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Analysis of nanostructural layers using low frequency impedance spectroscopy Hans G. L. Coster Part 3: Phenomenological Impedances

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Phenomenological Impedances Phenomenological impedances are not necessarily related to dielectric substructure. Manifest when: (1) The properties of the material is modulated by the electric current passing through the material and (2) The changes in the properties are time dependent Phenomenological impedances are strongly frequency dependent (decrease with increasing frequency) and are generally seen at low frequencies Can provide useful information about charge carrier transport processes

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Phenomenological impedance of a light bulb If the filament of the light bulb was a simple resistor then the current would be given by: However, the filament heats up because of the energy dissipation of the electric current and the resistance increases with temperature At low frequencies the temperature goes up and down during each cycle. The resistance changes with time during each cycle. Heating is rapid because the specific heat of the filament is small. Cooling is slower because the heat must be radiated away. At high frequencies (> ~10Hz) there is insufficient time for the filament to cool and it attains a constant, high, temperature.

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Electrical properties of a light bulb V= 240 V AC Consider a 60 Watt light bulb under normal (50Hz) operating conditions When cold the resistance is ~ 100 Maximum heating here Distorted sinewave With phase lead At low frequencies it appears as an inductor

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Photo-voltaic Cells: Basic structure n p Depletion Layer Electric potential profile

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Dielectric Structure: Equivalent circuit layers n p Depletion Layer

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Conductance dispersion with frequency 2 layer model fitted to data

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Capacitance Dispersion with frequency 2 layer model fitted to data We will initially look at the frquencies > 1 Hz

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Basic Parameters for Cell determined by the INPHAZE dielectric structure refinement software Depletion Layer Capacitance : 3.10 x 10 -3 Fm -2 343 nm Conductance: 13.3 S m -2 p type Si material Capacitance : 0.13 x 10 -3 Fm -2 842 nm Conductance: 630 Sm -2

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Diffusion and Recombination Current electrode recombination C* G* Complex Elements Back diffusion

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Photo-voltaic Cells n p Depletion Layer Narrower depletion layer Potential with forward bias It takes time for holes and electrons to diffuse into the depletion region. The properties are therefore both time dependent and current dependent giving rise to a phenomenological impedance with a phase lag that will manifest at very low frequencies

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Transport / Diffusion Capacitance and Conductance Data shows very large (3 orders of magnitude) dispersion of capacitance at frequencies < 1 Hz. Addition of an element with complex capacitances and conductances to model the charge injection transport polarisation allows that process to be characterized.

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Equivalent circuit n p Depletion Layer C* G* electrode C*=C R + j C X G* = G R + jG X

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Cell Data Derived Depletion Layer Capacitance : 3.10 x 10 -3 Fm -2 343 nm Conductance : 13.3 S m -2 (conductivity 4.7 x 10 - 6 Sm -1 ) Transport number/Diffusion : Impedance element C*=-0.0140 - j. 0.0310 Fm -2 G*= 150x104 + j.7.30x 108 Sm -2 p type Si material Capacitance : 0.13 x 10-3 Fm-2 842 nm Conductance : 630 Sm-2 (conductivity 43 x 10 - 3 Sm -1 )

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Conductance vs DC bias Depletion layer p type semiconductor layer (film)

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The Spectrometer Impedance range: 0.1 -10 10 Frequency: < 10 -2 – 10 6 Hz Impedance precision: 0.002% Phase resolution: 0.001 o Inphaze.com.au

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inphaze.com.au

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