129
Original scientific paper
Analysis of effects of dangling-bond defects in doped 
a-Si:H layers in heterojunction silicon solar cells with 
different electron affinities of ITO contacts
Jošt Balent, Franc Smole, Marko Topič, Janez Krč
University of Ljubljana, Faculty of electrical engineering, Laboratory of Photovoltaics and 
Optoelectronics, Ljubljana, Slovenia
Abstract:  The effects of dangling-bond defects in doped hydrogenated amorphous-silicon layers (p-a-Si:H and n-a-Si:H) in 
heterojunction silicon (SHJ) solar cells are studied in relation to applied Indium-Tin-Oxide (ITO) contacts with different electron 
affinities. A state-of-the-art numerical model of the SHJ solar cell was employed, including ITO contacts as full, volumetric 
semiconductor layers, applying the trap-assisted, band-to-band and direct tunnelling mechanisms at heterointerfaces in the device. 
The levels of dangling bond defect concentrations were varied in both p-a-Si:H and n-a-Si:H layers and ITOs with two different electron 
affinities were considered at both sides of the device. We show that the effects of the defects on the short-circuit current density, 
open-circuit voltage, fill factor and conversion efficiency of the device become more pronounced if ITOs with non-optimal electron 
affinities are used. Possibility to reach higher doping levels of the doped a-Si:H layers would mitigate the effects of its dangling bond 
states, which becomes more important if ITO electron affinity is not optimized to the doped a-Si:H layers. We demonstrate that the 
reduced efficiency due to the increase in dangling-bond density originates from the decrease of the fill-factor and open-circuit 
voltage, whereas the short-circuit current density has a small effect on efficiency for the chosen variation span. The reduction of the 
fill-factor is further explained by a drop in maximum-power-point voltage, which is more pronounced if optimization of ITO electron 
affinity is not taken into account.
Keywords: Silicon heterojunction solar cell; Opto-electrical simulation; Defect-states, Electron affinities
Numerična analiza učinkov defektov bingljajočih 
vezi v dopiranih plasteh iz a-Si:H v heterospojnih 
silicijevih sončnih celicah s kontakti ITO z 
različnimi elektronskimi afinitetami
Izvleček: Raziskali smo vpliv defektov bingljajočih vezi v dopiranih slojih hidrogeniziranega amorfnega silicija (p-a-Si:H in n-a-Si:H) 
v kombinaciji s kontakti iz indij-kositrovega oksida (ITO) pri heterospojnih silicijevih sončnih celicah (SHJ). Za raziskovanje notranjih 
in zunanjih lastnosti celice smo uporabili optoelektrične simulacije. Uporabljeni sodobni numerični model SHJ sončne celice je 
vseboval kontakte ITO, ki so bili modelirani kot dejanski polprevodniški sloji ter upošteval tuneliranje s pomočjo pasti, tuneliranje med 
energijskimi pasovi in tuneliranje znotraj energijskega pasu na heterospojih sončne celice. Spreminjali smo koncentracijo defektov 
bingljajočih vezi v p-a-Si:H in n-a-Si:H slojih pri dveh različnih elektronskih afinitetah kontaktov ITO na obeh straneh celice. Pokazali 
smo, da je vpliv defektov na izkoristek, polnilni faktor, napetost odprtih sponk in kratkostični tok bolj izražen, kadar elektronska afiniteta 
kontaktov ITO ni bila prilagojena dopiranim a-Si:H slojem. Ugotovili smo, da je zmanjšana učinkovitost zaradi povečanja gostote 
defektov bingljajočih vezi posledica zmanjšanja polnilnega faktorja in napetosti odprtih sponk, medtem ko kratkostični tok ni močno 
vplival na izkoristek znotraj izbranega območja variacije. Zmanjašanje polnilnega faktorja smo obrazložili preko upadanja napetosti pri 
maksimalni moči, ki se zmanjša še bolj občutno, kadar kontakti ITO niso optimizirani.
Ključne besede: heterospojne silicijeve sončne celice; optoelektrične simulacije; defektna stanja, elektronske afinitete
* Corresponding Author’s e-mail: jost.balent@fe.uni-lj.si 
Journal of Microelectronics, 
Electronic Components and Materials
Vol. 52, No. 2(2022), 129– 142
https://doi.org/10.33180/InfMIDEM2022.206
How to cite:
J. Balent et al., “Analysis of effects of dangling-bond defects in doped a-Si:H layers in heterojunction silicon solar cells with different elec-
tron affinities of ITO contacts", Inf. Midem-J. Microelectron. Electron. Compon. Mater., Vol. 52, No. 2(2022), pp. 129–142

