D E S I G N A N D O P E R A T I N G P R I N C I P L E S O F I I I -­‐ V S O L A R C E L L S A N T H O N Y M E L E C O C A P S T O N E A D V I S E R : D R . I A N S E L L E R S TABLE OF CONTENTS Abstract .......................................................................................................................................................................................... 3 Introduction ................................................................................................................................................................................. 3 Procedure ...................................................................................................................................................................................... 4 Photomask ................................................................................................................................................................................ 4 Modeling .................................................................................................................................................................................... 5 IV curve ................................................................................................................................................................................. 5 Internal and external quantum efficiency ............................................................................................................. 6 Calculations .................................................................................................................................................................................. 7 Results ............................................................................................................................................................................................. 8 Photomask results ................................................................................................................................................................ 8 Modeling results .................................................................................................................................................................... 9 Data fitting ........................................................................................................................................................................... 9 Modeling changes in cell structure ........................................................................................................................ 10 Conclusion .................................................................................................................................................................................. 12 References .................................................................................................................................................................................. 13 Appendix ..................................................................................................................................................................................... 14 Solar cell operation ............................................................................................................................................................ 14 Introduction ..................................................................................................................................................................... 14 Band gap ............................................................................................................................................................................ 14 P-­‐N junction ..................................................................................................................................................................... 15 Efficiency considerations ................................................................................................................................................ 16 Mask design ..................................................................................................................................................................... 16 General structure design ............................................................................................................................................ 17 ABSTRACT For this project, single-­‐junction1 III-­‐V2 photovoltaic cells3 were examined. This involved understanding the basics of general photovoltaic cell operation4 as well as the structure needed to make such a device possible. One of the components of the cell of particular interest was the photomask5, which would then be used by Dr. Ian Sellers’ research group to process their own photovoltaic cells. Looking into design and efficiency of solar cells was also a large component of this project. Overall solar cell efficiency6 is influenced by several factors. These factors concern themselves not only with the material involved in the growth of a cell, but also the way it has been grown. Additionally, the electrode design on the top of the cell is also important to the overall efficiency. These design choices lead directly into mathematical modeling for understanding on a further level. There are several ways to do this, and a couple different areas of the cell to be modeled were considered. However, because of time constraints, only one model was finished. This model has been developed to take advantage of any single junction solar cells regardless of design choices and lets the research group conduct various efficiency tests to see just how an assortment of choices can lead into highly efficient cells. Mathematica7 was used to do all of the modeling for this part of the project, and, the data for