Solar Cells 2
shoomoosh
class07SolarCells2020-08Carriertransport1.pptxCarrier transport (1)
Prof. Richard R. King
Solar Cells
EEE 565
Arizona State University
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Thank you !
Many thanks to
Prof. Steve Goodnick
for his slides on solar cells which appear throughout this class
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• Under nonequilbrium conditions (optical generation, electric fields), n and p are no longer given by their equilibrium values, and vary in space. Transport is related to particle flux (current density) through the continuity equation
• Under optical excitation, must add electron-hole generation and recombination
Nonequilibrium conditions
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• The main contributions to the current density Jn,p are given by two terms, representing drift and diffusion
where is the mobility (cm2/Vs) which depends on scattering processes due to crystal imperfections
• The mobility is the proportionality between the electric field and average carrier velocity
Transport
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• The mobility depends on scattering rate due to impurities and lattice vibrations
• Dn,p is the diffusion coefficient, given by the Einstein relation (nondegenerate conditions)
• The drift-diffusion model is a simplification of the Boltzmann transport equation, which is an equation of motion for the non-equilibrium distribution function f(k,r) (no longer the Fermi-Dirac function)
Transport
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Electron mobility versus temperature for different doping levels:
High purity Si (Nd< 1012 cm-3); time-of flight technique (Canali et al. [1973])
High purity Si (Nd< 4·1013 cm-3): photo Hall effect (Norton et al. [1973])
Nd= 1.75·1016 cm-3; Na = 1.48·1015 cm-3; Hall effect (Morin and Maita [1954]).
Nd= 1.3·1017 cm-3; Na = 2.2·1015 cm-3; Hall effect (Morin and Maita [1954]).
http:// www.ioffe.ru/SVA/NSM/Semicond/Si/electric.html
Transport: Mobility
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Li, S. S. and W. R. Thurber, Solid State Electron. 20, 7 (1977) 609-616.
Jacoboni, C., C. Canali, G. Ottaviani, and A. A. Quaranta, Solid State Electron. 20, 2 (1977) 77-89.
Electron Mobility vs. Donor Density
Hole Mobility vs. Acceptor Density
Transport: Mobility
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Velocity Field Characteristics of Electrons in Si
Velocity saturation due to hot carriers
Jacoboni, C., et al. , Solid State Electron. 20, 2(1977) 77-89.
Transport: High Fields
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Resistivity of n and p Si versus total impurity concentration
Transport: Resistivity
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• In 1 dimension, the continuity and drift diffusion equations for electrons are written
• If the electric field is small, the drift term can be neglected compared to diffusion, to give the 1D diffusion equation
Transport
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• Generation:
• Recombination due to traps
• Un,p is the net generation rate, the difference of the generation and recombination rates:
• Optical carrier generation is the main process in solar-electrical energy conversion
Generation / Recombination
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Low and high level injection
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With optical absorption, the carrier population is driven out of equilibrium
Assume the separate populations of electrons and holes are governed by their own quasi-Fermi energies, Efn and Efp
Ef
Efp
Ei
Efn
Ev
Ec
Quasi-Fermi energies
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Recombination of carriers in the space-charge region (SCR) can actually dominate at low currents. The general expression for recombination via trap levels in the bandgap is:
Under low level injection in n-type material,
nn = ND >> pn, and the above equation reduces to:
Trap-Assisted (TA) Recombination
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14
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