Delft University of Technology
Theoretical evaluation of contact stack for high efficiency IBC-SHJ solar cells
Procel, Paul; Yang, Guangtao; Isabella, Olindo; Zeman, Miro DOI
10.1016/j.solmat.2018.06.021 Publication date
2018
Document Version
Accepted author manuscript Published in
Solar Energy Materials and Solar Cells
Citation (APA)
Procel, P., Yang, G., Isabella, O., & Zeman, M. (2018). Theoretical evaluation of contact stack for high efficiency IBC-SHJ solar cells. Solar Energy Materials and Solar Cells, 186, 66-77.
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Theoretical Evaluation of Contact Stack for High Efficiency
IBC-SHJ Solar Cells
Paul Procel, Guangtao Yang, Olindo Isabella, and Miro Zeman
Delft University of Technology, PVMD group, Mekelweg 4, 2628 CD Delft, the Netherlands
Abstract
In this work we present a theoretical analysis of charge carriers transport mechanisms in IBC-SHJ solar cells. The concepts of contact and transport selectivity are correlated through the band bending at c-Si interface and are used to identify thin-film silicon parameters affecting fill factor (FF) and open-circuit voltage (VOC). Additionally, the transport of carriers is
associated to energy barriers at the conduction band for electrons and at the valence band for holes. In case of p-type contact, the transport of holes is mainly affected by activation energy and band gap of the p-type layer and work function of the TCO. In case of n-type contact, the activation energy and work function of the doped layer impact the most on transport of electrons. Selective transport is improved by maximizing the collection of majority carrier in each doped contact stack while blocking minority carriers. In particular, low activation energy values of doped layers are crucial to minimize energy barriers for majority carriers and increase the band bending at c-Si interface. Simulation results based on TCAD Sentaurus reveal that the FF increases as the activation energy of the doped layers is reduced. Also, for the p-type contact, the bandgap of p-type layer strongly affects the band bending at c-Si interface. Particularly, widening the bandgap of p-type layer enhances passivation and transport in terms of VOC and FF but work function mismatch between the p-type layer and
the related transparent conductive oxide (TCO) strongly increases as bandgap increases. This possibly makes the device less performant because it is more sensitive to activation energy of the p-layer in combination with the choice of the proper TCO. Considering realistic deposited layers, a wide bandgap p-type layer, in combination with low activation energy, potentially improves hole collection leading to maximal simulated FF = 86.8% and VOC = 754 mV for a
conversion efficiency η = 27.2%.
Introduction
Crystalline silicon (c-Si) solar cells dominates current photovoltaic market thanks to the material abundance, material stability, technological development and relatively high conversion efficiency [1]. Additionally, the photovoltaic (PV) market is pointing to the reduction of costs of generated power electricity by increasing solar cells efficiency. To achieve such an objective, research and development groups devoted several works on novel concepts to reduce device recombination losses and on advanced solar cell architectures [2]. Regarding solar cell architectures, interdigitated back contact (IBC) concept have constantly demonstrated record results [3]–[7] owing to the absence of front shading contact. Reducing contact recombination by means of passivating carrier-selective contacts concepts anticipate high open-circuit voltage (VOC) well above 715 mV for high [3], [8], [9] and low temperature
process [6], [10]–[16]. Based on thin-film Si alloys, the use of silicon heterojunction (SHJ) structures has become particularly interesting to industry for the low thermal budget fabrication process. Besides, this PV technology benefits from the tremendous experience the field acquired from thin-film Si PV applications, which offer flexibility in a wide range of fabrication parameters [17]–[20]. The combination of c-Si and thin-film Si-based materials has therefore resulted in outstanding VOC values between 740 and 760 mV [15], [21], [22],
anticipating record efficiency solar cells. In fact, an IBC architecture with SHJ contact stacks
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has recently yielded the world record efficiency for c-Si solar cells (ηrecord = 26.6 %) [21]. SHJ
as passivating carrier-selective contact consists of the deposition of hydrogenated intrinsic amorphous silicon (i-a-Si:H) layer for chemical passivation followed by the deposition of thin-film silicon-based doped layers to form either electron-selective or hole-selective contact, thus inducing a potential on c-Si that allows carriers collection [23] (field effect passivation). Looking into thin-film Si portfolio, there is a broad list of thin films based on alloys of Si with carbon or oxygen in different phases (i.e. amorphous and nano-crystalline), leading to specific material parameters that are of particular interest to build efficient contacts [13], [18], [24]– [28]. Thus, it is essential to investigate parameters of thin films that stand out for high efficiency SHJ solar cells.
In this context, earlier works on amorphous Si alloys studied carrier collection and passivation, identifying the doping in doped a-Si:H layers as crucial parameter [29], [30]. Similarly, other groups devoted experiments on solar cell demonstrators, using nano-crystalline Si alloys and reporting similar improvements in VOC and fill factor (FF) with respect to amorphous
counterparts [31]–[33].The improved induced potential was identified as the fundamental reason for VOC enhancement [34]. Moreover, Adachi et al. remarked the path for high
efficiency SHJ solar cells experimentally, showing that improving the passivation quality (VOC enhancement), FF also increases [35]. Mechanisms ruling FF are typically related to
solar cell resistivity losses, which are in turn linked to materials conductivity and contact resistance [36] [37]. However, carriers’ selectivity and transport at contact stacks can truly describe the inner physics of FF. To explain transport mechanisms, some theoretical works based of one-dimensional (1-D) numerical modelling have been previously reported, considering only thermionic emission as transport model at hetero-interfaces [38]–[41]. In this respect, TCO is typically modelled as a metal with a certain work function (WF), an approach that underestimates both tunnelling and transport at doped layer/TCO hetero-interface [42]. Concerning specifically IBC-SHJ solar cells, simulation works have limited the study to analyze properties of amorphous Si films [43], [44].
