The Progression of Perovskite Light Emitting Diodes (LEDs) in our Future

Blog, Journal for High Schoolers, Journal for High Schoolers 2021

Authors

J. Guzman, R. Schweyk, and L. Traore

Abstract

Over 1.5 billion incandescent and III-V Light Emitting Diodes (LEDs) are currently in use in the United States today. Whether used in headlamps, flashlights, or lamp lights, these LEDs are consuming up 136 billion kilowatt-hours on a yearly basis in the United States. However, there is a possible solution concerning the new progress of perovskite LEDs. If we were to replace all the light sources in the United States that are dominated by III-V LEDs and incandescent light bulbs with the current progression of perovskites, would the enegry savings outweigh the financial cost, and what would this look like for the future of perovskite LEDs. Limited to their operational stability, perovskites as they stand are not a viable replacement. However, with the rapid evolution of perovskite LEDs as well as their superior optoelectric properties, it is probable that in the near future they will play a fundamental role in our daily lives.

In order to understand the cost effciency of perovskites, one must consider the economies of scale. When a company mass produces perovskites, instead of considering each and every material created in a single perovskite, one must take into account buying in bulk quantities. Not only this, but one must examine the advantages in energy consumption for perovskites in comparison to III-V and incandescent LEDs.

In this investigation, we will analyze the viability of replacing III-V LEDs and incandescent light bulbs with next-gen perovskite LEDs with an emphasis on the current operation stability of perovskite LEDs, how the stability will improve in the next 5-10 years, and when they reach an operational stability that rivals or surpasses that of III-V and incandescent technologies. Overall, this report will demarcate when it will make financial sense to switch to perovskite LEDs on a national scale.

Background and Motivation

To understand what perovskite LEDs (PeLEDs) are, one must become familiar with what is available on the market. As of now the majority of the world utilizes Incandescent lights or LED bulbs as light sources. A light-emitting diode (LED) is a semiconductor light source that emits light when current flows through it. Before understanding the physics governing PeLEDs, we need to understand the ambipolar charge transport comprised of both holes and electrons that lead to light emission within PeLEDs.

Electrons can be described as subatomic particles with a net negative charge. Their most influential role is in the process of bonding individual atoms, known as atomic bonding. Electrons can be found in every element as they occupy the outer orbitals of an element. It is also important to understand electron flow, or in other words, current. This is essential when considering a semiconductor, as when a voltage is applied to a semiconductor, the protons (positively charged subatomic particles) are held stationary whereas the electrons flow with some drift velocity. An abundance of these charge carriers creates majority carriers, whereas a scarcity of these charge carriers creates minority carriers. This in turn induces a current through an electric field. This will be key in this investigation regarding some of the issues that currently face perovskite LEDs, including ion migration and Joule heating. Although similar to an electron in magnitude, holes have a net positive electronic charge associated with them. In essence, a hole represents the absence of an electron. Both however are charge carriers that are necessary for the current flow in ambipolar-based semiconductors.

Figure 1. Typical Peled device structure including price breakdown for each layer.

Electrons in the semiconductor recombine with holes as electron-hole pairs, releasing energy in the form of photons thus leading to light emission. While perovskite light-emitting diodes depend upon the perovskite active layer which is in the form of ABX3, in lead halide perovskites, A represents a cation, B represents lead, and X represents a halogen. In the most common lead halide perovskites, halogens tend to most regularly be chlorine, fluorine, iodine, and bromine, the cations usually represent cesium or methylammonium, and as stated above, B represents lead. For example, CsPbBr3 is a typical lead halide perovskite.

Perovskites were first invented in the early 1950s only emitting red, but later green emission was possible. However, the color blue was and still is challenging to create, being 150 times less stable than green and red. Blue’s instability limits a wide color palette for perovskites to display, therefore impeding perovskite commercialization. One of the particular advantages of PeLEDs over current generation LEDs is that PeLEDs emit light with very narrow emissions resulting in ultra-high color purity. Thus, Lead Halide Perovskites are actively researched for their light emission capabilities and their promise for next-generation lighting and display technologies.