130
J. Balent et al.; Informacije Midem, Vol. 52, No. 2(2022), 129 – 142
1 Introduction
The ever-growing demand for clean and affordable 
electrical energy opened up a substantial market for 
photovoltaics and other renewable energy technolo-
gies. In Photovoltaics the biggest market share (~95 %) 
belongs to the crystalline-silicon (c-Si) based solar-cell 
technology [1]. Of these, silicon heterojunction (SHJ) 
solar cells are gaining attraction with the potential to 
achieve high conversion efficiency, low temperature 
coefficients and competitive production costs. The 
current world-record efficiency of a c-Si-based ter-
restrial non-concentrating large area solar cell is 26.7 
% [2] and is achieved by the heterojunction structure 
in combination with interdigitated back contacting 
[3]. The SHJ cells utilize the benefits of both, conven-
tional (c-Si wafer-based) and thin-film (hydrogenated 
amorphous silicon - a-Si:H) technologies. A thorough 
understanding of the governing physical mechanisms 
in state-of-the-art structures of solar cells, such as SHJ, 
is crucial when designing cells at the limit of what is 
theoretically possible (~30 % for single junction de-
vices) [4]. Numerical modelling and simulations are an 
indispensable part of the R&D cycle as they unveil, of-
ten immeasurable, internal quantities of the solar cell, 
which determine its external characteristics. The study 
presented in this paper is based on detailed opto-elec-
trical modelling and simulations of SHJ solar cells. In 
particular, we analyse the effects of dangling bond de-
fects in doped a-Si:H layers in relation to indium tin ox-
ide (ITO) transparent conductive oxide (TCO) contacts 
with different electron affinities χ. Various numerical 
models emerged from the research of SHJ cells that 
vary in complexity and accuracy [5]–[14]. In this con-
tribution we used the Sentaurus TCAD software suite 
[15] to numerically model and study the device’s inter-
nal and external performance related to the mentioned 
effects for applied ITO electrodes with optimized and 
non-optimal electron affinities. While our previous 
work [16] was focused on combined effects of defect 
states at i-a-Si:H/c-Si interfaces and in p-doped a-Si:H 
(p-a-Si:H) and n-doped (n-a-Si:H) thin layers consider-
ing one pre-selected electron affinity of ITO layers, in 
this work we extend the study to structures where ITO 
contacts have different electron affinities (optimized 
and non-optimal). Solar cells with ITO/doped a-Si:H 
selective contacts have already been studied numeri-
cally [11], [17]–[21] however, the authors either used a 
Schottky barrier as a Dirichlet boundary condition to 
model the ITO contacts or focused on other parameters 
of ITO and a-Si:H. Studies have not been performed in 
relation to specific defect types in a-Si:H doped layers 
in combination with different work functions or elec-
tron affinities of ITO contacts. In our research we use a 
fully volumetric semiconductor model of ITO, including 
the accompanying trap-assisted (TAT), band-to-band 
(BBT) and direct tunnelling (DT) processes in simula-
tions. We focus our analysis primarily on the maximum-
power-point (MPP) operation of the solar cell, as this is 
the common operating condition of solar cells in a real 
scenario and is often not taken in consideration suffi-
ciently in such modelling studies. Quantitative results 
of the presented analysis reveal the impact of defects, 
in particular dangling-bond states in doped a-Si:H lay-
ers (especially in the p-a-Si:H layer) when using ITO con-
tacts with different electron affinities. It is necessary to 
study also the synergy between the defect states and 
the ITO electron affinity as they both have a big influ-
ence on the electronic state of the device (formation of 
the electric field needed for charge separation), which 
determines the efficiency of the cell. Additionally, the 
study aims to improve the physical understanding of 
the related effects. Simulation results are presented for 
the a-Si:H based selective contacts, however, the results 
can be usefully considered also in the design of the SHJ 
solar cells including novel materials for selective con-
tacts. e.g. metal-oxides and fluorides [8], [22]–[27].
2 Device structure and model
In our analysis we considered the following SHJ so-
lar cell structure (Fig. 1): ITO front cathode (70 nm), 
p-doped a-Si:H layer (p-a-Si:H, 10 nm), intrinsic a-Si:H 
passivation layer at p-side (i-a-Si:H, 5 nm), n-doped c-Si 
bulk absorber (n-c-Si, 150 μm) with interface regions 
at both i-a-Si:H/n-c-Si interfaces (2 nm), intrinsic a-Si:H 
passivation layer at n-side (i-a-Si:H, 5 nm), n-doped a-
Figure 1: Structure of the simulated solar cell. Optical 
simulations were done on the entire device whereas 
electrical simulations used ideal ohmic boundary con-
dition in lieu of the Aluminum layers.

131
Si:H layer (n-a-Si:H, 10 nm), rear anode ITO (100 nm)/
Al contact layer (500 nm). The ITO/p-a-Si:H and ITO/n-
a-Si:H layer stacks enable selective collection of gener-
ated holes and electrons at the cathode and anode, re-
spectively. The input parameters of layers and interface 
regions are described later.
The optical generation profile of the illuminated cell 
with standard AM1.5g spectrum was simulated with 
the SunShine simulator [28]. The coherent and incoher-
ent nature of light was accounted for in the thick and 
thin layers, respectively, together with the light scat-
tering and antireflection effects at the front and rear 
side of the device. Light enters into the device through 
the p-a-Si:H side (front) of the device in our basic case, 
however, selected simulation tests have been done 
also for the n-side illumination. In the simulated refer-
ence structure, the short-circuit current density (Jsc), 
calculated directly from optical generations in the n-
c-Si layer under AM1.5g solar spectrum, amounted to 
39.06 mA/cm
2
. The Optical generation profile was kept 
unchanged during sweeps of the investigated electri-
cal parameters (peak dangling bond defect density 
and doping of p-a-Si:H and n-a-Si:H layers, ITO elec-
tron affinity) to selectively indicate their effect on the 
solar cell performance. It should be noted that in this 
study we did not focus on the optical performance of 
the device. We chose the presented planar architecture 
instead of an interdigitated back-contact (IBC) solution 
to minimize external influences, such as lateral cur-
rents, normally present in IBC devices, to more clearly 
show the effects of defect density and ITO electron af-
finity on SHJ solar cell performance. Detailed optical 
simulations can be found elsewhere [10, 29]. 
Detailed electrical simulations of the device were per-
formed with the Sentaurus TCAD software suite [15], 
also used and validated for simulation of SHJ solar 
cell structures in previous publications [9], [10]. The 
material interfaces were generally considered as geo-
metrically flat in electrical simulations. The simulation 
domain in electrical simulations of the device was two-
dimensional, however, the problem at hand is one-di-
mensional. Therefore, the results of internal quantities 
were transformed in a one-dimensional function of 
the structure depth where applied. The temperature 
was kept at 300 K in all simulations. In the numerical 
description of the cell, the Drift-Diffusion model was 
employed to solve the Poisson equation coupled with 
the continuity equations for charge concentration in-
side the investigated solar cell structure. We used both 
Gummel and Newton solving schemes interchange-
ably to either ensure, or expedite the convergence of 
the simulations. The Fermi-Dirac statistics was used 
to accurately calculate free-charge density also in the 
regions of high effective dopant concentrations. Band-
gap narrowing and mobility dependence on dopant 
density was not included in the analysis, which short-
ened the simulation time with negligible effect on re-
sults as tested before for selected cases. The recombi-
nation of charge in the n-c-Si bulk was based on the 
parametrization first implemented by Richter et. al. 
[30], which includes both Auger and Radiative recom-
bination mechanisms and accurately calculates their 
impact on minority carrier life-times in a broad range 
of dopant concentrations and injection levels. The 
Shockley-Read-Hall (SRH) recombination in the n-c-Si 
bulk was modelled via life-time of minority carriers (10 
ms). In a-Si:H layers the defect states were represented 
by donor-like (don) and acceptor-like (acc) tail and dan-
gling-bond (db) states. The amphoteric nature of dan-
gling bonds was taken into account by two Gaussian 
functions, describing the so called +/0 and 0/- charged 
states [31]. The donor-like tail and the +/0 dangling-
bond states are positively charged when vacant and 
neutral when occupied by an electron. The acceptor-
like tail and so-called 0/- dangling-bond states are 
neutral when vacant and negatively charged when oc-
cupied by an electron. The defect-density distribution 
of tail-states (N
tail
) and dangling-bond states (N
db
) along 
the band-gap of the p-a-Si:H layer for the reference cell 
is presented in Fig. 2. 
Figure 2: Representation of defect-state distribution 
in a-Si:H layers of the reference cell (selected case is 
shown for the p-a-Si:H layer, see corresponding values 
of the parameters for all a-Si:H based layers in Table I). 
The red dashed and full lines present the donor-like tail 
and +/0 dangling-bond states. The blue dashed and full 
lines correspond to acceptor-like tail and 0/- dangling-
bond states.
However, all used defect-state parameters for the p-a-
Si:H, n-a-Si:H, i-a-Si:H layers, and the i-a-Si:H/n-c-Si in-
terface regions in the starting, reference cell are avail-
able in Table I. Regarding the defect-state variation, in 
this study we focused only on the values of the Gauss-
J. Balent et al.; Informacije Midem, Vol. 52, No. 2(2022), 129 – 142