In this work, we present first a detailed theoretical analysis of IBC-SHJ solar cell contact stacks to evaluate the competitive mechanisms of selectivity and transport towards optimal carrier collection. Afterwards, supported by advanced TCAD simulations, we identify key parameters of thin-film Si alloys impacting on both FF and VOC. Finally, we provide general
guidelines on the design of contact stack and rear geometry.
Selectivity and Transport
The concept of selectivity refers to the ratio between the conductivity of majority and minority charge carriers in a doped layer [45], [46]. The rationale is that selectivity accounts for collecting carriers inside c-Si absorber bulk in terms of carrier concentration at c-Si interface. Hence, within this work, with the terms carrier selectivity we indicate the collection of carriers at c-Si interface and with the term transport we describe the collection of carriers at the metal contact. Note that we use the following notation for subscripts related to contacts, carriers and materials: (i) n and p denote n-type or p-type contact stack, respectively; e and h denote electrons and holes, respectively; (iii) cSi and TCO denote crystalline silicon and transparent conductive oxide, respectively.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 (a) (b) (c) (d)
Figure 1. Schematic band diagram of n-type (a) and p-type (b) contacts of a SHJ solar cell under illumination. Distance r =
0 is set at c-Si / i-a-Si:H interface. EC,cSi (EV,cSi) and Efe (Efh) are conduction (valence) band energy level and Quasi-Fermi level of electrons (holes); qφn,cSi (qφp,cSi) is the band bending at the c-Si / i-a-Si:H interface for n-type contact (p-type contact). Patterned areas stand for energy barriers for electrons in conduction band and for holes in valence band (see
Selective transport section below). Schematic band diagram of n-type (c) and p-type (d) contacts of a SHJ cell at thermal
equilibrium. Ef is the Fermi level at equilibrium; qφ0,n,cSi (qφ0,p,cSi) is the band bending at the c-Si / i-a-Si:H interface for n-type contact (p-n-type contact) at equilibrium; φ0,n (φ0,p) is the electrostatic potential supported by i-a-Si:H / n-n-type layer (i-a-Si:H / p-type layer) at equilibrium; Eg,n (Eg,p) is the bandgap of n-type (p-type) layer and Ea,n (Ea,p) stands for the activation energy of n-type (p-type) layer; χn (χp) is the electron affinity of n-type (p-type) layer. Here we assume that the total thickness of i/n or i/p stacks is larger than the sum of space charge regions from c-Si and from TCO. Then, Ef,n = χn+ Ea,n and
Ef,p = χp+ Eg,p - Ea,p. Vbi is the built-in voltage and WTCO is the TCO work function. Carrier selectivity
Let us consider selectivity at the latest infinitesimal portion of c-Si, beneath the i-a-Si:H interface [46]:
where n and p denote electrons and holes concentration, and μe and μh are electron and hole
mobility. In c-Si, the nature of high selectivity imposes asymmetric carrier concentrations at a surface, since μn and μp are in the same order of magnitude. Accordingly, selectivity is
maximized by increasing the carrier concentration of one type of carriers, meaning the decrease of the other carriers by Fermi statistics.
In general, without explicitly mentioning the dependency from distance (r), the carrier concentrations at c-Si / i-a-Si:H interface (r = 0) are so defined:
TCO i/n material c-Si Jh Je rTCO 0 qn,cSi EC Efe Efh EV qh (r) En er gy , E Distance, r qe(r) TCO i/p material c-Si Jh Je rTCO 0 qp,cSi EC Efe Efh EV qh (r) En er gy , E Distance, r qe(r) qVbi,n En ergy, E Distance, r Vacuum EC Ef EV q0,n,cSi Ea,n Eg,p n q0,n c-Si i/n material TCO WFTCO WFTCO qVbi,p Eg,p p Ea,p En ergy, E Distance, r Vacuum EC Ef EV q0,p q0,p,cSi c-Si i/p material TCO
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where NC (NV) is the density of states in the conduction (valence) band for electrons (holes),
Efe,cSi (Efh,cSi) stands for Quasi-Fermi energy level of electrons (holes) at c-Si / i-a-Si:H
interface and EC,cSi (EV,cSi) is the conduction (valence) band energy. Thus, for n-contact and at
the c-Si / i-a-Si:H interface, is maximized when ΔEn,e = EC,cSi - Efe,cSi is a negative number
meaning that while, for p-contact and at the c-Si / i-a-Si:H interface, is
maximized when ΔEp,h = Efh,cSi – EV,cSi is negative by means of . Considering a
reference point in c-Si bulk beyond the space charge region (r = d), the electrostatic potential between c-Si and a-Si:H interface can be written as φn,cSi = [EC,cSi(d) - ΔEne(0)]/q for n-type
contact and φp,cSi = [EV,cSi(d) - ΔEph(0)]/q (see Figure 1a and 1b). Therefore, either n or p in
equation 2 are maximized when the junction electrostatic potential at each contact is also
maximized. As the band bending is the electrostatic potential multiplied by the elementary charge ( ), indicates band bending in the remainder of this work.
