Recent Progress in Vacuum-Deposited Small Molecule

Organic Solar Cells

By: Graeme Williams*

*Organic Optoelectronic Materials & Devices Laboratory, g3willia@uwaterloo.ca

Electrical and Computer Engineering

University of Waterloo. Waterloo, ON Canada. N2L 3G1.

Abstract.

While solution-coated organic solar cells (OSCs) have been a strong area of research for the

past decade, recent advances in the photovoltaics industry have suggested that vacuum-

deposited small molecule OSCs may yet have a promising future in organic photovoltaics. With

vacuum-deposited devices, researchers can remove many experimental variables that are

specific to solution processing, and instead focus on understanding and optimizing the device

physics. Furthermore, with many of the fundamental device architectures already developed,

researchers have recently sought improved device performance through the synthesis of new

donor materials and through the creation of new fabrication techniques. This review examines

these developments, with the vast majority of the work focused on three key areas: the

optimization of exciton dissociation through improved morphology of deposited layers, smart

materials synthesis for enhancement of device optical and electrical properties, and the

improvement of the OSC absorption-solar spectrum match. Optical modelling of the OSCs is

further performed to highlight the importance of the device design and architecture, especially

the device thicknesses, in absorbing the maximum amount of light. The knowledge obtained

from this literature review is used to explain the results from current leaders in vacuum-

deposited small molecule OSC efficiency.

Contents

1. Introduction ............................................................................................................................ 1

2. Small Molecule Organic Solar Cells: Early Developments ..................................................... 3

2.1. Multiple and Tandem Solar Cells ..................................................................................... 4

2.2. Mixed Layer and Bulk Heterojunction Solar Cells ............................................................ 6

2.3. Tandem p-i-n and Hybrid Planar-Mixed Molecular Heterojunction Solar Cells .............. 9

2.4. Optical Modelling of Organic Solar Cells by Transfer Matrix Formalism ....................... 10

3. Recent Progress in Organic Solar Cells ................................................................................. 12

3.1. New Donor Materials for Small Molecule Organic Solar Cells ....................................... 12

3.2. Novel Fabrication Techniques for Small Molecule Organic Solar Cells.......................... 17

3.3. Recent Giants in Small Molecule Organic Solar Cell Efficiency ...................................... 22

3.3.1. Optimized ‘p-i-n’ Tandem Organic Solar Cells ............................................................ 22

3.3.2. Highly Efficient Solar Cells Based on New Donor Materials ....................................... 24

4. Conclusions ........................................................................................................................... 27

References .................................................................................................................................. a

Appendix A – Modelling Assignment: Optical Modelling of Organic Solar Cells by Transfer

Matrix Formalism ......................................................................................................................... i

1

1. Introduction Solar cell technology is classified in terms of generations, where the first generation

technology refers to the most widely implemented single crystal silicon solar cell. Second

generation technology comprises most thin-film solar cells, which aim to surpass single crystal

silicon in output power per dollar on the terms of reduced costs. Organic solar cells (OSCs) fall

under this ‘second generation’ photovoltaics umbrella, and are unique in their approach as they

make use of aromatic hydrocarbon semiconductor materials. These materials offer potential

cost-saving advantages by elimination of silicon purification and processing steps. The organic

materials used in OSCs are instead prepared by batch chemical reactor syntheses. Since the

organic compounds can be tuned to have very high absorption coefficients, their thin films can

absorb strongly while using small amounts of raw material. Further, OSCs may be fabricated on

plastic substrates, allowing for form-fitting, flexible devices.

The realm of organic photovoltaics (OPVs) can be broken down into two primary

categories: small molecule and polymer. In terms of their implementation, small molecule

species are historically insoluble and are thus commonly vacuum-deposited by thermal

evaporation techniques. As an addendum to this point, while they are difficult to synthesize,

soluble small molecules are feasible and have recently become the subject of intense research

[1-5]. In contrast, polymer materials are more easily synthesized to be soluble in common

organic solvents. Polymer OSCs have garnered significant attention that may be attributed in

part to the realization of high efficiency OSCs comprised of a thiophene-based polymer and a

soluble fullerene derivative – specifically, poly(3-hexylthiophene) (P3HT) with phenyl-C61-

butyric acid methyl ester (PCBM). These OSCs have since been studied extensively, with over

1000 published papers between 2002 and 2010 [6]. The success of this materials system has

spurred massive research efforts into the smart fabrication of new donor polymers with

enhanced electrical, optical and morphological properties [7-12].

Recently, small molecule OSCs have shown their immense promise, with over 10%

power conversion efficiency (PCE) reported by both Mitsubishi and Heliatek [13, 14]. Further,

Heliatek’s vacuum-deposited tandem small molecule OSCs have shown unprecedented stability,

2

with virtually no degradation to efficiency in 1000-hour lifetime tests at 85oC. Given the batch-

to-batch variations and inherent difficulties associated in processing polymeric materials, small

molecules may be the most promising route for OPVs. To this end, by pursuing the precise

control in material synthesis and device fabrication offered by small molecule OSCs, limiting

factors toward efficiency as well as pathways toward degradation can be more easily identified

and isolated. The possible shift toward small molecule-based OPVs would be well in-line with

other forms of organic electronics, such as organic light emitting diodes (OLEDs), which are

largely small molecule-based devices owing to their significant efficiency gains over polymer-

based devices. Thus, this review focuses only on the vacuum-depositable small molecules,

noting that vacuum deposition has fewer experimental parameters and allows for simpler

control in device fabrication.

While organic solar cells have shown to be a promising approach toward economic solar

energy, their past successes rely on new materials development and unique device

architectures due to the inherent low mobility of the comprising organic materials. In

polymeric systems, the general approach toward high efficiency OSCs has been the formation

and optimization of a bulk heterojunction (BHJ) through solution processing techniques. Since

these techniques are largely unavailable to the thermally evaporated small molecule-based

systems, new approaches for efficiency enhancements must be devised. In the present review,

two critical areas of OSC device fabrication are discussed:

- the most prominent and promising materials for use in vacuum-deposited OSCs

- the clever techniques used for high efficiency vacuum-deposited OSCs

In order to provide a basis for more recent developments in literature, a historic outlook on

small molecule OSC device architectures is first provided, culminating in the tandem mixed

donor-acceptor devices developed in parallel by several research groups in 2004-2006. Optical

modelling techniques will be used to highlight the importance of this device structure. From

this cornerstone of research, more recent developments and the overall direction of research

until present day will be discussed.

3

2. Small Molecule Organic Solar Cells: Early Developments

Initial work

on small molecule

OSCs focused on the

study of bilayer

devices, following

the success of Tang

in 1986 [15]. In this

research, Tang

proposed a planar

heterojunction (PHJ)

comprised of an electron donating material and an electron accepting material. The lowest

unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) of the

donor and acceptor are offset to allow for splitting of photogenerated excitons into electrons

and holes. In Tang’s work, the donor material was copper phthalocyanine (CuPc) and the

acceptor material was 3,4,9,10-perylenetetracarboxylic bis-benzimidazole (PTCBI). An

illustration of a simple device based on this architecture along with the relevant energy levels is

shown in Figure 1. The most significant variation to this device is the replacement of PTCBI with

fullerene (C60) as the acceptor material and the occasional substitution of CuPc for Zinc

Phthalocyanine (ZnPc).

In any photovoltaic device, it is necessary to separate photo-generated excitons into

electrons and holes, and to collect these free carriers before they recombine. For the

aforementioned CuPc-PTCBI device, this process is accomplished as described below and

illustrated in Figure 1:

i. an impingent photon produces an exciton in either the CuPc or PTCBI layer

ii. the exciton diffuses to the CuPc-PTCBI interface to be separated into its constituent

electron and hole

iii. the free carriers are subsequently collected at their relevant electrodes

Figure 1 - A. Illustration of a Simple Planar Heterojunction Device Comprised of CuPc Donor and PTBI Acceptor. B. Associated Energy Levels

of the CuPc/PTCBI Device with Illustration of Light Harvesting Action.

4

Unfortunately, the exciton diffusion length for organic materials is generally very low. When

considering a simple bilayer OSC, the exciton diffusion length is generally much smaller than the

layer thicknesses required for efficient absorption of light. For example, one may use a 100nm

CuPc absorbing layer; however, only excitons formed within 10nm of the CuPc-PTCBI junction

will result in collectable electrons and holes [16]. In order to address this problem, two

approaches have been suggested: multiple or tandem solar cells, and mixed layer solar cells –

analogous to the bulk heterojunction used in polymer solar cells.

2.1. Multiple and Tandem Solar Cells

The ultimate goal of stacking PHJ solar cells in a tandem configuration is to have many

interfaces for efficient exciton dissociation while maintaining a summative thick film for

absorption of light. One may also absorb a broader spectrum of light through the use of

different donor/acceptor materials with different absorption characteristics. Since stacked

solar cells are effectively in series, they ideally have an open circuit voltage (VOC) equal to the

sum of the Voc values of the individual sub-cells. However, the short circuit current density (Jsc)

is effectively limited by the sub-cell with the lowest Jsc. The obvious downside of tandem solar

cells is the increased complexity to device fabrication and associated increase in costs with each

additional layer.

Following this rationale,

Peumans, Yakimov and Forrest

examined multiple junction OSCs

based on CuPc-PTCBI PHJs [16,

17]. An example two-stack PHJ

OSC is shown in Figure 2.

Deposition of two CuPc-PTCBI

devices in series would intuitively

result in the formation of an

inverse heterojunction. As such,

Figure 2 - Illustration of a Double Planar Heterojunction (Tandem) Solar Cell. Image adapted from Ref [16].

