2-1 Motivation
Fossil fuels such as oil and coal nature accumulated over the years, and finally exhausted. Use too much fossil fuel emissions of carbon dioxide caused by the greenhouse effect also very worried about the future of the Earth's environment. By the semiconductor manufacturing process of solar cells can convert sunlight directly converted into electrical energy, has long been one of the great hopes of alternative energy production methods.
Currently used as a power generation of solar cells mainly Flatbed polycrystalline silicon solar cells and single crystal silicon solar cell, solar cell grade silicon material quality equal to semiconductor grade silicon, so many high-quality silicon material needs. So many high-quality silicon material requirements, use of solar energy power generation goal to become very difficult. And to produce so many of the silicon wafer must also consume a lot of energy. A feasible method is the use of concentrating technology, and use a cheap lens or mirror to focus sunlight on a small solar cell, significantly reduce the amount of solar cells. Focus on one type of solar cell power
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generation system, the condenser the higher the magnification, and the higher the amount of conversion efficiency of solar cells used, the lower the cost of power generation.
III-V solar cell has two main aspects of concentrating solar energy power generation system with the help[7][8][9][10]
.
1. A higher rate of condenser: Silicon semiconductor material properties, silicon solar cell concentrator magnification is limited to about 200 times to 300 times, GaAs solar cells can be up to 1,000 times to 2,000 times.
2. Provide a higher conversion efficiency can practice: Single-crystal silicon solar cell production, 20% energy conversion efficiency is almost the upper limit, but InGaP / GaAs dual-junction solar electricity, you can reach 25 to 30%.
Among the various material systems of the solar cells, the III-V solar cell has been the forerunner of the power conversion efficiency (PCE)[11]. The multiple junction tandem cell can run as high as 40% in PCE, but is still bounded by the famous Shockley-Queisser limit[12]. To break through this limit, however, requires different thoughts in the solar cell. One of the possible solutions is to use intermediate band (IB) to increase the utilization of solar spectrum. It can be shown theoretically that the single band gap material with addition of IB can convert more than 60% of received solar energy into electricity [13].
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2-1-1 III-V solar cell
III-V semiconductor energy gap is direct bandgap. In theory, group III-V solar cell materials used in weight less and thin thickness than silicon. For the transfer of electrons and holes, thin materials only need to pass the shorter the distance you can reach the electrode, as long as the lattice of the material do not have too many defects in the natural loss of smaller, high cell efficiency. Another feature of the group III-V solar cells is the deployment of different bandgap materials, similar to the lattice dimensions of these materials can create stacked solar cell[2].
GaAs characteristics
GaAs as a direct bandgap materials at room temperature, the GaAs lattice
constant 5.6532Å band gap was 1.42 eV, its bandgap theoretically quite suitable
for the production of a single junction solar cell.
InGaP characteristics
InGaP material lattice constant match with GaAs, Ga and In, the proportion of
about 0.5:0.5 (a more precise figure is 0.51:0.49), and usually InGaP / GaAs
dual-junction solar cell, In0.5Ga0. 5P as the upper sub-solar material.
A typical Multijunction cells III-V solar cells construct the top anti-reflective layer, then the positive electrode, the top-level components for high-energy band gap of
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GaInP, followed by the tunneling junction. Next is low band gap in the underlying
components GaAs and then finally Ge substrate. and the back electrode. GaInP lattice
constant changes by the proportion of the adjustment of In and Ga, Ga and In is about
1:1, the lattice constant is very close to the GaAs lattice, these two kinds of materials
with very good access surface at the stress and defects can be reduced to a minimum,
and is conducive to electron transfer. In addition, the Tandem Cell theoretical
efficiency with upper and lower components of the energy gap with the absolute
relationship, with a bandgap of GaInP and GaAs is quite suitable for high theoretical
efficiency[14][15].
Fig. 2-1 Lattice constant versus energy gap
http://www.tf.uni-kiel.de/matwis/amat/semitech_en/kap_2/backbone/r2_3_1.html
2-2 Theory
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2-2-1 Physics of p-i-n solar cells
Semiconductor solar cells for an optimal design can absorb part of the conversion
of sunlight to produce voltage, current semiconductor photodetector. Semiconductor
materials absorb photons to produce electronic and electrical, combination of
semiconductor materials of different types of mixed together to form a diode, the
diode body built-in electric field will be electronic and electric separation, and in
particular the direction of current is potential difference at the p-n junction[16].