Figure 2. Joule heating that occurs in the electron transport layer, perovskite layer, and hole transport layer

Utilizing the knowledge above, we can now understand the fabrication process needed to build the most basic lead halide perovskite LED. The process begins with adding the bottom electrode ITO (indium tin oxide) to the glass substrate which is often used to create a conductive, transparent coating for the bottom layer. Next, the PEDOT: PSS layer is spun onto the ITO, or otherwise known as the hole transport layer, which is a polymer mixture composed of multiple sulfonyl groups created by sulfonic acid. One of the most key components of the perovskite LED includes the perovskite active layer itself. Created by the ABX3 structure, lead halide LEDs contain the most common compound in the perovskite layer as CsPbBr3 (cesium lead bromide), created by mixing CsBr (cesium bromide) and PbBr2 (lead bromide). It is also necessary to add TPBi, a man-made compound that plays the role of the electron transport layer, after the perovskite layer. Additionally, LiF (lithium fluoride) is added mainly to improve device performance and to align energy bands. Finally, the top electrode layer is added, Al (Aluminum). Towards the end of the fabrication process, LiF, Al, and TPBi layers are evaporated for the best stability of the perovskite. The culmination of these steps provides what we now can classify as the most basic perovskite LED (lead halide perovskite LED).

Considering all these factors required in the progression of perovskite LEDs, each and every component is essential in creating the most basic perovskite. In this report, we will further examine the cost analysis as well as the plausibility of our proposal. Given their current operational stability issues, we will predict how far into the future that these perovskite LEDs will be a suitable replacement for all the current incandescent and III-V LEDs in the United States.

Methods and Results

To analyze when the US can transition to perovskite LEDs rather than incandescent and III-V LEDs, one must consider the output power of these PeLEDs. White light is the current most often utilized color of light, consisting of a superposition of three colors: red, blue, and green light. Once one determines the amount of power each color individually consumes, we can sum up the wattages resulting in a final approximation of the amount of power white light would need to be at its best efficiency.

I. Power Analysis

When considering the power of each individual light source, the equation P=IV will be necessary to keep in mind. Boiled down to four specific steps, at this point one can thoroughly investigate the necessary amount of power needed to allow for a certain color of light to be emitted. First, one must gather the peak EQE (external quantum efficiency), the ratio between the amount of photons leaving the system to the amount of electrons entering, of the color[] Once this is gathered, use the EQE to characterize how much power the PeLED is consuming at that given operating point using J-V-L graphs. Similarly, one must do the same and compare this voltage number to a graph correlating J (current density) to voltage. This is one of the most important steps in the process as J is measured most commonly in mA/cm^2 which will be relevant in the step that follows. When understanding the equation P=IV, P represents power, I represents current, where V represents voltage. Then, one must input the data gathered into this equation. Although plugging in one’s value for V is simple, current is a bit more complicated. Since we are given units in mA/cm^2, one must multiply this value by the device area each perovskite substrate is created on, leaving with the overall current. Only then, will one be able to complete the calculation and solve for power.

After a thorough investigation of these criteria, we can begin the exact calculations. Take for instance red perovskite LEDs. Having a peak EQE currently at 17.8%, the corresponding voltage at the best efficiency occurs at 2.2 V. Similarly, the corresponding J value results in 8mA/cm^2, but must be multiplied by an area of 2.25 cm^2 as explained above. This has a result of approximately 41mW. Now, we can apply these same steps to green and blue perovskite LEDs. Green perovskite LEDs have their peak EQE at 21.63% being the highest of the three. With a voltage of 3.5 V and a current density value of 5mA/cm^2 both at the best efficiency of the perovskite, this results in a total of 63 mW. Although blue perovskite LEDs are still in development as are the others, blue perovskite LEDs have a long way to go in terms of stability and EQE as it is a very difficult color to produce. Containing a peak EQE of 10.11%, a voltage most efficient at 3.5 V, and a J value most efficient at 15 mA/cm^2, the power results in 118 mW .

