Transcript Extended Equivalent Circuit of a Solar Cell

Solar Cells
The electrical conductivity of
semiconductors
Conductivity increases as T decreases. Low T
sensors!
Extrinsic conduction
The density of free electrons for n
doping
ionization energy
necessary to release
electrons
from the donor atoms.
Effective
state density
For silicon crystals with a temperature of
T = 300 K,
NL = 3.22•1019 cm–3
ED = 0.044 eV
for phosphorus atoms as donors.
The density of free electrons for p
type semiconductorsA small amount of
energy can
release a freely
moving hole.
the effective state density
in the
valence band
density of the
acceptors
• (NV = 1.83•1019 cm–3
for silicon at T = 300 K, and EA = 0.045 eV
for boron)
The diffusion voltage created
• The charge neutrality within the
boundaries dn and dp of the space
charge region in the n-type and p-type
semiconductor region leads to:
The total width of the space charge
region
• When electrons are lifted from the valence
band into the conduction band and thus
released from the atom in the space
charge region, the electric field will pull
them into the n-region.
• Similarly, generated holes will move into
the p-region. This can be explained in the
energy band model by band bending in the
space charge region.
Solar cell principle with energy
band model
• the solar cell can only convert a part of the
photon energy into electrical current.
• For photon energies smaller than the band
gap, the energy is not sufficient to promote
an electron from the valence band to the
conduction band. This is the case for
wavelengths above:
• Not all the energy of photons with wavelengths
near the band gap is converted to electricity.
• The solar cell surface reflects a part of the
incoming light, and some is transmitted through
the solar cell.
• Furthermore, electrons can recombine with
holes. In other words, they can fall back to the
valence band before they are converted to
electricity.
Processes in an irradiated solar cell
• The solar cell only uses an amount of
energy equal to the band gap of the higher
energy of photons with lower wavelengths.
Excess energy, i.e. energy above the band
gap equivalent, is passed on to the crystal
in the form of heat.
• Hence, the share of the usable energy mainly
depends on the wavelength and the band gap.
• The external quantum collecting efficiency
ηext(λ) is the likelihood that an incident photon
generates an electron–hole pair. It is closely
related to the spectral response, which is a
measure of the part of the energy converted into
charge carriers.
Spectral response
external quantum collecting
efficiency
• In the absence of an external field, i.e. if a
solar cell is short-circuited, the
photocurrent IPh is generated. This current
can be calculated using the solar cell area
A, the spectral sensitivity S and the
spectrum of sunlight E(λ).
Photocurrent
• The irradiance E absorbed by the
semiconductor is a share of the incoming
irradiance E0. It depends on the thickness d
of the semiconductor and the materialdependent absorption coefficient α:
Comparison of semiconductors
• GaAs has an absorption coefficient for
light with a wavelength of about 1 μm of
α(GaAs)
app. 630 mm–1, whereas this value
decreases to α(Si) app. 7.2 mm–1 for
silicon.
• For both semiconductors to absorb the
same amount of light, the silicon will
have to be 87.5 times thicker than a GaAs
semiconductor.
The wavelength dependence of the
absorption coefficients must be considered
for an exact calculation.
Crystalline silicon solar cells should have a
thickness of at least about 200 μm for high
absorptions.
PRODUCTION OF SOLAR CELLS
AND SOLAR MODULES
• Crystalline silicon solar cells
Various semiconductor materials are suited
to solar cell production; however,
silicon is the most commonly used material
today.
• Silicon can mainly be found in quartz sand
(SiO2). The following reduction
process extracts silicon from the quartz sand
at high temperatures of about 1800°C
(3272°F):
Metallurgical
grade silicon
MG-Si, 98%Si
Another method: aluminothermic
reduction:
• However, silicon gained by this process
also has significant impurities. Silicon
used by the computer industry is so-called
electronic-grade silicon (EG-Si) for
the production of semiconductor devices. Its
impurity level is below 10–10 per
cent.
SOG-Si
• This high purity is not necessary for solar
cell production, in which solargrade
silicon (SOG-Si) is commonly used.
Nevertheless, purification processes
are needed for the production of SOG-Si.
• Silicon is mixed with hydrogen chloride or
chloric acid (HCl) in the silane process. An
exothermic reaction produces
trichlorosilane (SiHCl3) and hydrogen
(H2):
• Trichlorosilane is liquid at temperatures of
30°C. Multiple fraction distillations are
used to remove the impurities. The
chemical vapour deposition (CVD) process
is used for silicon recovery.
• Silicon is deposited as a thin silicon rod at
temperatures of 1350°C (2462°F), when the
trichlorosilane is brought into contact with
high-purity hydrogen:
• The end product is a high-purity silicon rod with
diameters of up to 30 cm (about 12 inches) and
lengths up to 2 m (about 80 inches). These rods
can be used for the production of polycrystalline
solar cells, which consist of a number of crystals,
rather than a single crystal. The crystals of
polycrystalline silicon are differently oriented and
separated by grain boundaries. They introduce
some efficiency losses.
• To increase solar cell efficiency, monocrystalline
material can be produced from polycrystalline
material applying the Czochralski or float zone
process.
• Seeding a single crystal at high temperatures
transforms the polycrystalline silicon to the
desired monocrystalline silicon. No grain
boundaries are present in the resulting material
and thus losses within a solar cell are reduced.
• The silicon slices, or so-called wafers, are cleaned and
doped in the following steps.
• Hydrofluoric acid removes any saw damage.
Phosphorus and boron are used for doping silicon to
create the p-n junction.