each of the cells I pulled key design choices from were obtained from Dr. Sellers. The model did produce mixed results, but can still be used in the future with a little more work. INTRODUCTION Solar cell design has been a subject of study since the first practical devices were fabricated in the 1950s. Of course, the cost of solar cells back then made it not worth the time and money needed to research these devices. The oil crisis in the 1970s is what first turned the world to wanting alternative forms of energy. Since then, although the crisis was short lived, research had begun to take off. By the 1980s, silicon cells had reached the 20% efficient milestone8. Today, solar cell technology is recognized as a viable means for alternative energy, but is facing its own crisis against other cheaper and more efficient forms of energy. To combat this, there are new and emerging solar cell technologies that are currently being researched. In addition, we are approaching the theoretical efficiency limit of single junction cell technology and continuing to drive down fabrication cost. This is where the project fits in. By creating the photomask for the solar cell, Dr. Sellers’ research group can fabricate and study their own cells and, with the model in the future amongst other methods, can create new ways to increase efficiency and drive down cost. 1 Single junction -­‐ Solar cells that use just one P-­‐N junction. Considered further in [P-­‐N junction] 2 III-­‐V – Refers to group III and V elements of the periodic table that that makes up a solar cell 3 Photovoltaic cell – An electrical device, also called a solar cell, which converts the energy of light directly into electricity by the photovoltaic effect 4 General photovoltaic cell operation – A brief introduction to solar cell operation is briefly discussed in [Solar cell operation] 5 Photomask – An opaque plate with holes or transparencies that allow light to shine through in a defined pattern. Also referred to as a photolithographic mask 6 Solar cell efficiency – Generally computed as power out divided by power in 7 Mathematica – A computational software program used in scientific, engineering, and mathematical fields and other areas of technical computing 8 Efficiency milestones – For comparison, today’s single junction efficiency is fast approaching the theorized limit of 33.5% by reaching into the upper 20% PROCEDURE PHOTOMASK The design of the photomask involved a very straightforward approach. Researching the design of the electrode patterns9 and then enacting such research was the basic idea involved here. Investigation into the design of the electrode patterns started with understanding just what is important for an efficient electrode pattern10. This research was aided by a previous design of III-­‐V electrode pattern [Error! Reference source not found.] provided by Dr. Sellers. FIGURE 1: THE PREVIOUS ELECTRODE DESIGN Realization of the photomask was achieved using L-­‐Edit11. In addition to the main electrode pattern, other patterns needed to be created within the photomask. While an electrode pattern such as [Error! Reference source not found.] defines the top of a typical cell, a second pattern is eeded to define the size and shape of the cell. This can also be seen in [Error! Reference source not found.] and is referred to here as the mesa12. It is larger than the 1mm2 mask by 10 micrometers on each side. Moreover, other cell sizes are desired for a couple reasons. 1mm2 sized cells are not the typical size for the type of high efficiency cells the research group is developing. Usually this is a 1cm2 cell. Furthermore, taking comparison measurements between different cell sizes is important for determining material quality. Finally, a few additional patterns were included so further measurements, such as resistance of the electrode contacts could be taken. All of these can be seen in the photomask [Error! Reference source not found.] below. 9 Electrode pattern – To avoid confusion, I use pattern here to refer to the various objects on the left side of the overall photomask [Error! Reference source not found.]. 10 Efficiency of an electrode pattern – Design considerations for the efficiency of the electrode pattern is discussed in [Mask design] 11 L-­‐Edit – A photomask design program from Tanner research 12 Mesa – This is an additional overlaying pattern that covers the first pattern and serves to define the size and shape of the cell. Where the first pattern represents what can be seen on the top of the cell, the mesa represents a shield of sorts for everything under it therefore defining the cell’s size and shape. All of the mesas are pictured on the right side of [Error! Reference source not found.] 13 IV curve – A graph that plots the current (I) against the voltage (V) of a solar cell FIGURE 2: THE ENTIRE PHOTOMASK MODELING IV CURVE The IV curve13 is one of the ways to model part of a solar cell’s design. This curve is important as it can tell us a few significant parameters about a particular cell. These parameters are the turn on voltage14 and the contact resistance of the cell. This curve is governed by [Equation 1]15 and can be seen by [Figure 3] on the next page. EQUATION 1: THE IV CURVE 13 IV curve – A graph that plots the current (I) against the voltage (V) of a solar cell 14 Turn on voltage -­‐ The voltage required to allow current flow 15 I
