. Have too thin a layer then there is not enough diamond to release the electrons efficiently.
– If the crystallinity is high, the electron mean free path (travel distance to collect the electrons) will be large. Making the device efficient but expensive. Too low then it will become cheap but inefficient.
– Highly doping the diamond will allow the released electrons to be collected more efficiently. But if it is too high it will scatter the released electrons reducing efficiency.
NDB nano battery will use a related but different design in order to include NDB’s novel integrated nanostructure. A structure that is designed to increase the NDB’s efficiency and power. This is based on the NDB technical team’s knowledge and experience of high energy electron/diamond interaction.