Solar cells need sunlight to work, so most of the solar cell in series with the battery,
there will be electricity generated when the sun first store to discharge to use for
non-sun. Basically, solar cells can absorb the solar spectrum energy is larger than the
semiconductor bandgap, and the amount of solar energy into electrical energy. All
electromagnetic radiation, including sunlight by photons with specific energy photons
have a wave nature, with the wavelength λ; photon energy and wavelength
corresponding relationship
E hc
(2-1) h is Planck's constant, c is the speed of light, only greater than the semiconductor material bandgap photons to generate electron hole pairs, so the solar spectrum is an
important consideration in the design of solar cells.
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When the sun light shines on this P-N structure, the P type and N-type
semiconductor due to the absorption of sunlight and produce electron - hole pairs.
Due to the depletion region provided by the built-in electric field, allowing the
semiconductor electron flow within the battery, through electrode leads to the current,
we can form a complete solar cell.
Relative to the original ideal diode, solar illumination light current is a negative
current. The solar cell current - voltage relationship is the ideal diode with a negative
current to the light, that is, illumination, the solar cell is an ordinary two diode
When the solar cell short-circuit, that is, V = 0, the short-circuit current, compared
with, that is when the solar cell short circuit, short circuit current is the incident
photocurrent, if the solar cell open circuit(open circuit), that is, I = 0, the open circuit
voltage (open-circuit voltage) was
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current multiplied by voltage, the former little corresponding to the voltage with
current in the current - voltage curve can be thought out a rectangle Fig.2-2, the area
of the rectangle is power, in order to facilitate analysis of solar cell device
characteristics from the current - voltage curve, in particular, the maximum power
voltage Vm and maximum power current Im shall be a rectangular area, and open
circuit voltage Voc withshort-circuit current (Isc) for the rectangular area ratio defined
fill factor, which is
Fig. 2-2 The solar cell IV curve
Semiconductor solar cells as an energy conversion element, most important, of course, the power conversion efficiency, output power with the ratio of the incident
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Which the incident power Pin can measure the incident light spectrum to determine.
Semiconductor solar cells is another important parameter is the quantum
efficiency as a measure of the photon conversion efficiency of the electronic, can be
divided into external electronic efficiency and internal efficiency.
The external electronic efficiency (EQE) means: a given wavelength of light
irradiation, the components can collect the maximum number of electrons and output
photocurrent with the ratio of the number of incident photons, can be expressed as
components can collect the output photocurrent of the maximum number of electrons
with the ratio of the number of photons absorbed, can be expressed as
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transmittance; and Wopt for is the so-called optical thickness, which is equivalent to the optical absorption length.
2-2-2 Detailed Balance Model
One of the fundamental limit on the power conversion efficiency of a solar cell was proposed by Shockley and Queisser [12]. This limit is based on detailed balance model.
Detailed balance provides a technique to evaluate the maximum efficiency of photovoltaic devices under ideal situation. The calculations for detailed balance model only consider the particle flux for electrons and photons. The theory can be easily used in the analysis of solar cell designs and thus serves as the basis for our research In the following, we will follow the derivation in ref. 17 to explain the detailed balance model, and its significance towards the device physics.
There are two simplest and most common basic assumptions in detailed balance:[12][17]
1. The mobility is infinite, allowing collection of carriers no matter where they are generated.
2. Complete absorption of all photons above the band gap.
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Fig. 2-3 The blackbody radiancy solar spectra at 6000 K[17]
For the source of light, the blackbody spectrum is most often used in theoretical analysis. The AM0 spectrum is useful for space-based photovoltaics. The AM1.5G spectrum is often used for non-concentration solar cells while the AM1.5D spectrum
is used for concentration devices[17]. Planck’s law for blackbody radiation
1
represents a photon flux per unit energy flowing out of a blackbody cavity, where E is the energy, h is Planck’s constant, c is the speed of light, k is Boltzmann’s constant, and T is the temperature of the blackbody.
The sun can be treated as an ideal blackbody, so the solar energy can be summed up as:
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flux flowing out of the blackbody, then (2-9) represents the absorbed total flux at the sun’s surface. For a solar cell on earth, the incident solar lights are almost the same as
the plane waves. Therefore the photon flux absorbed by the solar cell is actually decreased by a factor of
fs
(2-10) where is the solid angle subtended by the sun and the factor of 1 accounts for plane waves impingent on a planar surface. A standard value for fs is 2.1646×10-5 .