132
ian peak concentrations (
 +/0
db-peak
N , 
 0/-
db-peak
N ) and not the 
tail states, since it was indicated that they have a no-
ticeable effect on device performance [16] including 
indium-tin-oxide (ITO). The defective n-c-Si surfaces (in 
simulations 2 nm regions) passivated by i-a-Si:H layers 
are described by dangling-bonds only, presented by 
two Gaussian peaks (see parameters in Table 1) and 
were also kept constant in this study. The ITO layers 
were modelled as semiconductor layers to fully encom-
pass the band alignment with the a-Si:H layers, thus, 
taking into account the band-bending in both materi-
als forming the heterojunction [17]. The electrical input 
parameters for ITO and all other layers are summarized 
in Table 2 in the Appendix.
Regarding the transport mechanisms at heterointer-
faces, the transport through the i-a-Si:H/n-c-Si (encir-
cled 1a and 2a in Fig. 3) heterojunctions is mediated by 
the inclusion of the built-in thermionic emission model 
[32], where for particle fluxes across the interface, the 
condition of continuous quasi-Fermi level and carrier 
temperature is used [33]. The thermionic emission at 
these interfaces is also supported by the trap-assisted 
tunnelling in our modelling approach [34], [35], which 
is also applied to the ITO/a-Si:H heterointerfaces (encir-
cled 1 and 2 in Fig. 3).
The dominant tunnelling transport depends on the 
shape of the barrier [11], [21]. The transport through 
the ITO/p-a-Si:H barrier was modelled accordingly by 
the trap-assisted and band-to-band tunnelling, where-
as at the ITO/n-a-Si:H interface by the trap-assisted and 
direct tunnelling. We used only non-local tunnelling 
models (variation of band energies and electric field 
over depth fully considered, guaranteed zero current 
at equilibrium). The use of non-local models is neces-
sary since simpler, local models tend to underestimate 
the tunnelling current at low electric fields [37]. Direct 
(intra-band) and band-to-band tunnelling are consid-
ered as a sum of elastic (momentum of the particle is 
constant along the tunnelling path) and in-elastic or 
phonon-assisted (momentum changes across the tun-
nelling path) mechanisms and are based on [38] and 
[39]. Trap-assisted tunnelling is modelled similarly as a 
sum of elastic [34] and in-elastic processes [35]. 
In the reference cell the p-a-Si:H and n-a-Si:H layers 
doping densities were set to 2e19 cm
-3
 and 1.5e19 cm
3
, 
corresponding to activation energies of 300 meV and 
200 meV, respectively. Their electron affinity was set to 
3.9 eV and their mobility-gaps to 1.65 eV and 1.72 eV, 
respectively. All other material and tunnelling param-
eters used for the reference case are presented in Table 
2 in the Appendix.
Table  1: Defect-state parameters for a-Si:H layers and i-a-Si:H/n-c-Si interfaces
Quantity Symbol p-a-Si:H n-a-Si:H i-a-Si:H i-a-Si/n-c-Si
Tails
Tail peak concentrations
(cm
-3
eV
-1
)
1e+21 / 1e+21
[12]
1e+21 / 1e+21
[12]
1e+18 / 1e+18
[12]
/
Tail slopes
don
tail tail
/
acc
σσ
(meV)
120 / 70
[12]
60 / 40
[12]
120 / 70
[12]
/
Tail capture cross-sections 
(charged/neutral)
ch n
tail tail
/ CC (cm
2
)
1e-16 / 1e-16
[12]
1e-16 / 1e-16
[12]
7e-15 / 7e-17
[12]
/
Dangling bonds
Dangling bonds peak 
Gaussian concentrations
/0
dbpeak
N
+
/
(cm
-3
eV
-1
)
1.9e+19 / 1.9e+19
[12]
*
2e+19 / 2e+19
[12]
*
1e+16 / 1e+16
[12]
2.5e+17 / 
2.5+e17
[36] 
Dangling bonds std.  
deviations
(meV)
200 / 200
[12]
200 / 200
[12]
150 / 150
[12]
200 / 200
[36] 
Dangling bonds capture 
cross-sections 
(charged/neutral)
ch n
db db
/ CC (cm
2
)
5e-14 / 5e-15
[12] / [5]
5e-14 / 5e-15
[12]
2e-14 / 2e-15
[12]
1e-18 / 1e-19
[36] 
Dangling bonds peak  
energies
(eV)
1.1 / 1.3
[12]
0.45 / 0.7
[12]
0.9 / 1.1
[12]
0.46 / 0.66
[36] 
* 
dbpeak
N
 
values were changed from the reference in order to obtain realistic activation energies (300 meV and 200 meV) 
for the p-a-Si:H and n-a-Si:H layers, respectively. 
J. Balent et al.; Informacije Midem, Vol. 52, No. 2(2022), 129 – 142
don acc
tailpeak tail-peak
/ N N
0/
db-peak
N
−
/0 0/-
db db
/ σσ
+
/0 0/-
db db
/ EE
+