L, the light generated current (minority carrier flow current); IO, the dark saturation current (majority carrier flow current), n, the ideality factor, q, charge of an electron, k, Boltzmann’s constant, Rs and Rsh, series resistance of contacts and shunt resistance of contacts respectively. FIGURE 3: THE IV CURVE [Equation 1] also is an example of an implicit function16. The procedure for modeling this was unfortunately not easy. The fact that it is an implicit function means that an iterative method17 should work well. Unfortunately, attempting such a method resulted in a function that broke down and started diverging rather quickly. It was decided due to time that extracting the series resistance18 and shunt resistance19 of a cell was not as important as another modeling method that extracts different information about a cell and is a standard for measuring efficiency. INTERNAL AND EXTERNAL QUANTUM EFFICIENCY Internal and external quantum efficiency curves show the energy conversion rate of a solar cell at different wavelengths. Internal quantum efficiency shows this conversion rate after the losses of reflectivity20 and transmission21 have been determined while external quantum efficiency demonstrates the conversion rate with those losses22. These efficiency curves were modeled using similar equations, with the only difference being the reflectivity and transmission as a factor. Regardless, they both take on the form of [Error! Reference source not found.] that can be seen n the next page. [Error! Reference source not found.] is essentially a superposition of the currents generated in the three regions of the cell divided by the total input power either incident on the cell or already absorbed for EQE and IQE respectively. 16 Implicit function – A function f(x) that is defined implicitly by a relation between its argument and its value 17 Iterative method – A mathematical procedure that generates a sequence of improving approximate solutions for a class of problems 18 Series resistance – A resistance that results from the resistance of the contacts and affects a cell’s performance at high voltages 19 Shunt resistance – A resistance that results from poor quality of the material and affects a cell’s performance at low voltages 20 Reflectivity -­‐ Refer to the fraction of incident electromagnetic power that is reflected at an interface 21 Transmission – Property of a substance to determine the passage of light, with some or none of the incident light being absorbed in the process 22 Because of this fact, IQE curves always have a higher efficiency than EQE curves EQUATION 2: QUANTUM EFFICIENCY This will therefore generate a curve that shows us the percentage of energy conversion at any given wavelength. Embedded in the currents generated in each of the regions are different parameters and, when fitted to data, can be used to tell us different things about a particular cell. CALCULATIONS Quantum efficiency was modeled using the currents in the different regions. These currents all take on similar forms and an example can be seen in [Equation 3]. EQUATION 3: CURRENT GENERATED IN THE N REGION The important parameters of the cell are used to tailor fit this curve to any type of single junction photovoltaic cell. These parameters include factors not dependent on wavelength such as q23, xp24 wp25, sn26, ln27, dn28 as well as some parameters that are, such as intensity29 and α30. As an approximation, for R31, a single constant value was used, but it too does depend on wavelength. Modeling this as a function of wavelength, λ, we obtained the current generated by the N region at any given wavelength. And, modeling the other two similar current equations, we obtained the other regions’ current generation as well. This can be seen in [Figure 4] on the next page. By looking at [Figure 4], one can determine a few things. First, the cell structure can easily be seen. Noticing the different in generation between the N layer and the P layer tells us that the N region is much thicker than the P region32. One can also see that the space charge region33 is not very large 23 q – The electric charge carried by a single electron 24 xp –The size of the P region 25 wp – Depletion width of the P region 26 sn – Surface recombination velocity in the N region. Affects of the rate of recombination at the surface. Recombination is discussed further in [General structure design] 27 ln – Average diffusion length of an electron 28 dn – Diffusion coefficient of an electron 29 intensity – Refers the light incident on the cell at any given wavelength 30 absorption – Denoted, α, and refers to the absorption of light of a cell at any given wavelength 31 R – Reflectivity of a cell at any given wavelength 32 Layer generation – While it may seem backwards at first, solar cells are minority carrier diffusion driven and so this is actually correct. More on this can be found in the appendix something 33 Space charge region – Another term for depletion width as it does not generate much current. This tells us that doping of this particular cell is not too high since the space charge region’s size is directly proportional to the doping concentration. FIGURE 4: INTERNAL QUANTUM EFFICIENCY Finally, one can easily determine the band gap34 to be about 870 nm as that is where the QE graph ends. RESULTS PHOTOMASK RESULTS The photomask [Figure 2] has already been used to fabricate cells by Dr. Sellers’ research group. The first of these fabricated cells have been the results of the 1mm2 electrode pattern. This can be seen on the following page in [Figure 5] with green to show the second mask for clarity. Additionally, some optical microscope images of the fabricated cells can be seen on the next page as well in [Figure 6] with the left cell showing the 1mm2 electrode pattern applied to a cell, but without the second mask applied and the right cell showing the 1mm2 electrode pattern again already applied to a cell, but also the second mask applied, which can be seen by examining the edges of the cell. 34 Band gap – Discussed in [Band gap] FIGURE 5: 1MM^2 ELECTRODE PATTERN WITH SECOND MASK ON TOP FIGURE 6: 1MM^2 ELECTRODE PATTERN (LEFT) AND 1MM^2 ELECTRODE PATTERN WITH THE OVERLAYING SECOND MASK APPLIED (RIGHT) MODELING RESULTS DATA FITTING The model used in