5

the researchers made use of an ultrathin (ideally 5Å) silver layer to separate neighbouring

heterojunctions. At 5Å thickness, the silver layer forms islands that act as efficient

recombination centres. In this manner, holes from CuPc recombine directly with electrons from

PTCBI on the silver islands. As long as the rate of recombination surpasses the generation rate

of free carriers, there is no charge accumulation at this interface so there is no splitting of the

quasi-Fermi levels and no formation of the inverse heterojunction. Further, it is supposed that

carriers tunnel through interface dipoles at the metal island-organic interfaces (shown, for

example, at the PTCBI-Ag interface in Figure 2) [16]. The function of the multijunction OSC is

then as follows:

- Impingent light generates excitons in both the front and back cells

- The excitons are split into electrons and holes at the two CuPc-PTCBI interfaces

- The hole from the front cell is collected at the ITO contact and the electron from the

back cell is collected at the Ag contact

- The remaining electron in the front cell recombines with the remaining hole from

the back cell at the ultra-thin Ag layer

In effect, one generates photocurrent equivalent to a single cell; however, as illustrated in

Figure 2, the Voc of the multijunction OSC is the sum of the individual Voc values.

As a point of note, the stacking of cells cannot be repeated ad infinitum to achieve

unrealistically high open circuit voltage values. From the work in [17], the OSC with two

stacked cells performed best at 1-sun illumination, achieving optimal VOC and associated power

conversion efficiency (PCE) values of (2.5% PCE1) when compared to 3-cell and 5-cell OSCs. As

more cells are stacked, less light reaches the lower cells due to absorption of light from the

active CuPc/PTCBI layers and due to scattering or absorption of light by the Ag layers. As a

consequence, 5-cell OSCs, for example, would have to be run at unrealistically high light

intensities (>10 suns) to achieve peak efficiencies. In order to achieve such high light intensities

solar concentrators would be required, which would drastically increase the cost of the solar

cell and thus make any economic gains from using organic materials irrelevant.

1 All PCE values throughout this review are quoted for AM1.5, 100mW/cm

2 (1-sun) exposure unless specified

otherwise

6

2.2. Mixed Layer and Bulk Heterojunction Solar Cells

The common route to high efficiency polymer OSCs is the formation of the BHJ, which

comprises an active layer with mixed donor and acceptor species to allow for much thicker

films to better absorb sunlight. Thick films are possible because excitons will encounter donor-

acceptor interfaces with much higher probability, as these interfaces are distributed throughout

the entire active layer. This approach is prevalent in polymer OSCs given its ease in

implementation for solution-based fabrication – one can simply mix the donor and acceptor

species in the same solvent prior to doctor blading, spin-coating or spray-coating. It is also a

proven approach for small molecule OSCs, although there are significantly fewer variables

available to control the ultimate morphology of the mixed donor-acceptor layer.

The obvious downside of the bulk heterojunction is that the hole and electron mobilities

in the mixed layer are significantly reduced compared to the pure donor and acceptor layers.

Further, for a hole or an electron to be collected, they must be generated in a region of donor

or acceptor that is continuous to the anode or cathode. ‘Dead ends’ can lead to undesirable

charge accumulation and carrier recombination that ultimately decrease the solar cell

efficiency. The morphology of the mixed layer is thus very important and incredibly susceptible

to experimental variation. An ideal morphology is a bicontinuous distribution of donor and

acceptor phases, with pure phases on the order of nanometres for efficient exciton separation.

Gebeyehu et al. studied the BHJ approach to small molecule OSCs [18], making use of a

ZnPc-C60 blend as the active layer. Noting the likelihood for exciton quenching at the metal-

organic interfaces, the researchers employed charge carrier transport layers to contact the ITO/

Poly(3,4-ethylene dioxythiophene) poly(styrenesulfonate) (PEDOT:PSS) and LiF/Al anode and

cathode. The finalized device structure is shown in Figure 3. The hole-specific transport layer is

4,4’, 4’’-tris(3-methylphenylphenylamino) triphenylamine (m-MTDATA) doped with tetrafluoro-

tetracyano-quinodimethane (F4-TCNQ), denoted as p-m-MTDATA. The electron-specific

transport layer is dimethyl-perylene-tetracarboxylic-diimide (MPP) doped with Rhodamine B,

denoted as n-MPP. Strong doping of the transport layers is desired in order to minimize series

resistance across these layers, especially since they do not contribute to photocurrent.

7

By removing the risk for exciton

quenching at the electrodes, the active layer

thickness can be optimized with minimal concern

for pinholes and device shorting. Further, since

the charge transport layers are highly

conductive, their thicknesses may be altered in

order to optimize the electric field distribution

within the organic layers, placing the BHJ active

layer in the region of highest electric field

intensity. It should be noted that the positioning

of active layers to align with the peak electric

field is also of critical importance for tandem

solar cells, as multiple absorbing regions are

used. This topic will be discussed in greater

detail and the electric field will be modelled in

Sections 2.3 and 2.4 respectively.

The OSC described in Figure 3 has been

named the “p-i-n” OSC, as it makes use of a heavily hole-doped layer (P-m-MTDATA, the p-

region), an absorbing region with relatively poor electron and hole conductivity (ZnPc:C60 BHJ,

the i-region) and a heavily electron-doped layer (n-MPP, the n-region). The device therefore

bears strong resemblance to p-i-n solar cells commonly used in other thin-film technologies.

Such p-i-n OSCs have more recently been used in 6.1% PCE tandem cells [19], as will be

discussed in Section 3.3.1, and are likely the backbone behind Heliatek’s 10.7% efficient small

molecule OSCs. The presently examined OSCs illustrated in Figure 3 have been proven to be

capable of 1.0% PCE with a 1:2 ratio of ZnPc:C60.

Drechsel et al. later produced a comprehensive study of this particular ZnPc:C60 p-i-n

OSC, making observations specifically on the hole transport layer [20]. They found that the p-

doped m-MTDATA was a limiting factor on the fill factor and series resistance of their p-i-n cells,

Figure 3 - A. Illustration of a p-i-n Bulk Heterojunction Small Molecule Solar Cell.

B. Energy Band Diagram of the Short-Circuited Solar Cell. Image adapted from

Ref [3].

8

and therefore switched to the higher conductivity N,N,N’,N’-tetrakis(4-methoxyphenyl)-

benzidine (MeO-TPD). The researchers also stressed the importance of forming an Ohmic

contact between the organic layers and the adjacent organic layers, noting the strong likelihood

for dopant degradation with top-contact deposition. In order to avoid such degradation, a thin,

protective layer prior to top contact deposition was found to be desirable. Based on these

modifications and observations, the resulting ZnPc:C60 p-i-n OSC allowed for a 1.9% PCE [20].

In a similar vein, Uchida et al. investigated CuPc:C60 bulk heterojunction devices [21].

The researchers noted a marked improvement in PCE by inclusion of a neat C60 layer between

the CuPC:C60 BHJ and the top electrode, effectively forming a pseudo-'i-n' device. In this work,

they made use of a 2,9-dimethyl-4,7-diphenyl-1,10-phenanthroline (BCP) hole/exciton blocking

layer, which has a deep HOMO to block holes and to preclude exciton quenching at the top

contact. BCP serves a secondary purpose to protect

the neat C60 layer from damage during Ag

evaporation. Optimization of their layer thicknesses

allowed for 3.5% PCE and a notably smaller series

resistance when compared to the ZnPc:C60 devices by

Drechsel et al [20].

Following their successes in [21] and using the

same reasoning as applied with the p-i-n devices, Xue

et al. investigated their hybrid planar-mixed

molecular heterojunction (PM-HJ), as illustrated in

Figure 4 [22, 23]. In this case, instead of using heavily

doped transport layers, Xue et al. simply extended

pure CuPc and C60 layers from the mixed BHJ. This

device structure may be considered a subset of the p-

i-n device structure considered earlier, but the use of

pure donor and acceptor ‘p’ and ‘n’ layers to border

the mixed layer is ineffective in blocking excitons.

Figure 4 - A. Device Structure of the Planar-Mixed Molecular Heterojunction.

B. Image of the Band Structure for the Same. Image adapted from Ref [8].

9

Further, the absence of dopants in these layers results in increased series resistances. The

benefit of the PM-HJ is that the pure CuPc and C60 layers also contribute to photocurrent. If the

transport layers are designed to have thicknesses equal to the exciton diffusion lengths, most

excitons will reach a donor-acceptor interface for dissociation. As with their previous work, BCP

was used to block holes and excitons and to prevent damage to the organic layers during

evaporation of the silver contact. The optimized solar cells from this work achieved 5% PCE.

2.3. Tandem p-i-n and Hybrid Planar-Mixed Molecular Heterojunction

Solar Cells

Since both tandem OSCs and BHJ-based OSCs showed strong improvements in

efficiency, the natural extension of this research is to combine the two architectures. The

tandem configuration for p-i-n solar cells, where the ‘intrinsic’ layer is a ZnPc/C60 BHJ, was

studied by Maennig et

al. and the full device

structure is shown in

Figure 5.A [24]. The

researchers noted an

inherent difficulty with

the tandem

configuration, which

was mentioned briefly in

Section 2.3: it is difficult

to align both cells to be

placed in maxima of the impingent light's electric field within the device. In order to alleviate

this problem, Maennig and coworkers suggested optical modelling and, subsequently,

alteration of the thicknesses of the charge transport layers to optimize the optical field

distribution. These techniques are based on transfer matrix formalism and are described

further in Section 2.4. This work allowed for a PCE of 2.4%. Drechsel et al. later refined and

applied this technique to achieve a PCE of 3.8% for the same-structure cells [25].

Figure 5 - Device Structures for Bulk Heterojunction p-i-n Tandem Solar Cells by A. Reference [23] and B. Reference [25]. Images

adapted from the same.