133
3 Results and discussion
The goal of this analysis is to quantify and understand 
the effects related to different levels of defect states, in 
particular the dangling-bond Gaussian peaks (N
db-peak
), 
in the p-a-Si:H and n-a-Si:H layers in a SHJ solar cell, for 
different affinities of ITO contacts as well as different 
doping levels of the a-Si:H layers. 
We start the analysis with the energy band-diagrams 
of selected structures in thermal equilibrium (Fig. 3). 
The green, blue and red colours present the vacuum 
level, conduction and valence bands respectively. The 
fermi level is presented by the black line. Full lines 
depict the reference cell (parameters from Tables 1 
and 2). Electron affinity of ITO at both sides is marked 
(double-arrows) for the reference case. The electron af-
finities of ITOs in the reference cell at the p- and n-sides 
(χ
ITO p-side
 = 5.30 eV and χ
ITO n-side
  = 4.56 eV) of the device 
have been selected according to [40], presenting real-
istic values close to the optimum case with respect to 
the low work function mismatch (∆WF) between the 
ITOs and their adjacent doped a-Si:H layers (0.2 eV on 
both sides of the device) [19]. Please note that for our 
reference cell, to completely mitigate the mismatch of 
the work function just by manipulating the ITO elec-
tron affinity values, one would have to set them to 5.50 
eV and 4.36 eV for the p-side and n-side, respectively. 
This could be achieved only for the ITO on the n-side 
of the device, since min. and max. values of electron af-
finities at the selected doping levels of ITO correspond 
to 4.2 eV and 5.3 eV [40]. However, besides ITO, there 
are also other TCO’s that could be applied, namely Alu-
minum doped Zync-Oxide (AZO) and Antimony doped 
Tin-Oxide (ATO), as they both have high optical trans-
parency due to high band gaps (> 3.1 eV) and can be 
doped sufficiently to provide a low resistance contact 
[40]. Regarding the range of possible work functions, 
AZO work functions range from 3.1 eV to 4.5 eV and for 
ATO the range is from 3.8 eV to 5.2 eV [40]. Out of these 
three, ITO offers the highest possible work function of 
5.3 eV and is best suited for the ITO/p-a-Si:H contact 
stack. Other TCOs exhibit lesser optical or electrical pa-
rameters in comparison. A review of TCO material char-
acteristics and their application to various solar cells is 
available in [40] and [41], respectively. The alternative, 
non-optimal values for the electron affinities of ITOs 
was the same on both sides (χ
ITO p-side
 =  χ
ITO n-side
  = 4.93 eV) 
and resulted in a work-function mismatch of 0.57 eV 
(same for both sides). This type of symmetric mismatch 
allowed us to make a fair comparison between the two 
sides. During the analysis, we changed the electron af-
finity of ITO from its reference value to the non-optimal 
case on one side only, while maintaining the reference 
level on the other side. The dashed lines in Fig. 3 pre-
sent the energy bands of the case, in which we varied 
the electron affinity of ITO only on the p-side, while the 
dash-dot-dot lines present the variation on the n-side. 
Since similar conditions, with respect to the energetic 
barriers at the heterointerfaces occur also in the MPP 
condition, we did not show it in this graph for the sake 
of simplicity. At the p-side, the two barriers related to 
the heterojunctions hinder the flow of holes generated 
in the n-c-Si absorber towards the front ITO, whereas 
on the n-side they impede the flow of electrons toward 
the rear ITO contact.
Figure 3: Band-diagrams in thermal equilibrium of the 
SHJ cell with different electron affinities of ITO layers 
(χ
ITO
) at front (p-side) and rear (n-side) of the device (see 
values in the legend). The reference cell with optimal 
electron affinities of ITOs is presented by full lines. Sym-
bols E
V
, E
F 
, E
C
 and E
VAC
 correspond to the conduction-
band edge, Fermi level, valence-band edge and the 
vacuum level, respectively. Circled numbers 1, and 2 
mark the ITO/p-a-Si:H and ITO/n-a-Si:H interfaces, re-
spectively. Circled numbers 1a and 2a present the i-a-
Si:H/n-c-Si heterojunctions on the p- and n-side of the 
device, respectively.
In further analysis the N
db-peak
 parameter of p-a-Si:H 
and n-a-Si:H layer was chosen for variation since it was 
pointed out in our previous study that it has detrimen-
tal effect on device performance. The variation was 
done separately for p-a-Si:H and n-a-Si:H layer. In the 
presented simulation results we varied N
db-peak
 of both 
donor and acceptor states (0/- and +/0) simultaneously 
in a single layer. However, analysis showed that in the 
case of the p-a-Si:H layer the +/0 type of dangling-
bonds affects efficiency the most (see later discussion), 
whereas the n-a-Si:H layer is affected mostly by the 0/- 
type.
To illustrate and compare trends related to N
db-peak
 vari-
ation, a series of device simulations were performed 
where the N
db-peak
 peak value (height of Gaussian func-
tions) was varied independently of other defect state 
parameters. Besides the selected reference level of N
db-
J. Balent et al.; Informacije Midem, Vol. 52, No. 2(2022), 129 – 142

134
peak
 = 1.9e19 cm
-3
eV
-1
 and 2e19 cm
-3
eV
-1
 for the p-a-Si:H 
and n-a-Si:H, respectively, we also included an ideal-
ized case with zero N
db-peak
 (but tail states still present 
in the material) and the cases with strongly enhanced 
N
db-peak
 values up to and including 6e19 cm
-3
eV
-1
.
Besides electron affinities of ITO, two doping levels 
of p-a-Si:H and n-a-Si:H layers were also included in 
simulations (reference values and hypothetically high 
doping values of N
A
 = N
D
 = 3e19 cm
-3 
for p- and n-layer 
respectively). Note that the chosen value for the high 
levels of doping density presents a purely hypotheti-
cal case that cannot be achieved with normal a-Si:H 
material as they would result in the corresponding ac-
tivation energy values of ~0.2 eV and ~0.1 eV for the 
p-a-Si:H and n-a-Si:H layers, which is not achievable in 
praxis. This hypothetical case is used to indicate the ef-
fects related to materials where lower activation ener-
gies, and thus, higher effect of doping can be achieved, 
e.g. nano-crystalline silicon or other meta-materials 
such as metal oxides. With this hypothetical case we 
want to stress and quantify the importance of efficient 
doping of charge carrier selective layers in relation to 
different ITO contacts.
In Fig. 4a-b the black and red lines present cases with 
optimal (χ
ITO
 = 5.30 eV and 4.56 eV for the p-a-Si:H and 
n-a-Si:H layers respectively) and non-optimal electron 
affinity values of ITO layers (χ
ITO
 = 4.93 eV for both lay-
ers), respectively. The hypothetical case of high-doping 
values is presented with semi-transparent lines. The 
points on the graphs, presenting the reference case are 
also encircled.
The results presented in Fig 4a and 4b show that in gen-
eral the increase of N
db-peak
 starts to lower the efficiency 
of the device at all conditions, although the decreases 
start at different levels of defect states (N
db-peak
 values). 
Focusing first on the p-a-Si:H side of the cell (Fig 4a), in 
the case with nominal doping level and reference elec-
tron affinity of ITO at the p-side (full black line) we can 
observe that efficiency starts to rapidly drop, when N
db-
peak
 becomes greater than ~2e19 cm
-3
eV
-1
. Higher level 
of doping in this case (dashed semi-transparent black 
line) shifts this decline of efficiency to N
db-peak 
values of 
around 3.5e19 cm
-3
eV
-1
. In both cases, reducing the N
db-
peak 
parameter below the reference value will yield an 
increase in efficiency of less than 1 % when compared 
to the reference N
db-peak
. In case of nominal doping we 
increase the reference efficiency from 24.28 % to ~25 
% according to simulations. For higher doping this in-
crease is even less significant. Focusing now on the sec-
ond case, where the electron affinity of ITO at the p-side 
is not optimal and doping is nominal (full red line), we 
can observe that efficiency drops from the reference 
value of 24.28 % to 21.79 % even at the reference level 
of the N
db-peak
 parameter (1.9e19 cm
-3
eV
-1
). Additionally, 
we can see an even faster decline in efficiency as N
db-peak
 
