Solar cells
Semiconductor devices course - 2016
Alessandro Inglese
February 8th, 2016
Overview
•
•
•
•
•
•
From the p-n junction to the solar cell
Equivalent model
Solar cell characterization
Power losses
Solar cell design and trade-offs
State-of-the art and the future
P-n junction
p-Si
n-Si
+++++
+++++
+++++
-------------------
p-Si
When the
junction is
formed
n-Si
-
+
+
+
+
The diffusion of majority
carriers from the p-side to
n-side and vice versa
leaves behind
uncompensated “fixed”
charge that forms the
depleted region.
P-n junction (reverse bias)
SCR
SCR
When reverse bias is
applied:
•
Energy barrier
increases, such that
very few majority
carriers overcome the
barrier
•
The increased electric
field pulls majority
carriers away from the
junction
•
Drift of minority carrier
is still present, as it is
not impeded by the
junction electric field
(i.e. energy barrier).
This leads to the
small diffusion current
drift
diffusion
diffusion
holes drift
holes drift
P-n junction (reverse bias)
p-Si
n-Si
V
-
+
I
np0
Equilibrium
concentration - electrons
Equilibrium
concentration - holes
pn0
x
Saturation
current
(not to scale)
The figure shows the minority carrier concentration across the junction when:
• Reverse bias is applied
• The junction is kept in the dark
V
Illuminated P-n junction (reverse bias)
V
p-Si
n-Si
diffusion
-
I
+
Light-generated
carriers
drift
+
diffusion
-
-
-
drift
Light-generated
carriers
V
+
+
x
Incident light photo-generates electron-hole pairs in
• Depleted region (Space-charge region)
• Quasi-neutral regions (n-type and p-type)
Increased
saturation
current
This leads to increased saturation
current
Illuminated P-n junction (reverse bias)
•
Photogeneration dramatically increases minority carrier
concentrations. Saturation current thus increases due to the
following mechanisms:
– Drift of photo-generated carriers inside the junction
– Enhanced diffusion of minority carriers due to higher concentrations of minority
carriers (holes from n-side to p-side and viceversa for electrons).
This is the operation principle of light-detectors: solar cells and light
detectors are basically the same device. Depending on the external
bias, a solar cell can act as a light detector and vice versa.
Illuminated P-n junction – some formulas
• Aj is the junction area
• Gext is the generation rate
[cm-3/s] – proportional to light intensity
• wd is the width of the depletion layer
I photodepletion  qA j Gext wd
Photo-generated carriers inside the depletion
layer
p-Si
Diffusion of minority carriers
n(x)
I diff n  qA j Dn
x
I diff  p  qA j Dp
p(x)
x
Photo-generated carriers
 n  photo  Gext n  n p  Gext n
 p  photo  Gext p  pn  Gext p
n-Si
Photo-generated carriers
 n  p  Gext
Lp
Ln
We calculate the diffusion
current through a
simplification:
we linearize the carrier
concentrations
np is the electron concentration in the p-region
pn is the hole concentration in the n-region
x
Illuminated P-n junction – some formulas
 n p
is often referred to as carrier lifetime  average time between carrier
photo-generation and subsequent recombination
With the linearization in the
previous slide
Given that
L2n  Dn n
L  D p p
2
p
n p
x