To understand which are the individual layer parameters that improve contact selectivity, we consider thermal equilibrium conditions (see Figure 1c and 1d). In particular, perfect selectivity at n-type or p-type contact is achieved when the Fermi energy of c-Si at thermal equilibrium ( ) over-crosses conduction or valence band energy, respectively. In other words: and . Therefore, maximal values of stand for maximal selectivity by increasing collecting carrier density at c-Si / i-a-Si:H
interface. Accordingly, for n-type and p-type contacts, the electrostatic potential supported by each semiconductor of hetero-junction can be written as follows [47]:
where the subscript (·) stands for either n-type (n) or p-type (p) layer, is in general the band
bending, N(A,D) is the number of acceptors (A) and or donors (D) and (·) is the permittivity
coefficient. It is worth noting that in this approximation, we overlook i-aSi:H effect, since it is assumed very thin with negligible doping. Therefore, increases as the doping on deposited layers ( ) increases, leading also to a decrease of at n-type or p-type layer, assuming that N(A,D),cSi is constant as given parameter from absorber bulk. Then,
looking into built-in potential (Vbi) definition:
increases as enhances. Similarly, Vbi,(∙) is defined as the difference of Fermi
levels in both isolated semiconductors at thermal equilibrium:
where Ef,p (Ef,n) is the Fermi level at thermal equilibrium in the p-type (n-type) layer. Thus,
including activation energy (Ea) (see Figure 1c and d), we have:
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For thin-film Si alloys, electron affinity and are close to 4 eV, while the bandgap Eg can
be modified alloying carbon or oxygen with silicon. Then, the band gap increases shifting valence band energy [48]. Therefore, from equations 6 and 7, it appears that Ea and Eg are the
thin films key parameters to increase selectivity. Interestingly, in case of p-type contact, Vbi is
maximized by increasing the difference while, for the n-type contact case, Vbi is
maximized by minimizing . Therefore, selectivity (see equation 1) is enhanced by exploiting the Vbi.
Selective transport
In IBC-SHJ solar cells, collection of carriers involves transport through two hetero-interfaces: c-Si / i-a-Si:H and doped layer / TCO. Such hetero-interfaces exhibit discontinuities in the band diagram, building so-called energy barriers (see dashed areas in Figure 1a and 1b). In either the n-type or p-type contact stack, we define the energy barrier for electron (hole) the area under (above) the curve of conduction (valence) band between the two abovementioned interfaces and the EC,cSi(0) (EV,cSi(0)) level. Transport of carriers through these energy barriers
is described by two mechanisms: i) thermionic emission and ii) tunnelling. Both models are associated to transport of carriers across energy barriers or discontinuities. As described in Ieong et al. [49], the tunnelling for transport of electrons and holes is associated to the local generation rate G as follows:
where in this case the subscript (·) stands for either electrons (e) or holes (h), is the Richardson constant is the temperature, is the Boltzmann constant, is the electrical field, is the tunnelling probability at the doped material / TCO interface, ΔEe = Ee,cSi - Efe,cSi (ΔEh = Efh,cSi – Eh,cSi), ( ) is the energy of electrons (holes) in the conduction
(valence) band and ( ) is the Quasi Fermi-level of electrons (holes) at each hetero-interface, either c-Si / i-a-Si:H (cSi) or doped material / TCO. The term inside the logarithm correlates the density of filled states at the c-Si / i-a-Si:H interface with that of free states at the TCO interface (both sides of energy barrier) [50]. As the density of filled states at the c-Si / i-a-Si:H interface is associated to equation 2, maximizing the band bending additionally improves the transport of carriers. It is worth noting that transport of carriers in TCO is typically deployed on the conduction band by means of density of free states for electrons. Therefore, transport at n-contact / TCO is based on direct tunnelling and transport at p-contact / TCO interface is based on band to band tunnelling.
The tunnelling probability is calculated following Wentzel-Kramers-Brillouin (WKB)
approximation:
where is the reduced Planck constant and ( ) is the electrostatic potential in terms of potential barrier profile along the position r for electrons (holes). Since this work is based on SHJ, effective tunnelling masses of electrons me and holes mh are assumed constant
to 0.1 times the electron rest mass (m0) [51]. It is interesting that according to the patterned
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area inside the barriers exponentially influences . Hence, transport of carriers is improved by decreasing energy barriers.
In general, the energy barriers are defined by band offset at hetero-interfaces and inner band bending in the doped layers. Since c-Si interface is usually passivated by i-a-Si:H, then the band offset is defined by the thin i-a-Si:H passivating layer. Therefore, band offset at c-Si interface is assumed as a fixed parameter to account for high passivation quality. The band offset and induced band bending at doped material / TCO interface is instead constructed by the so-called work function (WF) mismatch, which accounts for the difference between the isolated Fermi energy levels of the doped material and of the TCO. Such band offset together with the induced band bending in the doped material define a Schottky barrier for carrier collection. Then, similar to band bending at the c-Si / i-a-Si:H interface, the proper Fermi energies conditions ( and ) reduce the band bending component in the energy barrier for p-type and n-type contact, respectively. Moreover, according to equation 3, energy barriers significantly decrease by increasing doping (i.e. decreasing Ea). Hence, the key parameters impacting on energy barriers size are WFTCO and
doped layer Ea.
At this point, we introduce the concept of selective transport, which is achieved by reducing energy barrier of collecting carriers and increasing energy barrier for no-collecting carriers. Therefore, selective transport for SHJ contact can be defined as:
where Tn (Tp) is the selective transport of electrons (e) and holes (p) at the n-type (p-type)
contact, and G denotes the local generation associated to the current of electrons or holes in either n-type or p-type contact through the c-Si / i-a-Si:H and doped layer / TCO interfaces. Similar to the concept of contact selectivity [46], the fundament of high selective transport is the asymmetry between transport of electrons and holes through the related energy barriers at the conduction and valence band. Due to particular working regime of solar cells, Tn and Tp
are not constant and illustrate the contact optimization problem in maximizing G for one type of carriers and minimizing it for the other. Additionally, the root of such selective transport is established in equilibrium conditions. Therefore, band diagrams on equilibrium evidence fundamental transport mechanisms as energy barrier size and band bending. The material parameters that impact on transport of carriers on IBC-SHJ devices are: TCO work function WFTCO, activation energy Ea and bandgap Eg of doped layers. In the following section, we
present a simulation analysis to understand the impact of these parameters on the device transport by looking at the computed FF.
Simulation Approach
To assess the impact of aforementioned material parameters on the external parameters of an IBC-SHJ solar cell, opto-electrical simulations were performed using TCAD Sentaurus [52]. The use of such an advanced device simulation environment is in this case instrumental as drift-diffusion equations are solved taking into account traps distributions, band structures, dopants and thickness of layers (i-a-Si:H, doped layers, TCO) alongside with tunnelling and thermionic emission transport mechanisms. In particular, we executed a 2-D opto-electrical modelling.
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Figure 2. Symmetry element of the IBC-SHJ considered as simulation domain. The front side comprises a randomly-generated micro-scale pyramidally-shaped texture compatible with industry standard and coated with a dual anti-reflective coating (ARC: SiO2 / SiNx). The bulk is n-type c-Si. The flat rear side features an n-type stack (i-a-Si:H / n-type thin-film Si-based layer / TCO / metal) in the role of back surface field and a p-type stack (i-a-Si:H / p-type thin-film Si-based layer / TCO / metal) in the role of emitter. The architecture is gapped and modelled with a quarter of circle characterized by a 1-μm wide radius.
As validation device, we considered an IBC solar cell featuring carrier-selective poly-Si-based passivating contacts (IBC-poly) [5]. Interfaces of emitter and back surface field with c-Si bulk are planar and separated by a curved gap, resulting from a self-aligned process [2]. Figure 2 reports the sketch of an IBC-SHJ solar cell symmetry element. Afterwards, we modelled a structure similar to that of IBC-poly [5] but replacing at the rear side the stack of tunnelling SiO2/poly-Si/Al with the stack i-a-Si:H / doped thin-film Si alloy / TCO / Ag. The
simulation approach is similar to the one described in [53]. Accordingly, the optical simulation is performed by a ray-tracing model featuring a Monte Carlo scheme combined with the transfer matrix method (TMM). The primary scope of this work is to analyse transport and selectivity. Although changing TCO work function and doped layers electrical parameters implies a certain variation in their optical behaviour [54], [55], we assume fixed wavelength-dependent complex refractive index of i-aSi:H, n-type and p-type doped layers [56] and TCO [57]. This choice is optically acceptable given that both contact stacks are located at rear side of the device.
The electrical simulation is based on ad-hoc drift-diffusion model, using state-of-art models [53], [58] for AM1.5G illumination. Table 1 summarizes models and parameters used in this work. Electrical parameters of i-aSi:H and doped layers such as traps energy distribution, electron affinity and mobility were accounted according to [58] but for brevity they are not
reported in Table 1. In order to vary the Ea, we adjusted accordingly the uniform doping
concentration in doped layers.
Transport mechanisms were modelled according to the non-local tunnelling model [49], [52], and thermionic emission to proper consider transport of carriers through energy barrier at c-Si / i-a-Si:H and doped layer / TCO hetero-interfaces. To avoid any lateral transport in low-mobility deposited layers, our IBC-SHJ device features full TCO and metal coverage at n-type and p-n-type contacts.
Regarding TCO layers, they were modelled as degenerate semiconductors [59] with , thus work-function mismatch and induced band bending are accurately taken into account.
Concerning TCO electrical parameters like electron affinity and WFTCO, a wide range of
values is reported in literature [59]. This is because of inherent properties of different types of TCO [54], [59], [60] and also TCO / semiconductor interfaces, for which dipole formation is allowed [59]–[63]. Within this work, we assume a constant TCO bandgap, carrier concentration and mobility (see Table 1) with a variable electron affinity and thus variable
Base (n-type) p contact n contact Metal Metal TCO i-a-Si:H i-a-Si:H TCO ARC: SIO2 /SiNX
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WFTCO. Accordingly, we focus our study on analysing WFTCO as concise and essential TCO
parameter affecting transport mechanisms through deposited layers.
In the following, we investigate the influence of WFTCO and Ea, Eg and thickness of doped
layers thickness on the FF as transport figure of merit. Aiming at the evaluation of transport mechanisms minimizing the recombination due to defects in c-Si in realistic devices, we set the device SRH parameters according to Table 1.
Table 1. Summary of general IBC-SHJ device parameters.
Model / Parameter Simulated Device Model / Parameter Simulated Device
Bandgap narrowing Schenk [64] i-a-Si:H band gap 1.7 eV
c-Si mobility Klaassen [65] Doped layer bandgap variable
1.7 eV otherwise Intrinsic carrier density Altermatt [66] 9.65 × 109 cm-3 at 300 K ITO bandgap 3.7 eV
Free carrier statistics Fermi-Dirac TCO work function (WFTCO)
variable
4.7 eV [59] otherwise Intrinsic
recombination
Richter [67] Carrier concentration in TCO
1x1020 cm-3
bulk SRH lifetime 10 ms TCO electron or hole mobility 50 or 30 cm2/V s Surface SRH Surface Recombination Velocity 0.1 cm/s i-a-Si:H thickness 5 nm
Bulk resistivity 5 Ωcm TCO thickness 80 nm
Electron affinity i-a-Si:H and doped layers
4 eV Substrate thickness 100 μm
Tunneling mass for i-aSi:H and doped layers
0.1m0 *
[51] Pitch 650 μm
*
m0 is electron rest mass
Results and discussion
Activation energy of doped layers
In this section, the transport of carriers at p-type and n-type contacts is evaluated as a function of the doped layers Ea. To this purpose, Ea was varied from 35 (35) meV to 410 (300) meV
for p-type contact (n-type contact). These ranges were decided based on different doping concentrations, featuring traps and charge distribution as reported in [58]. To evaluate individually the transport of carriers at n-type or p-type contact, the other contact was assumed as perfect by setting Ea = 30 meV. Then, simulations were performed assuming
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Figure 3. Simulated FF as a function of Ea at n-type (left) and p-type contact (right) for 7-nm thick doped layers and with respect to different WFTCO. Patterned regions correspond to typical Ea of a-Si:H doped for n- and p-contact
Figure 3, shows the FF as a function of Ea for different WFTCO. In general, we observe that FF
decreases as Ea increases. In fact, as Figure 4 depicts for the case of p-type contact and as
previously discussed, high Ea values increase the energy barrier experienced by majority
carriers and decrease the energy barrier for minority carriers. Additionally, band bending at c-Si interface, which is also associated to Ea, decreases with increasing Ea. Therefore, low
values of Ea enhance transport selectivity in terms of both energy barrier size and band
bending at c-Si interface. Similarly, still depending on the Ea, the TCO-induced band bending
at doped layer / TCO interface modifies the size of the energy barriers, explaining the dependence of FF on Ea in case of low (high) WFTCO values for p-type (n-type) contact.
Figure 4. Band diagrams at equilibrium of p-type contact stack for different activation energy of the p-type layer (Ea,p). Here, p-type layer thickness is 7 nm and WFTCO is 4.7 eV. Patterned areas indicate energy barriers for electrons (conduction band) and holes (valence band). ΔE is related to the band bending at the c-Si interface (see Equation 2 in Carrier selectivity section above). Decreasing Ea,p, the energy barrier for holes decreases while the energy barrier for electrons increases.
Effect of TCO and doped layers thickness
Figure 5 shows the effect of WFTCO on FF for different Ea. In case of p-type contact, an
increase in FF is observed by increasing WFTCO. On the contrary, in case of n-type contact, FF
degrades for WFTCO values higher than 4.7 eV. Interestingly, for both contact stacks, FF
becomes insensitive to WFTCO for Ea values lower than 100 meV. As discussed above, lower
Ea (i.e. higher doping) hinders the effect of induced band bending in doped layers
(specializing equation 3 for the doped layer / TCO interface). Changing WFTCO, the size of
energy barriers is modified as illustrated in Figure 6. Simulation results demonstrate that two conditions could be implemented to improve the FF: (i) high Ea and WFTCO larger than 5.1 eV
0 50 100 150 200 250 0.40 0.50 0.60 0.70 0.80 FF (-) Ea,n (meV) WFTCO = 5.2eV WFTCO = 4.7eV WFTCO = 4 eV 0 100 200 300 400 500 0.76 0.78 0.80 0.82 0.84 0.86 FF (-) Ea,p (meV) WFTCO = 4.4 eV WFTCO = 5.1 eV WFTCO = 5.3 eV EC Ef EV En er gy , E Distance, r Ea,p = 400 meV E Ea,p = 300 meV En er gy , E Distance, r E Ea,p = 100 meV E ~ 0 En er gy , E Distance, r
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or smaller than 4.7 eV for p-type or n-type contact, respectively; or (ii) Ea lower than 100
meV for any WFTCO. Thus, the option (i) is limited by TCO material and processing parameters [54], [63]. Moreover, additional complexity comes from the fact that increasing
WFTCO, the conductivity of the TCO commonly decreases and vice-versa. On the other hand,
the option (ii) allows to use more types of TCO materials since only maximizing free states at
TCO / doped layer interface matters in terms of Ee,TCO - Efe,TCO (see equation 8).
Figure 5. Simulated FF as a function of WFTCO at n-type (left) and p-type (right) contact for 7-nm thick doped layers and
with respect to different Ea,n and Ea,p, respectively. Patterned areas correspond to typical work function values of ITO with 90 wt % In2O3 and 10 wt % SnO2 [54], [68].
Figure 6. Band diagrams at equilibrium of p-type contact stack for different work function of TCO (WFTCO). Here, p-type
layer thickness is 7 nm and Ea,p is 300 meV. Patterned areas indicate energy barriers for electrons (conduction band) and holes (valence band). ΔWF indicates work function mismatch at the TCO/p-layer interface. Increasing WFTCO, the energy barrier for holes shrinks, but energy barrier for electrons expands.
In case of even thinner doped layers, the work-function mismatch at doped layer / TCO interface eventually impacts on the band bending at c-Si interface. Indeed, for relatively high Ea and depending on WFTCO, the thickness of doped layers can be calibrated to maximize
transport leveraging on the trade-off between optimal band bending at c-Si interface versus the size of the energy barriers.
The aforementioned degradation of FF for relatively large work-function mismatch is mitigated by increasing the thickness of doped layer as reported in Figure 7 and 8. Indeed, thicker doped layers build wider energy barriers, but also reduce the influence of WFTCO on
band bending at c-Si interface. From our simulations, we found that to isolate the effect of
3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 0.30 0.40 0.50 0.60 0.70 0.80 0.90 FF (-) WFTCO (eV) Ea,n = 230 meV Ea,n = 185 meV Ea,n = 120 meV 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 0.78 0.80 0.82 0.84 0.86 0.88 FF (-) WFTCO (eV) Ea,p = 400 meV Ea,p = 300 meV Ea,p = 100 meV EC Ef EV WFTCO = 4.4 eV En er gy , E Distance, r WF WFTCO = 4.7 eV En er gy , E Distance, r WF WFTCO = 5.1 eV En er gy , E Distance, r WF
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
WFTCO, the minimum thickness of doped layer has to be larger than the sum of depletion
region from both interfaces inside deposited layers.
Therefore, as simulated device accounts for full TCO / metal coverage, the transport of carriers through thin-film Si layers until metal contact is mostly one-dimensional (1D).
Accordingly, aforementioned FF trends as a function of WTCO and doped layer thickness are
in agreement with those presented in [69], in which front and rear contact SHJ solar cell is also simulated considering a 1D approach.
Figure 7. Simulated FF as a function of WFTCO for n-contact (left) and p-contact (right) for Ea,n = 230 meV and Ea,p = 400 meV and with respect to different thicknesses of di/n or di/p stack, respectively. Patterned areas correspond to typical work
function values of ITO with 90 wt % In2O3 and 10 wt % SnO2 [54], [68].
As discussed above, the selective transport T is the ratio between competitive transports of charge carriers at each contact in terms of Ge and Gh (see equation 11). Accordingly, to
evaluate T, we extracted the generation of carriers associated to current flows through the p-type and n-p-type contacts. For the sake of the simplicity, we executed the simulations in JSC
conditions, when the flow of collected carriers is maximized owing to the band alignment for transport of collecting carriers, and for di/p = 15 nm.
Figure 8. Band diagrams at equilibrium of p-type contact stack for different thickness di/p of i-a-Si:H and p-type layer. In
these cases, we set WFTCO = 4.4 eV and Ea,p = 400 meV. Patterned areas indicate energy barriers for electrons (conduction band) and holes (valence band). ΔE is related to the band bending at the c-Si interface (see equation 2 in Carrier selectivity section above). Increasing di/p shields band bending into c-Si induced by the TCO.
3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 0.30 0.40 0.50 0.60 0.70 0.80 0.90 FF (-) WFTCO (eV) di/n = 10nm di/n = 15nm di/n = 25nm 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 0.78 0.80 0.82 0.84 0.86 FF (-) WFTCO (eV) di/p = 10 nm di/p = 15 nm di/p = 25 nm EC Ef EV di/p = 10 nm En er gy , E Distance, r E di/p = 15 nm En er gy , E Distance, r E di/p = 25 nm E En er gy , E Distance, r
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 (a) (b) (c) (d)
Figure 9. (a) Gp,h, (b) Gp,e, (c) Tp, and (d) FF as a function of activation energy Ea,p and WFTCO. Low activation energy is the dominant parameter that improves hole collection in terms of Gp,h, T and FF.
In case of p-type contact, Figure 9 shows the trends of Gp,h, Gp,e and FF as a function of Ea,p
and WFTCO. We observed that the collection of holes Gp,h depends more on Ea,p than WFTCO
(see Figure 9a); while Gp,e depends on both parameters (see Figure 9b). Indeed, Gp,e lowers
by decreasing Ea,p and also increasing WFTCO. By evaluating Tp in Figure 9c, we observed
that Gp,h trend dominates over Gp,e. Indeed, such an effect is confirmed as transport indicator
in terms of FF, as Figure 9d depicts. Therefore, the increment observed in FF for lower Ee,p is
explained in terms of increment of Gp,h; while the rise of FF for higher WFTCO is ascribed to
the reduction of Gp,e in the p-type layer. Additionally, Ea,p is the dominant parameter that
describes mostly Tp and FF behaviour.
In case of n-type contact, Figure 10 shows the trends of Gn,h, Gn,e and FF as a function of Ea,n
and WFTCO. We observed in Figure 10a that the collection of holes Gn,h does not significantly
vary within our simulation domain (i.e variation is smaller than one order of magnitude). On the other hand, Gn,e shows a sharp increase for WFTCO values higher than 4.6 eV and Ea,n
values larger than 250 meV (see Figure 10b). Such an effect is expressed in terms of Tn
decrease (see Figure 10c). In fact, Tn behaviour explains the trend of FF (see Figure 10d) in
terms of hindering transport of holes (Ge,h). It is worth noting that collection of electrons does
not demonstrate a clear improvement within our simulation domain due to inherently smaller barrier size in the conduction band compared to valence band energy barrier.
50 100 150 200 250 300 350 400 4.2 4.4 4.6 4.8 5.0 WF TC O ( eV ) Ea,p (meV) 0.00 4.13x1013 8.25x1013 1.24x1014 1.65x1014 2.06x1014 2.48x1014 2.89x1014 3.30x1014 Gp,h (cm-3 s-1) 50 100 150 200 250 300 350 400 4.2 4.4 4.6 4.8 5.0 WF TC O ( eV ) Ea,p (meV) 1.92x109 2.88x109 3.85x109 4.81x109 5.77x109 6.73x109 7.70x109 8.66x109 9.62x109 Gp,e (cm-3 s-1) 50 100 150 200 250 300 350 400 4.2 4.4 4.6 4.8 5.0 WF TC O ( eV ) Ea,p (meV) 0.00 1.94x104 3.89x104 5.83x104 7.78x104 9.72x104 1.17x105 1.36x105 1.55x105 Tp (-) 50 100 150 200 250 300 350 400 4.2 4.4 4.6 4.8 5.0 WF T C O ( e V ) Ea,p (meV) 0.8224 0.8281 0.8337 0.8394 0.8451 0.8508 0.8565 0.8621 0.8678 FF (-)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 (a) (b) (c) (d)
Figure 10. (a) Gn,h, (b) Gn,e, (c) Te and (d) FF as a function of activation energy Ea,n and WFTCO. Low activation energy and low WFTCO hinder holes currents inside n-type contact in terms of Gn,h. Note that Gn,e is almost constant for all the simulated domain.
Band gap of highly-selective p-type contact
As discussed above, band bending at c-Si interface in case of p-type contact depends on the bandgap of the p-type layer (see equation 6). Consequently, to understand this relation and its impact on FF and Voc, we performed a set of simulations changing the bandgap on the p-type
layer. As Figure 11 illustrates, both FF and VOC ameliorate as Eg,p increases. Such an effect is
ascribed to the improved band bending at c-Si interface that increases hole-filled states, as it is observed in Figure 12. According to equation 6, the band bending at c-Si interface depends on the difference Eg,p - Ea,p, meaning that increasing Eg,p relaxes the contribution of Ea,p in
maximizing the band bending. For instance, the typical bandgap of p-type thin-film Si is around 1.7 to 1.8 eV, featuring Ea,p in the range between 30 and 400 meV. According to our
simulations, with this type of material, band bending at c-Si interface is maximized to 0.84 eV for Ea,p = 30 meV, leading to a Eg,p-Ea,p difference of around 1.7 eV. Similar effect is obtained
if Eg,p increases to 2.1 eV but with a relaxed Ea,p value of 300 meV. Indeed, according to our
simulations, FF values above 86% are achieved for Ea,p values lower than 400 meV, if band
gap values are higher than 1.8 eV (see Figure 11). Moreover, the FF improvement is more than 1% abs, if the band gap increases from 1.7 to 1.8 eV for 400 meV Ea,p. Nevertheless,
50 100 150 200 250 300 3.8 4.0 4.2 4.4 4.6 WF T C O ( e V ) Ea,n (meV) 4x108 7x109 1x1010 2x1010 3x1010 4x1010 4x1010 5x1010 6x1010 Gn,h (cm-3 s-1) 50 100 150 200 250 300 3.8 4.0 4.2 4.4 4.6 WF T C O ( e V ) Ea,n (meV) 1x1013 9x1014 2x1015 3x1015 4x1015 4x1015 5x1015 6x1015 7x1015 Gn,e (cm-3 s-1) 50 100 150 200 250 300 3.8 4.0 4.2 4.4 4.6 WF T C O ( e V ) Ea,n (meV) 1.0x105 1.7x106 3.2x106 4.8x106 6.3x106 7.9x106 9.5x106 1.1x107 1.3x107 Tn 50 100 150 200 250 300 3.8 4.0 4.2 4.4 4.6 WF T C O ( e V ) Ea,n (meV) 0.5810 0.6169 0.6527 0.6886 0.7245 0.7604 0.7963 0.8321 0.8680 FF (-)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
depending on Ea,p and WFTCO, the energy barrier size for both holes and electrons clearly
increases due to work function mismatch (see Figure 12). In fact, low Ea,p values (i.e. 35 mV see Figure 11) are crucial to mitigate this effect.
Figure 11. Simulated FF (left) and VOC (right) as a function of Eg for p-type contact and for di/p = 25 nm and WFTCO = 4.7
eV.
Figure 12. Band diagrams at equilibrium of p-type contact stack for different bandgap of p-type layer. In these cases, Ea,p = 400 meV, WFTCO = 4.7 eV and di/p = 25 nm. Patterned areas indicate energy barriers for electrons (conduction band) and holes (valence band). ΔE is related to the band bending at the c-Si interface (see equation 2 in Carrier selectivity section above). ΔWF indicates work-function mismatch at the p-type layer / TCO interface. Increasing Eg,p increases band bending at c-Si interface but also ΔWF.
The increase in Voc is explained in terms of reduced recombination in defective doped layer.
Looking into recombination (R) at c-Si / i-a-Si:H interface [70], we have:
where n and p stand for free carrier density, NDB is the density of dangling bonds, VTH is the
thermal velocity and is the capture cross section of neutral and charged states. When increasing the band bending at c-Si interface, the recombination at each contact stack decreases and becomes less sensitive to NDB. Indeed, in this condition the Fermi energy level
is close to conduction (valence) band, resulting in ( ) for n-type (p-type) contact. Hence, a strong band bending at c-Si interface is crucial and it can be engineered by
1.4 1.6 1.8 2.0 2.2 0.80 0.82 0.84 0.86 0.88 FF (-) Eg,p (eV) Ea,p = 400 meV Ea,p = 300 meV Ea,p = 35 meV 1.4 1.6 1.8 2.0 2.2 0.50 0.55 0.60 0.65 0.70 0.75 Voc ( V) Eg,p (eV) Ea,p = 400 meV Ea,p = 300 meV Ea,p = 35 meV EC EF EV Eg,p = 1.4 eV En er gy , E Distance, r E WF Eg,p = 1.7 eV En er gy , E Distance, r E WF Eg,p = 2.2 eV E ~ 0 En er gy , E Distance, r WF
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
deploying doped thin films of Si (alloys) with proper Ea for the n-type contact and with proper
Eg in combination with Ea for the p-type contact.
In thin-film Si technology, reduced Ea values are attained by increasing the doping in
amorphous structures, but Ea are limited to about 200 meV [71]. Lower Ea values correspond
to doped hydrogenated nano-crystalline Si (Si:H) alloys [32]. In particular, a doped nc-Si:H layer requires special growth conditions that eventually damage the i-a-nc-Si:H passivation layer [31], [32]. Accordingly, the so-called incubation layer, which consists of a few nanometers of doped a-Si:H, is necessary to start nano-crystalline phase growth while preserving the i-a-Si:H passivation [72]–[74]. Thus, achieving low Ea from the very beginning
of the doped layer deposition is technologically challenging and limits the band bending at c-Si interface (see Figure 13 (left), where ΔE is not minimized). To overcome such limitation, one can alternatively use doped wide bandgap thin-film Si films alloyed with carbon or oxygen that can induce stronger band bending than doped a-Si:H layers. In fact, a p-type contact stack featuring wide Eg,p material such as SiOx:H (1.7 - 2.2 eV) [24], [25], [55] and
SiCx:H (1.4 - 2.1eV) [20], [48], [75] exhibits maximized band bending at c-Si (see Figure 13
(right), where ΔE ~ 0). As a result, the use of wide bandgap doped p-type layer as incubation layer potentially boosts both FF and VOC as reported in Table 2. Simulated structures are
insensitive to WFTCO, because doped layers feature 50 meV Ea,p at doped layer / TCO
interface in a similar way than in Figure 5.
Figure 13. Band diagrams at equilibrium of p-type contact stack featuring (left) a-Si:H-based incubation layer (high Ea,p) or (right) wide bandgap incubation layer (high Ea,p). Patterned areas indicate energy barriers for electrons (conduction band) and holes (valence band). In both diagrams, Ea,p decreases until 50 meV as p-type layer thickness increases, emulating the growth of doped nc-Si:H. The usage of a wide bandgap (Eg,p = 2 eV) incubation layer (Ea,p = 400 meV) in the right-hand side diagram enhances the band bending at c-Si interface (ΔE ~ 0). Note that here we assume WFTCO = 4.7 eV as exhibited by
typical ITO material.
Table 2. Summary of external parameters of IBC-SHJ solar cells featuring different p-type doped incubation layers. The p-type doped layer in contact
with the TCO is p-type nc-Si:H (Eg,p = 50 meV).
Incubation layer JSC
(mA/cm2)
VOC (mV) FF (%) η (%)
p-type a-Si:H 41.4 744 84.9 26.2
p-type SiOx or p-type SiCx 41.5 754 86.8 27.2 p-nc-Si:H i-aSi:H EC Ef EV E Energy, E Distance, r
high Ea,p low Ea,p high Ea,p low Ea,p
p-nc-Si:H p-SiOx:H or p-SiCx:H i-aSi:H EC Ef EV E ~ 0 Energy, E Distance, r
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Lateral transport
Finally, to understand the impact of rear geometry on lateral transport in IBC-SHJ solar cells, we performed simulations changing the n-type finger width, p-type finger width and pitch size and assuming optimized contact stacks. For the sake of simplicity, within these simulations, the width of metal and TCO fingers corresponds to the width of doped layer fingers. Figure 14 presents FF as a function of half pitch and coverage of p-type contact over pitch. Similar to IBC homo-junction c-Si solar cells [76], minimal pitch leads to higher FF, but optimal p-type finger coverage remains constant to a value of 60%. This results from the trade-off between holes and electrons transport mechanisms. In fact, due to the inherent band alignment at hetero-interfaces, the transport of electrons to be collected tends to be more efficient than that of holes.
Figure 14. FF as a function of half pitch and coverage of p-type contact over pitch. It is observed that longer pitches increase the path of carriers to be collected, thereby affecting the FF. The FF is optimal for coverage of p-type contact over pitch of around 60%.
Conclusions
In this work, we have presented a theoretical analysis of the transport mechanisms in IBC-SHJ solar cells. The study has been performed by means of an advanced opto-electrical modelling platform based on TCAD Sentaurus. The concepts of carrier selectivity and selective transport were used to identify the parameters of doped thin-film Si layers affecting FF and VOC. It was shown that both concepts are related to the band bending at c-Si interface.
In this respect, maximizing carrier selectivity is equivalent to maximizing filled states at the c-Si interface, improving transport at hetero-interfaces. Additionally, the transport of carriers is also related to energy barriers in the conduction band for electrons and in the valence band for holes. Accordingly, in case of p-type contact, the parameters that impact on band bending at c-Si interface and energy barriers were identified as the doped layer bandgap and activation energy and the TCO work function. In case of n-type contact, these parameters are the doped layer activation energy and the TCO work function.
The concept of selective transport was also introduced and defined as a comparison of generation rate associated to transport at hetero-interfaces between majority and minority carriers. Accordingly, selective transport is improved maximizing the collection of majority carriers and minimizing the collection of minority carriers.
Simulation results confirmed that low activation energy values in doped layers are crucial to minimize energy barriers and increase band bending at c-Si interface. Moreover, low activation energy values also reduce the effect of TCO work function mismatch making the device insensitive to TCO work function. Indeed, in general, FF increases by reducing activation energy of doped layers. If the activation energy of doped layers at hand is still relatively high, then a TCO with work function larger than 5.1 eV (lower than 4.7 eV) enhances holes (electrons) collection in p-type (n-type) contact. The negative effect that the
300 400 500 600 700 800 900 1000 1100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 p-cont ac t / Pit ch (-) Half Pitch (m) 0.8222 0.8269 0.8317 0.8364 0.8412 0.8459 0.8506 0.8554 0.8601 FF
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
TCO work function might eventually inflict to the band bending at c-Si interface is mitigated by increasing the thickness of the doped layers. In this sense, a shielding thickness should be larger than the sum of the inner depletion regions at c-Si / i-a-Si:H and doped layer / TCO interfaces.
Concerning the evaluation of selective transport T, simulation results evidence a clear correlation with the FF within the considered parameters space of Ea and WFTCO. From this
analysis, in case of p-type contact, low Ea,p improves carrier collection, while high WFTCO
blocks the flow of electrons inside p-type deposited layers. In case of n-type contact, low Ea,n
values block the flow of holes, but do not improve electron collection.
The band gap of p-type layer strongly affects the band bending at c-Si interface and therefore both passivation and transport in terms of VOC and FF, respectively. Simulation results
revealed that Eg,p-Ea,p values above 1.7 eV maximizes band bending at c-Si interface to values
above 840 meV. However, as bandgap increases, work-function mismatch at doped layer / TCO interface strongly increases, making the performance of the device more sensitive to the doped layer activation energy. In thin-film silicon-based layers, low activation energy can be only achieved in nano-crystalline phase. Thus, to simulate a realistic device, we emulated the formation of an amorphous incubationlayer in the first nanometers of the doped layer above the passivating i-a-Si:H. This very thin layer hampers the positive influence of low activation energy in nano-crystalline doped layers. Therefore, we deployed a wide bandgap material in the role of incubation layer in combination with doped nc-Si:H with a layer characterized by narrower bandgap but slightly higher activation energy. In this way we could concurrently minimize the band bending at c-Si interface and avoid the work-function mismatch at doped layer / TCO interface. From this approach, record conversion efficiency up to 27.2% is predicted with VOC-max = 754 mV and FFmax = 86.8%.
Finally, lateral transport was evaluated in terms of pitch and width of n-type and p-type contacts. Similar to IBC homo-junction c-Si solar cells, small pitch increases FF. Specifically for IBC-SHJ cells, n-type and p-type contacts should ideally cover 40% and 60% of the pitch, respectively.
Acknowledgements
The authors gratefully acknowledge Dr. Rene van Swaaj for useful discussions and Miss Aurora Saez Armenteros for simulations related to the lateral transport analysis. This work is performed in the framework of NextBase project, that has received funding from the European Union’s Horizon2020 Programme for research, technological development and demonstration under Grant Agreement no. 727523.
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