parameter surpasses the 2e19 cm
-3
eV
-1 
mark. Of note is 
the observation, that in this case, reducing the N
db-peak
 
significantly below its reference level (1.9e19 cm
-3
eV
-1
) 
(a)
(b)
Figure 4: a) Efficiency vs. N
db-peak
 defect density varia-
tion in p-a-Si:H and b) in n-a-Si:H layer. Full lines rep-
resent nominal doping concentration of a-Si:H doped 
layers, whereas the dashed semi-transparent lines rep-
resent hypothetical high doping concentration (3e19 
cm
-3
). Cells with optimized values of the adjacent ITO 
electron affinity are presented by black curves (5.30 eV 
for the p-side and 4.56 eV for the n-side). Red curves 
present the non-optimal values (4.93 eV for both p- 
and n-side of the device). The case for the reference cell 
(Table 2, Appendix) is circled. It has to be noted that 
when the electron affinity of ITO is varied on one side of 
the device, the electron affinity of ITO at the other side 
is set to the reference (optimized) value.
J. Balent et al.; Informacije Midem, Vol. 52, No. 2(2022), 129 – 142

135
mitigates the negative effects of non-optimal electron 
affinity of ITO. Higher doping (dashed semi-transparent 
red line) has again a similar effect as before, as it de-
lays the onset and slows down the decline in efficiency 
until N
db-peak
 surpasses the 3.5e19 cm
-3
eV
-1
 mark. Reduc-
ing the defect density below 1.9e19 cm
-3
eV
-1 
does not 
significantly improve the efficiency also in this case. In 
general, the negative effects of increasing the defect 
density are amplified when ITO electron affinity is not 
optimized (high enough) for the p-a-Si:H layer. The ef-
fect can be mitigated by higher doping levels of the pa-
Si:H. Additional simulations showed that variation of 
the ITO band-gap has a much lower effect on efficiency 
than the electron affinity at different N
db-peak
 values (not 
shown here).
The general trends regarding sensitivity of efficiency 
to the N
db-peak
 parameter are similar also for the n-a-Si:H 
layer. Although, it can be observed in the reference case 
of electron affinities of ITO at the n-side that the effi-
ciency is much less sensitive to defects in the n-a-Si:H 
layer than that in the p-a-Si:H layer. Further simulation 
results (not shown in the graphs) revealed that this sen-
sitivity trend remains almost the same when the device 
is illuminated from either the p- or n-side, and is also 
independent of the doping type of the c-Si wafer (n- or 
p-type). Further on, for simulations where non-optimal 
selection of electron affinities (in this case χ
ITO
 = 4.93 eV) 
for the ITOs at both p- and n-side of the device (not in-
cluded in Fig. 4) the sensitivity of the efficiency to vari-
ations of N
db-peak
 in the p-a-Si:H and in the n-a-Si:H layer, 
surprisingly becomes comparable. It has to be noted 
that the differences between the reference (close to 
optimal) and the alternative values of the ITO electron-
affinity for both sides are the same but differ in the sign: 
∆ χ
ITO
 = 0.37 eV for the p-side and ∆ χ
ITO
 = -0.37 eV for 
the n-side. Additional simulations revealed that using 
an electron affinity value of 4.36 eV for the ITO at the 
n-side, which completely mitigates the work function 
mismatch, does not yield any increase in efficiency be-
cause the work function mismatch at the p-side already 
presents a bottle-neck even when an optimized value 
of electron affinity (5.3 eV) is used for ITO at the p-side.
A close comparison of the cases where non-optimal 
electron affinities were applied to ITOs on the p- and 
n-sides (red lines in Figs. 4a and 4b) and the N
db-peak 
 val-
ues were set to their reference values (1.9e19 cm
-3
eV
-1
 
and 2e19 cm
-3
eV
-1 
for p-a-Si:H and n-a-Si:H respectively) 
revealed a significant difference between the efficien-
cies (21.79 % and 24.06 % for the p- and n-side respec-
tively), despite the same work-function mismatch on 
both sides (∆WF=0.57 eV). This is due to a difference 
in the distribution of defect states in p-a-Si:H and n-a-
Si:H, with the distribution in p-a-Si:H affecting the cell 
more severely compared to n-a-Si:H [16]. Additionally, 
one can observe in Fig. 3, that the conduction band of 
the ITO and the valence band of p-a-Si:H do not over-
lap at the heterojunction (encircled 1 in Fig. 3), which 
means that BBT is not very efficient, thus the transport 
of charges across the barrier on the p-side is heavily 
dependent on TAT. On the n-side, however, the trans-
port across the barrier (encircled 2 in Fig. 3) relies on 
both TAT and Direct tunnelling, which makes the tun-
nelling on the n-side more efficient compared to the 
p-side [9], [11], [21] in this case. On a related note, opti-
mal electron affinity of the ITO on the p-side also brings 
the mentioned energy bands closer together when 
compared to the non-optimal case (Fig 3.), which not 
only decreases the work function mismatch, but also 
improves BBT tunnelling efficiency. The effect is even 
more pronounced when hypothetically high doping is 
applied to the p-a-Si:H as activation energy decreases 
and makes the bands come closer together even more 
(not shown in Fig. 3). In contrast, on the n-side (encir-
cled 2 in Fig. 3), the lower (optimal) value of the ITO 
electron affinity separates the conduction band of ITO 
from the valence band of n-a-Si:H even more, which 
does not affect the tunnelling noticeably, since BBT is 
not a factor on this side. However, it does lower the DT 
barrier height and improves the transport of electrons 
towards the anode. Similar to the p-side, this effect is 
even more pronounced when hypothetical levels of 
doping are applied. 
In order to see which tunnelling mechanism is domi-
nant at the ITO/p-a-Si:H and ITO/n-a-Si:H heterointer-
faces under various conditions (different electron af-
finities of ITO and various doping levels of the doped 
a-Si:H layers), we performed simulations where we 
applied only one tunnelling mechanism at the time 
at a specified ITO/a-Si:H heterointerface. The results 
showed, that TAT is the dominant tunnelling mecha-
nism at the ITO/p-a-Si:H heterointerface for both opti-
mal (5.3 eV) or non-optimal (4.93 eV) values of ITO elec-
tron affinity as well as for both realistic (2e19 cm
-3
) and 
hypothetical (3e19 cm
-3
) effective doping density lev-
els of the p-a-Si:H layer. Simulations indicated that the 
contribution of BBT is negligible compared to TAT in 
this case. These observations are also in accordance to 
predictions published in [21]. At the ITO/n-a-Si:H side, 
however, according to simulation results either TAT 
or DT on their own can provide a sufficient transport 
path and yield almost identical efficiencies for both ITO 
electron affinity values, as well as for both realistic and 
hypothetically high effective doping levels of the n-a-
Si:H layers.
Note, that the change in electron affinity of ITO affects 
(i) band offsets between the ITO and a-Si:H as well as 
(ii) the work function mismatch between the materials, 
that influences the space-charge-region (SCR) prop-
J. Balent et al.; Informacije Midem, Vol. 52, No. 2(2022), 129 – 142