10

Xue and coworkers pursued a similar tandem device structure based off of their PM-HJ

device structure. The tandem device is illustrated in Figure 5.B, where they separate the two

cells by a PTCBI/Ag cluster/m-MTDATA stack [26]. The Ag cluster stack buried in m-MTDATA

acts as an efficient recombination centre. Since CuPc absorbs at ~550nm-750nm and C60

absorbs at ~350nm-550nm, the researchers proposed asymmetric thicknesses of the sub-cells,

where the front cell absorbs short wavelengths (thicker pure C60 layer) and the back cell

absorbs long wavelengths (thicker pure CuPc layer). By optimizing the optical field distribution,

taking this asymmetry into consideration, Xue et al. were able to achieve 5.7% PCE.

Note that in a very brief period of time the proposed structure for the OSC

encompassed four major avenues of device structure: planar heterojunction, tandem planar

heterojunction, bulk heterojunction and tandem bulk heterojunction. The bulk heterojunction

may be further broken down into the simple BHJ and the p-i-n heterojunction. A simple

variation of the p-i-n heterojunction, denoted as the PM-HJ, relies on extending the individual

components of the BHJ as pure layers to border the BHJ. By incorporating this PM-HJ into a

tandem device, researchers ultimately achieved 5.7% PCE [26], which remains one of the

highest efficiencies for small molecule OSCs reported in literature.

2.4. Optical Modelling of Organic Solar Cells by Transfer Matrix Formalism

Optical modelling of OSCs can be accomplished by transfer matrix formalism, which is

detailed in a more rigorous manner in Appendix A2. As noted previously, optical modelling

allows for placement of the peak electric field in the 'active region' of the device – generally the

regions comprising of either, or both of, the donor or the acceptor. Shifting the optical field can

be accomplished by use of thick optical spacer layers comprised of high conductivity inorganic

semiconductors [27], or heavily doped materials [19]. The optical spacers must ideally avoid

significant increases to the series resistance of the devices. Since the generation of excitons is

proportional to the intensity of the impingent optical field, this is a simple and cost-effective

approach to drastically improve the efficiency of OSCs.

2 Note: Appendix A was completed for the extra modelling assignment for ECE632

11

In order to demonstrate the power of this technique, consider three device structures

discussed in Section 2.1-2.3:

i. A simple PHJ device with ZnPc donor and C60 acceptor

ii. A PM-HJ device with ZnPc donor and C60 acceptor

iii. A PM-HJ device in tandem configuration with ZnPc donor and C60 acceptor

The specific layer thicknesses, the modelling methodology and the MATLAB code written to

generate these models are provided in Appendix A. The electric field intensity for the first two

devices, assuming AM1.5 1-sun input radiation, is shown in Figure 6. For the PHJ device the

peak electric field occurs at the ITO/ZnPc interface, a region with generally high recombination

currents, clearly limiting the device performance. By making use of a PM-HJ device the peak

electric field can be shifted toward the ZnPc and ZnPc:C60 BHJ layers, allowing for much

improved device performance.

The third, tandem device is shown in Figure 7.A. For this device, the peak electric field

nearly occurs at the 0.5nm gold layer used to separate the sub-cells. This is also a poor location

for the peak electric field, as excitons are likely to recombine and provide zero photocurrent in

the immediate vicinity of the gold clusters. As a point of note, for simplicity, the gold clusters

have been modelled as a continuous layer of 0.5nm thickness with bulk properties for the

complex refractive index. This is not a completely realistic scenario, and additional ellipsometry

measurements are required to ascertain the optical constants of ultra-thin gold layers.

Figure 6 - Distribution of the Squared Absolute Optical Electric Field in A. a ZnPc/C60 PHJ OSC and B. a ZnPc:C60 PM-HJ OSC

12

In order to improve the electric field distribution, an optical spacer of p-doped ZnPc in

the second sub-cell has been modelled and is shown in Figure 7.B. This optimized device

structure allows for the original peak electric field to be shifted into the BHJ layer of the second

sub-cell. The BHJ layer of the first sub-cell aligns with a plateau of the electric field.

Unfortunately, the peak electric field occurs in the ITO layer, which does not contribute to

photocurrent. This stresses the need for further modelling, and highlights the inherent

difficulty in optimizing the layer thicknesses for maximum exciton generation.

3. Recent Progress in Organic Solar Cells

3.1. New Donor Materials for Small Molecule Organic Solar Cells

Recent research has focused on the development of new donor materials with superior

spectral match, improved electrical properties and better morphology for high efficiency

devices. The field of OPVs is now such a vast and rapidly growing field that it is well beyond the

scope of this review to provide useful discussion on all material developments. As such, the

present goal is to identify the most promising vacuum depositable materials, and to discuss the

most interesting merits of their research. However, the reader is encouraged to examine the

exhaustive review by Mishra and Bauerle, which lists the output characteristics of most new

small molecules for OSCs developed since 2005 [4]. Furthermore, the reader may be interested

Figure 7 - Distribution of the Squared Absolute Optical Electric Field in a ZnPc:C60 PM-HJ Tandem OSC A. without an Optical Spacer and B. with an Optical Spacer

13

in one of several reviews on the synthesis of new soluble small molecule OSC materials [1-3],

the most recent of which is quite extensive.

Following the successes of CuPc and ZnPc, many groups investigated other metal-

phthalocyanines for applications in OSCs. Yuen et al. examined a large subset of these

materials in unoptimized PHJs and BHJs, including metal-free Pc, MgPc, AlClPc, GaClPc, ClInPc,

TiOPc and VOPc [28]. Wang et al. focused on TiOPc and ClInPc donors specifically, noting their

strong sensitivity to solvent annealing treatments [29]. In particular, OSCs made from both

TiOPc and ClInPc exhibited substantially improved device properties with when exposed to a

chloroform vapour – TiOPc PHJ devices shifted from 1.3% to 3% PCE and ClInPc PHJ devices

shifted from 2.6% PCE to 3.3% PCE. The authors attribute this improvement to the increased

roughness with solvent annealing, which is purported to increase the contact area with C60 in a

PHJ device configuration. Chloroform-based solvent annealing was also shown to red-shift the

absorption band of TiOPc films, but had little effect on the absorption properties of ClInPc films.

In a similar vein,

Bamsey et al. employed

tetrahydrofuran (THF) instead

of chloroform solvent

annealing on ClInPc films and

noted a strong red-shift in the

ClInPc absorption band as

well as the EQE spectra, as

shown in Figure 8.C [30]. The

researchers used this

technique to create a

heteromorphic film, where

the first portion of the ClInPc

film was deposited and

solvent annealed, and the second portion was subsequently deposited without solvent

Figure 8 - A. Illustration of a ClInPc/C60 PHJ OSCs with 3 Types of ClInPc Films with Different Solvent Treatments. B. Associated IV

Characteristics of the ClInPC/C60 PHJ OSCs. C. Associated EQE Spectra of the Same. Figure adapted from Ref. [33].

14

annealing. This is illustrated in Figure 8.A.III. The resulting device thus exhibited a broad

absorption spectrum, spanning both the absorption of the un-annealed film and the annealed

film, and had improved device characteristics, as shown in Figure 8.B. As a point of interest, the

Voc of this device was found to be in between that of the un-annealed and the annealed device.

Fujishima et al. studied tetraphenyldibenzoperiflanthene (DBP) as a replacement to Pc

species for the acceptor material [31]. The authors note DBP’s strong absorption throughout

500-600nm, which aligns well with the peak emission from the solar spectrum. DBP further

exhibits a HOMO at 5.5eV compared to the 5.2eV of CuPc. In general, the theoretical maximum

Voc can be found as the difference between the HOMO of the donor and the LUMO of the

acceptor. Given a LUMO of 4.5eV for C60, the maximum Voc for CuPc-based cells is 0.7V, while

the maximum Voc for DBP cells is 1V. Experimentally, the authors observed an improvement

from 0.7V to 0.9V when switching from CuPc/C60 to DBP/C60 PHJ OSCs. The highest PCE

observed for DBP/C60 PHJ cells was found to be 3.6%.

Wagner et al. focused on diindenoperylene (DIP) to improve upon the inherent charge

transport limitations of CuPc:C60 and ZnPc:C60 blends. DIP is a perylene derivative with

absorption peaks spanning a large portion of the visible spectrum, from 375nm to 550nm with

tail-end absorption extending beyond 600nm. The researchers sought improved electrical

properties of their DIP films through improved morphology, which they found could be

controlled strongly by varying substrate temperature during deposition. An optimal substrate

temperature of 100oC was found. PHJ devices employing a C60 acceptor were shown to have a

PCE of 3.9% with a very high fill factor of 74.3% and a strong Voc of 0.9V. The impressive fill

factor is proof of the high quality of the deposited film – in particular, its high hole mobility and

low concentration of trap states.

Forrest and coworkers, (creators of the PM-HJ OSC and the 5.7% PCE tandem PM-HJ

OSCs [26]), shifted their focus toward squaraines and their derivatives. Wang et al. synthesized

2,4-bis[4-N,N-diisobutylamino-2,6-dihydroxyphenyl] squaraine (SQ), which exhibits a strong

absorption peak at ~700nm [32]. The authors note that further modification of the amine

donors or the aryl groups can allow for absorption into the near-IR – up to 1000nm. The

15

presently examined SQ was chosen due to its capacity to withstand molecular degradation

during sublimation, allowing it to be vacuum deposited. Further, this SQ has a relatively deep

HOMO (5.3eV), which allows for a large Voc. OSCs were fabricated with the structure:

IT/SQ/C60/BCP/Al. 3.2% PCE cells were attained for the thinnest SQ layer thicknesses (65-110Å).

Further studies on squaraines are detailed in Section 3.2 and Section 3.3.

Several groups have investigated triphenylamine (TPA) derivative donors to improve

reproducibility of their OSCs by removing direction-dependent transport properties [33-35].