this project to produce valid quantum efficiency curves for different data did have mixed results. These results can be seen explictly in [Figure 7] on the next page. FIGURE 7: DATA FITTING OF EXTERNAL QUANTUM EFFICIENCY The optical absorption used in this project is the reason for the inability to fit the data properly. This is believed to be the case and not something else for example, because of what is happening in the upper regime of the wavelength. The model used here has a different band gap than the cell’s data shows. This means that the absorption for the model is different to the absorption of the data. The absorption used in the model was the result of experiment on pure Gallium Arsenide35 while the cell being modeled was not structured using pure Gallium Arsenide. The material itself has been doped, which affects absorption. Additionally, other factors may contribute to the altering of the cell’s absorption. To correct this, a transmission measurement is required to determine the real absorption happening within the material. MODELING CHANGES IN CELL STRUCTURE The model is able to predict what changes cell structure and quality will have on efficiency36. This is shown explicitly on the next page in [Figure 8] by using the same cell structure as the model in [Figure 4]. Since the P region’s contribution was rather large, increasing the surface recombination velocity decreases the internal quantum efficiency quite a bit. The numbers used here are actually realistic recombination velocity numbers, with the original blue line representing the introduction of a highly doped window layer37 to reduce such effects. 35 A common III-­‐V material used due to its ideal properties for solar cells 36 Other considerations in solar cell efficiency design are discussed further in [General structure design] 37 Window layer – The top layer in the solar cell that serves to act as a “window” so to speak in that it allows the transmittance of light. It is sometimes highly doped to act as a passivation layer, which reduces the effects of surface recombination FIGURE 8: SHOWING THE EFFECTS OF SURFACE RECOMBINATION VELOCITY ON OVERALL IQE FIGURE 9: THE EFFECTS OF DECREASING THE DIFFUSION LENGTH OF THE HOLES ON OVERALL IQE [Figure 9] conversely shows the reduction in contribution of the model’s N region structure by reducing the length that the charged carriers38, in this case the holes, can travel. By reducing the distance of travel, carriers become less likely, or are even unlikely entirely, to travel and be collected by the surface. As such, the contribution of that region will decrease as seen. The numbers used here were mostly for effect only and are in no way typical values for the diffusion length of holes. CONCLUSION This project involved creation of both a photomask for cell fabrication and a model to measure created cells’ efficiency. The different electrode designs on the photomask were based off a typical III-­‐V design given to me by Dr. Sellers. The photomask is now currently in use by Dr. Sellers research group to fabricate cells. The model was obtained from the derived superposition of currents within the solar cell’s different regions. This model depended on various parameters and with the use of fitting, can be used to extract such parameters. However, the absorption used for the model cannot be used generically as I did. One must use the absorption specific to that cell (or at least a better approximation than pure material) if a good result is desired. Regardless, the model, as it is now, can predict changes in cell structure and quality of any single junction cell by altering the parameters that determine the overall quantum efficiency of the cell. 38 Charged carriers – A particle free to move in the material that carries an electric charge. Discussed further in appendix something REFERENCES http://en.wikipedia.org/ Nelson, Jenny. The Physics of Solar Cells. London: Imperial college Press, 2003. http://pveducation.org/ http://www.volker-­‐quaschning.de/articles/pv-­‐basics/index.php APPENDIX SOLAR CELL OPERATION INTRODUCTION The sun blankets the earth in solar energy every single day. The life on this planet would not be possible without it. Some living beings, such as animals, rely indirectly on the sun for life. Others, such as plants harness the sun’s energy directly. Solar cells can directly harness the sun’s energy as well. On the simplest level, Solar cell operation works by absorbing light, and the accompanying energy, and then being able to use that energy to do useful electrical work. The processes that make this happen are discussed in the following sections. BAND GAP Light incident on the cell is absorbed by all semiconductors and, just how much energy it takes to free an electron depends on that particular semiconductors band gap. FIGURE 10: THE BAND GAP [Figure 10] shows a separation between the valence band39 and conduction band40 of a generic semiconductor. This separation involves a potential difference41 that is typically overcome by absorption of light. In general, all the light with energy above the band gap is absorbed while light with energy below the band gap is not. Promotion42 of an electron into the conduction band from 39 Valence band -­‐ The highest range of electron energies in which electrons are normally present 40 Conduction band – The range of electron energies that are high enough to free an electron from binding with its atom to move freely within the material of the structure 41 Potential difference – Referring here to the electric potential, V. Also called voltage. 