Solar Cells: Optical and Recombination Losses
4.2 Recombination Losses .1 General Concepts.1General Concepts
When we illuminate a solar cell, more and more electrons are energetically lifted into the conduction band and become available for the generation of an electric current.
They “jump over” the forbidden zone. This process is called “photo-generation”.
Now, the question arises: how do the electrons come back into the valence band?
The semiconductor has a high conductivity under illumination. As soon as we switch off the light, the semiconductor loses its increased conductivity again. The electrons, thus, leave the conduction band after a certain time and recombine with the holes in the valence band. The time between generation and recombination we call the lifetimeτ. The holes also have a lifetime.
The lifetime is defined by the equation
τ(n)=n/(R(n)) (4.14)
τ lifetime
n excess carrier density R recombination rate
This equation indicates how long the excess carriersnexist before they recom-bine again. The recombination process is governed by the recombination rate R.
For “direct-bandgap” semiconductors like GaAs, see Sect.4.1, this is relatively fast, because after the thermalisation, e.g. after the release of surplus energy to the crystal lattice, the electron jumps directly into the valence band by skipping over the forbidden zone and recombines there with a hole. The momentum of the electron does not have to be changed.
4 Solar Cells: Optical and Recombination Losses 89
For an “indirect-bandgap” semiconductor such as silicon, this is not so easy. In this case, the momentum of the electron must also be changed. Here, a third parti-cle is needed, for example, a phonon from the crystal lattice,13which provides the necessary change of momentum. This process has a low probability because now three particles have to interact with each other. Therefore, the lifetimeτof the car-riers of “indirect-bandgap” semiconductors is larger than the lifetime for carcar-riers of
“direct-bandgap” semiconductors. This is advantageous for silicon solar cells. On the other hand, the mobility of charge carriers is greater in some direct semiconduc-tors like GaAs. Nevertheless, the diffusion length, defined as√
Dτ (square root of lifetime times diffusion constant), according to (4.13), is only 30–50μm for GaAs and approximately 1200μm for Si.
4.2.2 Recombination
As soon as an electron from the conduction band unites with a hole in the valence band, recombination takes place. We distinguish here between four different types of recombination:
1. Radiative recombination
2. Shockley-Read-Hall recombination 3. Auger recombination
4. Surface recombination 1. Radiative Recombination
In radiative recombination, when an electron recombines with a hole, the released energy is emitted as a photon; this is illustrated in Fig.4.12.
Therefore, it is the reverse process of absorption. This process is more pronounced, the higher the concentrations of electrons and of holes are:
Rrad =B
np−ni2
(4.15)
Fig. 4.12 Illustration of the process of radiative recombination. An electron gives its energy during recombination to a photon with the energyE=hν[4]
13The crystal lattice is the regular three-dimensional arrangement of the atoms.
90 S. Leu and D. Sontag
ni denotes the intrinsic density of charge carriers14and is in Standard SI units15: 1010cm−3for silicon
n,p are the concentrations of electrons and of holes for electrons:n=n0+n
for holes:p=p0+p
n0,p0 number of electrons, holes in the unexcited (dark) intrinsic state n,p excess carriers: electrons, holes
B is the constant of radiative recombination
B is a temperature-dependent and material-dependent constant and characterizes radiative recombination. In silicon it has, at room temperature, the value: BSi =
~10−15cm3s−1.
In gallium arsenide, we have, at room temperatureBGaAs=~10−10cm3s−1: this is, thus, a value that is 100,000 times larger than for silicon. This shows that radiative recombination occurs less frequently and is not so important for indirect-bandgap semiconductors such as silicon—when compared to direct-bandgap semiconductors, such as gallium arsenide. Radiative recombination is a material-inherent type of recombination and does not depend on impurities or doping. It is present in all semiconductors.
2. Shockley-Read-Hall (SRH) Recombination
In all semiconductors there are also defects caused by impurities, such as oxygen, carbon or iron. If these impurities (defects) are located on crystal lattice sites of the silicon wafer, they lead to additional energy levels within the bandgap. These energy levels are easier to reach for electrons and holes. They can climb down like on a staircase, which is easier for them, than crossing the whole bandgap in one step.