TPA has a unique propeller-like structure, which is responsible for its glass-like or amorphous

film-forming properties, as illustrated in Figure 9. As such, it is feasible to obtain a reasonable

degree of isotropy in carrier mobility, which makes TPA simple to incorporate into both vertical

and lateral device structures. Cravino et al. ([33]) specifically examined

thienylenevinylenetriphenylamin

e functionalized with peripheral

dicyanovinylene groups (TDCV-

TPA) with the following

molecular design goals:

- create an internal

charge transfer to

shift the TPA

absorption band to

better match the solar

spectrum

- preserve or enhance the high oxidation potential (deep HOMO) of TPA

- achieve high hole mobility

Their unoptimized TDCV-TPA/C60 PHJ achieved a PCE of 1.9% with a very high Voc of 1.2V. This

is attributed to the as-designed HOMO of 6eV for TDCV-TPA that allows for a theoretical

maximum Voc of 1.5V. It is feasible that the Voc of these devices could be improved even

further. More recently, Kagayama et al. ([34]) examined tris[4-(5-phenylthiophen-2-

Figure 9 - Illustrations of TPA Derivatives, including A. TDCV-TPA (Ref. [36]) and B. TPTPA (Ref. [37]).

16

yl)phenyl]amine (TPTPA) as a donor, which exhibits absorption in the 400nm range. When

incorporated into a PHJ with C70, the researchers achieved a PCE of 2.2% and Voc values of 0.9V.

Roquet et al. ([35]) examined a TPA derivative with thienylenevinylene conjugated

branches and electron-withdrawing indanedione or dicyanovinyl groups. Depending on their

solubility, these TPA derivatives were used in either solution-coated BHJ cells with a PCBM

acceptor or vacuum-deposited PHJ cells with a C60 acceptor. The authors showed that they

could easily tune the EQE spectra by altering one arm of the TPA base molecule. To this end,

they observed a shift in the peak response from 480nm to 550-580nm by functionalizing one

TPA arm with an indanedione or malononitrile group. The HOMO of TPA derivative was also

shown to be tunable, allowing for a maximum Voc of 0.96V.

Lloyd and coworkers studied (triisopropylsilylethynyl)pentacene (TIPS-pentacene) due

to the ~50nm bathochromic shift of its primary absorption peak compared to the well-studied

pentacene [36]. TIPS-pentacene further exhibits a HOMO that is 0.28eV lower than that of

pentacene, allowing for an improved Voc when coupled with C60. With proper thermal

annealing treatments, TIPS-pentacene was shown to form crystallites and provide high hole

mobility, in much the same manner as pentacene (in spite of the TIPS functionalization). While

TIPS-pentacene dissolved in toluene, it was insoluble in more common organic solvents such as

chloroform, chlorobenzene and dichlorobenzene. As such, the researchers spun thin films of

TIPS-pentacene and subsequently vacuum-deposited C60 to create PHJ devices. In spite of

various optimization approaches, devices only showed a maximum PCE of 0.5% PCE.

Noting the success of thiophenes in P3HT:PCBM solar cells, many researchers studied

oligomers based on thiophenes. In contrast to their polymeric counterparts, oligomers are

comprised of less than twenty monomer units, and are thus much easier to fabricate and purify

in a controlled manner. In an idealized scenario, they may offer the improved conductivity and

film-forming properties of polymers, but have the control and reproducibility of small

molecules. Xia et al. studied Triarylamino and Tricyanovinyl as well as Diarylamino and

Dicyanovinyl End-Capped Oligothiophenes (PhN-OFOT(2,3)-TCN) and diPhN-OFOT(2,3,4)-DCN

respectively) [37, 38]. The indices (2,3) and (2,3,4) indicate the number of monomer units

17

within the oligomer chain (for example, PhN-OFOT(3)-TCN) is a 3-unit oligomer). The PhN-

OFOT(2,3)-TCN species showed a strong absorption peak at ~680-690nm and a broad shoulder

at ~530nm, while diPhN-OFOT(4)-DCN had absorption peaks at ~450nm and ~580nm. As with

P3HT-based OSCs, these thiophene oligomers showed strong improvements to morphology

with thermal annealing that allowed for improved electrical characteristics when incorporated

into PHJ OSCs. The maximum PCEs for PhN-OFOT(2)-TCN and diPhN-OFOT(4)-DCN PHJ OSCs

(formed with a C60 acceptor) were 1.3% and 2.67% respectively. While the Voc values for both

species were quite high at 0.8 to 0.9V, the fill factors remained quite low at 40-50%, limiting

device efficiency.

3.2. Novel Fabrication Techniques for Small Molecule Organic Solar Cells

Substantial efforts have been dedicated to enhancing the PCE of small molecule OSCs

through specialized fabrication techniques. The most basic techniques involve improving film

morphology through substrate heating during deposition, or by thermal annealing treatments

and solvent annealing treatments. For solvent annealing treatments, the deposited film is

exposed to a solvent-saturated environment to change the film morphology. More recently,

researchers have investigated more esoteric approaches to improving device efficiency. Some

of the more successful approaches are detailed throughout this section.

Tandem OSCs can provide significant PCE improvements by implementation of different

donor/acceptor combinations for better spectral match to the solar spectrum. However, as

noted in Section 2.1, these devices suffer from substantially increased device complexity and

device costs. In order to address this limitation, Yuen et al. examined a simple parallel device

structure employing multiple donor species in a mixed/planar device structure [39]. A

representative parallel device structure is shown in Figure 10, along with the device’s energy

levels. Yuen and coworkers first deposited a thin layer of ZnPc to allow for strong light

absorption at ~620nm. A mixed ClInPc:C60 layer was subsequently deposited to allow for strong

light absorption at ~730nm. In regular device operation, photogenerated electrons from ZnPc

are transferred to the C60 in the ClInPc:C60 layer and subsequently to the pure C60 layer to be

collected at the Al cathode, whereas holes are transferred to the ITO directly. The ClInPc:C60

18

layer forms a BHJ, where

photogenerated electrons

are transferred to C60/Al

and holes easily flow

through the thin ZnPc layer

to be collected at the ITO

anode. The result is a

device that offers higher Jsc

than either the ZnPc/C60

PHJ device or the ClInPc:C60 BHJ device alone, and a Voc in between the Voc values of the

constituent devices. As a consequence, the parallel device offers a substantially improved PCE

of 1.8%, compared to 0.9% for the ZnPc/C60 PHJ OSC and 1.3% for the ClInPc:C60 BHJ OSC.

A similar approach was applied by Wong et al. with a ‘CuPc/rhenium benzathiazole

complex:C60/C60’ device [40]. In this manner, CuPc allowed for absorption over 600-800nm,

while the rhenium complex provided absorption in the range of 400-500nm. The EQE of these

cells exhibited reasonably strong absorption over most of the visible range, with only a slight

valley in the 500-550nm region. These OSCs were shown to be capable of 1.72% PCE. Kim et al.

also employed this methodology, by swapping the pure ZnPc layer in a ZnPc:C60 PM-HJ with a

PdPc layer to extend the absorption range of the OSC [41]. Their finalized structure was:

‘ITO/PdPc/ZnPc:C60/C60/ N,N′-dihexyl-perylene-3,4,9,10-bis(dicarboximide) PTCDI-C6/BCP/Ag’.

The researchers observed strong improvements to the EQE, with visible photocurrent

contributions from both the ZnPc and the PdPc species. This allowed for an increase in PCE

from 3.2% for the PM-HJ ZnPc:C60 cell to 3.7% for a PdPc/ZnPc:C60/C60 cell.

In the work by Kim et al. [41], as well as subsequent studies in [42], PTCDI-C6 was used

as an interlayer between C60 and the traditional hole/exciton blocking layer, BCP. The inclusion

of the PTCDI-C6 layer improved Jsc by improving the EQE across all wavelengths in the visible

spectrum. The use of PTCDI-C6 was also shown to drastically reduce device sensitivity to the

thickness of the BCP layer. For devices without PTCDI-C6, BCP thicknesses greater than 10nm

Figure 10 - A. Illustration of the Parallel Device Structure B. Energy Levels of the Same. B Adapted from Ref. [42].

19

drastically reduce the FF and Jsc. In contrast, devices with PTCDI-C6 can have BCP thicknesses

up to 20nm before device performance is negatively affected.

One may consider several reasons for the decreased OSC performance with increasing

BCP thicknesses:

- BCP has a very low LUMO, which may hinder collection of electrons with the

formation of a continuous BCP film at larger film thicknesses

- At higher film thicknesses, BCP may be more prone to unfavourable partial

crystallization that results in the formation of grain boundaries and trap states

- the deposition of the top metal electrode results in metal doping of the BCP layer,

which would be less prevalent at larger BCP film thicknesses

The deposition of PTCDI-C6 was shown to substantially increase the surface roughness, which

could be reasoned to address any of the above theories. More specifically, with higher surface

roughness, the ‘effective thickness’ of the BCP layer is reduced.

Noting the improvements made to OSC efficiency by insertion of inter-layers at the

organic-cathode interface, Hirade et al. sought to study and improve upon the organic-anode

interface [43]. As a first point of interest, the researchers show that the traditional hole-

extraction layer, PEDOT:PSS, is an efficient exciton quencher that can substantially reduce

device performance. As such, Hirade and coworkers employed TPTPA as an electron and

exciton blocking layer due to its much larger energy gap of 2.7eV compared to the energy gap

of the chosen donor, DBP. Since TPTPA has a comparable HOMO to that of DBP and a hole

mobility exceeding DBP, no substantial losses to device performance were expected. Insertion

of TPTPA into DBP/C60 PHJ device granted a substantial improvement in Jsc and a slight

improvement in FF, resulting in a shift in PCE from 3.9% to 5.3%. This improvement was

verified to be purely due to exciton blocking effects and not due to morphological variations, as

no variations in the active layer structure were observed by x-ray diffraction and

photoluminescence measurements.

