Abstract
α-voltaics harvest electron-hole pairs created as energetic α particles collide with and ionize electrons in a semiconductor, creating δ-rays. After ionization, charged pair production continues through δ-ray impact ionization events and the Auger relaxation of core-shell holes created through K-shell ionization events. Secondary ionization events are quantified using the TPP-2M model, the fraction of K-shell ionization events is determined using the energy-loss Coulomb-repulsion perturbed-stationary-state relativistic theory, and the relaxation of the resulting holes is treated with a fully ab initio approach using multiple Fermi golden rule calculations for ranges of carrier concentrations and temperatures. The limiting rate is 15 ns^{−1} for small carrier concentrations and high temperatures, as compared to the radiative core-shell relaxation rate estimated here at 20 ns^{−1}, indicating that Auger modes contribute significantly. Moreover, the K-shell ionization events are shown to dominate for low energy α particles and vanish for high energy ones. Thus, the efficiency loss due to energy dissipation in the fuel layer is mitigated, which is demonstrated by the analysis of a layered fuel-voltaic device with an efficiency from 20% to 14% for fuel layers between 5 and 10 μm thick. The design of a α-voltaic integrated with a thermoelectric generator is suggested for improved efficiency and the system-level mitigation of radiation damage and geometric inefficiency.
This research was in part supported by POSTECH WCU, National Research Foundation of Korea (R31-30005).
I. INTRODUCTION
II. EFFICIENCY
III. ELECTRON SHOWER
IV. K AND L-SHELL IONIZATION
V. AB INITIO CORE-SHELL KINETICS AND EFFICIENCY
VI. LAYERED-DEVICE EFFICIENCY
VII. RADIATION DAMAGE
VIII. BN α-VOLTAIC AS A TOPPING CYCLE
IX. CONCLUSION
Key Topics
- Ionization
- 56.0
- Carrier generation
- 13.0
- Energy transfer
- 11.0
- Phonon electron interactions
- 11.0
- Semiconductors
- 11.0
Figures
The ionization and relaxation of electrons in an α-voltaic. Primary K (1) and L-shell (2) ionization events, secondary δ-ray impact ionization events (3) and Auger K-shell hole relaxation (4), as well as nonradiative relaxations ((5a) and (5b)): electron and hole phonon emissions) are shown. These interactions describe the manner in which charged-pairs are generated in an α-voltaic. The density of states (D_{e} ) for c-BN and the ELFs [ ] for c-BN at the L ^{ 1 } and K-shell ^{ 2 } (boron) edges. The latter are used in the TPP-2M model ^{ 3,4 } to describe impact ionization (3) and can be extended to the primary ionizations (1,2). Here, the fraction of (1) to (2) is determined with ECPSSR theory.
The ionization and relaxation of electrons in an α-voltaic. Primary K (1) and L-shell (2) ionization events, secondary δ-ray impact ionization events (3) and Auger K-shell hole relaxation (4), as well as nonradiative relaxations ((5a) and (5b)): electron and hole phonon emissions) are shown. These interactions describe the manner in which charged-pairs are generated in an α-voltaic. The density of states (D_{e} ) for c-BN and the ELFs [ ] for c-BN at the L ^{ 1 } and K-shell ^{ 2 } (boron) edges. The latter are used in the TPP-2M model ^{ 3,4 } to describe impact ionization (3) and can be extended to the primary ionizations (1,2). Here, the fraction of (1) to (2) is determined with ECPSSR theory.
Variations in , the probability that a δ ray of energy causes an ionization with energy less than or equal to E_{I} , for L (top) and K (bottom) shells. Probabilities of 0.5, 0.8, and 0.95 are shown.
Variations in , the probability that a δ ray of energy causes an ionization with energy less than or equal to E_{I} , for L (top) and K (bottom) shells. Probabilities of 0.5, 0.8, and 0.95 are shown.
Variations in the ionization cross sections (in atomic units) for boron, nitrogen, and boron nitride as a function of α particle energy (using ECPSSR theory as implemented by ISICS). As it shows, K-shell and boron interactions will dominate for small , and L-shell and nitrogen interactions will dominate for large .
Variations in the ionization cross sections (in atomic units) for boron, nitrogen, and boron nitride as a function of α particle energy (using ECPSSR theory as implemented by ISICS). As it shows, K-shell and boron interactions will dominate for small , and L-shell and nitrogen interactions will dominate for large .
Variations in and as a function of the . As α particle slows down, it interacts more strongly with the core shell of boron and a large proportion of all ionization events create core-shell holes. The integrated probability shows the average probability for an α-particle entering c-BN with energy and illustrates the benefit of the strengthening core-shell interaction with decreasing particle energy.
Variations in and as a function of the . As α particle slows down, it interacts more strongly with the core shell of boron and a large proportion of all ionization events create core-shell holes. The integrated probability shows the average probability for an α-particle entering c-BN with energy and illustrates the benefit of the strengthening core-shell interaction with decreasing particle energy.
The electronic bandstructure of cubic boron nitride (calculated using VASP). An example of Auger and radiative K-shell hole relaxation modes are shown with the initial (i, j) and final (μ, ν) Auger electron states indicated.
The electronic bandstructure of cubic boron nitride (calculated using VASP). An example of Auger and radiative K-shell hole relaxation modes are shown with the initial (i, j) and final (μ, ν) Auger electron states indicated.
(a) Variations of the Auger relaxation rate as a function of core-shell hole energy for 8^{3} and 21^{3} k meshes, where results for the latter are averaged among the five nearest neighbors. The average rates are also indicated. (b) Variations of the average Auger and scaled Auger relaxation rates as a function of and . Each , extrapolated , and extrapolation method for simulations with , and are listed. The parentheticals (2), (4), and (5) describe the number of convergent simulations with averaged in order to quantify . Note that the behavior at represents the true behavior in the continuum.
(a) Variations of the Auger relaxation rate as a function of core-shell hole energy for 8^{3} and 21^{3} k meshes, where results for the latter are averaged among the five nearest neighbors. The average rates are also indicated. (b) Variations of the average Auger and scaled Auger relaxation rates as a function of and . Each , extrapolated , and extrapolation method for simulations with , and are listed. The parentheticals (2), (4), and (5) describe the number of convergent simulations with averaged in order to quantify . Note that the behavior at represents the true behavior in the continuum.
A layered fuel-α-voltaic device integrated with a TEG. The device concentrates the heat generated in the device and funnels it through the TEG in order to meet its thermal requirements and maintain a reasonably efficient life-span.
A layered fuel-α-voltaic device integrated with a TEG. The device concentrates the heat generated in the device and funnels it through the TEG in order to meet its thermal requirements and maintain a reasonably efficient life-span.
Variations in the overall efficiency and for varying fuel layer thicknesses, L_{f} . Here, is artificially separated from and , ignoring the non-linear interaction between the three terms, such that its rapid decay is illustrated.
Variations in the overall efficiency and for varying fuel layer thicknesses, L_{f} . Here, is artificially separated from and , ignoring the non-linear interaction between the three terms, such that its rapid decay is illustrated.
Tables
List of the relevant efficiencies, their values, and selected, influential terms. is zero by assumption. and are for to 10 μm.
List of the relevant efficiencies, their values, and selected, influential terms. is zero by assumption. and are for to 10 μm.
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