Table (1) Values used to calculate the total power of red, green, and blue perovskites LEDs

The data above is reasonable as one must consider the amount of energy each color consumes as a total. Utilizing the equation E= \frac{h c}{\lambda} , the colors with the largest wavelengths will result in the least energy, and understanding the equation P= \frac{E}{t} , the greater the energy, the greater the power. When analyzing each color with this information, blue has the smallest wavelength and therefore consumes the largest amount of power. In contrast to blue, red has the longest wavelength so, in turn, has the least amount of power, whereas green falls in between the two.

Since all of these perovskites are currently not at a competitive EQE or stability to replace incandescent and III-V LEDs, it is important to understand how much they need to improve. State-of-the-art green LEDs reside at an approximate 38.4% EQE whereas red LEDs reside at 35.48%. The reason why these values are at such a high percentage is for the very reason of optical lenses. Optical lenses are utilized to ultimately direct light in a single forward direction. EQE is only measured by the forward light emission of the perovskite LEDs. Keeping this into consideration, when perovskite LEDs do indeed reach this level, it will be the logical solution as a replacement. However, this now begs the question of when we will be able to replace all current incandescent and III-V LEDs with perovskite LEDs in the future, and what does the future of blue perovskite LEDs look like.

II. PeLED Operational Lifetime and EQE Estimates:

In order to predict commercialization of PeLEDs, one must consider the following factors: blue’s current and predicted EQE, Red, green, and blues’ projected operational lifetime in 10 years and their operational lifetime using ion migration suppression methods.

Figure 3. Ion migration and the movement of halide ions.

Blue EQE Prediction:

Currently, blue perovskite LEDs are not at their maximum external quantum efficiency. In comparison to green and red which have come close to reaching their maximum EQE, blue is still behind. Knowing that green and red’s projected maximum EQE is around 25%, blue is expected to reach this maximum of 25% as well. In order to predict when blue perovskite LEDs would reach their maximum EQE, this investigation first gathered blue EQE from the years 2016-2021. With the information collected this research created a graph displaying the points to form a line of best fit. To create the line one had to find the average between the points. This average made the equation of Y= -825.58/x +50. Note that when using this equation one must use the last two digits of the year for “X”, for example in 2016, use 16 for x. This equation grows asymptotically because blue’s EQE would eventually plateau and approach a maximum of 25%. This means that in the year 2034 (12 years), blues predicted EQE will reach 25 percent (view equation (A) for solution and figure (6) for growth).

In addition, all red, green, and blue perovskite LED colors are significantly behind the operational lifetime of an LED thus withholding perovskite commercialization. This however is temporary as advances and predictions can be made to show when perovskite LEDs will surpass LEDs. First, the research started by predicting each color’s operational stability within the next ten years. This would help understand how rapidly perovskites are truly growing. In order to do so, research gathered papers that reported each color’s operational stability throughout the years.

Predicted Blue PeLED Operational Lifetime in 10 years:

Starting with blue, in 2019, blue’s operational stability was 14.5 minutes, 51 minutes in 2020, and 81.3 minutes in 2021. With this data, one can create a line of best fit to average the points, create a growth rate, and predict future operational stability. Once done, research was able to average the data to formulate an equation of Y=33.4x-619.1, note that to again predict the years following, one must use the last two digits of the year. With this information, one replaced 31 to our x, representing 2031(10 years from now). This means that by the year 2031, blue would reach a predicted operational lifetime of 7 hours (view equation (B) for solution and figure 7 for growth).

It is important to notice that blue’s operational lifetime growth is linear. This is extremely valuable since blue is the most challenging color to create due to its large bandgap which will be further explained once compared to red and green’s operational lifetime growth.

Predicted Red PeLED Operational Lifetime in 10 years:

Just like blue, the investigation took similar steps to predict red perovskites’ operational stability in 10 years. Again, one collected red’s previous operational stability throughout the years using research papers to predict a growth rate. In 2017, red operated for 16 hours; it increased to 30 in 2018 and currently in 2021, 317 hours. This data is a bit different from blue since it grows exponentially. Therefore instead of using a line of best fit that is linear, research made it exponential. This has to do with the fact that red is a much easier color to accomplish than blue allowing it to advance faster. With that said, the red exponential equation is y=0.0000273735 \times 2.6169^{x} found by the average between points. With this equation, one imputed the year 31, representative of 2031 into the x of the equation. This shows that by the year 2031 red is predicted to operate at 726,735 hours, an extremely noticeable difference between our current operational stability( view equation (C) for solution and figure 8 for growth).