20

Beyond the insertion of additional sensitizing and carrier extraction/blocking layers,

many efficiency enhancement techniques have been dedicated to the improvement of the

donor/acceptor morphology and crystallinity. In order to achieve nanoscale phases of pure

donor and acceptor in their BHJs, Sakai et al. alternated deposition of very thin layers of donor

(D) and acceptor (A) to form a

‘DADADA. . .’ stack [44]. The

researchers used 1-2nm of

pentacene and C60 for the

donor and acceptor

respectively. The stack is

illustrated in Figure 11 along

with a cross-sectional scanning

electron microscope (SEM)

image. Since these films are

not perfectly continuous at 1-

2nm, their alternating

deposition results in the

formation of an interpenetrating bicontinuous network. Sakai and coworkers substituted a 12-

layer ‘DA’ stack for the mixed layer in a PM-HJ OSC to obtain the following device structure:

ITO/PEDOT:PSS/Pentacene(20 nm)/ [C60(2nm)/Pentacene(2nm]6 /C60/BCP/MgAg

This OSC achieved a PCE of 1.58%, which is a 68% improvement over the PCE of a simple

pentacene/C60 PHJ OSC. The improvement was attributed to a substantial increase in

conversion of excitons into electrons and holes. This improvement is reasonable, as the spacing

between pure pentacene and C60 phases is on the order of 1-2nm, which is much lower than

the exciton diffusion lengths for these materials. Increasing the number of stack layers beyond

twelve served to increase the series resistance, which deteriorated the PCE.

Yang and coworkers followed a similar approach, instead using CuPc as the donor and

C60 as the acceptor in a ‘DADADA. . .’ stack [45]. The authors note the preferable formation of

Figure 11 - Illustration of the Pentacene-C60 Repeating Donor-Acceptor Stack Architecture with a Cross-Sectional SEM Image

of the Same. Figure adapted from Ref. [47].

21

pure C60 and pure CuPc crystalline domains due to the relatively large C60-C60 and CuPc-CuPc

interaction energies versus those of the CuPc-C60 molecular pair. At a 12-layer ‘DA’ stack (6 of

donor and 6 acceptor layers), the interfacial area was found to be 11-times that of a simple

bilayer heterojunction. When incorporated into a PM-HJ device, their 12-layer CuPc-C60 stack

allowed for a PCE of 4.4%.

Wei et al. sought to achieve an interpenetrating, bicontinuous BHJ by strongly increasing

the roughness of the first-deposited ultra-thin squaraine donor material [46]. In this manner,

when the acceptor material is deposited, it fills the gaps and valleys, allowing for a high

interfacial area. In order to achieve a very high roughness, Wei and coworkers deposited 6.2nm

SQ films and converted them to polycrystalline films by both thermal annealing as well as

dichloromethane (DCM) solvent annealing. This shifted the RMS roughness from 0.9nm to

1.9nm. The resultant film also exhibited a much higher exciton diffusion length owing to its

large crystallites. With a 110oC thermal annealing temperature combined with DCM solvent

annealing, the researchers achieved 4.6% PCE devices.

Yu et al. noted that the crystallinity of their ZnPc donor layers could be improved with

the weak epitaxy growth (WEG) technique [47]. In this technique, an 8-nm precursor ‘inducing’

layer is used to assist in the growth of crystalline ZnPc, and the precursor and ZnPc depositions

are performed at high substrate temperatures (155oC). Aside from its ability to help form

crystalline ZnPc, the inducing layer was chosen to be 2,5-bis(4-biphenylyl)-bithiophene (BP2T),

owing to its:

- HOMO of 5.3eV, which aligns well with that of PEDOT:PSS (5eV)

- Low LUMO of 2.8eV, which helps to block excitons and electrons from reaching the

PEDOT:PSS layer and ITO contact

- high hole conductivity to allow for minimal series resistance losses

The deposition of ZnPc on BP2T resulted in the growth of long ZnPc fibres, as opposed to the

globular structures when deposited on ITO directly. Furthermore, the deposition of ZnPc onto

BP2T was shown to decrease the RMS roughness from 3.38nm to 2.42nm compared to

deposition directly on ITO. The authors note that, for their devices, the reduced roughness

22

helps to reduce surface-state-induced recombination. Selected area electron diffraction (SAED)

indicated that a ZnPc grain on a single domain of BP2T had only one orientation, which verifies

that this technique does result in some degree of epitaxial growth. WEG methods were

compared to regularly fabricated devices in both the PHJ and PM-HJ configuration. For the PHJ

devices, WEG improved the PCE from 1.2% to 2.1%. For the PM-HJ devices, WEG improved the

PCE from 1.8% to 3.1%.

3.3. Recent Giants in Small Molecule Organic Solar Cell Efficiency

3.3.1. Optimized ‘p-i-n’ Tandem Organic Solar Cells

Karl Leo and coworkers (of Heliatek fame and creators of the ‘p-i-n’ OSC architecture)

focused on the optimization of tandem cells based on p-i-n sub-cell architectures, using much

of the knowledge gained and described throughout Section 2. Riede et al. noted that, while

single junction OSCs are capable of achieving theoretical efficiencies on the order of 10-11% on

their own, tandem cells are necessary to surpass 15% PCE [19]. The researchers thus

considered a tandem system involving two sub-cells that ultimately allowed for a PCE of 6.1%

(illustrated in Figure 12, with sub-cell structures and full chemical names listed below):

- ITO/n-C60/C60/F4-ZnPc:C60 (1:1)/DiNPB/p-DiNPB/n-C60/Al (red-absorbing)

- ITO/n-C60/C60/DCV6T:C60 (2:1)/BPAPF/p-BPAPF/p-DiNPB/n-C60/Al (green-absorbing)

The following new small molecule or oligomer species were used:

- DiNPB: N,N ′ -diphenyl-N,N ′ -bis(4 ′ -(N,N-bis(naphth-1-yl)-amino)-biphenyl-4-yl)-

benzidine

- F4-ZnPc: tetra-fluoro zinc phthalocyanine

- DCV6T: α ,ω -bis-(dicyanovinylsexithiophene)-Bu(1,2,5,6) [48]

- BPAPF: 9,9-bis[4-(N,N-bis-biphenyl-4-yl-amino)phenyl]-9H-fluorene

Furthermore, ‘p-‘ and ‘n-‘ denote p- and n-doping with NDP9 AND NDP1 respectively –

materials that are proprietary from Novaled [49].

23

The complete cell structure therefore makes use of both ZnPc and a dicyanovinyl-

substituted oligothiophene as its donor materials. These materials complement each other

well, allowing for absorption over the entire visible spectrum. As a point of note, both species

were deposited at elevated substrate temperatures in order to improve the BHJ morphology.

Before considering the much more complicated tandem cell, one may first consider each

individual sub-cell:

The ‘red’ OSC uses a F4-ZnPc:C60 BHJ. F4-ZnPc is four-times fluorinated ZnPc, with a

reduced ionization potential (~HOMO) from -5.11eV to -5.46eV compared to regular ZnPc. This

occurs as a consequence of the electron-withdrawing nature of fluorine. The reduced HOMO

results in an increase in Voc of the OSC. When mixed with C60 as a BHJ, F4-ZnPc exhibits a

primary absorption peak at ~630nm, a shoulder at ~720nm and tail absorption extending above

800nm. Considering the specifics of the p-i-n stack, the DiNPB layer is the ‘p’ layer, the F4-

ZnPc:C60 layer is the ‘i’ layer and the C60 layer is the ‘n’ layer. The n-C60 layer adjacent to ITO

makes Ohmic contact with ITO and acts as an exciton blocking layer. The p-DiNPB layer is

Figure 12 - Illustration of the 6.1% Efficiency Tandem Organic Solar Cell and its Constituent Sub-Cells developed by Riede et al. Figure Adapted from Ref. [19].

24

similarly used to block excitons and to allow for easy passage of holes. The added thickness of

the p-DiNPB and n-C60 layers improves the positioning of the optical field within the devices, as

was determined by the same modelling methods described in Section 2.4.

The ‘green’ OSC uses a DCV6T donor material, where the 6 indicates 6 repeat monomer

units in the oligomer. When mixed with C60, DCV6T exhibits an absorption peak at ~570nm

with a broad shoulder extending well into the blue wavelengths. Considering the specifics of

the p-i-n stack, the BPAPF layer is the ‘p’ layer, the DCV6T:C60 layer is the ‘i’ layer and the C60

layer is the ‘n’ layer. BPAPF is chosen for the ‘p’ layer to better match the ionization potential

of DCV6T. A doped BPAPF layer is then used to reduce device series resistance and to make

contact with the p-DiNPB layer.

The tandem cell stacks the green sub-cell onto the red sub-cell, with the cells separated

by the p-DiNPB/n-C60 recombination contact. This contact has been detailed separately in [50]

for its use in tandem cell applications. It is a replacement to the previously used metal island

recombination layer described in Section 2.1. The tandem cell also makes use of a substantially

thicker p-doped DiNPB layer as an optical spacer to ensure the maxima in the optical field occur

in the i-regions of both cells. A peak efficiency is found using an optical spacer thickness of

165nm. Due to the sensitivity to optical field distribution, the authors also note that the

performance their tandem cells is strongly affected by the angle of measurement. Both Jsc and

PCE are found to drop with an increasing angle of light.

3.3.2. Highly Efficient Solar Cells Based on New Donor Materials

Steinmann et al. studied merocyanine dye MD376 as a donor in various configurations

of solar cells, including: standard BHJ solar cells, PM-HJ solar cells and the same in tandem

configurations [51]. MD376 exhibits a relatively broad absorption peak at ~610nm. For the

non-tandem devices, an optimal thickness of 50nm BHJ was used to achieve 4.3% PCE. When

incorporated into a PM-HJ, the PCE was further improved to 5%. All devices exhibited relatively

large Voc values of ~1-1.1V. The best tandem configuration device employed the following

device structure:

25

ITO/MoO3 (15nm)/MD376 (5nm)/MD376:C60 (1:1, 20nm)/Al(1nm)/MoO3 (15nm)/MD376:C60 (1:1, 30nm)/C60 (5nm)/ BPhen (6nm)/Ag

An Al (1nm)/MoO3 (15nm) recombination layer was used to separate the individual sub-cells.