42 Promotion – This process is also referred to as generation the valence band also creates what is called a hole43. [Figure 10] represents the electron with a red sphere and a hole by a blue sphere. The electron and hole are collectively referred to as charged carriers. P-­‐N JUNCTION In the discussion of solar cells, it is vital to introduce the P-­‐N junction. The P-­‐N junction is the region of cell that is the direct result of bringing two differently doped44 regions, a P doped45 region and an N doped46 region, into contact with each other. FIGURE 11: THE PN JUNCTION (LEFT); THE IV CURVE (RIGHT) The result is that the extra holes from the P doped side and the extra electrons from the N doped side diffuse across the boundary. This continues to happen until a fixed ion region results from the diffusion. This fixed ion region has an associated built-­‐in electric field (and therefore a potential), which prevents further diffusion of the holes and electrons of these two regions. This process can be seen in explicitly on the left side of [Figure 11]. To continue diffusion of the electrons and holes, the potential difference must be decreased. This can be accomplished by reducing the electric field by applying a bias to the P-­‐N junction. This can be seen on the right side of [Figure 11]. By increasing the voltage, and therefore reducing the potential of the space charge region, we eventually see the current increase as diffusion can once again happen. This current flow is called majority carrier current flow because it is the majority carriers that cause the current to arise. This is also the basis of a diode47 as well as a solar cell operating in the dark. 43 Hole – The absence of an electron that can be thought of as a positive particle 44 Doping – The act of purposefully introducing impurities into a semiconductor to increase conduction 45 P doping – Adding atoms with a missing valence electron or adding atoms with added holes. Boron is an example 46 N doping – Adding atoms with an extra valence electron. Phosphorous is an example 47 Diode -­‐ A semiconductor device with two terminals, typically allowing the flow of current in one direction only FIGURE 12: THE IV CURVE REPRESENTING THE EFFECT OF ILLUMINATION ON A CELL Under illumination, however, electrons and holes are generated from the absorption of light all over the cell. If this happens in the N region, the holes generated will not be the majority in that region and thus, will flow back to the P side. Conversely, if it happens in the P region, the electrons generated will flow back to the N side.48 This type of flow is called a minority carrier flow and it is opposite to the majority carrier flow. The result of this is seen above in [Figure 12]. The cell will appear to generate negative current, but this is merely convention since the minority carrier flow is opposite to the majority flow. In addition, one can see the maximum amount of power possible by a typical solar cell by studying the point where the current and voltage are at their respective maximum. EFFICIENCY CONSIDERATIONS MASK DESIGN The electrode designs seen in the photomask in [Figure 2] are extremely important for solar cell efficiency. [Figure 13] on the next page, is a close up of the 1cm2 cell. The electrode pattern is designed in such a way to optimize absorption and the flow of charged carriers. The long electrodes that reach down to the bottom of the cell are called fingers. These let the contacts extract as many of the carriers as possible from all over the cell while also not interfering too much with the absorption by being very thin. Additionally, they are wide enough to reduce the resistance as much as possible. The structure on the top of the cell is as large as possible to reduce resistance further as the carriers from all over the cell flow from the fingers to the load. In addition, the electrode pattern has been designed to be a 10% contact to surface area ratio. This has been researched to be an optimum balance between flow of carriers and absorption. The other electrode patterns on the photomask have also taken these design considerations into account. 48 Space charge region – Additionally, if it happens in the space charge region, the holes and electrons are swept away in either direction since no carriers can exist in this region FIGURE 13: THE 1CM^2 ELECTRODE DESIGN GENERAL STRUCTURE DESIGN Investigation into [Modeling changes in cell structure] discussed this briefly, but other considerations in design are important. In general, for good solar cell design, there needs to be an optimum band gap. An optimum band gap is one that trades off the potential difference with the amount of light that can actually be absorbed. Since a combination of both are needed to generate power, both are important to have. Additionally, strong optical absorption is required. This is directly proportional to material quality as well as the contact design on top of the cell. In the same vein, reflectivity of light must be low. One way in which this can be accomplished is by using anti reflection coatings. Moreover, carrier collection should be efficient. This requires long diffusion lengths, high mobility of the carriers and low recombination49 rates. There are different strategies to make this happen, and some of them have their own tradeoffs to be considered50. And as discussed above in [Mask design], the electrode design should make use of low resistance contacts. Of course, in addition to all of this, in manufacturing is of the utmost importance that the semiconductor be built with care so as not to cause defects in the material, which can cause their own problems such as what was discussed with shunt resistance in [IV curve]. 49 Recombination – Essentially the opposite of generation in that an electron that has been generated relaxes back into the valence band before it has been collected 50 Recombination rates – Surface recombination is discussed further in [Modeling changes in cell structure], but in general, increasing doping to increase conduction, also increases surface recombination.