Predicted Green PeLED Operational Lifetime in 10 years:

Again the research repeated the same process, this time gathering green’s perovskite operational stability to help figure out what the operational lifetime would look like in 10 years. The research found that in 2016 the green perovskite’s operational stability was ten hours, 2 years later in 2018 the LEDs operated for 46 hours, and finally, in 2021 the perovskites operated to their current maximum of 208 hours. This allowed the creation of a line of best fit that was exponential, being the average of the points y=0.0033 \times 1.169^{x} . Then use the equation to input the last two digits of the year into x as 31, representing 2031(10 years from 2021). Results in green’s operational lifetime to be 39,105 hours (view equation (D) for solution and figure 9 for growth). This operation stability for the year 2031 is a bit smaller than red’s considering that red is the most efficient.

Knowing that the blue’s bandgap is the widest, it directly correlates to the growth rate. The bandgap denotes the minimum energy required to excite an electron into a state that allows it to conduct current in the conduction band. The valence band is the lower energy level, and if there is a gap between this level and the higher energy conduction band, energy must be added to allow electrons to flow. As described, green and red have smaller band gaps which cause longer operational stability and exponential growth. Blue however has a wider bandgap which causes shorter operational stability and linear growth. Blue requires more energy to emit a photon because of the higher energy band gaps ultimately compromising the efficiency of perovskites.

Figure 4. Red, green, and blue Perovskites’ band gap width in comparison to one another.

III. PeLED Commercialization Viability

Red PeLED Commercialization:

Now that sufficient equations for each color have been gathered, predictions of commercialization can be considered. In order to find when each color can accomplish commercialization, one must acknowledge that an average LED can last 6 ×106h. Using this information, one can use the red perovskite equation to input 6 ×106h as our “ Y “ representing the operational stability to help find “X” our year. Doing so one can use 0.0000273735*2.16953^{x}=10^(6)*6h , this answer would result in 33~34, representative of the year 2034. This means that by the year 2034 the red perovskite should be able to compete with LEDs. (view equation (E) for solution)

Figure 5 displays blues highest EQE throughout the years and its recent progress. Figure 6 displays the equation ​​Y= -825.58/x+50, the line of best fit from figure 5, and predicts in which blue perovskite reaches maximum EQE. Figure 7 Displays the equation Y=33.4x-619 To help predict the operational lifetime of the blue perovskite in 10 years.

Figure 8 Displays the equation y=0.0000273735 x 2.6169^x to help predict the operational lifetime of the red perovskite in 10 years. Figure 9 displays the equation y=.0033 x 1.69116^x To help predict operational lifetime of the green perovskite in 10 years.

Green PeLED Commercialization:

One can repeat the process for the green perovskite where we utilize our equation to input our desired operation lifetime. By replacing our “Y“ as 6 ×106h simplified to 10^{6}*6 =.00336293*1.69116^{x} is equivalent to 40 representing 2040 years of commercialization. By the year 2040 green perovskites are estimated to commercialize (view equation (F) for solution)

Blue PeLED Commercialization:

Lastly, for the blue perovskite, one must solve for the estimated year which was (33.4x)-619=10^{6}*6h equal to the year

Figure 8 Displays the equation y=0.0000273735 x 2.6169^{x} to help predict the operational lifetime of the red perovskite in 10 years. Figure 9 displays the equation y=.0033 x 1.69116^{x} . To help predict operational lifetime of the green perovskite in 10 years.

179659, 179659 representative of the year 181,659.25. This year appears different in comparison to the other perovskite predicted commercialization year in which they were in the years 2000. To convert the number as one did for red and green one added 2000 which resulted in blues predicted commercialization year to be 181,659.25. ( view equation (G) for solution)

Blue is immensely behind, however, this is without taking into account advances that will be made in the future. For one, one must consider the fact that these numbers do not utilize ion migration joule heating suppression methods in addition to new research and studies that will specifically help advance the blue perovskite.

