Study of the recombination on silicon micropillar
solar cells by impedance spectroscopy
Armand Girard-Noyer1, Anna Dalmau Mallorqui1, Olivier Demichel1, Thomas Moehl2, Anna Fontcuberta i Morral1
Laboratory of Semiconductor Materials , 2 Laboratory of Photonics and Interfaces
Objectives
Equivalent circuit of a solar cell in AC mode
The aim of this project was to determine the carrier lifetime of silicon micropillar solar cells. It is
known that recombination processes in silicon based solar cells affect dramatically the efficiency of the device. However, it is rather difficult to measure the carrier lifetime.
Impedance spectroscopy measurements were carried out on silicon micropillar solar cells and
the band structure of the device was determined as well as the carrier lifetime as a function of
the pillar diameter.
C
In alternative current, a solar cell can be modelled as:
• RP represents the leakage current within the junction
• C the space charge separation
• RS represents the series resistance
Rs
Rp
Impedance of the equivalent circuit
Fabrication method
Z=
Top-down approach:
RP
RS +
1 + jωRP C
- Im(Z)
1
Rs + Rp
2
0
Rs
Re(Z)
R
Rs + Rp
Representation in the complex Z’ - Z’’ plane for different potentials:
Photolithography
Reactive ion etching
35,000
POCl3 diffusion
30,000
-Im(Z)/Ohm
25,000
n-shell
p-core
By fitting each semi-circle, the series
resistance, the parallel resistance and
the capacitance are extracted as a
function of the applied voltage.
20,000
15,000
10,000
5,000
ITO
0
-5,000
-10,000
0
Radial pn-junction
Re(Z)/Ohm
Impedance vs. diode IV curve
I
50,000
The parallel resistance is inveresly proportional to the amount of recombination occuring
within the pn-junction. As the barrier height of the junction decreases with the applied bias,
the leakage current increases and the parallel resistance decreases.
For small amplitude sine waves:
1.5x105
5.0x10-9
R
C
E0 ,I0
1
× ∆E +
2
d2 I
dE 2
E0 ,I0
× ∆E 2 + ... ≈
dI
dE
E0 ,I0
× ∆E
∆E
Z(ω) =
∆I
0
1.0x105
4.0x10-9
C (F)
∆I =
dI
dE
Rp (Ohm)
I0 + ∆I × sin(ωt + φ)
5.0x104
3.0x10-9
E
0.0
E0 + ∆E × sin(ωt)
The capacitance in reverse bias is the ratio between the permittivity of the semiconductor
and the depletion width.
-1.0
-0.5
2.0x10-9
0.0
C(V ) =
ε0 εr
w(V )
Since the depletion width decreases with the
applied bias, the capacitance is expected to increase with the potential.
Bias (V)
Lifetime measurements
Mott-Schottky plot
The inverse square capacitance is related to the doping level and the built-in voltage by the
so-called Mott-Schottky relationship:
For
τ = Rp C
1
2 NA + ND
=
(Vf b − V )
C2
qεr ε0
NA
The lifetime can be splitted into bulk and surface lifetime:
2
1
1
=
(Vf b − V )
2
C
qεr ε0 NA
1
1
1
1
4S
=
+
=
+
τ
τbulk τsurf ace
τbulk
Φ
N D NA
The acceptor density is determined from the slope
of the Mott-Schottky plot (1/C2 = f(V)):
d
Lifetime of charge carriers within the junction is expressed by:
1
C2
dV
=
where S is the surface recombination velocity and Φ the pillar diameter. The lifetime decreases
with the pillars diameter consistent with an increase of the surface-to-volume ratio
2
1
qεr ε0 NA
The flat-band potential corresponds to 1/C2 = 0.
From this potential, one can determine the built-in
potential:
Vbi = Vf b − kT /q
Sample
A
B
Acceptor density N
1.89·1017
1.21·1017
A
(cm − 3 )
Built-in voltage (V
1.13
1.11
bi )
Determination of the Indium Tin Oxide top electrode work function
ITO thin films have different conductivity, transparency and surface structures, depending on
the deposition method.
ITO/p-type silicon junction leads to the following band structure:
φIT O
Built-in voltage and doping level are determined from the Mott-Schottky plot. Knowing
the electron affinity of the silicon and its band
gap, one can calculate the ITO work function
according to:
φIT O = Vbi + φSC
Vbi = φIT O − φSC
Work function of the ITO was found to be 4.65
eV.
The depletion width calculated from the doping profile shows that depending on the applied
voltage and the pillar diameter, pillars are not always fully depleted.
Impedance spectroscopy is an efficient method for lifetime measurements as a
function of an applied bias.
Conclusions
From impedance spectroscopy measurements, determination of:
• the built-in voltage
• the top electrode work function
• the doping level
Full band structure of the device
From impedance spectra, the band structure of the device was fully determined
• carrier lifetime as a function of the voltage
• silicon micro-pillars are not necessarly fully depleted but it depends on the bias.
Impedance spectrscopy is a suitable method
for carrier lifetime determination
Acknowledgements: