MSc Physics and Astronomy
Science for Energy and Sustainability
Master Thesis
Theoretical and experimental efficiency
estimates of ultra-thin, flexible silicon for
photovoltaic cells
by
Pepijn Koppejan
Student number UVA: 12134635
Student number VU: 2655654
60 ECTS
September 2019 - June 2020
Supervisor:
dr. Esther Alarc´
on Llad´
o
Daily supervisor:
Nasim Tavakoli
Second reviewer:
dr. Elizabeth von Hauff
Pepijn Koppejan
3D photovoltaics, AMOLF
July 3, 2020
Abstract
Thin film, flexible photovoltaic cells have a great variety of possible applications, including integration in windows and as solar foils. Thin crystalline silicon films have yet to catch up with other flexible technologies in terms of solar conversion efficiency. Several studies have therefore used light trapping mechanisms to enlarge the optical path and couple light to the silicon waveguides. This thesis will use disordered hyperuniform nanopatterns for the purpose of increasing the conversion efficiency by coupling the light to waveguiding modes. With PC1D simulations we have successfully shown an increase from 12.1% of an unpatterned case to over 22% with nanostructures. Moreover, NextNano3simulations showed
the challenges of making a solar device with contacts for 1µm thick silicon due to the doping concentrations and whether the metal back contact resulted in an Ohmic or Schottky contact. These simulations explain the troubles of electrochemically proving the increased efficiency of our nanopatterned silicon.
Contents
1 Introduction to thin film photovoltaics 1
2 Background 3
2.1 Photovoltaics . . . 3
2.2 Electrochemistry . . . 8
3 Light trapping using hyperuniform nanopatterns 12 4 Device simulations using PC1D 14 4.1 PC1D . . . 14
4.2 Realistic efficiency estimate of ultra-thin silicon . . . 16
4.3 Comparing bulk silicon wafers with ultra-thin silicon membranes . . . 18
4.4 Evaluating different lifetimes in 1µm silicon . . . 20
4.5 Comparison with other ultra-thin devices . . . 24
4.6 Conclusion . . . 25
5 Measuring light trapping with photoelectrochemistry 26 5.1 Experimental set-up . . . 26
5.2 NextNano3 . . . . 29
5.3 Proof of concept . . . 32
5.4 MC-EC on patterned ultra-thin silicon . . . 34
5.5 Conclusion . . . 38
6 Conclusion and Outlook 39
Acknowledgments 40
References 41
1
Introduction to thin film photovoltaics
Back in 1839, French physicist Edmond Becquerel first observed the photovoltaic (PV) effect in which sunlight is converted to electricity [5]. It took 66 years before a scientific foundation for the effect was described; the first to do so was Albert Einstein [12]. From that point on, small contributions in the field were made, primarily on growth mechanisms of semiconductors. The first next landmark happened in 1950, when Bell labs produced a solar cell to be used in space. The research in solar cells advanced quickly and in 1954 the first modern solar cell was produced with an efficiency of approximately 6% [7]. In the present, several materials, configurations and growth techniques are investigated to produce commercially available solar cells indicating the growth that this field has undergone. Figure 1.1 shows the increasing efficiency over time for several different technologies, from 1976 to the present [40].
Figure 1.1: The best research solar cells over time [40].
The EU has set a 2030 goal that at least 32% of the European energy generation has to come from renewable energy. In 2018 this share was up to 18%, well on its way to meet the end goal. However, to fully realize the energy transition from coal to renewables, large photovoltaic modules will not solely meet the demand [26]. Furthermore, the 21st century has put the focus on economical development parallel to
the energy transition, which introduces several environmental issues [67]. This ’3E-trilemma’ combined with the high demand for solar panels requires a different, more practical approach: thin film technology. Thin films have been researched since the beginning (the green line in Figure 1.1) and have different possibilities compared to thick (∼200 µm) silicon solar cells. Thin film cells are more lightweight and
Chapter 1
flexible compared to robust thick silicon PV. Moreover, where current PV modules are mainly placed on rooftops, thin film technologies can be integrated into new unused areas for light conversion, for example directly in the walls or windows of buildings [59]. Examples of thin films integrated into everyday life are ample. Possibilities include rolling out a solar foil to charge a phone (1.2a), integrating solar cells into architecture (1.2b), or laying down artistic foils on fields (1.2c, an artist impression).
Unfortunately, the efficiency of crystalline silicon based thin films is relatively low (∼ 15% for a 10µm wafer) and needs to be increased to make the above examples affordable. The most efficient current thin film cells are namely made from organic materials (17.4%), cadmium telluride (22.1%) or perovskites (25.2%). These materials, however, have several challenges to overcome, such as toxicity, stability and scarcity. Silicon, on the other hand, is the best understood material for electronics, easy to fabricate, cheap and earth-abundant, making it advantageous for PV [38]. The challenge therefore is to bring crystalline silicon to the same efficiencies as the other thin film technologies.
This thesis will explore the possibilities of enhancing the efficiency of 1 µm thick silicon by introducing several nanopatterns that trap light and increase the optical path length (Chapter 3). The presented work uses both simulations (Chapter 4.6) and experiments (Chapter 5.5) to demonstrate this increased conversion efficiency, which could help bridge the gap towards industry standard ultra-thin crystalline silicon foils.
Figure 1.2: The future of thin films. a) a solar foil that could be rolled up to charge a phone. b) thin films integrated int a building. c) artist impression of an artistic solar foil rolled out on a field.
2
Background
This chapter explains and discusses the theory and background necessary to understand this thesis. The chapter will introduce basic photovoltaic nomenclature, equations and processes, and give a brief overview of electrochemical characterization techniques.
2.1
Photovoltaics
2.1.1
IV-curve
The most important parameters in a solar cell are found in the corresponding IV curve. A typical IV curve of an illuminated solar cell is based on the diode equation:
I = I0 exp( qV kBT − 1 − Iphoto (2.1)
with I the current, I0 the saturation current, Iphoto the light generated current, V the voltage, q the
electron charge, kBBoltzmann’s constant and T the temperature. The (-1) term is only relevant for very
small voltages, namely to ensure that at V=0, J=0 in the dark. The equation can be plotted to find an IV curve (Figure 2.1, with several relevant points that will be discussed in the following sections. The convention is that the current is negative, to get a positive value the equation is multiplied by (-1).
From this plot, the maximum efficiency of a solar cell is found by optimizing the product of Jmpp
and Vmpp. However, the conversion efficiency (Eq. 2.4 0 is typically described in terms of short-circuit
current density (Jsc, Eq. 2.2), open-circuit voltage (Voc, Eq. 2.3), fill factor (FF, the red square in Figure
2.1) and the incoming power (Pin).
The corresponding circuit is shown in Figure 2.1b for an ideal solar cell. Figure 2.1c includes the series and shunt resistance in the circuit for a non-ideal solar cell.
J = J0 exp qV nkBT − 1 − Jphoto, (2.2) Voc = nkBT q ln Jphoto J0 + 1 (2.3) η = VocJscF F Pin = VmppJmpp Pin (2.4)
2.1. PHOTOVOLTAICS Chapter 2
Figure 2.1: a) A typical IV curve, showing Isc, Voc, FF and the maximum power point. On the right
the equivalent circuit for an ideal solar cell (b) and a non-ideal solar cell (c), including shunt and series resistance. Figure taken from [36] and [52]
Photocurrent density
The efficiency thus depends on both the photocurrent and the saturation current. The photocurrent density (Jph) is defined as the current at V=0 and depends on the absorption in the semiconductor and
the illumination intensity [52]. Moreover, Jphis contingent on the carrier generation rate which describes
the excitons that are created and therefore describes the amount of absorption. The carrier generation rate as a function of depth x is defined as [18]:
g(x) = n X i=1 αi λi hc dEi dλ exp(−αix)∆λi (2.5)
with α the absorption coefficient and λ the wavelength. Saturation current density
The open-circuit potential (Voc) depends on the photocurrent and the saturation current and is defined as
the voltage when I=0[52]. The saturation current is connected to electron-hole recombination, of which three types are dominant in silicon: radiative, Shockley-Read-Hall (SRH) and Auger recombination, shown in Figure 2.2.
Radiative recombination, or band-to-band recombination, depends on the radiative recombination rate B, the equilibrium electron and hole density (n0and p0), and is the excess carrier density (δn) [46]:
τrad=
1 B(n0p0δn)
(2.6) SRH describes the recombination via trap states created by lattice defects. The defects are located in the energy gap and allow electrons to occupy a state between the conduction and valence band, after which it recombines with an hole that is attracted due to a Coulomb interaction [52]. The lifetime is given by: τSRH = 1 cnNT n(-type) (2.7) τSRH = 1 cpNT (p-type) (2.8)
with cn and cp the electron and hole capture coefficient, respectively. It is seen that the lifetime is
proportional to the trap density NT.
Auger recombination involves three charge carriers. During recombination, the exciton transfers its energy and momentum to an electron in the conduction band or a hole in the valence band. The extra
2.1. PHOTOVOLTAICS Chapter 2
energy causes the electron to be excited higher into the conduction band. In the case of a hole, it is excited into lower levels of the valence band. Thereafter, the excited electron or hole moves back to the edge of the band by transferring the excess energy to phonons [52].
For high injection τAuger =
1 (Cn+ Cp)
(2.9) For low injection
τAuger = 1 CnNdop2 (n-type) (2.10) τAuger = 1 CpNdop2 (p-type) (2.11)
where Ca represents the ambipolar Auger coefficient and is the addition of the Auger coefficients for
electrons and holes (Cn and Cp, respectively). It should be noted that these equations are only valid for
high doping conditions (>1018), for lower doped silicon Coulomb interactions and phonon participation influence the probability of Auger recombination. The complete parametrization for silicon is done [47], yet goes beyond the scope of this thesis.
The recombination mechanisms described above all occur in the bulk; on the material’s surface re-combination also transpires due to dangling bonds forming trap states in the energy gap. The surface recombination is defined by the surface recombination velocity[52]:
Sr= νthσNsT (2.12)
where ν is the thermal velocity, NsT the surface trap density and σ the capture cross-section.
The total lifetime (τ ) is defined as the sum of all lifetimes above: 1 τ = 1 τrad + 1 τSRH + 1 τAuger + 1 τsurf ace (2.13) Finally, the lifetime is inversely linked to the saturation current: the lower the lifetime, the higher the recombination and therefore the higher the saturation current, according to [45]:
∆n τ ∼ J0(ND+ ∆n)∆n qW n2 i (2.14) with ∆n the excess carrier concentration, W the thickness, ND the doping concentration and q the
electron charge.
Figure 2.2: Depiction of different recombination mechanisms in a solar cell: radiative, Shockley-Read-Hall (trap-state) and Auger. Figure taken from [61]
2.1.2
Charge carrier statistics
The current-voltage characteristics in an illuminated diode are derived from charge carrier statistics. The following equations describe the carrier statistics under thermal equilibrium when there is no external force applied and the system remains unperturbed.
2.1. PHOTOVOLTAICS Chapter 2
The concentrations of electrons and holes in a semiconductor are given by the product of the density of state function and the distribution function. The result is integrated across the entire energy band [52]. n = 4π 2m ∗ n h2 32 p E − EC | {z } density of states × 1 1 + expE−EF kBT | {z } Fermi-Dirac distribution p = 4π 2m ∗ n h2 32 p E − EV | {z } density of states × 1 − 1 1 + expE−EF kBT | {z } Fermi-Dirac distribution (2.15)
where m∗ is the effective mass, E the energy level and h Planck’s constant. After simplification Eq.2.15 yields: n = NCexp EF− EC kBT p = NVexp EV − EF kBT (2.16)
with NC and NV the effective density of the conduction band and valence band, respectively.
Fur-thermore, for an intrinsic semiconductor at equilibrium, n=p and thus: n2i = np = NCNVexp EV − EC kBT = NCNVexp − Eg kBT (2.17) Most semiconductors are either positively or negatively doped to influence the charge carrier statistics. Under the assumptions that the dopants are uniformly distributed and all dopants are ionized at room temperature, the semiconductor obeys:
for n-type materials: n ≈ ND p = n 2 i n ≈ n2i ND (2.18)
for p-type materials: p ≈ NA n = n 2 i p ≈ n2 i NA (2.19)
The equations above describe the electron and hole density in both doped and undoped semicon-ductors. The excess carrier concentration (∆n=n-ni) is used to find the saturation current density and
several simulation programs solve the equations to, for instance, simulate band diagrams and generate IV curves.
2.1.3
Theoretical limit
The efficiency of a photovoltaic cell is limited by several physical processes, first described by Shockley and Queisser [51]. The so-called Shockley-Queisser limit assumes that each photon with energy above the bandgap produces an exciton, that only radiative recombination occurs, and that all charge carriers are extracted. The maximum limit set by Shockley and Queisser is at 33% for a single pn-junction. The losses in efficiency can be assigned to the open-circuit potential and found in Eq. 2.20 and Figure 2.3.
2.1. PHOTOVOLTAICS Chapter 2
A solar cell can be seen as a heat engine and there exists a limit on the amount of heat that can be converted into entropy-free energy, this is the first loss in a solar cell (5%). The minimal losses of a heat engine are in the Carnot cycle, where there is no increase in energy. Furthermore, entropy losses due to the mismatch between the incident and emitted solid angle account for a further 7% decrease in efficiency, the entropy of light losses in Eq.2.20. Photons with energy smaller than the bandgap will be lost and decrease the efficiency even further, whilst photons with energy larger than the bandgap will create hot electrons that thermalize back to the band edge and lose energy in the form of heat. Other forms of recombination, e.g. Auger and Shockley-Read-Hall lower the quantum efficiency (QE) and therefore the final efficiency further.
Incomplete light trapping could prevent photons from being absorbed, which is the final loss mecha-nism discussed here. The theoretical absorption limit is known as the Lambertian limit and defined as 4n2, with n the refractive index [66]. However, this limit is only valid for incident angels of π/2, for other
angles the Lambertian limit is described by 4n2/sin2θ [22].
With further light trapping schemes and light management to minimize entropy losses, single junction photovoltaic devices could reach efficiencies of over 40% [43].
qVoc= Eg 1 − T Tsun | {z } Carnot engine −kBT ln Ωemit Ωsun | {z } entropy of light + ln 4n 2 I | {z }
incomplete light trapping
− ln(QE) | {z } Quantum efficiency (2.20)
with Egthe bandgap of the material, T the temperature of either the device or the sun, Ω the solid angle,
n the refractive index and QE the quantum efficiency.
Figure 2.3: The efficiency limits in a solar cell, with solutions to minimize the losses. Taken from [43]
2.1.4
Ultra-thin Si photovoltaics
Absorption in semiconductors depends on the thickness of the active layer. In ultra-thin silicon, below 10 microns in thickness, the width of the absorption layer is not adequate to produce a high output current. To enhance the current, the optical path in the absorbing layer must be enlarged. Solutions involve a perfect back reflector so that the light crosses the material twice, as opposed to a single pass. Most research goes beyond the double pass system and employs light scattering techniques that trap light inside the material by coupling it to the waveguiding modes and elongate the optical path.
Experimentally confirmed efficiencies greater than the double pass absorption are, however, scarce. For 10 µm silicon, an efficiency of 15.7% and Jsc of 35.4 mA/cm2 has been obtained by fabricating an
inverted nanopyramid structure in combination with a metal back reflector [6]. Thinning down to 3 microns in thickness, the same inverted pyramid structure experimentally showed a Jsc of 25.3 mA/cm2,
an enhancement of 40% from 18.3 mA/cm2measured on non-textured silicon [19]. On a 1.1 micron thick
silicon membrane, a conversion efficiency of 8.6% was obtained by using rounded inverted nanopyramids, coined ’nanocups’, in combination with a passivation layer [10]. These possibilities of enhancing the optical path length are supplemented by several theoretical studies. A combination of front surface
2.2. ELECTROCHEMISTRY Chapter 2
grating and rear metal nanoparticle grating has theoretically reached a Jsc of 29.7 mA/cm2 [50]. A Jsc
of 35.5 mA/cm2, for 1 µm silicon, was obtained by introducing slanted conical-pores into the material and adding a silver back reflector [14]. The absorption with slanted conical-pores even exceeds the Lambertian limit. It should, however, be noted that the numbers presented by Eyderman are most likely overestimated, yet present a remarkable absorption in ultra-thin silicon and provide insight in the possibilities of nanostructuring to enhance light trapping and the figures of merit for photovoltaic cells.
2.2
Electrochemistry
Electrochemistry is a broad field concerned with physical, chemical and electrical processes and reactions in (semi)conductors or at the interface of ionic conductors and electronic conductors or semiconductors [2]. This section will introduce the prominent features occurring in an electrochemical reaction and the measuring techniques used.
2.2.1
Semiconductor-electrolyte interface
In the experimental part of this thesis, a semiconductor-electrolyte interface is formed. The semiconductor contains trapped states on the surface which are filled with electrons and adsorbed ions. Counter charges are provided by ionized donors or acceptors in the semiconductor and by an accumulation of oppositely charged ions from the electrolyte solution. The solution also contains water molecules that surround the charged ions due to water’s large dipole moment, forming a layer between the adsorbed ions and the free moving ions in the electrolyte, known as the Helmholtz layer [63]. The double layer is formed due to the equilibration of the chemical potential and the Fermi energy. This semiconductor-electrolyte interface is depicted in Figure 2.4.
Figure 2.4: The electrolyte-semiconductor interface. At the surface of the semiconductor additional charges are located forming a Helmholtz layer. Adapted from [63].
2.2.2
Band structure
Upon creation of the semiconductor-electrolyte interface, several electrochemical processes thus occur and the band structure changes accordingly. The experimental part of this thesis will use NaCl as electrolyte and boron doped silicon as the semiconductor.
For positively doped silicon, the Fermi level energy is below that of the NaCl solution. Electrons will, therefore, flow from the electrolyte into the semiconductor, making the electrolyte more positive, while the semiconductor becomes more negatively charged. The excess charge is distributed in the depletion region with the consequence that the valence and conduction band look differently compared to bulk semiconductor. The changed charge in this depletion region leads to higher charge differences between the semiconductor surface and the electrolyte. The closer to the surface, the higher this difference and the bands will bend. Band bending happens in such a way that the Fermi levels of the semiconductor and the electrolyte will align, whilst the position of the bands at the interface remains at the same place.
2.2. ELECTROCHEMISTRY Chapter 2
The depletion region forms an electric field, excess electrons in the region will be pushed towards the electrolyte, while excess holes will travel to the bulk (Figure 2.5a and b) [3].
A bias potential can alter the behaviour of the semiconductor. The applied potential will be distributed over the Helmholtz layer and the depletion region, changing the amount of bend bending. With a negative potential applied to a p-type semiconductor the barrier will increase, which is crucial for harvesting charges at both ends. Vice versa, a positive potential applied to a p-type semiconductor can result in no band bending (Figure 2.5c) [3].
Under illumination of the semiconductor (Figure 2.5c), electrons will be excited to the conduction band and move to the electrolyte, which will be oxidized. Simultaneously, the created holes will go into the bulk material, separating the charges; all happening under influence of the applied electric field. With a counter and working electrode attached the system has a closed circuit and a photovoltaic cell is formed (Figure 2.5d).
Figure 2.5: The stages of band bending in a p-type semiconductor in contact with an electrolyte. a) The junction before contact. b) The junction after contact, bending of the conduction and valence band is visible. c) The junction under illumination, an electron is excited to the conduction band and moves to the electrolyte under influence of the electric field, where it will reduce the redox couple. The hole travels to the bulk material. d) Contacts are added to the junction and a photovoltaic cell is created. An excited electron takes part in the redox reaction after which it leaves the system through the counter electrode and enters via the working electrode. The hole travels in the opposite direction. Adapted from [3]
2.2.3
Photo-electrochemical reaction
The photovoltaic cell depicted in Figure 2.5d shows a redox reaction where H2is produced at the cathode
and O2 at the anode (Eq. 2.21). The reaction is widely researched and commonly known as solar water
splitting. The hydrogen produced by the solar water splitting reaction can be used as a renewable energy storage method [62, 4, 23, 64]. Cathode : 2H++ 2e− → H2 Anode : H2O → 1 2O2+ 2H ++ 2e− (2.21)
2.2. ELECTROCHEMISTRY Chapter 2
A study by Oh et al. [41] measured the current density on both a silicon nanowire array and planar silicon on the photocathode using the photo-electrochemical reaction of Eq. 2.21. Moreover, Hou et al. [24] measured the current density of planar and nanowired silicon, with a focus on wavelengths larger than 680 nm under an intensity of 28 mW/cm2, finding a current density just below 12 mA/cm2. Both studies demonstrated that solar water splitting can be used to measure the current density of several different silicon structures, including a planar wafer, without the need for a front contact that creates the typical p-n junction.
The experimental part of this thesis will adopt that proven concept of solar water splitting reactions to measure the current density of ultra-thin nanopatterned silicon (Chapter 5.5).
2.2.4
Electrochemical measurement techniques
The previous sections focused on the physical processes happening during an electrochemical measurement and the consequences thereof. The following sections will describe the possible techniques involved in this thesis.
One such technique is electrochemical deposition in which a metal is deposited onto a substrate from the electrolyte under the influence of an applied electric field. Applications of the techniques are found in circuit boards, plating, read and write heads, and magnetic recording media [11]. Furthermore, it is shown that gold, copper and platinum can also be deposited on semiconductors, with n-type silicon as example [42].
The electrical industry is focusing on downsizing and fabricating devices on the micro and even nanoscale. In order to accomplish fabricating devices on that scale with electrochemistry, Meniscus Confined Electrochemical Deposition (MCED) can be used instead of the common electrochemical cell. This technique deposits metals from an electrolyte onto a substrate with the use of a micro-pipette that has a nozzle opening of several hundred nanometers to several micrometers. MCED has been used for wire fabrication [25], copper microwire fabrication [37] and polymer nanostructures [34].
Two types of measurements are performed, the first one being cyclic voltammetry (CV). A CV measurement is often used to investigate oxidation and reduction reactions, but can also be used to explore other reactions involving electron transfer. A CV applies a parameter to the system and measures the output, in most cases a potential is applied and the current measured [13].
This thesis will use the Biologic 470 model, which requires several input parameters. The most important parameters to consider are the initial potential, four sweep potentials, the sweep rate and the number of cycles. A potentiostat will apply the voltage until the inserted sweep potential is reached after which the potential is increased or decreased until the next inserted value is reached. After the fourth potential is reached, the first cycle is completed. Finally, the sweep rate determines the pace in V/s at which the potential is increased and decreased. This process is shown in Figure 2.6a. For the measurements intended in this thesis, and thus the creation of an IV curve, the first, third and fourth sweep potentials are set at the same value. The second sweep potential determines the final applied potential of the IV curve.
The second experiment is a chronoamperometry (CA) measurement that measures the current as a function of time at a set applied potential. For the Biologic 470 model, the potential can be increased in three steps; however, for measurements on a solar cell, one potential suffices. The parameters that can be altered are found in Figure 2.6b.
The solar simulator can be chopped so that it constantly alters whether the sample is illuminated or in the dark. For both CV and CA, the difference between the photo- and dark current is then seen clearly.
2.2. ELECTROCHEMISTRY Chapter 2
Figure 2.6: The parameters involved in cyclic voltammetry (a) and chronoamperometry (b). CV contains four different sweep potentials, the initial potential, sweep rate and number of cycles. CA contains three different potential steps and the initial potential.
3
Light trapping using hyperuniform nanopatterns
Most light trapping mechanisms employ periodic structures, whereas random textures or nanoparticle distributions are also widely investigated [49, 54]. A different approach to increase the theoretical pho-tocurrent density of 18.3 mA/cm2[19] is to use a fairly new class of patterning: disordered hyperuniform
(HUD).
Hyperuniformity is mathematically defined as a system in which the number variance of particles in an area with radius R grows more slowly than the volume of that window for large R. The density fluctuations in the window are thus concealed at large length scales [57, 58]. The mathematical theory is depicted in Figure 3.1. A random (Figure 3.1a), square periodic array (Figure 3.1b) and a disordered hyperuniform array (Figure 3.1c) are illustrated with a window Ω and radius R. Solely the density fluctuation of the square periodic and hyperuniform point patterns remain equal for increasing R, i.e. the number of points inside the window does not change. Therefore, any periodic array is by definition also hyperuniform; the difference lies in the term ’disordered’ which distinguishes the system from random and periodic arrays.
Figure 3.1: Theory of hyperuniform point patterns, depicted with window Ω with radius R and center x0.
a) random point pattern, b) periodic point pattern, and c) hyperuniform point pattern. For a periodic and hyperuniform pattern the density fluctuation is negligible with growing R and the number of points inside the window remain almost constant. Taken from [57]
HUD designs are found in many biological systems, such as photoreceptors in birds [27], self-organized immune receptors [33] and in the structure factor of prime numbers [69]. Black butterflies, for instance, only reflect 0.2% of incoming light due to underlying hyperuniform nanostructures [9, 20]. In photonic crystals, HUD exhibit tunable, complete photonic band gaps, similar to photonic crystals [16, 17]. Con-sequently, HUD designs can be used to control light propagation, extraction and absorption [21, 30, 15]. The structure factor determines how incident light is scattered and can be controlled with HUD. Contrary to random and periodic designs, HUD can thus determine to which wave vectors light is scattered
Chapter 3
to create distinguishable patterns in k-space. The structure factor is defined as:
S(~k) = 1 N " N X m=1 exp(i~k · ~rm) #2 (3.1) where k represents the wave vector in reciprocal space and r the position of the particles. By modifying k to match the desired pattern in reciprocal space, several point patterns can be determined and optimized [21]. Two HUD designs for light trapping by coupling light to the silicon waveguiding modes, coined ’holes’ and ’honeycomb’, are designed based on solving the structure factor for ~r.
A near-HUD design based on density wave structures, ’spinodal’, is constructed by considering random superpositions of cosine wave functions with wave vectors solved from the desired structure factor [32, 56]:
Φ(~r) =
Nq
X
j=1
cos( ~qj· ~r + φj) (3.2)
with Nq homogeneously distributed random wavevectors, and φj random phases in the (0,2π) range. A
two-phase dielectric function is then defined for:
(r) = (
1, Φ(r) < Φ0
2, Φ(r) ≥ Φ0
, (3.3)
with 1and 2the dielectric permitivities and φ0 the filling fraction. With specific boundary conditions
at a fixed height the spinodal structure separates from the silicon to form a zebra-like pattern.
The Scanning Electron Microscope (SEM) images for these three structures are presented along with their structure factor and absorption in Figure 3.2. The HUD patterns have only an inner bound in k-space, while for the spinodal structure an outer bound is defined as well. All three designs show a ring in k-space that is most confined for the spinodal pattern due to the outer bound. Finally, the absorption plot shows a large increase in absorption for the three patterned wafers with respect to the flat case. For long wavelengths, the absorption is even higher than the Lambertian limit, indicating that the hyperuniform patterns trap light efficiently.
To quantify the enhanced absorption and translate it to the figures of merit for a silicon solar cell, experimental measurements and theoretical simulations are performed in the next chapters.
Calculations and designs of the structures have been done in the groups of Marian Florescu (University of Surrey) and Riccardo Sapienza (Imperial College London). Fabrication of the structures, Fourier microscopy and absorption measurements have been done at AMOLF.
Figure 3.2: SEM image and corresponding structure factor for the two HUD designs (holes and honey-comb) and one nearly-HUD (spinodal) used in this thesis. Clearly visible is the ring in k-space. On the right the absorption plot showing an increase in absorption for the hyperuniform structures with respect to the flat case. For long wavelengths the absorption is larger than the Lambertian limit.
4
Device simulations using PC1D
Thick silicon wafers are industry standard when it comes to photovoltaic cells; thin silicon cells could in the future be used as flexible solar cells or be integrated in architecture. Thick wafers have more light trapping as a result of more absorbing material and have therefore generally a higher short circuit current and overall power conversion efficiency. On the other hand, a thicker layer introduces more recombination and thus a lower open circuit potential. For thin film silicon to become viable, a higher Jsc is thus required, which can be achieved by light trapping mechanisms. This chapter explores, by
simulations, the possibilities and results of such light trapping schemes and tries to answer the question whether ultra-thin silicon could theoretically be used for thin film, flexible purposes.
4.1
PC1D
4.1.1
Useful equations
Simulations were done with PC1D software to find Jsc, Vocand the efficiency for silicon films. PC1D solves
five semiconductor equations: two Boltzmann transport equations (Eq. 4.1), two continuity equations (Eq. 4.2) and Poisson’s equation of electrostatics (Eq. 4.3). These equations together with charge carrier statistics (mentioned in Chapter Background) and the relevant boundary conditions for the device, all simulations can be performed.
Boltzmann equations
PC1D applies four assumptions to the Boltzmann transport equations, being that there is no carrier-carrier scattering, there are no hot carrier-carriers, the carrier-carrier mobility is isotropic, and the energy bands are rigid. Moreover, the temperature is assumed to be constant and the magnetic fields are neglected. The equations are denoted with Jn and Jp as the current density for electrons and holes, respectively, µ
the mobility of either electrons or holes, and n and p the electron and hole density. E represents the quasi-Fermi energy for electrons and holes.
Jn= µnn∇EF n
Jp= µpp∇EF p
(4.1)
Continuity equations
The continuity equations in semiconductors account for what occurs to the electrons and holes in the material. The equations contain a drift-diffusion term accounting for the flow of electrons and holes, a photogeneration term (GL) and a recombination term (Up and Un).
There are, however, again a few assumptions made in each term. The photogeneration term does not include multiple carrier pairs, two-photon absorption processes with an intermediate step and photon recycling. Furthermore, PC1D uses a two-carrier model, meaning that electrons and holes are created and annihilated in pairs and cannot exists on their own, which is valid for high-quality materials with a low concentration of occupied defect states. For materials with a higher occupied trap state concentration,
4.1. PC1D Chapter 4
the two-carrier model shows small deviations, yet not to a degree that will affect the outcome significantly. The recombination term in the continuity equations incorporates Shockley-Read-Hall, Auger and band-to-band recombination. j ∂n ∂t = ∇ · Jn q + GL− Un ∂p ∂t = ∇ · Jp q + GL− Up (4.2) Poisson’s equation
The Poisson equation relates electric potential ψ to the volume charge density ρ, with the material’s permittivity. Again, PC1D uses a two-carrier approximation, which for Poisson’s equation results in neglecting charges in trap states. Moreover, the assumption is made that all dopants are ionized, which is valid at room temperature or higher.
∇ · (∇ψ) = −ρ (4.3)
4.1.2
Set-up
Figure 4.1 is a schematic picture of the device simulated in PC1D, with the c-Si absorption layer in blue and a 5 nm diffusion layer, in order to make a pn junction between the two layers, in red. The emitter and base contact are also depicted. PC1D allows the user to change several parameters of the device in three different parts: the device itself, the material and the excitation. On the device side, the front and rear surface can be passivated, the area can be changed, and reflection can be adjusted. The material part allows for a change in the material’s parameters, such as the dielectric constant, doping level and recombination lifetimes. For c-Si, however, PC1D holds a file that already contains most of the parameters. Finally, the excitation part allows the user to change the illumination intensity. In like manner, PC1D already contains the AM1.5G spectrum for 1 Sun, which only needs to be loaded into the simulation.
Figure 4.1: Device schematic with the adjustable simulation parameters as depicted in PC1D. In red a 5 nm first diffusion layer and in blue the c-Si absorption layer, the emitter and base contacts are also visible in the schematic.
4.2. REALISTIC EFFICIENCY ESTIMATE OF ULTRA-THIN SILICON Chapter 4
4.2
Realistic efficiency estimate of ultra-thin silicon
4.2.1
Parameters
PC1D is used to model and simulate a 1 µm silicon solar cell with the parameters displayed in Table 4.1. These values correspond to state-of-the-art advanced HE-Tech devices as reported by Liu [31]. The values reported in Table 4.1 will be standard throughout this chapter, unless specified otherwise.
Constant parameters Value
Exterior rear reflectance 100%
Base contact 2 Ω
Emitter peak doping 6 ×1018cm−3
Background doping 1017
Bulk recombination 500 µs
Rear surface recombination 1 cm/s Front surface recombination 100 cm/s
Table 4.1: Used parameters for PC1D simulations of the 1 µm Silicon solar cell.
In order to specify the device for our case with front surface texturing, internal reflection is added to the model. From the absorption measurements in Figure 3.2, the short-circuit current density (Jsc)
is calculated and the internal reflection parameter in PC1D is modified until the calculated Jsc matches
the simulated Jsc. Moreover, for the three different structures (honeycomb, holes and spinodal) the front
surface recombination was increased due to the extra surface generated by texturing. The enhancement factor differs per structure as a honeycomb structure requires more etching compared to holes and has therefore a larger surface area and thus a larger surface recombination velocity (SRV) enhancement factor. These factors are calculated as the ratio of textured surface area and flat surface area.
4.2.2
Efficiency, V
ocand J
scWith increased internal reflection and a SRV enhancement factor, Vocand efficiency can now be obtained
and are presented in Table 6.12. The internal reflection value for the textured devices is close to the theoretical Lambertian limit and therefore approaches 100% in PC1D. A substantial increase in both Jsc
and efficiency is seen between an unpatterned and nanopatterned surface, whereas Voc drops by only
1.7% at the most (Honeycomb structure). Interestingly, the light trapping for the Honeycomb structure is more effective and shows a higher Jsc than the hole structure, yet due to the large Voc the overall
device efficiency is 0.1% lower. The corresponding I-V and efficiency curves for all four surface textures are displayed in Figure 4.2 and also show the vast increase in Jsc and efficiency.
SRV enhancement factor Internal reflection Voc (V) Jsc (mA/cm2) Efficiency (%)
Flat 1 59.5 0.769 18.4 12.1
Holes 1.75 96.25 0.770 32.4 21.2
Honeycomb 3.274 96.5 0.756 32.6 21.1
Spinodal 2.37 97.32 0.764 33.8 22.1
Table 4.2: Results of PC1D simulations with the values presented in Table 4.1. Internal reflection is altered until it matches the calculated Jsc from the theoretical absorption in Figure 3.2
4.2. REALISTIC EFFICIENCY ESTIMATE OF ULTRA-THIN SILICON Chapter 4
Figure 4.2: I-V curves (a) and efficiency curves (b) corresponding to different front textured surfaces. The colors represent the different structures: no structure (blue), honeycomb (red), holes (orange) and spinodal (yellow).
4.2.3
Validation of the model
A study by Yoshikawa [68] pushed the limit of a 165 µm thick amorphous silicon/crystalline silicon heterojunction solar cell to 26.3 % (± 0.5), 2.7 % higher than any other silicon solar cell. The high efficiency was obtained by using an interdigitated back contact (IBC) of n-type a-Si and p-type a-Si to separate electrons and holes. The front surface was passivated and an anti-reflection coating was added. Moreover, pyramidal texturing was applied to the front for light trapping purposes, similar to our goal. Overall, the device produced by Yoshikawa could be considered the Adv. HE-tech device in Table 4.1 in the aforementioned study of Liu [31]. To validate the use of Adv. HE-tech parameters in PC1D both models are compared.
The numbers from Yoshikawa’s study and results obtained using PC1D with Adv. HE-Tech parame-ters, both for a 165 µm wafer, are found in Table 4.3. Voc values for the flat and hole designs are similar
while the honeycomb and spinodal structure both have a lower Voc value. This observation could be
explained by the enlarged surface area and SRV, leading to more losses in Voccompared to the a-Si/c-Si
IBC-HJ. On the other hand, for all structures Jsc is significantly higher and the spinodal structure even
approaches the theoretical limit of 29.1%. However, the a-Si/c-Si IBC-HJ device has poor light trapping compared to the Lambertian limit, with a reported 1.7% loss in Jsc for the longer wavelength range of
900-1200 nm compared to the theoretical maximum Jsc, which is mainly attributed to light trapping
be-low the Lambertian limit, parasitic absorption in the electrodes, and transmission losses and for a small part (∼0.1%) to front surface reflectance. The PC1D simulations assume no parasitic absorption and light trapping close to the theoretical limit due to the added surface patterns and have therefore a Jsc
∼0.6% lower than the theoretical maximum Jsc of 43.7 mA/cm2. As a consequence, the efficiencies are
1.1, 1 and 1.2% higher, for holes, honeycomb and spinodal structures, respectively, compared to a-Si/c-Si IBC-HJ device. The parameter values used in PC1D are thus more idealized than current experimental results prove they can be. However, the final efficiencies are still lower than the ultimate theoretical limit of 29.1% for a silicon solar cell. With some more research, Yoshikawa even expects to be able to get to 27.1 % efficiency, approximately the efficiency obtained using PC1D for both the hole and honeycomb structure, while the spinodal pattern is 0.3% higher.
After the comparison made above, it is safe to conclude that the parameters for an Adv. HE-tech device are a good approximation of the highest measured silicon solar cell to date. It is very likely that in the coming years the efficiency will match the efficiency in PC1D with the Adv. HE-tech parameters.
4.3. COMPARING BULK SILICON WAFERS WITH ULTRA-THIN SILICON MEMBRANESChapter 4
Device Voc (V) Jsc(mA/cm2) efficiency (%)
No patterns 0.744 40.2 25.5 HUD (holes) 0.743 43.0 27.3 HUD (honeycomb) 0.739 43.1 27.2 spinodal 0.741 43.3 27.4 a-Si/c-Si IBC-HJ [68] 0.744 42.3 26.3 ± 0.5 Theoretical limit [68] 0.752 43.7 29.1
Table 4.3: A comparison between Yoshikawa’s study [68] and results obtained using PC1D with Adv. HE-Tech parameters, all for a 165 µm wafer.
4.3
Comparing bulk silicon wafers with ultra-thin silicon
mem-branes
4.3.1
The case without surface patterning
Figure 4.3 displays the Voc, Jsc and efficiency of an unpatterned 1µm silicon membrane using PC1D
simulations. For market-standard silicon with a thickness of 165 µm a Vocof 0.74 V, Jscof 40.2 mA/cm2
are obtained with a total efficiency of 25.5 % under the conditions in Table 4.1. Going towards an ultra-thin silicon membrane, the optical absorption length becomes greater than the thickness of the absorbing layer, resulting in a decrease in Jsc and efficiency. As a result, the amount of absorbed light
that is converted to current is gradually decreasing for thinner wafers. Interestingly, however, the opposite trend is seen for the Voc until approximately 10 µm, where the potential is increasing with decreasing
thickness. The reason is that thinning down silicon reduces the bulk recombination rate (Shockley-Read-Hall and Auger recombination) and therefore increases the voltage. The major contribution to the total recombination rate in ultra-thin membranes is the surface recombination since surface area dominates over volume for thin films. As the total surface area does not change for different thicknesses, the voltage thus goes up. Only for ultra-thin silicon below 10 m the open-circuit voltage drops again slightly, caused by the rapid decrease in Jsc. The relation towards SRV will be elaborated upon in section 4.4. The final
results for a 1 m silicon wafer are a Voc of 0.77 V, Jsc of 18.5 and total efficiency of 12.1% (Table 6.12),
4.3. COMPARING BULK SILICON WAFERS WITH ULTRA-THIN SILICON MEMBRANESChapter 4
Figure 4.3: Open-circuit voltage Voc, short-circuit current density Jsc and solar cell efficiency for p-type
silicon with increasing thickness. For Voc the part from 1 to 15 m is displayed in the top corner.
4.3.2
The case with surface patterning
The necessity for extra light trapping schemes in ultra-thin cells to boost efficiency is clear; the first part of Figure 4.3, between 50µm and 1µm, shows a massive fall in efficiency as the most of the light is not absorbed in the ultra-thin layer. Silicon wafers of more than 10 microns in thickness are still showing efficiencies over 20% and are thus a valid option for flexible, thin film silicon solar cells. Even thinner wafers, down to a single micron are not profitable at all yet. Therefore, the three different surface textures (honeycomb, hole and spinodal) are introduced in order to increase the conversion efficiency to a value over 20%. Figure 4.4 shows the enhanced results of the four added surface patterns, plotted against thickness. Voc first increases with increasing thickness and after approximately 10 microns in thickness,
it decreases constantly due to more bulk recombination mechanisms in the absorbing layer. However, efficiency increases rapidly in the first part and flattens out around 30 microns to a relatively constant value. This increase in efficiency is mostly caused by an increased Jsc, which in turn is the result of more light absorption in bulk material. The contribution due to a dropping Voc is substantially lower than
the increase in Jsc. For that reason, the efficiency and Jsc curve show the same behaviour at the same thicknesses.
Both Figures 4.3 and 4.4 thus show the same trends: a decrease in current and efficiency, while the voltage increases with decreasing thickness. However, as mentioned before, the final efficiency is enhanced majorly, reaching 22% for the 1 µm spinodal structure. The two HUD and one near-HUD thus improve the efficiency of ultra-thin silicon to above 20% and for the best case are only 3.4% lower than bulk industry-standard silicon.
4.4. EVALUATING DIFFERENT LIFETIMES IN 1µM SILICON Chapter 4
Figure 4.4: Open-circuit voltage Voc, short-circuit current density Jsc and solar cell efficiency for p-type
silicon with the four different surface texturing plotted against thickness.
4.4
Evaluating different lifetimes in 1µm silicon
After comparing thin film silicon with bulk wafers, it is important to study the effect of other relevant parameters that affect the efficiency of photovoltaic cells. Especially bulk recombination lifetime and surface recombination velocity have a considerable impact on the efficiency of photovoltaic devices. It is therefore relevant to alter these parameters in PC1D simulations to be able to comment on the feasibility of ultra-thin silicon.
4.4.1
Bulk recombination lifetime
Firstly, efficiencies of the four devices (flat, holes, honeycomb and spinodal) are calculated with a range in bulk recombination lifetime (τ ) of 1 µs to 2 ms, plotted in Figure 4.5. Different bulk lifetimes translate to the quality of silicon, considering high-quality silicon has a high bulk lifetime and vice versa. Figure 4.5 clearly shows a decrease in Voc of between 30 mV (honeycomb structure) and 50 mV (flat), while
Jsc remains constant. Lifetimes below 100 s are sufficiently short in a 1 m for electrons and holes to
recombine before they are extracted at the contacts. From Voc and Jsc it is expected that efficiency will
also decrease with decreasing lifetimes. However, the change in Vochas only a marginal influence and the
cell efficiency is hardly affected by a 200 fold increase in bulk recombination lifetime from 1 µs to 2000 µs. The efficiency in ultra-thin nanopatterned silicon only drops by approximately 2%. This observation is explained by the fact that a 1µm silicon membrane is too thin for bulk recombination to play a major role in recombination losses. Bulk lifetime thus has minimal influence on thin film Si and lower quality silicon can, therefore, be used for thin films without a major loss in efficiency.
On the other hand, an increase in lifetime in a 200 µm Si wafer does affect efficiency significantly. An increase of 100 to 2000 µs leads to an absolute efficiency increase of ∼1.7 in percentage terms. Very short lifetimes below 100 µs even show a fast decrease in efficiency. For bulk values, the black line in Figure 4.5, the efficiency loss is ∼9% in absolute terms, which is considerably greater than the 2% for nanopatterned ultra-thin silicon. For thicker wafers, it is, therefore, necessary to use silicon with the highest possible quality to minimize bulk recombination losses.
4.4. EVALUATING DIFFERENT LIFETIMES IN 1µM SILICON Chapter 4
Figure 4.5: Efficiency plotted against the logarithm of bulk recombination lifetime for the four different structures. The efficiency plot also contains efficiency of bulk 200 µm silicon as reference (black line). The dotted line is set at 500 µs.
4.4.2
Surface recombination velocity
The same comparison of ultra-thin silicon with surface recombination velocity is made, Figure 4.6. An increase in SRV from 100 to 1500 for the flat surface results in an absolute decrease in efficiency of 1.2 percent; for textured surfaces, the decrease in efficiency is about 2 absolute percentage points. Comparable to the simulations for different lifetimes, Jsc remains constant with different SRV values; the change in
efficiency comes from the change in Voc, with a decrease of approximately 60 mV in the range 100
cm/s to 1500 cm/s. Compared to the standard lifetime value of 500 µs in Figure 4.5, the change in efficiency is much more pronounced for a range of SRV values. This observation can be explained by the fact that the surface area to volume ratio for a 1 µm silicon membrane is very large and surface recombination thus dominates over bulk recombination. SRV is therefore more important to optimize than bulk recombination lifetime.
For 200 µm bulk wafers the decrease in efficiency is comparable to thin film silicon, which indicates that proper surface passivation is required for all thicknesses to minimize efficiency losses at the surface.
4.4. EVALUATING DIFFERENT LIFETIMES IN 1µM SILICON Chapter 4
Figure 4.6: Efficiency plotted against the logarithm of SRV values for the four different structures. The efficiency plot also contains efficiency of bulk 200 µm silicon as reference (black line).
4.4.3
A closer look at the saturation current density
In order to better comprehend the losses due to bulk lifetimes and surface recombination velocities, Figure 4.7 shows the power conversion efficiency as a function of the saturation current density and the photocurrent density, for unpatterned silicon. In our model, the optical losses are negligible and Jphoto
is therefore equal to Jsc.
The effect of bulk lifetime is firstly investigated. Figure 4.7a shows the efficiency as a function of three different bulk lifetimes, 100 µs (blue), 500µs (orange) and 1000µs (green), for different thicknesses. Clearly visible is the high recombination and therefore lower efficiency for the case of 100 µs, which shows a Jdark of almost 30 fA/cm2. The cases of 500 µs and 1000 µs nearly follow the same trend, with 1000
µs showing a slightly better efficiency, as previously seen in Figure 4.5 for the 1 µm silicon.
Secondly, the effect of surface recombination is displayed in Figure 4.7b for two different surface recombination values, 100 cm/s (blue) and 1000 cm/s (orange). Both curves have the same shape, with the 1000 cm/s curve shifted upwards, to a Jdarkof ∼17 fA/cm2for 1 µm thickness. For 200 µm the curve
goes to approximately 28 fA/cm2. The slope of the graph and thus the delta in efficiency for different
4.4. EVALUATING DIFFERENT LIFETIMES IN 1µM SILICON Chapter 4
Figure 4.7: Power conversion efficiency versus Jdarkand Jphotofor different thicknesses. a) Bulk lifetimes
of 100 µs, 500µs and 1000µs. b) SRV values of 100 cm/s and 1000 cm/s. The white lines are at efficiencies of 10, 13, 16, 19, 22, 25 and 28%.
4.4.4
Changing SRV and bulk lifetime in 200 µm silicon
To further put the 1 µm device into perspective and compare with a 200 µm solar cell, the PC1D simulations were repeated for an absorbing layer thickness of 200 µm with the three different surface textures. By comparing two extreme cases for each parameter (SRV and bulk recombination) separately, table 4.4 is produced. Table 4.4a shows Voc, Jscand efficiency for SRV of 100 cm/s and 1000 cm/s, while
bulk recombination is kept at 500 µs. The other electronic parameters are as used throughout this work and listed in Table 4.1. Because of the small effect of SRV to the total efficiency in bulk Si, the Voc is
the same (within two decimal spaces) for all the designs, while extra light trapping mechanisms provide a significant increase in Jsc, and hence total efficiency of up to 2 percent.
In Table 4.4b SRV is held constant at 100 cm/s and τ is altered from 500 µs to 5000 µs. The trend touched upon earlier is once more seen: bulk recombination does affect efficiency by an approximate absolute increase of 0.5 percent for all surface textures. It can, therefore, be concluded that surface texturing could also increase efficiency in bulk silicon slightly, yet is critical to bring ultra-thin silicon to an acceptable efficiency of over 20 percent and compete with other flexible photovoltaic devices. This will be further discussed in the next section.
Table 4.4: Results of PC1D simulations for a 200 µm Silicon solar cell. For comparison an SRV of 100 cm/s and bulk lifetime of 500 and 5000 µs (top), and bulk lifetime of 500 µs and SRV of 100 and 1000 cm/s (bottom) are displayed in the same table.
4.5. COMPARISON WITH OTHER ULTRA-THIN DEVICES Chapter 4
4.5
Comparison with other ultra-thin devices
The final goal of ultra-thin silicon is to produce flexible solar cells which can, for example, be easily incorporated in day-to-day architecture. Different materials and devices are constantly being researched and fabricated, often leading to yearly improvements. One of these examples is an amorphous sili-con/crystalline silicon heterojunction, with a record efficiency of 14.0 % in a 3.4 µm device. Besides silicon, two other materials are widely investigated, being copper indium gallium selenide (CIGS) and cadmium telluride (CdTe). The former reached an efficiency of 23.4% [39] and 23.3% with a concentrator to 14 Sun conditions ([65]), while the latter is set at 22.1% [53]. A different approach to flexible, thin film photovoltaic cells is to use organic materials, with the world record currently at 17.4% in a two junction device of 150 nm PBDB-T:F-M as the front cell and 110 nm PTB7-Th:O6T-4F:PC71BM as rear cell [35].
With over 20% efficiency, ultra-thin nanopatterned silicon is competing with CIGS and CdTe devices, as all three far outweigh organic photovoltaic cells.
On the other hand, perovskite solar cells are also considered a thin film photovoltaic technology. They, however, show efficiencies far greater and more promising than any other thin film device mentioned above. The current world record is set at 25.2% for perovskite cells and 29.1% for perovskite-silicon tandem devices [40]. Perovskites do have different challenges to overcome, mostly related to toxicity and stability and are a completely different class of photovoltaics [1].
The efficiencies of the aforementioned flexible, thin film devices are displayed in Table 4.5.
Device efficiency (%) Institute
CIGS (concentrator) 23.3 NREL
CIGS 23.4 Solar Frontier
CdTe 22.1 First Solar
Amorphous Si:H (stabilized) 14.0 AIST
Organic PV 17.4 SJTU-UMass
Perovskite 25.2 Korea University
Spinodal textured ultrathin Si 22.1 This work
Table 4.5: Other flexible, thin film solar cell devices and their efficiencies, based on NREL’s Best Research-Cell Efficiency Chart [40].
4.6. CONCLUSION Chapter 4
4.6
Conclusion
In this chapter, it is shown that ultra-thin silicon could overcome its major huddle in comparison with bulk silicon wafers: a low efficiency. Simulations in PC1D have shown that by texturing the surface of a 1 µm silicon membrane, efficiencies over 21% can be reached. Three different surface textures have been explored, namely holes, honeycomb and spinodal. Of these three, the spinodal structure showed the greatest promise for light trapping and the biggest increase in conversion efficiency. On the other hand, the hole pattern required the least amount of modification to the surface and thus had a relatively small increase in surface area compared to the honeycomb and spinodal pattern. Therefore, the holes showed the largest Vocof the three structures. The full set of simulations can be found in Appendix 6.
Furthermore, simulations showed that an increase in bulk lifetime did not affect thin film silicon, while bulk wafers are influenced; the simulation with increasing SRV led to the same conclusion. This means that the quality of silicon does not affect the efficiency of thin films, while bulk materials are highly dependent on the quality and could potentially drop up to almost 2 percent for each parameter.
Comparing ultra-thin nanotextured silicon to other thin film devices showed that our designs can likely compete with CIGS and CdTe devices in terms of efficiency; perovskite solar cells are only 2 percent higher.
This chapter answers the question whether silicon could be used for thin film, flexible intentions. By evaluating different surface textures and comparing them to the efficiencies of other thin film devices, it can thus be concluded that ultra-thin silicon can be a suitable option for thin film devices, providing additional light trapping schemes are incorporated.
5
Measuring light trapping with photoelectrochemistry
The previous chapter concluded that ultra-thin film silicon can show relatively high efficiencies and current densities if a hyperuniform nanostructure is added. With the theoretical analysis completed, this chapter will proceed towards measuring the current density of the aforementioned thin films and try to experimentally prove and justify the numbers presented earlier.
5.1
Experimental set-up
The silicon sample to be measured is 10 millimeters in length with structures of 150 by 150 microns. It is thus too small to measure a photocurrent using a standard electrochemical cell. We, therefore, use a micro-pipette with an opening diameter of several 100 µm diameter, the exact diameter differs per pipette. Other equipment includes the Bio-Logic Model 470 Scanning Electrochemical Workstation, which is connected to the Bio-Logic 3300 bipotentiostat. A model VCAM3 video microscope is used to be able to visualise the position of the micro-pipette tip with respect to the substrate. Finally, a solar simulator is used to illuminate the sample. The set-up is depicted in Figure 5.1.
The micro-pipette is filled with 0.1 M NaCl solution and a platinum wire is inserted as the counter electrode, after which the micro-pipette is mounted to the Scanning Electrochemical Workstation. It is then lowered in small steps of several micrometers until the meniscus touches the membrane; the camera will have to be zoomed in and refocused along the movement of the pipette. A bias potential is then applied and the output current is measured during a cyclic voltammetry experiment.
Figure 5.1: General set-up of the experiments including an electrochemical workstation, bipotentiostat and video microscope.
5.1. EXPERIMENTAL SET-UP Chapter 5
Electrochemical cell
Reference measurements on silicon without nanopatterns are performed in a standard electrochemical cell, with an opening of 0.20 cm2, as illustrated in Figure 5.2. A holder is placed on top of the frame of the
workstation which holds the cell in place. After filling the cell with the electrolyte, the working electrode is attached to the back of the cell, and the platinum counter electrode and the reference electrode are inserted in the electrolyte. A cyclic voltammetry experiment is used to measure the current.
Figure 5.2: a) The general set-up modified for an electrochemical cell with an opening of 0.20 cm2, placed in a holder on top of the frame. The working electrode is attached to the cell, and the counter and reference electrode are inserted in the electrolyte. The counter electrode is a platinum wire.
Scanning electrochemical microscopy
The measurements on the nanopatterned ultra-thin films are adapted from meniscus confined electro-chemical deposition (MCED), to form a meniscus confined electroelectro-chemical cell (MC-EC). A back contact to the silicon wafer is made of indium gallium (InGa) and the sample is placed on copper and connected as the working electrode. The pipette is filled with an electrolyte and a platinum wire is inserted as the counter electrode. The pipette is brought into contact with the sample until a meniscus is formed between the sample and the pipette. This is summarized in Figure 5.3.
5.1. EXPERIMENTAL SET-UP Chapter 5
Figure 5.3: a) The general set-up modified for scanning electrochemical microscopy. The pipette is mounted and lowered until a meniscus is formed on the sample. The counter electrode is a platinum wire and the working electrode is stainless steel on which the sample is placed. The picture is taken during measurement and the sample is under illumination. b) The same set-up under illumination, the pipette is lowered until it forms a meniscus on the sample. c) A meniscus is formed between the sample and the pipette, salt deposition from the electrolyte is seen on the tip of the pipette. The reflection of the pipette on the sample is also seen.
Pipette fabrication
There are two steps in the fabrication of the pipette. First, a 100 mm borosilicate capillary from World Precision Instruments is pulled using a P-1000 micro-pipette puller of Sutter Instruments. The capillaries have an outer diameter of 1 mm and an inner diameter of 0.58 mm. A 160 nm glass rod is annealed to the inside of the capillary to create more capillary action and ease the filling process. The capillaries are placed in the micro-pipette puller and gently pulled apart until the pipette breaks in two pieces of approximately 50 mm long. The two created micro-pipettes now have a nozzle of approximately 1 µm in radius, which is too small to form a meniscus large enough to cover the nanostructures and measure a current. The details of the pulling program can be found in Appendix 6
The second step in the fabrication process is therefore to grind the pipettes using a pipette grinder. The pipette is placed in the holder and a rotating disk is used to grind the pipettes until the preferred nozzle size is reached. The height of the holder can be altered in such a way that the pipette only slightly touches the rotating disk so that the nozzle is ground gradually. Furthermore, the rotating disk is wet to make the entire process easier and reduce the chance of breaking the pipette tip. After the grinding process, the nozzle of the pipette will be several hundreds of micrometres in diameter, producing a relatively large meniscus that covers the nano-structure and can be used to measure the current.
5.1.1
Sample fabrication
Samples are fabricated by Nasim Tavakolil
The ultra-thin silicon films were made by Norcada Inc., a company specifying in micro-electromechanical systems, and had a boron doping density of around 1014 cm−3. The membranes (1.3 x 1.3 mm2 or 4.8 x
4.8 mm2) were attached to a 10 x 10 mm2 silicon frame. The frame was 300 µm thick and ensured safe
handling and stability of the silicon membrane. The hyperuniform nanopatterns were added by electron beam lithography and ion etching.
The sample was firstly spincoated with HDMS as adhesion layer and CSAR as positive e-beam lithog-raphy resist. After that, the sample was placed in the e-beam lithoglithog-raphy, where the nanopatterns were
5.2. NEXTNANO3 Chapter 5
imprinted. The sample was left to develop and the broken polymers dissolved. Finally, the sample was etched with Hbr and O2. The left-over resist was lifted off, making the sample ready for electrochemical
measurements.
Several thin films are then brought to the sputter coated where a thin layer of 100 nm of either aluminium or gold is added to the back of the film, forming a junction with silicon.
5.2
NextNano
3To optimize the results for the experiments to be conducted later, NextNano3, a program to simulate electronic and optical properties for nanotechnologies [60], is used to explore the band structure in ultra-thin silicon with three different back contacts, being silver, gold and aluminium. NextNano solves the Schr¨odinger, Poisson and drift-diffusion equations for 1D, 2D and 3D objects (Eq. 5.1,5.2 and 5.3). Note that the Poisson and drift-diffusion equations are also solved in PC1D simulations to obtain the electrical properties. For our purposes of exploring band bending of a junction with a metal, a 1D simulation suffices.
1D-Schr¨odinger equation:
i¯h∂
∂tΨ(r, t) = ˆHΨ(r, t) (5.1)
ψ is the wavefunction as a function of position and time and ˆH the Hamiltonian Poisson equation:
∇ · (∇ψ) = −ρ (5.2)
with ψ the electric potential, ρ the volume charge density and the material’s permittivity. Drift-diffusion equations: Jn= qnµnE + qD~ n ∂n ∂x Jp= qpµpE + qD~ p ∂p ∂x (5.3)
with J the current density, q the electron charge, n and p the electron and hole density, D the diffusion constant and E the electric field vector.
A template written by Greg Snider (University of Notre Dame) entitled ’1D Schr¨odinger-Poisson tutorial’, is used as a starting point, only minor changes required. The program would then simulate and plot the band structure according to the input parameters. These parameters include, for example, doping density, material and thickness. The most important code can be found in Appendix 6.
5.2.1
Metal work functions and the effect on band bending
NextNano3 requires the user to specify whether the junction is a Schottky or Ohmic contact. To do so,
the work functions of the three different metal back contacts, silicon and silicon dioxide are needed. A work function is an important material property indicating the thermodynamic energy needed to bring an electron from the bulk to the vacuum level. In a metal-metal junction, the Fermi levels of both metals align at equilibrium, equivalent to a p-n junction. In a metal-semiconductor junction, e.g. back of a solar cell, the Fermi levels align again, with two possible outcomes. For a p-type semiconductor, an Ohmic junction is formed when the work function of the metal is larger than that of the semiconductor, or a Schottky junction is formed if the work function of the metal is smaller than that of the semiconductor. For n-type semiconductors the opposite is true: a Schottky junction is formed if the work function of the metal is larger than the work function of the semiconductor. Considering that in a p-type semiconductor the current is primarily hole current, an Ohmic junction results in an accumulation of holes at the interface where they recombine with electrons from the metal. For each recombination, an extra hole can fill the empty place, generating a constant current. The other case, a Schottky junction forms a barrier between the metal and semiconductor as the majority carriers are now not able to travel to the metal [55, 29]. Such a barrier would be preferable in photovoltaic devices to separate charges at the interface and protect recombination due to reverse charges.
5.2. NEXTNANO3 Chapter 5
The back contact of a solar cell, and especially of an ultra-thin cell with an extremely thin layer of absorbing material, should be chosen carefully. Important is that a Schottky barrier will form so that charges can be separated. Figure 5.4a shows the work functions of several metals (aluminium, gold and indium gallium) that could be used as a back contact for ultra-thin silicon. Additionally, the valence band, conduction band and Fermi level of silicon and silicon dioxide are depicted as those are the semiconductors that will form the junction [28]. In Figure 5.4b and c the difference, as explained before, between an Ohmic and Schottky junction are seen. Only an Au has a work function larger than the work function of silicon and is thus the metal expected to show upwards bend bending. Ag, Al and InGa show a lower work function and are therefore expected to show downwards bend bending in a junction with silicon. Moreover, this means that Au is predicted to form an Ohmic junction, while Ag, Al and InGa form a Schottky junction.
Figure 5.4: Work functions of the metals used as back contact aluminium, silver, gold and indium gallium. The work functions of the semiconductors used in the experiments, silicon and silicon dioxide, are also included. The used values are for the < 100 > orientation. b) and c) schematic overview of a Schottky junction and Ohmic junction, respectively. Adapted from [28].
5.2.2
Simulation results for ultra-thin silicon without native oxide
The results from the simulations produced with NextNano are found in Figure 5.5. The figure represents the band structures of 1 µm thick silicon in contact with the metal on one side and the electrolyte on the other side. The horizontal axis represents the position within the silicon relative to its thickness. Position 1000 nm thus represents the back of the silicon sample and is hence the part where the silicon and metal form a junction. The vertical axis presents the energy of the bands relative to the Fermi level which is set at 0V.
From figures 5.5a, 5.5b and 5.5c (Ag, Au and Al, respectively) it can be seen that only for the gold contact the conduction and valence bands bend upwards. For both Ag and Al the bands bend downwards, as predicted above. Moreover, the different doping densities, ranging from 1013to 1015cm−3play a crucial role in the band structure, found in Figure 5.5d. For low doping levels, the difference in energy between the junction and the bulk is almost negligible, especially in the case of Ag (0.01 eV). The different metals also account for different depletion regions, as for an Au junction the depletion region is approximately 300 nm wide, while the depletion regions for Ag and Al are more than half the thickness (600 nm and 800 nm, respectively). The energy difference for Al is the highest of the three metals, for high doping levels, which makes up for the large depletion region.