They, thus, act on the charge carriers as recombination centres. Iron introduces an energy state that is located in the middle of the Si bandgap. Iron is, thus, attractive for both electrons and holes and acts as a strong recombination centre. Ni, Cu, Au and oxygen precipitates—also promote recombination and are strong lifetime-killers.
SRH recombination is the predominant type of recombination in silicon photovoltaic solar cells. In particular, it will take place in different steps as shown in Fig.4.13[5]:
• An electron can be trapped by the defect, Case I
• A hole can be trapped by the defect, Case III.
On the other hand, electron-hole pairs can also be generated starting from the defect states:
14The intrinsic carrier densityniis the density of carriers in an undoped sample of the same material (here: crystalline silicon), which is not subjected to any external field or other activation (e.g. light).
Its value (for silicon) is at room temperature approximately 1×1010cm−3.
15«SI units» refers to theInternational System of Units(SI, abbreviated from the FrenchSystème international[d’unités]); it is the modern form of the metric system and is the most widely used system of measurement.
4 Solar Cells: Optical and Recombination Losses 91 holes stay in the defect state for different durations and finally recombine (Case I for electrons and Case III for holes). Conversely, electrons (Case II) or holes (Case IV) can be emitted from the defect state.EDdenotes the energy levels of defect states (impurities) that represent the recombination centres [6]
• The trapped electron can be lifted back from the defect state into the conduction band, Case II
• Finally, a trapped hole can be returned to the valence band, Case IV.
The SRH recombination rateRSRH is dependent on the number (density)NDof defect states lying within the bandgap and on their energy levelsED. It also depends on the capture cross-sections of the defect states for the capture of electrons (σn) or for holes (σp) and finally it depends on the densitynof electrons in the conduction band and the densitypof holes in the valence band—and also and on the thermal velocityνthof the charge carriers
RSRH = np−n2i
τn(n+nSRH)+τp(p+pSRH) (4.16) where nSRH and pSRH are auxiliary variables, which in their turn depend on the intrinsic density ni of free carriers and on the position (energy)ED of the defect states with respect to the Fermi-level.
ni is the intrinsic density of charge carriers and is for silicon 1010 cm−3 (see Footnote 14).
92 S. Leu and D. Sontag
Fig. 4.14 Representation of Auger recombination with the two different cases:
electron-electron-hole recombination, characterized byCnand electron-hole-hole recombination, characterized byCp[4]
τn=(σnVthND)−1 (4.20)
The lifetime of the electrons in the conduction band isτnand the lifetime of the holes in the valence band isτp.
SRH recombination is based on impurities and other defects within the semi-conductor. In order to reduce SRH recombination, with the goal of increasing solar cell efficiencies, one must minimize the density of defects. This is possible—in the case of silicon—through a skilful design of the crystallization process of silicon, by exploiting the different segregation properties of the impurity atoms. Nevertheless, to take the example of iron impurities, impurity concentrations below 1012cm−3can hardly be achieved. Note that even after crystallization, it is possible to further reduce impurity concentrations by a suitable gettering16process (see Chap.5).
3. Auger Recombination
In Auger recombination, the energy released when one electron jumps from the conduction band into the valence band is transferred to a third particle. The energy can be given over to an electron or to a hole. The first case is called electron-electron-hole recombination and the second case is called electron-electron-electron-hole-electron-electron-hole recombination.
The two cases are shown in Fig.4.14.
In electron-electron-hole recombination, the relationship for the corresponding Auger recombinationRaug(e) is given by (4.21)
Raug(e)=Cnn2·p (4.21)
And if an electron and two holes are involved, then we have, by analogy:
Raug(p)=Cpp2·n (4.22)
16The gettering process reduces contaminants in a wafer and increases the carrier lifetime.
4 Solar Cells: Optical and Recombination Losses 93
Since both processes run in parallel, the following relationship holds:
Raug=n·p·
Cn·n+Cp·p
(4.23) For silicon, we have:Cn≈Cp≈10−30cm6s−1.
To fabricate a solar cell, we need doping. This unavoidable doping mainly causes Auger recombination. The higher the doping, the stronger that Auger recombination will be. Doping will lead to many defects.
Today’s most common solar cells use p-type silicon.p-type silicon is, to start with, doped with boron. Thepn-junction is then realized by overcompensation with phosphorus. Low phosphorus doping can reduce Auger recombination, but in this case, the n-region (emitter17) has a higher resistivity and it becomes difficult to obtain low contact resistances by metallisation. Emitter sheet resistances above about 100/are difficult to contact (metallisation) without losing cell efficiency.
It is often the case that the resistance and thickness of the emitter are not known.
This makes it difficult to determine the properties required for the metallization.
With the four point probe18 one can measure the sheet resistivity. From this the optimal metallisation can then be determined. The sheet resistance depends on both the resistivity and the thickness.
Explanation of Sheet ResistanceRs
The term “sheet resistanceRs” is often used in semiconductor industry when screen-printed pastes or other thin layers are employed. It is a very important parameter for characterizing thin films and plays a decisive role in photovoltaics in the assessment of metallization layers.
When we apply a metal contact to the emitter of a solar cell, we basically should know the resistivity and the thickness of the emitter, in order to optimize the metal contact. It is often the case that the resistance and thickness of the emitter are not known. This makes it difficult to design the metallization. On the other hand, the sheet resistivity of a homogenously doped emitter can be measured very easily.
The sheet resistance resistivity is defined as follows:
Rs=ρ/T (4.24)
ρ specific resistance (mm);
T (here:) thickness of the layer (mm);
Rs sheet resistance or sheet resistivity (/square) or (/).
Rs depends both on the specific resistance ρ ( mm) or more precisely on ρ (mm2/mm) and on the thicknessT(mm). The units used forRsare (mm2/[mm×
17The term emitter is often used in photovoltaics within the description of apn-junction. Inp-type silicon then-region is called emitter whereas inn-type silicon thep-region is called emitter.
18Four measuring probes are placed on the cell at a constant distance from each other and on a straight line. A current is driven through the two outer probes and the two inner probes measure the voltage. An alternative is to use the Electrochemical Capacitance-Voltage (ECV) method. This method measures additionally the active carrier concentration profiles in semi-conductor layers.
94 S. Leu and D. Sontag
mm]) or simply. Since the sheet resistanceRsrefers to a surface, one writes ohm/, whereis dimensionless.Rsgives an indication of how the metallization is to be real-ized. And as mentioned before it is easy to measure. If, for example, the phosphorous is driven into the p-type silicon for formation of thepn-junction19a sheet resistivity between 97 and 205 / results. 97/ can be achieved, for example, with a phosphorus concentration of 8×1019; 205/with a phosphorus concentration of 3.3×1019(low concentration). 97/leads in our example to a specific resis-tance of 31×10−3mm (4.24) and the semiconductor can be contacted optimally with silver fingers. A higher sheet resistivity of e.g. 205/cannot be optimally contacted without losing efficiency. The reason for this is that the dark currentJo
increases strongly at very low doping concentrations under the metal contacts [7].
This leads to low cell efficiencies. In this way thepn-junction can be evaluated by means of sheet resistivity.
4. Surface Recombination
A large part of the recombination within solar cells can be attributed to surface recombination. The neighbouring lattice atoms are missing on the surface, so that foreign atoms, especially oxygen, can accumulate. Additionally, doping with for-eign atoms, for example with phosphorous, also contaminates the surface and even intensify the recombination. As an example: In the case of ap-type silicon wafer, the phosphorus dopant enters from the surface. Finally, and most importantly, the metal contacts are lying on the surface—these contacts introduce additional contaminants and, act, thus as very active recombination centres. In the metal contacts (like in all metals), the Fermi level EF lies within the Conduction Band. Therefore, there are very many free electrons in these contacts which are just ready and waiting to swallow all holes, which reach the metal layer. Metal contacts are, thus, zones of very high surface recombination. The theoretic treatment of surface recombination is similar to that of SRH recombination. For the production of solar cells, the reduc-tion of surface recombinareduc-tion by passivareduc-tion of the electrically active recombinareduc-tion centres has the highest priority. The surface recombination velocityS is a variable with the unit cm s−1; it indicates how fast charge carriers recombine on the surface.
Surface recombination can be calculated for electrons (e) or for holes (h). In the following it is calculated for holes. Inp-type bulk material electrons are the minority carriers, but at the front-surface holes are the minority carriers because of the doping used for the formation of thepn-junction. For holes, surface recombination velocity Shdepends on the capture cross-sectionσh, on the density of electrons at the surface neand on the thermal velocityνthaccording to the following equations:
Sh=σhneνth (4.25)
If we now multiply the surface recombination velocityShwith the density of holes nh, we get the surface recombination rate.
19Thepn-junction is typically 350 nm thick.
4 Solar Cells: Optical and Recombination Losses 95
Rsurf-h=Shnh (4.26)
As an example: the surface recombination velocities are about 200–600 cm s−1 for standard solar cells and about 60–80 cm s−1for PERC cells (see Chap.5).
Inn-type bulk material holes are the minority carriers, but at the surface electrons are the minority carriers because of the formation of thepn-junction. The surface recombination velocity for electronsSecan be calculated similarly as in (4.25) and (4.26).
References
1. P. Würfel, Physik der Solarzellen, inSpektrum akademischer Verlag, 2. Auflage (Spektrum Hochschultaschenbuch, 2000). ISBN 3-8274-0598-X
2. E. Hecht, A. Zajac,Optics, 4. Auflage (Addison-Wesley Longman, Amsterdam, 2003). ISBN 0-321-18878-0, S. 402
3. H.-P. Sperlich,Meyer Burger Technologie AG, Analyse 2014, anlässlich einer Studie zusammen mit der Westsächsischen Hochschule Zwickau
4. T. Marvart, L. Castaner,Solar Cells: Materials, Manufacture and Operation(Elsevier, 2005).
ISBN 1856174573
5. W. Shockley, W.T. Read, Phys. Rev.87, 835 (1952); R.N. Hall, Phys. Rev.83, 228 (1951) 6. K. Lauer, Untersuchungen zur Ladungsträgerlebensdauer in kristallinem Silizium für
Solarzellen(Universitätsverlag Ilmenau, 2005)
7. S. Werner, E. Lohmüller, S. Maier, S. Mourad, A. Wolf, Challenges for lowly-doped phosphorous emitters in silicon solar cells with screen-printed silver contacts, in7th International Conference on Silicon Photovoltaics, Silicon PV 2017. Energy Procedia124, 936–946 (2017)
Sylvère Leu was from 2008 to 2017 with the Meyer Burger Group, where he became a member of the executive board, as Chief Innovation Officer and Technology Officer (CIO/CTO).
Since his retirement in 2017, he is active as technology con-sultant, for the Meyer Burger Group. Sylvère graduated from the Swiss Federal Institute of Technology in Zürich (ETHZ). He additionally obtained a Master’s Degree in Business Adminis-tration at the University of St. Gallen (HSG). As a Swiss pio-neer, Sylvère Leu started to work in photovoltaics 30 years ago.
He constructed an industrially relevant laminator and sun sim-ulator in his own company. Beside his job he worked as an associate lecturer at University of St. Gallen (HSG), for several years, in the field of industrial production. At the end of 2005 he was charged with building up an integrated 250 MWp photo-voltaic facility, including wafer, cell and module manufacturing, in Germany.
96 S. Leu and D. Sontag
Detlef Sontagis Senior Technologist for Solar Cells at Meyer Burger (Germany) GmbH. since 2015—one of the world’s lead-ing PV equipment manufacturlead-ing companies. He graduated as a physicist at the University of Konstanz in 2000, and obtained his Ph.D. degree in 2004 working on novel wafer materials for Pho-tovoltaics. In 2004 he joined Deutsche Cell GmbH, a subsidiary of Solar World AG, as quality assurance engineer with insights in the industrial crystalline silicon PV manufacturing processes along the whole value chain from block casting via cell pro-cessing to module assembling. Detlef Sontag joined the equip-ment manufacturer Roth & Rau AG as Senior Principal for cell technology in 2009. There he supported the planning and com-missioning of the Technology centre and worked actively on the development of cell technologies like PERC and HJT including project coordination of corresponding R&D-projects.