• Gaseous dopants are mixed with a carrier gas such as
nitrogen (N2) or oxygen (O2) for gas diffusion, and this
gas mixture flows over the silicon wafers.
The impurity atoms diffuse into the silicon wafer
depending on the gas mixture, temperature and flow
velocity.
Etching cleans the surface of the doped semiconductor.
• Finally, cell contacts are added. A screen
printing process adds the front and rear
contacts. Materials for the contacts are
metals or alloys of aluminium or silver. The
rear contact usually covers the whole cell
area. Thin contact fingers are used for the
front contacts, because they obstruct and
reflect sunlight. Only a minimum of the
cell’s surface should be covered by
contacts in order to optimize light capture.
• Finally, an antireflective coating is added
to the solar cell. This coating reduces
reflection at the metallic silicon surface.
Titanium dioxide (TiO2) is mostly used for
the coating and gives the solar cell its
typical blue colour.
Solar Cell Structure and Front View of a Crystalline
Silicon Solar Cell
Module sizes
• To avoid climatic damage several solar
cells with an edge length between 10 and
21 cm are combined in a solar module for
cell protection. Many modules are made
up of 32–40 cells; however, other module
sizes with significantly more or fewer cells
exist.
Thin film modules
• Besides crystalline silicon, thin film
modules hold promise for the cells of the
future.
They can be made of amorphous silicon
and other materials such as cadmium
telluride (CdTe) or copper indium
diselenide (CuInSe2 or CIS).
• Thin film modules can be produced using
a fraction of the semiconductor material
necessary for crystalline modules and
this promises lower production costs in
the medium term.
ELECTRICAL DESCRIPTION OF
SOLAR CELLS
• Simple equivalent circuit
• A photovoltaic solar cell is a large area
diode. It consists of an n-type and ptype
doped semiconductor with a resulting space
charge layer.
Typically, a non-irradiated solar cell has
nearly the same behaviour as a diode.
Therefore,a simple diode can describe the
equivalent circuit.
• The equation of the cell current I depends
on the cell voltage (V =VD) with the
saturation current IS and the diode factor
m:
• The thermal voltage VT at a temperature of
25°C is VT = 25.7 mV. The magnitude of
the saturation current IS is of the order of
10–10–10–5A.
• The diode factor m of an ideal diode is
equal to 1; however, a diode factor
between 1 and 5 allows a better
description of the solar cell characteristics.
Photocurrent
• A current source connected in parallel to
the diode completes the simple equivalent
circuit of an irradiated solar cell. The
current source generates the photocurrent
Iph, which depends on the irradiance E and
the coefficient c0:
• Kirchhoff’s first law provides the current–
voltage characteristics of the simple solar
cell equivalent circuit illustrated in the
following figures shows the characteristic
curves at different irradiances):
Simple equivalent circuit of a solar
cell
Influence of the Irradiance E on the I-V
Characteristics
of a Solar Cell
Extended equivalent circuit
• The simple equivalent circuit is sufficient for
most applications. The differences between
calculated and measured characteristics of real
solar cells are only a few per cent. However,
only extended equivalent circuits describe the
electrical solar cell behaviour exactly, especially
when a wide range of operating conditions is to
be investigated.
• Charge carriers in a realistic solar cell
experience a voltage drop on their way through
the semiconductor junction to the external
contacts.
• A series resistance RS expresses this
voltage drop. An additional parallel
resistance RP describes the leakage
currents at the cell edges.
The following figure shows the modified equivalent circuit including both
resistances.
Extended Equivalent Circuit of a Solar Cell (One-diode Model)
• The series resistance RS of real cells is in
the range of several milliohms (mΩ), the
parallel resistance RP is usually higher
than 10 Ω.
• The following figures illustrate the
influence of both resistances in terms of
the I-V characteristics.
Influence of the Series Resistance RS on the I-V Characteristics of
a Solar Cell
Influence of the Parallel Resistance RP on the I-V Characteristics
of a Solar Cell
Kirchoff’s nodal law
• With
• provides the equation for the I-V
characteristics of the extended solar cell
equivalent circuit:
• Can be solved by Newton’s method.
Given
voltage
Two diode model
Further electrical solar cell
parameters
• The voltage of a short-circuited solar cell is
equal to zero, in which case, the short
circuit current ISC is approximately equal to
the photocurrent IPh.
• Since the photocurrent is proportional to
the irradiance E, the short circuit current
also depends on the irradiance:
• The short circuit current rises with
increasing temperature.
• The standard temperature for reporting
short circuit currents ISC is usually ϑ =
25°C.
• The temperature coefficient αISC of the
short circuit current allows its value to be
estimated at other temperatures:
• For silicon solar cells, the temperature
coefficient of the short circuit current is
normally between
• If the cell current I is equal to zero, the
solar cell is in open circuit operation. The
cell voltage becomes the open circuit
voltage VOC.
• The I-V equation of the simple equivalent
circuit, provides VOC when setting I to zero:
• Since the short circuit current ISC is
proportional to the irradiance E, the open
circuit voltage dependence is:
• The temperature coefficient αVOC of the
open circuit voltage is obtained similarly to
the short circuit current. It commonly has a
negative sign. For silicon solar cells, the
temperature coefficient is between
• αVOC = –3•10–3/°C and αVOC = –5 • 10–3/°C.
• In other words, the open circuit voltage
decreases faster with rising temperature
than the short circuit current increases.
• The power curve has a point of maximal
power. This point is called the maximum
power point (MPP).
I-V and P-V Solar Cell Characteristics with Maximum
Power Point (MPP)
Electrical solar cell parameters