Comparison of the device physics principles of planar and radial p-n junction nanorod solar cells

TL;DR: In this paper, a device physics model for radial p-n junction nanorod solar cells was developed, in which densely packed nanorods, each having a pn junction in the radial direction, are oriented with the rod axis parallel to the incident light direction.

Abstract: A device physics model has been developed for radial p-n junction nanorod solar cells, in which densely packed nanorods, each having a p-n junction in the radial direction, are oriented with the rod axis parallel to the incident light direction. High-aspect-ratio (length/diameter) nanorods allow the use of a sufficient thickness of material to obtain good optical absorption while simultaneously providing short collection lengths for excited carriers in a direction normal to the light absorption. The short collection lengths facilitate the efficient collection of photogenerated carriers in materials with low minority-carrier diffusion lengths. The modeling indicates that the design of the radial p-n junction nanorod device should provide large improvements in efficiency relative to a conventional planar geometry p-n junction solar cell, provided that two conditions are satisfied: (1) In a planar solar cell made from the same absorber material, the diffusion length of minority carriers must be too low to allow for extraction of most of the light-generated carriers in the absorber thickness needed to obtain full light absorption. (2) The rate of carrier recombination in the depletion region must not be too large (for silicon this means that the carrier lifetimes in the depletion region must be longer than ~10 ns). If only condition (1) is satisfied, the modeling indicates that the radial cell design will offer only modest improvements in efficiency relative to a conventional planar cell design. Application to Si and GaAs nanorod solar cells is also discussed in detail.

Figures

FIG. 1. sColor onlined A conventional planar solar cell is ap-n junction device. Light penetration into the cell is characterized by the optical thickness of the materialf,1/a, noting that the absorption coefficienta is wavelength dependentssee Sec. III Bdg, while the mean-free path of generated minority carriers is given by their diffusion length. In the case shown, light penetrates deep into the cell, but the electron-diffusion length is too short to allow for the collection of all light-generated carriers.

FIG. 5. sColor onlined Relative light absorption—absorbed power for photons with energy greater than the band-gap energy vs thickness, for silicon and gallium arsenide.

FIG. 6. sColor onlined Short-circuit current densityJsc vs cell thicknessL and minority-electron diffusion lengthLn for sad a conventional planarp-n junction silicon cell andsbd a radial p-n junction nanorod silicon cell. In both cases the short-circuit current density is unaffected by decreasing the trap density in the depletion region. In the radialp-n junction nanorod case, the cell radiusR is set equal toLn, a condition that was found to be near optimal.

FIG. 7. sColor onlined Open-circuit voltageVoc vs cell thicknessL and minority-electron diffusion lengthLn for sad a conventional planarp-n junction silicon cell andsbd a radialp-n junction nanorod silicon cell. In both cases the top surface shown in the plot has a depletion-region trap density fixed at 1014 cm−3, so thattn0,tp0=1 ms, while the bottom surface has a depletion-region trap density equal to the trap density in the quasineutral region, at each value ofLn. In the radialp-n junction nanorod case, the cell radiusR is set equal toLn, a condition that was found to be near optimal.

FIG. 8. sColor onlined Efficiency vs cell thicknessL and minority-electron diffusion lengthLn for sad a conventional planarp-n junction silicon cell and sbd a radialp-n junction nanorod silicon cell. In both cases the top surface shown in the plot has a depletion-region trap density fixed at 1014 cm−3, so that tn0,tp0=1 ms, while the bottom surface has a depletion-region trap density equal to the trap density in the quasineutral region, at each value of Ln. In the radialp-n junction nanorod case, the cell radiusR is set equal to Ln, a condition that was found to be near optimal.

FIG. 9. sColor onlined Short-circuit current densityJsc vs cell thicknessL and minority-electron diffusion lengthLn for sad a conventional planarp-n junction gallium arsenide cell andsbd a radialp-n junction nanorod gallium arsenide cell. In both cases the short-circuit current density is unaffected by decreasing the trap density in the depletion region. In the radialp-n junction nanorod case, the cell radiusR is set equal toLn, a condition that was found to be near optimal.

FIG. 11. sColor onlined Efficiency vs cell thicknessL and minority-electron diffusion lengthLn for sad a conventional planarp-n junction gallium arsenide cell andsbd a radial p-n junction nanorod gallium arsenide cell. In both cases the top surface shown in the plot has a depletion region trap density fixed at 1014 cm−3, so thattn0,tp0=1 ms, while the bottom surface has a depletion-region trap density equal to the trap density in the quasineutral region, at each value ofLn. In the radialp-n junction nanorod case, the cell radius R is set equal toLn, a condition that was found to be near optimal.

FIG. 10. sColor onlined Open-circuit voltageVoc vs cell thicknessL and minority-electron diffusion lengthLn for sad a conventional planarp-n junction gallium arsenide cell andsbd a radial p-n junction nanorod gallium arsenide cell. In both cases the top surface shown in the plot has a depletionregion trap density fixed at 1014 cm−3, so thattn0,tp0=1 ms, while the bottom surface has a depletion-region trap density equal to the trap density in the quasineutral region, at each value ofLn. In the radialp-n junction nanorod case, the cell radiusR is set equal toLn, a condition that was found to be near optimal.