136
erties of the ITO/a-Si:H heterointerface, which will be 
discussed later. At the p-a-Si:H side, an increase in elec-
tron affinity of ITO also increases band offsets, resulting 
in higher barriers for electrons and holes (see Fig. 3), 
which could potentially reduce tunnelling efficiency. 
However, we observed an increase in efficiency when 
electron affinity was increased, which means that the 
possible negative effects of increased band offsets are 
far outweighed by the positive effects of decreasing 
the work function mismatch. At the n-side, the reduc-
tion of electron affinity results in smaller band offsets 
as well as a reduction in the work function mismatch 
and higher efficiency as well. The results indicate, that 
changes in band offsets due to variation in electron af-
finity of ITO in the presented range do not significantly 
affect tunnelling efficiency at the ITO/a-Si:H interface, 
but the same changes in electron affinity define the 
work function mismatch, and thus affect the SCR prop-
erties of the interface, as will be explained later. Note, 
that tunnelling must be applied at ITO/a-Si:H heteroin-
terfaces for the cell to function properly, as explained 
in our previous publication [16]. We would like to state 
here, that tunnelling is already good enough in both 
cases of ITO electron affinity on both sides when defect 
density is not extremely high (N
db-peak
  <  3e19  cm
-3
eV
-1
 
as efficiency of the cell is above 20 % in those cases. 
Therefore, the main reasons for the observed efficiency 
trends when ITO electron affinity is varied and defect 
density is increased have to be related to other mecha-
nisms. 
To further examine and explain the efficiency trends 
presented in Fig. 4a, we show in Fig. 5a-c also simula-
tion results of the fill-factor (FF), short-circuit-current 
density (J
SC
) and open-circuit voltage (V
OC
) of the cell as 
a function of the N
db-peak
 parameter in the p-a-Si:H layer. 
From now on, we will focus on the p-side of the device, 
recognizing that the defects in the p-a-Si:H layer have 
a stronger impact on the performance of the device 
under the given circumstances. Similar to the previous 
figures, the black and red curves in Fig. 5a-c show cas-
es with optimal χ
ITO
 (5.30 eV on the p-side and 4.56 eV 
on the n-side), and non-optimal χ
ITO
 values (4.93 eV on 
both sides). The solid and dashed lines correspond to 
the nominal (2e19 cm
-3
) and hypothetically high (3e19 
cm
-3
) doping levels, respectively. The simulation point 
corresponding to the reference cell (Table 2, Appendix) 
is circled.
Detailed comparison between the graphs in Fig. 5 re-
veals that FF and V
OC
 are more sensitive to N
db-peak
, fol-
lowed by J
SC
. For the highly doped p-a-Si:H layer one 
can observe almost no decrease in J
SC
 even for extreme-
ly high N
db-peak
 values, which has to be considered as a 
hypothetical (idealised) case. These observations also 
corroborate the statement that tunnelling is sufficient 
regardless of the chosen ITO electron affinity values. 
Let us now examine the effects of dangling-bonds in 
the p-a-Si:H layer on J(V) curves for some selected cells 
considering nominal doping levels (N
A p-a-Si:H
 = 2e19 cm
-3
) 
in Fig. 5d. The grey line represents the reference cell 
(Tables 1, 2) with reference (optimal) electron affinity 
of ITOs and the reference N
db-peak
  =  1.9e19  cm
-3
eV
-1
 in 
p-a-Si:H. The black curve corresponds to the cell with 
increased N
db-peak
 = 2.5e19 cm
-3
eV
-1
, the remaining pa-
rameters are the same as for the reference cell (Tables 
1 and 2). The red curve presents the case with a non-
optimal electron affinity of ITO (χ
ITO p-a-Si:H
 = 4.93 eV) and 
increased N
db-peak
 . The selected curves reflect the trends 
observed for the related parameters (J
SC
, V
OC
, FF) in the 
region of moderate increase in N
db-peak
. J(V) curves in-
dicate that besides lower V
OC
, the FF decreased mostly 
due to the drop of the voltage at the maximum power 
point (V
MPP
) as indicated in the figure. The same gen-
eral trend is observed for all cells, with different elec-
tron affinity of ITO layers, however the scale of change 
is different. The drop in V
MPP
 is more pronounced when 
non-optimal electron affinity of ITO is used, and even 
more-so when defect states are increased. Of note is 
also the observation that applying non-optimal elec-
tron affinity of ITO alone decreases the FF in a similar 
manner as increasing only the defect states since V
MPP
 
drops in both cases.
We found that the explanation for the decrease of V
MPP
 
and V
OC
 can be related to the Poisson equation and 
how the total charge (free holes and electrons, ion-
ized dopants and trapped charge) determines the final 
voltage of the cell when electron affinity of ITO and 
dangling-bond defect states are varied. In our previ-
ous publication [16] we explained in great detail how 
the voltage drops due to increased defect density 
and related charge re-distribution as the electric field 
that is needed for charge separation becomes weaker. 
We also explained that work-function mismatch dic-
tates the amount of ionized ITO charge that needs to 
be screened in the adjacent a-Si:H layer in order to 
obtain a sufficient electric field in the c-Si bulk that is 
needed for charge separation and good MPP voltages 
[16]. When ITO with a non-optimal electron affinity is 
applied, as was the case here, the work function mis-
match is increased. Then, higher dangling-bond defect 
density reduces the charge-screening capability of the 
p-a-Si:H which leads to an even lower electric field and 
the observed trends of low V
MPP
 and V
OC
. 
Changes in electron affinity of ITO directly affect the 
ITO work function. When the work function of ITO is 
smaller than that of p-a-Si:H (the difference is referred 
to as work function mismatch), electrons (mediated by 
tunnelling) flow from ITO toward p-a-Si:H and a posi-
tively charged part of the space-charge-region (SCR) is 
J. Balent et al.; Informacije Midem, Vol. 52, No. 2(2022), 129 – 142