G n  n p
Ln

G n
Ln
pn G p  pn G p


x
Lp
Lp
Ln and Lp are the diffusion lengths
for electrons and holes respectively
I photo  I photodepletion  I diff n  I diff p  qA j G(wdep  Ln  L p )
P-n junction – forward bias
+
When forward bias is applied:
drift
diffusion
•
Energy barrier is decreased
•
Drift of minority carriers from the p-side to
the n-side still takes place (same current
as for reverse bias).
•
Due to the low energy barrier, majority
carriers start overcoming the barrier such
that a diffusion current is formed. This
majority carrier current flows in the
opposite direction with respect to the
saturation current
Illuminated P-n junction – forward bias
When the p-n junction is illuminated, the considerations for
the photo-generated current under inverse bias are still
valid. However, the diffusion current depicted in the
previous slide also takes place and partially compensates
the photo-generated current. Hence,
net current
I photo  I directbias
+
V>0
Iphoto
Idirect-bias
-
We have a device with positive
voltage between cathode (+) and
anode (-) and current is flowing
from the anode (-) to the cathode
(+).
It is generating power!
Solar cell – operation region
Equivalent model
I
Iload
LightDetector
(V<0, I<0)
Iphoto
V
Solar cell
(V>0, I<0)
Iphoto
I load  I photo  I diff  I photo  I s (e
Idiff
qV
kT
1)  I photo  I s e
qV
kT
Diffusion current
shown at slide 10 which
obeys the p-n junction
current equation
Solar cell characterization
Equivalent model –
open circuit voltage
+
I
Voc = open-circuit voltage
Iphoto
Idiff
Voc
-
V
Equivalent model –
short circuit current
Iphoto
Isc = short-circuit current
Iphoto
Isc
Solar cell characterization
The Isc depends on several factors, namely:
•
•
•
•
the area of the solar cell;
the number of photons (i.e., the power of the incident light source).
the spectrum of the incident light.
the optical properties (absorption and reflection) of the solar cell
(discussed later);
• the collection probability of the solar cell (discussed later)
Solar cell characterization
When Isc and Voc, no power is
generated
Output Power is maximized at a
specific point (Vmax,Imax) of the I-V
diagram
P  Vload I load
dP
dVload
0
Vload VM
Solar cell characterization
The area of the rectangle is the
maximum generated power
I
A fill factor can be defined in order
to quantify the “squareness” of the
I-V curve
Voc
V
Max power
Iphoto
VM I M
FF 
Voc I sc
Voc
Isc
Optimal operation
point, where output
power is maximized
Isc
Solar cell characterization
Efficiency
Pmax FF Voc  I sc


Pin
Pin
Pin is the incident light power
Efficiency is defined as the ratio of output power from the solar cell to input
power from the sun.
Efficiency depends on:
• The spectrum and intensity of the incident sunlight
• Solar cell temperature.
• Power losses
Solar cell characterization
Solar radiation is filtered by the
atmosphere such that it is
attenuated before it reaches the
Earth’s crust.
Some wavelengths are missing,
due to gas absorption in the
atmosphere.
Further attenuation is caused by
nitrogen and particles (e.g. dust)
Solar cell characterization
The distance that light covers through the atmosphere strongly
depends on the position of the Sun
AM >1
AM1
A parameter, called air mass (AM),
defines the ratio between the
distance effectively covered by
light and the shortest possible path
length (i.e. when sun is overhead).
AM 
Estimation of the incident power. In
scientific literature AM=1.5
1
cos( )
The intensity of sunlight can be determined
as a function of air mass from this
empirical equation:
Pin  1.1 I 0  0.7 AM
0.678
I 0  1.353
kW
m2
Solar cell structure
Solar cell – Power losses
Surface reflection
Metal contacts with finite resistance
Bulk resistance
Metal contacts with finite resistance
Bulk recombination
Surface
recombination
The equivalent model shown at slide
13 holds only in the ideal case.
Solar cell
•
Front and rear metal contacts always show finite resistance (ohmic
losses)  Series resistance
•
Ohmic losses also in the shunt diode due to the finite resistance of
doped silicon  Shunt resistance
Equivalent model
Iphoto
Idiff
Rshunt
Rseries
Iload
These resistances directly
impact the short circuit
current and open-circuit
voltage.
Effect of series/bulk resistance (ohmic loss)
Rseries=0 Ω Rshunt=∞
Rseries=5 Ωcm2 Rshunt=∞
As a rule of thumb, series resistance
affects the “squareness” of the I-V
curve (it directly impacts the fill-factor).
The effect on Voc and Isc often remains
negligible.
The shunt resistance mainly affects the
Voc and the fill-factor.
Rseries=0 Ω Rshunt=26 Ωcm2
A combination of series and shunt
resistances leads to reduced fill-factor,
Isc and Voc (see next slide).
Effect of series/bulk resistance (ohmic loss)
• Shunt resistance is normally
related to the solar-cell geometry.
Reducing the cell thickness
generally leads to reduced shunt
resistance
• Series resistance mainly depends
on the quality of the metallization
used to create the contacts (type
of metal, metallization design etc.)
Optical losses
• Reflectivity of bare silicon is approx. 30%.
This means that at least 30% of the
incoming radiation is lost by reflection.
• To minimize the power loss by reflection,
there are two approaches:
1. Deposition of an anti-reflective
coating such that n0<n1<n2. The
thickness is chosen so that the
wavelength in the dielectric material
is one-quarter the wavelength in the
air. In formulas,
t
0
4n1
Note that zero reflection is achieved only with a single wavelength!! In solar cells zero
reflection is achieved with wavelengths of 0.6 μm, where the solar spectrum shows a peak
(see slide 18)
Optical losses
2. Texturing: surface treatment such that
needles and piramides are formed. Light
gets trapped within the pyramides through
multiple reflections.
In the industrial state-of-the-art, this is
accomplished through the generation of
the square based pyramides.
Black silicon
Texturing can be brought to the
nano-scale by creating very small
needles. Due to the very small
reflectivity, silicon becomes black,
since all the incoming radiation gets
trapped within the needles.
Research on black silicon
currently done at Aalto!
Bulk recombination
Light breaks the covalent bonds
and generates eletron-hole pairs
BUT not all the photogenerated
carriers are transferred to the
metal contacts
Some of them recombine
before reaching the metal
contacts
Bulk recombination
Ec
Incident
light
Illumination promotes an electron
from the valence to the
conduction band
Ev
Non-radiative recombination
Radiative recombination
Auger recombination
SRH recombination
Ec
Ec
Defects, vacancies,
recombination centers…
Ev
Ev
Unlikely to happen
in silicon because
it is an indirect
semiconductor
Ec
Photon emission
Ev
Bulk recombination – SRH model
Defects in the semiconductor introduce intermediate states within the
bandgap which trap photogenerated electrons and holes
Such intermediate states are generated by:
• Metal impurities (Fe, Cu, Ni etc.)
• Crystal defects (dislocations, vacancies,
stacking faults etc.)
• Organic contaminants (e.g. dust)
• Inorganic contaminants (e.g. sodium)
Light-induced degradation
Research currently done by me!
Solar-cell efficiency loss
within about one day of
illumination
Cu metal impurities have
been shown to cause such
phenomenon
Surface recombination
Silicon surface is often a very active recombination center. At the
interface between air and surface, the crystalline structure of the
semiconductor suddenly interrupts. The missing covalent bonds are
replaced by the so-called ”dangling bonds” with impurities at the surface
Surface passivation
In order to avoid the formation dangling bonds, a ”passivation” layer is
grown or deposited on the surface, such that the silicon atoms form
covalent bonds with the the passivation layer.
Passivation
passivation
Silicon
Si atoms
Covalent bonds
Common passivation materials are:
• Silicon dioxide (SiO2)  naturally grows when silicon is exposed to oxygen (oxidation)
• Silicon Nitride (SiN)  deposited through CVD or PECVD
• Aluminum oxide(Al2O3)  deposited through ALD
Research on novel passivation materials currently done at Aalto!
Surface recombination
Solar cell must not be too thick,
otherwise the photogenerated
carriers recombine before
reaching the front and rear
contact
Thickness is a design trade-off
Photon penetration rate follows
an exponential law e  ax
Solar cell has to be thick enough
to capture approx. all the incident
1
radiation
ts 

