Analysis of nanostructural layers using low frequency impedance spectroscopy

1
Analysis of nanostructural layers using low
frequency impedance spectroscopy
Part 3 Phenomenological Impedances
Hans G. L. Coster
2
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
3
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 (gt 10Hz) there is
insufficient time for the filament to cool and it
attains a constant, high, temperature.
4
Electrical properties of a light bulb
Consider a 60 Watt light bulb under normal (50Hz)
operating conditions
When cold the resistance is 100 W
Maximum heating here
Distorted sinewave With phase lead
At low frequencies it appears as an inductor
5
Photo-voltaic Cells Basic structure
n p
Y
Electric potential profile
Depletion Layer
6
Dielectric Structure Equivalent circuit layers
n p
Depletion Layer
7
Conductance dispersion with frequency
2 layer model fitted to data
8
Capacitance Dispersion with frequency
2 layer model fitted to data
We will initially look at the frquencies gt 1 Hz
9
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
• 
  

10
Diffusion and Recombination
Complex Elements
Current
C
electrode
Back diffusion
G
recombination
11
Photo-voltaic Cells
Narrower depletion layer
n p
Y
Potential with forward bias
Depletion Layer
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
12
Transport / Diffusion Capacitance and Conductance
Data shows very large (3 orders of magnitude)
dispersion of capacitance at frequencies lt 1 Hz.
Addition of an element with complex capacitances
and conductances to model the charge injection
transport polarisation allows that process to be
characterized.
13
Equivalent circuit
n p
electrode
C
G
CCR j CX
Depletion Layer
G GR jGX
14
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)

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)
Transport number/Diffusion Impedance
element C-0.0140 - j. 0.0310
Fm-2 G 150x104 j.7.30x 108 Sm-2
15
Conductance vs DC bias
p type semiconductor layer (film)
Depletion layer
16
The Spectrometer
Impedance range 0.1 -1010 W
Frequency lt 10-2 106 Hz
Impedance precision 0.002 Phase resolution
0.001 o
Inphaze.com.au
17

• inphaze.com.au