137
weaker electric field (needed for charge separation) in 
the n-c-Si absorber when the SCR is not well contained 
in the p-a-Si:H. The mentioned changes affect the re-
distribution of charges throughout the device, which 
also determines the external voltage. 
In order to mitigate the negative effect of the work 
function mismatch, that lowers the voltage (V
MPP
 and 
V
OC
) and FF, at the ITO/p-a-Si:H (n-a-Si:H) heterointer-
face, the negative (positive) charge in the p-a-Si:H (n-a-
Si:H) layer must be able to screen the opposite charge 
in the SCR of ITO. The screening capability of a-Si:H de-
Figure 5: a) FF, b) V
OC
, c) J
SC
 vs. N
db-peak
 defect-density variation in the p-a-Si:H layer. Full lines correspond to nominal 
doping density of p-a-Si:H layer (2e19 cm
-3
), whereas dashed lines represent the device with high doping density 
N
A p-a-Si:H
 = 3e19 cm
-3
). Devices with reference (optimal) values of the ITO electron affinities are presented by black 
curves (χ
ITO
 = 5.3 eV for the p-side and 4.56 eV for the ITO at the n-side). Red curves correspond to cases where ITOs 
are not optimal (χ
ITO
 = 4.93 eV for both p- and n-side of the device). The legend in a) applies also to b) and c). d) J(V) 
curve for the reference cell (grey) and selected cases with high N
db-peak
 (2.5e19 cm
-3
eV
-1
) and ITO electron affinity at 
the p-side set to 5.30 eV (black) and 4.93 eV (red). All presented cases were simulated at nominal doping level of the 
p-a-Si:H layer (2e19 cm
3
).
(a)
(c)
(b)
(d)
formed on the ITO side of the ITO/p-a-Si:H heterojunc-
tion (due to ionized donor atoms), whereas the nega-
tively charged part of the SCR forms in the p-a-Si:H due 
to ionized acceptor dopants and neutralized +/0 states 
(that are now occupied by electrons that came from 
ITO and no longer contribute to the positive charge). 
The resulting electric field is oriented in the opposite 
direction than the electric field at the i-a-Si:H/n-c-Si 
heterojunction. As the work function mismatch is in-
creased, the SCR is broadened even deeper into the 
p-a-Si:H region. The broadening of this SCR is actu-
ally depleting the p-a-Si:H layer, which can result in a 
J. Balent et al.; Informacije Midem, Vol. 52, No. 2(2022), 129 – 142

138
pends on effective doping concentration, defect den-
sity and layer thickness. Thicker layers with high doping 
concentrations and low defect density are capable of 
screening more ITO charge. The increase in dangling-
bond defect density mitigates the positive effect of 
doping and reduces the screening capability of the 
layer. In addition, as we discussed in our previous pub-
lication [16], an increase in peak dangling-bond defect 
density (N
db-peak
) in the p-a-Si:H layer reduced both V
OC
 
and FF, whereas J
SC
 changed only slightly. The drop in FF 
was explained by lowering of the V
MPP
, whereas J
MPP
 was 
observed to be almost unaffected, since at MPP con-
ditions, total recombination was still far smaller com-
pared to optically generated current. We concluded, 
that an increase in N
db, peak
 reduces efficiency especially 
due to lower V
MPP
 (
SC OC MPP MPP
in in
J V FF JV
Eff
PP
⋅⋅ ⋅
== ). 
To explain the drop in V
MPP
 we followed the Poisson’s 
equation, which relates charge distribution to the volt-
age between the terminals. A thorough analysis of total 
charge and all of its components (free charge, trapped 
charge in defect states and ionized dopant atoms) re-
vealed that the increase in N
db-peak
 in p-a-Si:H resulted in 
a reduction of positive charge in the SCR of ITO and a 
reduction of negative charge in the SCR of p-a-Si:H. The 
reduction of negative charge in p-a-Si:H was shown to 
be an increase in positive charge in the p-a-Si:H layer 
due to unoccupied +/0 dangling-bond states, that 
are positioned at energies where they are unlikely to 
be occupied by an electron and remained positively 
charged. We used the Poisson’s equation and showed, 
that this virtual shift of positive charge from ITO into 
the p-a-Si:H layer due to an increase in N
db-peak
 resulted 
in the observed reduction in V
MPP
. We also showed, that 
0/- states remained neutral and did not significantly af-
fect the total charge in p-a-Si:H. All of the above is true 
also for all the cases presented in this work (both dop-
ing levels and dangling-bond defect densities).
Before moving on to conclusions, we would like to pro-
vide a brief commentary regarding the reference effi-
ciency of our simulated device (24.28 %), where both 
ITO layers have optimal electron affinity values (5.3 
eV and 4.56 eV for the p- and n-side, respectively). It 
has been reported that SHJ cells have the potential to 
reach efficiencies as high as ~27 % [9]. However, this 
can be achieved by employing additional layers, such 
as p-type SiC
x
 or SiO
x
 and using the IBC architecture. 
Without these additional layers, the record cell, made 
by Kaneka, reached efficiency of 26.7 % [42], thanks to 
the IBC design, that allows for high J
SC
 = 42.65 mA/cm
2
. 
In comparison, our reference cell, that uses optimized 
ITO layers, achieves J
SC
 = 39.02 mA/cm
2
. Should we cal-
culate the efficiency of our reference cell, by using the 
J
SC 
of the record cell, we would get efficiency around 
26.5 %, which is also in accordance to the simulations 
presented in other publications that were simulating 
and optimizing IBC SHJ solar cells [9]. Therefore, the 
difference between the efficiencies of IBC and planar 
architectures can be mostly attributed to better J
SC
 of 
IBC devices. In addition, the V
OC
 and FF values of our ref-
erence cell simulations are very similar to the ones re-
ported for the record cell and comparable to the ones 
presented in [9].
4 Conclusion
We applied opto-electrical modelling of a SHJ solar cell 
to study ITO/doped a-Si:H selective contacts in terms 
of ITO electron affinity and dangling-bond Gaussian 
peaks (amphoteric defects) of the doped a-Si:H layers. 
In the simulation structure, the ITO layer at the p- and 
n-side of the device was considered as a full semicon-
ductor layer. DT, BBT and TAT tunnelling mechanisms 
were included in simulations at ITO/doped a-Si:H se-
lective contacts. We demonstrated that optimizing the 
electron affinity of the ITO layers is critical when the 
doped a-Si:H layers are insufficiently doped or have 
high concentrations of dangling-bond defect states. 
We showed that optimization of electron affinity of ITO 
is especially important at the p-side of the device due 
to a less favourable trap distribution and poorer tun-
nelling efficiency compared to the n-side. We showed 
that the ITO at the p-a-Si:H layer should have electron 
affinity as high as possible (~5.3 eV) in order to mini-
mize the work function mismatch (which was only 0.2 
eV in this case), as higher values of the work function 
mismatch can deplete the p-a-Si:H layer to the point, 
where it is unable to sufficiently screen the positive 
charge in the space-charge-region of ITO, resulting in 
a diminished electric field in the n-c-Si absorber, and 
consequently poor charge separation capability of the 
cell, leading to a reduction in FF and V
OC
. Conversely, 
the ITO at the n-a-Si:H layer should have electron affin-
ity as low as 4.56 eV (work function mismatch is 0.2 eV 
in this case). Lower values of electron affinity enabling 
lower work function mismatch on the n-side did not 
further improve efficiency, due to the already present 
work function mismatch at the p-side (0.2 eV in the 
optimal case). Low values of V
OC
 also confirmed poor 
charge-separation capability of the cell, when electron 
affinity of ITO results in a higher work function mis-
match between the ITOs and doped a-Si:H layers. We 
demonstrated that the work function mismatch be-
tween ITO and doped a-Si:H layers makes the solar cell 
efficiency more sensitive to increased dangling-bond 
defect states in the doped a-Si:H layers as higher dan-
gling-bond defect density reduces the layers’ ability to 
screen the charge in the SCR of ITO as it negates the 
positive effect of doping. We also observed that when 
J. Balent et al.; Informacije Midem, Vol. 52, No. 2(2022), 129 – 142