Similarly, The solar cell may be treated as an ideal blackbody at some temperature Tc. When a voltage V is applied across the device, due to the increased carrier injection, the p-n junction will see an increase in radiative recombination proportional to the Boltzmann factor, which is similar to what we saw in the forward bias current formula, and the expression for radiative recombination is thus given as
where A is the surface area of the device and q is the elementary charge. Similarly,
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the recombination rate due to non-radiative transitions is
electron-hole pair populations must be zero; thus:
AfAfs s U cAR
RAc I qU R R
Iq current density of the solar cellThe maximum efficiency is approximately 44% for the sun with an energy gap value of 1.1 ev.
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Fig. 2-4 Efficiency versus band gap/eV
2-2-3 Intermediate band
For increasing the efficiency of solar cell we add the intermediate band in the structure to absorbs additional lower energy photons, Intermediate band can be by several means like (lone pair bands, low dimensionality superlattices, quantum dots, impurities), Fig. 2-5 is the original design of the intermediate band solar cell. The traditional solar cell had only one band gap. By adding intermediate band, we can extend our absorption into longer wavelength region. In theory, the cell added intermediate band, its efficiency can exceed the Shockley and Queisser efficiency for ideal solar cells[12][13][18]
.
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Fig. 2-5 The original design of the intermediate band solar cell
We assume that the photons in the absorption process of this structure, including the electronic conversion process ACV between the valence band and conduction band electrons in the valence band and intermediate band conversion process AIV in as well as electronic band in the middle band and conduction band between the the conversion ACI; we assume that the photons are absorbed to produce a free electron-hole pairs the same time, the electron-hole pairs will be the opposite compound emit photons, so we will use the detailed balance deduced. Like the model of SQ of derivation, we assume that any irreversible process, the following derivation is derived under the assumption of an ideal solar cell of the following seven:
The ideal condition 1 (IC1): Suppose that any non-radiative recombination process
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takes place between any two energy levels.
The ideal condition 2 (IC2): assume that the carrier has infinite mobility.
The ideal condition 3 (IC3): assume that the composition of the external current, only the conduction band of free electrons and the valence band free holes, and the middle band in any of the electron and hole flow external.
The ideal condition 4 (of IC4): assume that the battery is thick enough to absorb all the incident photons, in order to ensure that all three conversion process will occur.
The ideal condition 5 (IC5): assume that the bottom of the battery or other locations are set to have a perfect mirror to ensure that the photon escaping from the battery to the front area.
The ideal condition 6 (of IC6): Suppose that in any photon energy range, only a photoelectric conversion process will occur.
The ideal condition 7 (IC7): assume that the light in the isotropic within the battery.
As shown, we assume that the three quasi-Fermi levels were ∈FC, ∈ FI, and ∈ FV the battery chemical potential μCV in = the the ∈FC-∈FV, the μCI = ∈FC,-∈ FI, μIV = ∈FI- ∈FV;
set the energy gap between the energy gap between the conduction band and valence band is set to ∈G, the conduction band and intermediate band ∈C, the energy gap between the intermediate band and the valence band is set to ∈I, andlocated ∈I <∈C, we can consider the incident photon energy ∈ will have the following four absorption
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modes:
1. ∈ <∈ I: no photon is absorbed.
2. When ∈I <∈ <∈C: the photon is absorbed and lead to the transition between
the electron and hole in the middle of the band and the valence band.
3. When and ∈C <∈ <∈G: photons are absorbed and lead to electron-hole interband transitions in the conduction band and the middle
4. ∈G <∈: the photon is absorbed and lead to electron and hole in the conduction band and valence interband transitions.
Assume that the cell has a maximum condenser 46000 times, the incident photons
and emit the photon flux will meet the following thermodynamic equation [3]: (2-17)
Where T is temperature, c is the speed of light, h is Planck's constant, μ is the chemical potential; μ set to 0 and T is set to sun the temperature TS, you can get the
incident photon flux . Then we can get the flow to the external current conduction band to meet the following formula:
(2-18) Output current in an external potential difference is equal to the conduction band and valence band between the Fermi gradient qV = μCV = μCI + μIV. In the absence of
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any current outflow from the middle band, so you can launch the current conservation equation:
( 2 - 1 9 )
calculate the maximum power divided by the incident radiant power
(σ is the Boltzmann constant) can be the theoretical maximum efficiency.