IV. Pathways to enhance PeLED performance and stability

Ion Migration Suppression Strategies:

As of now, there are many methods utilized to counteract migration and joule heating. One being B-site engineering. B site engineering is doping B-site cation ions with metal ions like Mn2+. Traps in the mid-gap can prevent electrons from recombining with holes, ultimately limiting the perovskite as light cannot emit. Reducing traps allows electrons to fall freely without encountering any obstructions. The addition of Mn2+ reduces the trap density, which results in less ion migration. Mn2+ can lower defect density (the number of defects ) in perovskites, reducing ion migration and resulting in greater operational stability. With that said, a study that utilized this method caused blue perovskites to operate 1,440 times longer than their original undoped perovskites. This study also applied B-site engineering to red perovskites allowing them to operate for 305 times longer than the undoped perovskites.

The second method was using Precursor Solution Composition Optimization. There are three crystallinity orders in a perovskite (substrate). There is amorphous, which means there is no discernible order. There is crystalline, where everything is in order and visually is similar to a checkerboard. Lastly, Polycrystalline indicates that halide ions can be arranged and slightly distributed in tiny groupings. There are pockets of small groups in polycrystalline thin films that will be in order. However, grain boundaries will exist inside the limits of those groupings.

In a polycrystalline material, a grain boundary is a point where two grains, or crystallites, meet. Grain boundaries are two-dimensional defects in the crystal structure that reduce the material’s electrical and thermal conductivity. This indicates that there are flaws in the device that cause it to degrade. Halide ions, such as bromide, chloride, or iodide, can easily cross grain boundaries since they have the lowest activation energy.

These halide ions are at grain boundary cusps, and because they are not strongly attached to the group, they can be whisked away by the electric field, resulting in ion migration. Halide ions are being swept across and concentrated at some point due to the electric field being applied to the layer, which is producing the most segregation. Instead of employing a cesium bromide, we can use a different method. CsTFA-derived films have a flatter energy landscape (a more homogenous energy level distribution for charges), a more stable crystal structure, superior optical characteristics, and reduced ion migration as compared to the CsBr method.

As a result, such grain boundaries get passivated, or the lead halide ions become more difficult to respect within the magnetic field. This causes tighter films where there are no bubbles, (effectively a sheet compared to cesium bromide with defects), less ion migration occurs. A research group utilized Precursor Solution Composition Optimization which allowed for green perovskites to operate 17 times more efficiently.

Applying Precursor Solution Composition Optimization to Green PeLEDs:

Our research can then apply these numbers to the current undoped operational lifetime. Precursor Solution Composition Optimization allows green perovskites to function 17 times more efficiently. Therefore one first had to find a number multiplied to 17 to then calculate to 10^(6)*6 h resulting in 352,941h. One can then calculate the year our “X” in which green will be able to reach 352,941h. Solving for the year 35 representative of in the year 2035, green will be able to commercialize ( view equation (H) for solution).

Applying B-site Engineering to Red PeLEDs:

Applying B site engineering red perovskites will be able to operate 305 times longer in comparison to our original predictions. One must find the minimum number that can be multiplied with 305 (305 representing how many times more the perovskite would last being doped) to be equivalent to 10^(6)*6h.

Set of equations A-J is processes taken in order to predict blue EQE (A), Blue perovskite estimated operational lifetime in ten years(B), Red perovskite estimated operational lifetime in ten years (C), Green perovskite estimated operational lifetime in ten years (D), Predicted Red perovskite commercialization year (E), Green perovskite commercialization year (F), Blue perovskite commercialization year (G), Green perovskite estimated commercialization year using Precursor Solution composition optimization(H), Red perovskite estimated commercialization year using B-site Engineering(I) and Blue perovskite estimated commercialization year using B-site Engineering(J).

This number is 19,672h, now replacing it for “Y” representing operational lifetime, into our red perovskite equation. Let us solve for “X” resulting in 26 representing the year 2026. This method allowed for the reduction of 7 years, in comparison to not using any ion migration suppression methods ( view equation (I) for solution).