Photons with sub-bandgap energy
Not all the photons are absorbed
Ephoton=hv
The photon, whose energy depends on
the wavelength, promotes an electron to
the conduction band only when
E photon  Egap
Photons with E<Egap are not absorbed
This implies that only a portion of the
solar spectrum is actually absorbed by
the semiconductor
Absorption coefficient
Si
Sub-bandgap photons (non-absorbed
radiation)
λ
2·
ν
With Si small
frequencies (large
wavelengths) are not
absorbed
Shockley–Queisser limit
• Maximum theoretical efficiency of a solar cell using a p-n
junction to collect power from the cell.
• Efficiency limit of a single-junction solar-cell when all the
rest is assumed ideal (ideal contacts, no surface
recombination, no reflactance losses etc.).
In a single junction solar cell the
maximum conversion efficiency
is 33.7% and it is achieved
when Egap=1.34 eV!
Shockley–Queisser limit
• Based on this theoretical calculation, silicon is a
favourable material, since its energy gap (Egap=1.12 eV)
is close to the maximum
• However, even in the best case, only 33.7% of the
incoming radiation can be turned into electricity.
Record efficiency with crystalline Si solar-cells is
≈ 25%.
The only way to break this theoretical limit is to
use multi-junctions of materials with different
energy gaps
References
http://www.pveducation.org/
H.J.Möller “Semiconductors for solar-cells”, Artech House
1993
A.Kitai “Principles of Solar Cells, LEDs and diodes” – The
role of the p-n junction , Wiley 2011
S.Dimitrijev ”Principles of Semiconductor devices” – Oxford
University Press - 2006