Note that the first cell has an effective ‘p-i’ structure, whereas the second cell employs an ‘i-n’

structure. Bphen, 4, 7-Diphenyl-1, 10-Phenanthroline, is used as a replacement to BCP, acting

as a protective layer for metal deposition and to block holes and excitons. This device exhibited

a PCE of 4.7% and a very high Voc of 2V. The EQE spectra and IV characteristics for MD376-

based devices are shown in Figure 13.A.

Lin et al. made use of DTDCTB donors in PM-HJ devices, where DTDCTB is described as a

“ditolylaminothienyl moiety and an electron-withdrawing dicyanovinylene moiety bridged by

electron-accepting 2,1,3-benzothiadiazole” [52]. DTDCTB films exhibit a strong and broad

absorption band at 700nm with tail-end absorption extending beyond 900nm, and a secondary

absorption band at 430nm. The authors combine DTDCTB with C70 to allow their PM-HJ OSCs to

absorb over the entire visible spectrum. DTDCTB further exhibits a HOMO of 5.3eV in a thin

Figure 13 - EQE/Absorption (top) and IV Characteristics (bottom) of A. MD-376:C60 PM-HJ OSCs (Solid Line = Single Cell; Dashed Line = Tandem Cell) (Ref. [54]). B. DTDCTB:C60 and DTDCTB:C70

PM-HJ OSCs (Ref [55]). C. Mixed 1-NPSQ:DPASQ/C60BHJ OSCs at Different Mixing Ratios and Varying Annealing Treatments (Ref [57]).

26

film, allowing for a reasonably large Voc of 0.8V when paired with either C60 or C70. When

incorporated into a PM-HJ structure with an MoO3 hole extraction layer and a BCP exciton

blocking layer, devices were shown to be capable of 5.8% PCE. The EQE spectra and IV

characteristics for DTDCTB-based devices are shown in Figure 13.B.

Following their successes with the SQ devices detailed in Section 3.1 and 3.2, Forrest

and coworkers studied further squaraine derivatives. In particular, Wei et al. developed 2,4-

bis[4-(N-phenyl-1-naphthylamino)-2,6-dihydroxyphenyl] squaraine (1-NPSQ), a material based

on SQ, but with its isobutylamines substituted for the less bulky arylamines [53]. As a

consequence, 1-NPSQ undergoes more -stacking between donor molecules to improve hole

mobility and hole collection. In OSC performance, this is manifested as substantially reduced

series resistance and a strong improvement in fill factor. The electron-withdrawing arylamine

also serves to decrease the HOMO energy from 5.1eV to 5.3eV, thereby increasing the

theoretical Voc of the device. Finally, 1-NPSQ exhibits a slightly red-shifted absorption band

compared to SQ, with peak absorption at ~700nm and tail-end absorption to ~810nm. As with

the SQ species described in Section 3.2, thermal annealing 1-NPSQ increases both the

crystallinity and roughness of its film, allowing for increased contact area with the subsequently

deposited C60. The optimally annealed device (90oC / 10 minutes) had a PCE of 5.7%, with a Voc

of 0.9V, a FF of 64% and a Jsc of 10 mA/cm2.

Xiao et al. further improved the squaraine-based OSC efficiency by blending 1-NPSQ

with the complementary blue-shifted SQ molecule, [2-[4-( N , N -diphenylamino)-2,6-

dihydroxyphenyl]-4-diphenylamino] squaraine (DPASQ) [54]. DPASQ exhibits a peak absorption

at ~530nm. When both DPASQ and 1-NPSQ donors are used in combination with C60 acceptor

the entire visible spectrum may be captured. This is illustrated by the absorption

characteristics of these materials in Figure 13.C (top). With a HOMO of 5.4eV, the experimental

maximum Voc for DPASQ cells was found to be 1V. When employing a mixed donor layer, the

Voc generally varies in between that of 1-NPSQ and DPASQ; however, the maximum Voc of 1V

can be achieved at a mixing ratio of 1:2 1-NPSQ:DPASQ. Unfortunately, the maximum Jsc is

achieved at a mixing ratio of 2:1 1-NPSQ:DPASQ. The addition of DPASQ helps improve the EQE

27

from 500-600nm; however, increasing the concentration of DPASQ beyond 50% substantially

decreases the contribution from 1-NPSQ in the 600-700nm region, thus deteriorating the Jsc.

In order to further improve the cell performance, solvent annealing with DCM was

performed, and a 1,4,5,8-napthalene-tetracarboxylic-dianhydride (NTCDA) / PTCBI optical

spacer was added between the C60 and Al layers. Addition of the optical spacer resulted in an

increase in short circuit current, which followed from the fact that the peak electric field

intensity better overlapped with the active layers. Solvent annealing further increased the

short circuit current and improved the FF to a very high value of 72%, but decreased the Voc

from 1V to 0.8V. In spite of the decreased Voc, this optimized, solvent-annealed OSC exhibited

an impressive PCE of 5.9%. The IV characteristics for the various iterations of these devices are

shown in Figure 13.C (bottom).

4. Conclusions

Organic electronics, and OPVs in particular, are a rapidly developing and constantly

evolving field. While soluble organic materials, including polymers and soluble small molecules,

offer substantial cost benefits due to their potential ease of fabrication, they typically exhibit

poor reproducibility. The high number of experimental variables makes these systems

inherently difficult to study. As such, in order to obtain a fundamental understanding of the

efficiency limitations and degradation mechanisms of OSCs, the insoluble and vacuum-

deposited small molecules are of particular interest. The most basic OSC architectures formed

by thermally evaporated small molecules are the PHJ, BHJ, tandem PHJ and tandem BHJ OSCs.

The BHJ cells may be further refined into p-i-n solar cells, where the ‘i’ layer is the BHJ. A

common subset of the p-i-n solar cell, denoted as the PM-HJ, simply borders the ‘i’-layer with

pure donor and acceptor layers for the ‘p’ and ‘n’ layers respectively. In all of these systems,

with a strong emphasis on tandem OSCs, the distribution of the electric field within the device

layers has been identified as a significant factor to limit the PCE. In order to address these

concerns, researchers have adapted transfer matrix formalism to identify the position of the

peak electric field in any OSC.

28

The focus of OPVs has shifted from the realization of new device architectures to the

creation of new donor materials and to the optimization of the current systems by clever

fabrication techniques. With regard to the first point, research groups have studied a wide

range of different materials with varying degrees of success. The most successful alternative

donor materials in literature include F4-ZnPc, DCV6T, DTDCTB, MD376 merocyanine dye and

squaraine derivatives, allowing for PCEs ranging from 5% to 6.1%. These materials were all

designed specifically for their broad absorption bands, as well as their relatively deep HOMO

levels for enhanced Voc values.

Device optimization and refinement has focused on the addition of inter-layers for

enhanced electrical properties, light absorption or material crystallization. Several groups have

successfully increased the absorption range of their OSCs by the insertion of a thin secondary

donor layer immediately prior to the deposition of their primary donor BHJ. Meanwhile, other

researchers have investigated improved morphology by additional or modified deposition

techniques. Some methods are simple, such as strong annealing treatments to create an

interdigitated network of donor and acceptor materials, while others involve substantial

deviations from regular fabrication – such as WEG, or the deposition of stacks comprised of

alternating ultra-thin (1-2nm) layers of donor and acceptor.

New materials development and further device optimization techniques, such as those

detailed in this review, should eventually allow for 15% PCE OSCs. Unfortunately, there are still

a number of hurdles that must be surpassed before OSCs are a viable commercial product.

With meagre device lifetimes, the degradation study of OSCs is still a very young field that

requires massive research efforts. Further, most OSCs to date have been fabricated as lab-scale

devices with device areas typically less than 1cm2. Scaling up these devices and integrating

them into panels will prove to be difficult, especially with the commonly high OSC series

resistances. Regardless, with OSC efficiencies already above 10% and Heliatek quoting device

harvesting factors 15-25% higher than crystalline silicon and other thin-film solar technologies,

it is clear that OPVs are quickly becoming a strong competitor in the solar industry.

References [1] M. T. Lloyd, et al., "Photovoltaics from soluble small molecules," Materials Today, vol.

10, pp. 34-41, Nov 2007. [2] J. Roncali, "Molecular Bulk Heterojunctions: An Emerging Approach to Organic Solar

Cells," Accounts of chemical research, vol. 42, pp. 1719-1730, Nov 2009. [3] B. Walker, et al., "Small Molecule Solution-Processed Bulk Heterojunction Solar Cells,"

Chemistry of Materials, 2011. [4] A. Mishra and P. Bäuerle, "Small Molecule Organic Semiconductors on the Move:

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i

Appendix A –Optical Modelling of Organic Solar Cells by Transfer Matrix

Formalism

Modelling of the electric field within the OSC can be used to accurately determine the

layer thicknesses required to obtain maximum OSC efficiency. This approach relies on the

notion that the generation rate of excitons is proportional to the intensity of the optical field

within the cell. The electric field throughout the device is dependent on the reflection and

absorption of light due to variations in the complex refractive index of the various OSC layers.

The transmittance and reflectance of light can thus be modelled by Fresnel equations. The

electric field can be further plotted by transfer matrix formalism, as has been shown by

Pettersson et al. and Sievers et al. [55, 56].

This appendix has been created for the extra modelling assignment for ECE632. It

outlines the methodologies and mathematics employed in transfer matrix formalism. MATLAB

code has been written to reproduce the results described in literature. Complex indices of

refraction for common OSC materials have been taken from literature and are used to evaluate

the electric field in various device configurations. The results of some of these models have

been described for their application in actual devices in the body of this report (Section 2.4).