Applying B-site Engineering to Blue PeLEDs:

The same process can then be repeated for the blue perovskite. Instead, however, ion suppression made the operational lifetime 1440 times longer. The research found the minimum number that could be multiplied to 1440 (1440 representing how many times more the perovskite would operate for, being doped) to be equivalent to 10^{6}*6h . Resulting in 4166h, which was used to represent Y operational lifetime into our blue perovskite equation. Then research proceeded to solve for X as our estimated year. Doing so, formulated the number 143 representing the year 2143 when the blue perovskite would be able to commercialize (view equation (J) for solution). Although this is significantly sooner than the undoped blue perovskite commercialization prediction there are still other factors one must consider. Since perovskites are rapidly evolving there are still numerous studies and ion suppression methods that can be applied. With this in mind, new research can be applied to all color’s estimated commercialization year. Regardless of red and green being able to commercialize sooner than blue, blue is still a color with great improvements expected over the next few years.

V. Modeling the Economies of Scale towards Mass Production

To evaluate the total cost of mass-producing perovskite LED materials in the project of replacing all light sources in the US, we would need to apply economies of scale to our calculations. Economies of scale is the total average cost savings obtained by an enterprise for a greater quantity of production. As production increases, the total average cost decreases, resulting in a lesser total cost than the sum of the price per unit. In the generic model, the variables P1 and P2 represent the cost of production, and the variables Q1 and Q2 represent the quantity of production, and with an increase in the quantity of production (Q value), there is a gradual decline in the cost of production.

Figure 10 describes the asymptotic model developed from TPBi costs at 2g and 5g and describes the decreasing growth rate of costs as production increases.

Our model evaluating costs, considering the impacts of economies of scale, was developed from a quotation by the Stanford Congreve Lab for TPBi, providing numbers for price at different numbers of grams. From these numbers, we were able to gather initial price numbers and establish a trend. The numbers initially provided were $566.00 for 2 grams and $1341.00 for 5 grams, thus $283.00/g and $268.20/g respectively, while the cost for 1 gram is between $600 and $700. The development of a model for economies of scale necessitated the development an asymptotic graph model based on these numbers, given costs for 2 grams and 5 grams respectively, to calculate the price per gram for 10,000 grams and price for bulk production of 1 billion at this rate.

For an increase in gram quantity by a factor of 2.5, there is a 5.23 % decrease in cost. This number was achieved by subtracting 268.20 from 283, the respective price per gram for 2 grams and 5 grams, and evaluating that percentage of the resulting 14.8. By this model, we can calculate a projected $169.69/g for 10,000 grams, and a projected $1.70/g for 1 billion. The asymptotic model for TPBi prices for increasing gram quantities follows this trend. Having calculated our model for the TPBi layer, we can then apply it similarly to each layer, which would be expected to follow a similar price trend.

To apply these numbers, we must consider the fact that for TPBi, 10,000 grams amounts to 1,000,000 substrates. For the ITO layer, $250.00 is the approximate price for 100 substrates, and by an increase in substrate by a factor of 250, there is a 0.05% decrease in cost per substrate. For 1,000,000 substrates, the cost can be estimated to be $237.48, a mere fraction of a cent per substrate at that quantity. Similarly, an approximate $125.00 corresponds to the quantity of 100 substrates for the PEDOT layer, and by the same process, the total cost for 1,000,000 substrates can be estimated to be $118.74. For the CsPbBr3 layer, the original costs were found to be for $38.00 CsBr and for $10.64 for PbBr2 for 1 substrate, and once more by the same process, the cost for 1,000,000 substrates can be estimated to be $34.29 for CsBr and $9.60 for PbBr2. For the LiF layer, $1 corresponds to the price of LiF for 1 substrate, and for 1,000,000 substrates, the cost can be calculated to an approximate $0.90. Finally, $0.27 corresponds to the price for 1 substrate in the Aluminum layer, and the cost for 1,000,000 substrates can be similarly estimated to $0.24. These costs were originally gathered from Sigma-Aldrich and Ossila.