Calculation results shown in Fig. 2-6, calculated in arbitrary ∈I, ∈G maximum efficiency corresponds to the intermediate band, perfect backlit mirror and the largest condenser the theoretical maximum efficiency) curve; results showed that with the middle of the band structure of photoelectric conversion efficiency can reach 63.1%, 40.7% higher than that of SQ the model calculation results.
Fig. 2-6 Intermediate band theoretical maximum efficiency of the cell.
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2-2-5 Quantum Dot Solar Cell
We can divide the photocurrent into three sections, where the first and second are current generated from n and p-type regions and the final is current generated from QD’s structure. For one thing, at the p-type region, we can define the scope is extended from Z=0 to Z=Zp.
Fig. 2-7 Schematic structure of energy-band diagram of p – i – n QD solar cell.
Because of the standard equations for electron current density and electron continuity, we can figure out the distribution of minority carriers and obtain the electron–hole generation rate [18].
Gp
,z
1 R
F
e x p
z
(2-20) QD’s
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Which is under room temperature situation and where R(λ) is the surface reflection coefficient and a(λ) is the light absorption coefficient of GaAs. For overall understanding, we should find out the inconvenient part of solar flux F(λ). In this we make use of the model of solar spectrum described by a black body curve at the temperature of 5760 K, and acquire that
constant, and T1=5760K.
To follow we induce continuity equation since the excess electrons.
generation current only in proportion to the Dn=ә△n(x)/әx section . On account of the boundary conditions we can obtain
Finally, by solving the continuity equation we have
a , the total photocurrent collected by p-type region is equal to
01
j d Jnp n
(2-25)
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where λ1 is the absorption cut-off wavelength. Similarly, we can obtain the
photocurrent of the intrinsic and n-type region by the same derivation. The final short-circuit current Jsc can be written as:
Jsc=fi(Jnp+Jpn+Ji) (2-26) The results obtained from equations (2-20) to (2-23) are generic and no quantum dots effects are considered. To properly include the contribution from quantum dots, we have to modify several things. First, the carriers generated from bulk GaAs and quantum dots can be calculated separately using similar concept in equation (2-20) to (2-23). However, when we consider the summation of all currents and the solar cell circuit model, the ordinary current-voltage relation: J=Jsc-J0[exp(eV/kT)-1], needs to be changed. The saturation current J0 can be divided into two components: one from the edge of depletion layers (js,bulk), and the other from interior of depletion region(js,QD) [19]. By detailed balance between the radiation and thermal equilibrium, these components can be written in the form of: [19][20]
defined by percentage of i-region volume occupied by quantum dots (denoted by P):
Eg,eff=(1-P)×Eg,bulk+P×Eg,QD. For the bulk case, the Aeff and Eg,eff(=Eg,GaAs) can be found in regular textbook [19] [21]. The resultant J0 is the combination of the js,bulk, and
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js,QD. With J0 changed due to quantum dots, we can calculate the I-V (or J-V) characteristics of a quantum dot device more accurately. Second, the spectral absorption line shape of quantum dot needs to be considered when we model the generation rate G(λ,z) in equation (2-20). The shape of absorption of quantum dot can directly affect the photo-generated currents and thus the efficiency of the solar cell. In the ideal case, the quantum dot absorption is a delta function located at the discretized levels. However, in practical case, the quantum dot absorption is broadened by the non-homogenous size distribution of the dots, and imperfect of the material. The Fig.
2-8 shows our simulation on the single junction device in the ref. [22],
(a) (b) (c)
Fig 2-8. QD layer thickness and QD volume density impact to (a)Jsc (b) Voc(C) efficiency[19]
The shape of absorption of quantum dot can directly effect the photo-generated currents and thus the efficiency of the solar cell. In the ideal case, the quantum dot absorption is a delta function located at the quantum dot discretized levels. However,
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in practical case, the quantum dot absorption is broadened by the non-homogenous
size of the dots, and imperfect of the material. Usually a Lorentzian line shape is used
[22].
2-2-4Tunnel Junction
The wide bandgap tunnel junction connecting the InGaP and GaAs two
The wide bandgap tunnel junction connecting the InGaP and GaAs two