Modelling Theory

We consider a plane wave of light incident on a superstrate OSC. The behaviour of the light at

any interface can be described by Fresnel coefficients, which can be organized in an

interference matrix for an arbitrary interface of material j and material k:

(1)

, where tjk and rjk are the complex transmission and reflection coefficients:

(2)

ii

(3)

, where nj and nk are the complex indices of refraction for materials j and k respectively – for

example, nj=n+i*, where n is the real part and is the imaginary part of the refractive index.

The interference matrix can then be rewritten as:

(4)

The propagation of light through a given layer j may similarly be described by a 2x2 matrix:

(5)

, where

, is the wavelength of light and dj is the thickness of the layer.

We consider both the forward and backward propagating complex quantities of electric field

along an axis ‘x’, denoted as E+(x) and E-(x). The electric field of light as it interacts with a series

of ‘m’ layers (i.e. as light passes through the organic solar cell) can be described by the total

system transfer matrix, also known as the scattering matrix (S):

(6)

, where E0 refers to the electric field of light just as it approaches the front side of the solar cell,

and Em+1 refers to the electric field of light just as it exits the back side. Further, S can be

written as the product of all interference and propagation matrices:

(7)

The reflection and transmission coefficients of the m-layer stack may be written as:

(8)

iii

(9)

Since the glass substrate is generally quite thick, it is cumbersome and impractical to include it

in the transfer-matrix calculation. Following the approach by [56], the intensity of the light

after it has passed through the substrate can instead be calculated as:

(10)

, where I0 is the intensity of the incident plane wave, Ts is the transmittance of the substrate, Rs

is the reflectance of the substrate, s is the absorption coefficient of the substrate, ds is the

thickness of the substrate and R is the reflectance of the remaining layers of the OSC.

The reflectance of the remaining layers of the OSC can be found as:

(11)

The intensity of the input light varies with wavelength and is defined by the AM1.5 1-sun solar

spectrum.

Using Is, the incident electric field, after passage through the substrate, can be found as:

(12)

For the purposes of this model, ES effectively refers to E0+ in equation (6) above.

In order to calculate the electric field at a specific distance x within layer j, it is necessary to

break apart the total system transfer matrix into partial transfer matrices. One may define

S=Sj’LjSj’’, where Sj’ is the partial transfer matrix prior to layer j, Sj’’ is the partial transfer matrix

after layer j, and Lj is the propagation matrix for layer j, as defined in equation (5) above. Sj’

and Sj’’ may be written as:

(13)

iv

(14)

The complex reflection and transmission coefficients may then be written as

,

,

and

.

Further, the internal transmission coefficient relating to the propagation of light in the forward

direction can be found as:

Finally, the total electric field in layer j at a distance x from its interface with layer (j-1) can be

written as:

(15)

Since the input intensity and the complex indices of refraction are a function of wavelength, the

electric field is necessarily a function of wavelength. The square of the absolute value of the

electric field at each point x can be integrated across the wavelengths of the input light to

provide the total electric field.

Input Data

For simplicity, the range of wavelengths considered is 300nm to 800nm. The 1-sun, AM1.5

input spectrum was obtained from the National Renewable Energy Laboratory (NREL) and is

available at http://rredc.nrel.gov/solar/spectra/am1.5/

Complex indices of refraction were obtained by digitizing graphs found in literature. The data

was subsequently interpolated and smoothed to generate 1nm spacing between data points in

the range of interest. The following sources were used to obtain the data:

BCP: [57]

v

CuPc: [58]

C60: [55]

glass: [59]

ITO: [59]

PEDOT:PSS: [59]

P3HT:PCBM (1:1) BHJ: [60]

ZnPc: [61]

ZnPc:C60 (1:1) BHJ: [24]

Metal complex indices of refraction were obtained from http://refractiveindex.info/

Printouts of the complex indices of refraction are available upon request.

MATLAB Implementation and Output

In order to demonstrate the basic implementation of this model, the following P3HT:PCBM BHJ

device is modelled:

Layer 0: Glass, thickness = 0.7mm

Layer 1: ITO, thickness = 100nm

Layer 2: PEDOT:PSS, thickness = 30nm

Layer 3: P3HT:PCBM (1:1), thickness = 70nm & 200nm

Layer 4: Aluminum, thickness = 100nm

Layer 5: Air

All thicknesses are representative of a realistic device structure capable of producing 2-3% PCE

in a laboratory device. 70nm P3HT:PCBM would be fabricated by spincoating from a

chlorobenzene solvent. 200nm P3HT:PCBM would be fabricated by spinning at higher weight

percents from a dichlorobenzene solvent.

The code used for this model is available at the end of this document. The output figures are

shown below in Figure A.1 with the various layers labelled.

vi

Figure A.1 - Distribution of the Squared Absolute Optical Electric Field in a P3HT:PCBM BHJ OSC with A. 70nm P3HT:PCBM and B. 200nm P3HT:PCBM

From Figure A.1-A, it is clear that a large portion of the electric field falls in the PEDOT:PSS and

ITO regions. Since these regions are non-absorbing and they do not contribute to

photocurrent, a significant portion of the incident light is effectively wasted. Increasing the

P3HT:PCBM layer thickness to 200nm (Figure A.1-B) helps to isolate the original peak within the

active layer; however, a secondary electric field peak arises in the ITO/PEDOT:PSS region.

In order to better isolate the electric field within the active region, a final P3HT:PCBM thickness

of 130nm is chosen. The results are shown below in Figure A.2.

Figure A.2 - Distribution of the Squared Absolute Optical Electric Field in a 130nm P3HT:PCBM OSC

vii

This device is shown to have a significantly improved electric field distribution, with the

maximum electric field centred within the active region of the device.

In order to further verify the power of this technique, the following device configurations are

also examined:

i. A simple PHJ device with ZnPc donor and C60 acceptor glass(0.7mm)/ITO(100nm)/ZnPc(30nm)/C60(30nm)/BCP(5nm)/Al(100nm)

ii. A PM-HJ device with ZnPc donor and C60 acceptor glass(0.7mm)/ITO(100nm)/ZnPc(30nm)/ZnPc:C60(20nm)/C60(30nm)/BCP(5nm)/Al(100nm)

iii. A PM-HJ device in tandem configuration with ZnPc donor and C60 acceptor glass(0.7mm)/ITO(100nm)/ZnPc(30nm)/ZnPc:C60(20nm)/C60(10nm)/Au(0.5nm)/ZnPc(10nm)/ZnPc:C60(20nm)/C60(30nm)/BCP(5nm)/Al(100nm)

For these devices, the MATLAB code was modified to include additional layers as required. This

additional MATLAB code is available upon request.

The squared electric field distributions for devices i and ii are shown in Figure A.3. As shown in

Figure A.3-A, the electric field distribution is quite poor, with very little possible absorption by

C60 and a large portion of the electric field in the ITO. Incorporation of these materials into a

PM-HJ device, however, improves the positioning of the electric field, shifting its peak to the

ZnPc:C60 BHJ.

Figure A.3 - Distribution of the Squared Absolute Optical Electric Field in A. a ZnPc/C60 PHJ OSC and B. a ZnPc:C60 PM-HJ OSC

viii

The electric field distribution is further complicated by the implementation of the tandem

device, as shown in Figure A.4. The ideal electric field would have two peaks, centred at each

of the ZnPc:C60 BHJs. However, as shown in Figure A.4-A, which is the device based off of iii

above, the peak electric field occurs almost nearly at the Au metal cluster interface between

the two sub-cells. This is non-ideal, as photogenerated excitons will recombine directly in this

region before splitting into their constituent electrons and holes.

In order to better align the electric field, a 130nm p-doped ZnPc optical spacer can be added

and the thickness of the BHJ layer closer to the Al electrode can be increased to 30nm, as

shown in Figure A.4-B. In this case, the original local maximum shifts directly into the ZnPc:C60

BHJ. The minimum occurs within the optical spacer as desired, and the second BHJ occurs

within a plateau of the electric field. Unfortunately the absolute maximum electric field occurs

within the ITO layer, which is non-absorbing and does not contribute to device photocurrent.

This stresses the strong sensitivity of the system to any changes in the layer thicknesses. To this

end, further optimization is required to achieve the optimal electric field distribution.

Figure A.4 - Distribution of the Squared Absolute Optical Electric Field in a ZnPc:C60 PM-HJ Tandem OSC A. without an Optical Spacer and B. with an Optical Spacer

ix

%******************************************************* %Electric Field Calculation by Transfer Matrix Formalism %*******************************************************

%Author: Graeme Williams %Contact: g3willia@uwaterloo.ca %This model has been completed for the extra modelling assignment in ECE %632

%Description: This function maps the square of the absolute value of the %electric field within a stack of m layers with known complex indices of %refraction. %Devices are considered to be fabricated superstrate, such that the light %first passes through a substrate of a given thickness.