Finally, from our calculated value of 3 to 4 cents for the cost of 1 substrate for a perovskite LED, we can apply our model to find this number at mass production, which would amount to an approximate fifth of a cent for a gram increase by a factor of 2.5. At production of 1 billion, the price would be about 11 million USD.

VI. Financial, Performance, and Energy Analysis of Transitioning to PeLED-based Lighting

After taking a cumulative approach to this research of perovskite LEDs, the ultimate question of if the price of perovskite LEDs is worth the energy consumption can finally be answered. Considering the equation P = \frac{E}{t} where P equates to power, E equates to energy, and t equates to time, it is possible to calculate the energy of each color perovskite LED given power and time. Finally, one must combine all these values to find the total energy the US would have to use to power lighting with perovskite LEDs. Considering these perovskites will be at the level where they can compete with current LEDs, one must assume each color perovskite is at their maximum EQE of 25%. The calculations proceed as follows: ((0.063*1.1)+(0.041*1.4)+(0.118*2.5))*(60*60*6*360*328,200,000) . By multiplying each power value by specific numbers to approximate them to be around 25% EQE, this would give us a better and more accurate representation of the future. Multiplying this by 3,600 gives our value in hours rather than seconds, and final multiplying by the amount per year for every person in the US. This equates to approximately 1.5*10^{15} kWh. Compared to the 136 billion kWh the US uses in energy consumption a year to fuel light emission, this does not seem to be a logical fit currently, but with joule heating methods along with the rapid improvements of these perovskite LEDs, they are sure to reach the stability and energy of regular LEDs in the future.

VII. Cumulative Research Prediction of White Peled

Taking into account power analysis, operational stability, and economies of scale, research is sufficient to help predict how much power a white PeLed would utilize, how long the peled would operate for, and how much the product would cost the U.S as a whole. As previously stated the blue Peled has an operational lifetime of 81 min noticeably behind the green and red Peled operational lifetimes, therefore if one were to utilize multiple blue peled in one white Peled it would help increment lifetime. For example, to create a white PeLED one red, green, and blue peled is needed. However one could utilize ten blue PeLEDs to increment the lifetime by 10 times as long as only one blue peled is used at a time. Nevertheless, there are limitations such as the cost of having multiple PeLEDs in one unit or utilizing an extreme amount of power to operate. Therefore as all colors currently stand research would only utilize 173 blue LEDs. Particularly, 173 blue perovskites in one white Peled because this would allow for the operation to increase to 207 hours (This lifetime being close to green Peleds current operational stability which is at 208 hours). Research multiplied the power needed to light up a blue Peled by 173. Finally adding the power needed to operate one green and one red Peled. The power for this Peled would equate to 20.518 kW. According to calculations 173 blue PeLEDs, one red and one green in one unit to supply the U.S population would cost 128 million. As they currently stand, they would not be the best alternative.

However, research can also calculate the lifetime of the white Peled in 16 years. It is important to consider how the white Peled would change in the future. Particularly in 16 years, since the green perovskite has reached operational stability of 1 million. At this time the blue perovskite would operate for a total of 10 hours, and could potentially operate for 1,000 hours using 100 blue Peled in one unit. This amount of blue Peleds would take less energy as time progressed, the power calculating to a total of 11.9 kW to operate one white LED in the year 2037. The cost of the white Peleds is 127 million dollars to fully transition. This number is lower in cost for a longer operational lifetime and less power needed compared to where they currently stand. It is also important to consider that in the future there could be new advances to combat ion migration which could also improve power, operational lifetime, and cost.

Challenges Encountered

We are currently facing many problems when considering the stability of PeLEDs. At the moment being unstable, the goal for the future of perovskite LEDs is to eventually increase the stability of each perovskite, however, there are some issues that need to be solved that are preventing us such as ion migration, joule heating, etc.

Before understanding the problems with ion migration, we first must understand the meaning of an electric field. An electric field is a field that physically surrounds electrically charged particles which allows for the repulsion and attraction of other electrically charged particles. Ion migration occurs in the perovskite layer, where either cations or anions, typically halide ions (anions) in lead halide perovskites, as seen in figure 3, approach either the negative or positive side of the electric field, which creates unevenness throughout the perovskite. Once they congregate near the terminals, any sort of light emission will be uneven which in turn compromises the performance of the device. This is solely due to the electric field.

Joule heating occurs in the electron transport layer, the perovskite layer, and the hole transport layer. Joule heating allows for and creates heat, which is produced by current flowing in the material. The problem with this is that it can raise the temperature of the material by up to 40 degrees celsius which also, in turn, allows for degradation of the material and a decrease in instability. Any material is optimized at 200k, which progressively regresses as temp increases, which decreases current since electrons are more scattered. No flow amounts to no current, which results in no light emission. This is solely based on a thermal effect.

Another contributing factor to perovskite degradation is bandgap width, this can cause problems with operational lifetime, particularly with the color blue. The reason why red is the most efficient color is due to its small band gap width. Blue for example has the widest band gap width out of the three colors, this means that there is more energy that must move an electron. As for red, which has the smallest band gap width, the electron does not need as much energy to the dropdown. With smaller band gaps, we are able to have greater stability for red and green. For blue, since the color has a wider bandgap, occasionally the electron gets trapped in the middle of the bandgap; this area is called the midgap. Here the perovskite cannot emit light, as light emission does not occur in the mid-gap, only when the electron falls. This is one of the major problems faced as band gap width is not something that can be changed. Unlike green and red which have longer operational lifetimes, blue currently faces this problem and will continue to face it. In addition, the traps in the mid-gap also affect the operational lifetime to not only the blue perovskite. Therefore jeopardizing particularly the blue perovskite lifetime.

Another challenge encountered was the lack of perfect accuracy for our model of economies of scale. The economies of scale model utilized to calculate the cost values at various quantities is an imperfect measure of estimates. The model is based on very small quantities of TPBi, thus it could have been made more accurate if costs for larger quantities had also been provided for comparison. Additionally, all estimates are based on the model for TPBi, so they are expected to have slightly more inaccurate estimates for the other materials. However, although it does not specifically account for such inaccuracies, the model is itself an estimation and only approximates the trend in cost change at larger scales.

Conclusion

Whether keeping into account each individual color of perovskite LEDs or the culmination of them all together, they most undoubtedly will play a fundamental role in our future. Each aspect explained upon in the preceding sections of this paper show countless evidence of the rapid evolution of these perovskites when considering either the power of each color, their operational stability, or the price of each perovskite.

The power analysis played an equally important role in determining the reliability of each perovskite. Considering the equation P=IV, the peak EQEs of each color, applying J-V graphs, and combining them collectively to get a final value for power, all portray the importance of the power analysis. As the rise of each color’s EQE continues, so will the efficiency of perovskites, which perhaps may be the most important factor in transitioning from III-V and incandescent LEDs to perovskites. With joule heating methods, perovskites are improving at exponential rates being very promising to their future.

By utilizing previous perovskite operational lifetimes there was sufficient information to predict if Peleds are worth the transition. Starting with the prediction of EQE for the blue perovskite, where research proved to show growth is rapid. Green and red perovskites too have shown extreme n operational lifetime improvements for the future. While the blue perovskites do seem to struggle, there are advances such as B-site engineering and precursor solution composition optimization to combat their short operational stability. Most importantly, the current white Peleds would not be a reasonable transition with the blue perovskite being the largest setback. However, with time we can be sure to see white Peleds thrive.

A significant consideration to evaluating the cost of transitioning to lighting by perovskite LEDs was economies of scale. At the high number of production necessary for this replacement, the total financial estimate could not be made accurately by multiplying the price per unit by the intended number of units, as such a calculation would overestimate the actual cost. Thus, the reduction in increase was calculated based on the original prices gathered from Sigma-Aldrich and Ossila. The economies of scale assumed for these calculations was a continued 5.23 % decrease in cost per gram for a quantity increase by a factor of 2.5, and by the model we used, this amounts to the LED cost of a fraction of a cent for a gram increase by that trend. Currently, to supply the U.S population with next-generation lighting, it would cost $128 million.

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