%All input complex index of refraction matrices are defined as: %| WAVELENGTH | Re(n) | Im(n) | %| 300 | x0 | y0 | %| ... | .. | .. | %| 800 | x500 | y500 |

%Variables c = 299792458; %speed of light, m/s eps_0 = 8.854187817620*10^-12; %vacuum permittivity, F/m

%------------------------------------------------------------------------- %INPUT DATA %Spread of wavelengths lamset = [300:1:800]'*(10^-9); %300nm to 800nm

%Number of data points along the x-dimension per layer x_pts = 100; %in reality, will actually be x_pts + 1

%Input Light Intensity %Listed by NREL, available: http://rredc.nrel.gov/solar/spectra/am1.5/ I0 = AM1p5(:,2);

%Note: Due to its thickness, the glass substrate will be excluded from the %transfer matrix methods. Intensity of light through the glass will be %calculated separately d_glass = 0.7*10^-3; %m R_glass = [n_glass(:,1), ((1 - n_glass(:,2))./(1 + n_glass(:,2))).^2]; T_glass = [R_glass(:,1), (1 - R_glass(:,2))]; alpha_glass = 30; %m^-1, roughly k_glass = lamset*(alpha_glass)/(4*pi);

%Layered Structure %n0 - Air to Glass n_0 = n_glass(:,2) + i*k_glass(3); T_s = T_glass(:,2); R_s = R_glass(:,2); alpha_s = alpha_glass; d_s = d_glass;

x

%1 - ITO n_1 = n_ITO(:,2) + i*n_ITO(:,3); xi_1 = (2*pi*n_1)./lamset; alpha_1 = n_ITO(:,3)*(4*pi)./lamset; d_1 = 100*10^-9; %100nm, in m %2 - PEDOT:PSS n_2 = n_pedot(:,2) + i*n_pedot(:,3); xi_2 = (2*pi*n_2)./lamset; alpha_2 = n_pedot(:,3)*(4*pi)./lamset; d_2 = 30*10^-9; %30nm, in m %3 - P3HT:PCBM n_3 = n_p3pc(:,2) + i*n_p3pc(:,3); xi_3 = (2*pi*n_3)./lamset; alpha_3 = n_p3pc(:,3)*(4*pi)./lamset; d_3 = 70*10^-9; %70nm, in m %4 - Al n_4 = n_Al(:,2) + i*n_Al(:,3); xi_4 = (2*pi*n_4)./lamset; alpha_4 = n_Al(:,3)*(4*pi)./lamset; d_4 = 100*10^-9; %100nm, in m %5 - Air (assume vacuum for simplicity) n_5 = zeros(501,1); %-------------------------------------------------------------------------

%------------------------------------------------------------------------- %Calculation of overall reflection and transmission coefficients %& Definition of parameters for subsequent analysis

%Initializing variables for later use R = []; T = []; t1_plus = []; r1_pp = []; t2_plus = []; r2_pp = []; t3_plus = []; r3_pp = []; t4_plus = []; r4_pp = [];

%Looping through the wavelengths 300nm to 800nm for j=1:501 %*** Across n0 to n1 %Interface Matrix I_01 = [ ( (n_0(j) + n_1(j))/(2*n_0(j)) ), ( (n_0(j) - ... n_1(j))/(2*n_0(j)) ); ( (n_0(j) - n_1(j))/(2*n_0(j)) ), ... ( (n_0(j) + n_1(j))/(2*n_0(j)) )];

%*** Through n1 %Layer Matrix L_1 = [exp(-i*(xi_1(j)*d_1)), 0; 0, exp(i*(xi_1(j)*d_1))];

%*** Across n1 to n2 %Interface Matrix I_12 = [ ( (n_1(j) + n_2(j))/(2*n_1(j)) ), ( (n_1(j) - ... n_2(j))/(2*n_1(j)) ); ( (n_1(j) - n_2(j))/(2*n_1(j)) ), ...

xi

( (n_1(j) + n_2(j))/(2*n_1(j)) )];

%*** Through n2 %Layer Matrix L_2 = [exp(-i*(xi_2(j)*d_2)), 0; 0, exp(i*(xi_2(j)*d_2))];

%*** Across n2 to n3 %Interface Matrix I_23 = [ ( (n_2(j) + n_3(j))/(2*n_2(j)) ), ( (n_2(j) - ... n_3(j))/(2*n_2(j)) ); ( (n_2(j) - n_3(j))/(2*n_2(j)) ), ... ( (n_2(j) + n_3(j))/(2*n_2(j)) )];

%*** Through n3 %Layer Matrix L_3 = [exp(-i*(xi_3(j)*d_3)), 0; 0, exp(i*(xi_3(j)*d_3))];

%*** Across n3 to n4 %Interface Matrix I_34 = [ ( (n_3(j) + n_4(j))/(2*n_3(j)) ), ( (n_3(j) - ... n_4(j))/(2*n_3(j)) ); ( (n_3(j) - n_4(j))/(2*n_3(j)) ), ... ( (n_3(j) + n_4(j))/(2*n_3(j)) )];

%Through n4 %Layer Matrix L_4 = [exp(-i*(xi_4(j)*d_4)), 0; 0, exp(i*(xi_4(j)*d_4))];

%*** Across n4 to n5 %Interface Matrix I_45 = [ ( (n_4(j) + n_5(j))/(2*n_4(j)) ), ( (n_4(j) - ... n_5(j))/(2*n_4(j)) ); ( (n_4(j) - n_5(j))/(2*n_4(j)) ), ... ( (n_4(j) + n_5(j))/(2*n_4(j)) )];

%Calculating the total transfer matrix for this lambda S = I_01*L_1*I_12*L_2*I_23*L_3*I_34*L_4*I_45;

%Calculating the total reflectance and transmittance parameters r = S(2,1)/S(1,1); t = 1/S(1,1);

%Calculating the parameters wrt power/intensity R = [R; abs(r^2)];

%********************************************************************** %Calculating partial transfer matrices (for position-dependent %intensity calculations - see below) S1_p = I_01; S1_pp = I_12*L_2*I_23*L_3*I_34*L_4*I_45; S2_p = I_01*L_1*I_12; S2_pp = I_23*L_3*I_34*L_4*I_45; S3_p = I_01*L_1*I_12*L_2*I_23; S3_pp = I_34*L_4*I_45; S4_p = I_01*L_1*I_12*L_2*I_23*L_3*I_34; S4_pp = I_45;

%Calculating relevant transmission and reflection parameters

xii

r1_pp = [r1_pp; S1_pp(2,1)/S1_pp(1,1)]; r2_pp = [r2_pp; S2_pp(2,1)/S2_pp(1,1)]; r3_pp = [r3_pp; S3_pp(2,1)/S3_pp(1,1)]; r4_pp = [r4_pp; S4_pp(2,1)/S4_pp(1,1)];

t1_plus = [t1_plus; (S1_p(1,1) + S1_p(1,2)*r1_pp(j)*... exp(2*i*xi_1(j)*d_1))^(-1)]; t2_plus = [t2_plus; (S2_p(1,1) + S2_p(1,2)*r2_pp(j)*... exp(2*i*xi_2(j)*d_2))^(-1)]; t3_plus = [t3_plus; (S3_p(1,1) + S3_p(1,2)*r3_pp(j)*... exp(2*i*xi_3(j)*d_3))^(-1)]; t4_plus = [t4_plus; (S4_p(1,1) + S4_p(1,2)*r4_pp(j)*... exp(2*i*xi_4(j)*d_4))^(-1)];

end %-------------------------------------------------------------------------

%------------------------------------------------------------------------- %Calculation of the internal transmittance through the glass substrate T_int = (T_s.*exp(-alpha_s.*d_s))./(1-(R.*R_s.*exp(-2.*alpha_s.*d_s))); %-------------------------------------------------------------------------

%------------------------------------------------------------------------- %Calculation of position-dependent reflection and transmission coefficients

%Defining the inital electric field intensity based on: %I=(c*n*eps0/2)*abs(E)^2 E0 = sqrt(2*(I0.*T_int)./(c*n_glass(:,2)*eps_0));

%Initializing variables for later use E1 = []; E2 = []; E3 = [];

%Layer 0 (substrate) Is = I0.*T_int;

%Layer 1-3 %Splitting layers into finite segments %Layer 1 delta_d1 = d_1 / x_pts; d1_pts = [0:delta_d1:d_1]; %Layer 2 delta_d2 = d_2 / x_pts; d2_pts = [0:delta_d2:d_2]; %Layer 3 delta_d3 = d_3 / x_pts; d3_pts = [0:delta_d3:d_3]; %Layer 4 delta_d4 = d_4 / x_pts; d4_pts = [0:delta_d4:d_4];

%Looping through the wavelengths for j=1:501

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for k=1:(x_pts+1) E1(j,k) = E0(j) * t1_plus(j)*(exp(i*xi_1(j)*d1_pts(k)) + ... r1_pp(j)*exp(i*xi_1(j)*(2*d_1-d1_pts(k)))); E2(j,k) = E0(j) * t2_plus(j)*(exp(i*xi_2(j)*d2_pts(k)) + ... r2_pp(j)*exp(i*xi_2(j)*(2*d_2-d2_pts(k)))); E3(j,k) = E0(j) * t3_plus(j)*(exp(i*xi_3(j)*d3_pts(k)) + ... r3_pp(j)*exp(i*xi_3(j)*(2*d_3-d3_pts(k)))); E4(j,k) = E0(j) * t4_plus(j)*(exp(i*xi_4(j)*d4_pts(k)) + ... r4_pp(j)*exp(i*xi_4(j)*(2*d_4-d4_pts(k)))); end end

%Integrating intensity across the visible spectrum Esq1 = abs(E1).^2; Esq2 = abs(E2).^2; Esq3 = abs(E3).^2; Esq4 = abs(E4).^2;

xvals = AM1p5(:,1); Esq1sum = []; Esq2sum = []; Esq3sum = []; Esq4sum = [];

for k=1:(x_pts+1) y1vals = Esq1(:,k); y2vals = Esq2(:,k); y3vals = Esq3(:,k); y4vals = Esq4(:,k);

Esq1sum = [Esq1sum, trapz(xvals,y1vals)]; Esq2sum = [Esq2sum, trapz(xvals,y2vals)]; Esq3sum = [Esq3sum, trapz(xvals,y3vals)]; Esq4sum = [Esq4sum, trapz(xvals,y4vals)]; end

%Plotting the output data total_y = [Esq1sum Esq2sum Esq3sum Esq4sum]; x1max = max(d1_pts); x2max = max(d2_pts) + x1max; x3max = max(d3_pts) + x2max; x4max = max(d4_pts) + x3max; total_x = [d1_pts (x1max + d2_pts) (x2max + d3_pts) (x3max + d4_pts)]; p1 = plot(total_x,total_y, 'red'); p1_axis = axis;

%Drawing vertical lines to visually separate layers hold on line([x1max x1max], [0 p1_axis(4)]) line([x2max x2max], [0 p1_axis(4)]) line([x3max x3max], [0 p1_axis(4)]) line([x4max x4max], [0 p1_axis(4)])