139
ITO electron affinity at the p-a-Si:H (n-a-Si:H) layer is 
lower than 5.3 eV (higher than 4.56 eV) and doping is 
nominal (2e19 cm
-3
 and 1.5e19 cm
-3
 for p-a-Si:H and n-
a-Si:H, respectively), only the FF (and not V
OC
 or J
SC
) can 
be improved by lowering the dangling-bond defect 
density below the reference level (1e19 cm
-3
eV
-1
). In 
contrast, J
SC
 was affected only at extremely high levels 
of defect densities even when electron affinity of ITO 
at the p-a-Si:H (n-a-Si:H) was lower (higher) than 5.3 eV 
(4.56 eV). We also concluded that tunnelling efficiency 
at the ITO/a-Si:H interface is not significantly affected 
by the changes in the band offsets, caused by variation 
in electron affinity of ITO, whereas the changes in the 
work function mismatch, as the SCR properties of the 
heterointerface were changed, affected the cell sig-
nificantly. An increase in electron affinity of ITO at the 
p-a-Si:H layer results in increased conduction and va-
lence band offsets, but the reduction in work function 
mismatch outweighs the negative impact of increased 
barrier heights and an increase in efficiency was ob-
served, whereas a reduction in electron affinity of ITO 
at the n-a-Si:H layer results in even lower band offsets 
as well as a reduction in work function mismatch. It 
was also shown that TAT is the dominant transport 
mechanism at the ITO/p-a-Si:H heterojunction for all 
presented cases. At the ITO/n-a-Si:H interface, both DT 
and TAT provide an efficient transport path and yield 
very similar results when either of the two is applied 
as the only tunnelling mechanism at that interface. 
Results presented in this paper give indications for 
acceptable defect levels in doped amorphous-silicon 
layers in relation to optimality of ITO electron affinity 
for the ITO/a-Si:H selective contacts and can serve as a 
roadmap when designing selective contacts with alter-
native materials for SHJ cells.
Table 2: Input parameters for the reference case
Quantity Symbol n-c-Si p-a-Si:H n-a-Si:H i-a-Si:H i-a-Si:H/n-c-Si ITO
Relative Dielectric 
Constant
e r
11.9
[43]
11.9
[43]
11.9
[43]
11.9
[43]
11.9
[43]
8.9
[44]
Electron Affinity
χ 
(eV)
4.05
[12]
3.9
[12]
3.9
[12]
3.9
[12]
4.05
[12]
5.3 / 4.56 
(p-side/n-side)
[40]
Band-gap 
(Mobility-gap)
E
gap
 
(eV)
1.12
[36] 
1.65
[12]
1.72
[12]
1.70
[12]
1.12
[36]
3.7
[9]
Effective Doping 
Conc.
DA
/ NN
(cm
-3
)
2e+15 / 0
[12]
0 / 2e+19
[12]
1.5e+19 / 0
[12] *
2.2e+15 / 0
[12]
2e+15 / 0
[12]
1e+20 / 0
[9]
Density of States
CV
/ NN
(cm
-3
)
2.8e+19 
/ 
3.1e+19
[43]
2e+20 
/ 
2e+20
[43]
2e+20 
/ 
2e+20
[43]
2e+20 
/ 
2e+20
[43]
2.8e+19 
/ 
3.1e+19
[43]
4.12e+18 
/ 
1.17e+19
[44], [45]
SRH 
life-times
eh
/ ττ
(ms)
1 / 10
[36]
/ / /
1/10
[36]
/
Mobilities
eh
/ µµ
 
(cm
2
/Vs)
1342 / 452
[43]
10 / 1
[12]
10 / 1
[12]
10 / 1
[12]
1342 / 452
[43]
50 / 30
[9]
Tunnelling mass 
(DT, TAT and BBT)
m* /
0.1
[9]
0.1
[9]
0.1
[9]
0.1
[9]
0.1
[9]
Trap volume  
( TAT )
V
trap
 
(μm
-3
)
/
1e-11
[8]
1e-11
[8]
1e-11
[8]
1e-11
[8]
/
Huang-Rhys con. 
( TAT )
H
rhys
/
2
[8]
2
[8]
2
[8]
2
[8]
/
Phonon Energy 
( TAT )
E
ph
 
(meV)
/
37.78
[8]
37.78
[8]
37.78
[8]
37.78
[8]
/
Coupling factor 
(DIRECT, BBT)
g
e
/g
h
/
1 / 1
[9]
1 / 1
[9]
1 / 1
[9]
1 / 1
[9]
1 / 1
[9]
* Effective doping concentration was changed from the reference to obtain realistic activation energy for the n-a-Si:H 
layer (200 meV)
5 Appendix
J. Balent et al.; Informacije Midem, Vol. 52, No. 2(2022), 129 – 142

140
6 Acknowledgments
The authors acknowledge the financial support from 
the Slovenian Research Agency-ARRS (program P2-
0415 and PhD funding for J.B.).
7 References
1. F. ISE, ‘Photovoltaics Report’ , 2020. [Online]. Avail-
able: https://www.ise.fraunhofer.de/content/
dam/ise/de/documents/publications/studies/
Photovoltaics-Report.pdf
2. M. A. Green, E. D. Dunlop, J. Hohl‐Ebinger, M. 
Yoshita, N. Kopidakis, and X. Hao, ‘Solar cell effi-
ciency tables (version 56)’ , Progress in Photovolta-
ics: Research and Applications, vol. 28, no. 7, pp. 
629–638, 2020, 
 https://doi.org/10.1002/pip.3303.
3. K. Yoshikawa et al., ‘Silicon heterojunction solar 
cell with interdigitated back contacts for a pho-
toconversion efficiency over 26%’ , Nature Energy, 
vol. 2, p. 17032, Mar. 2017.
4. A. Richter, M. Hermle, and S. W. Glunz, ‘Reassess-
ment of the Limiting Efficiency for Crystalline Sili-
con Solar Cells’ , IEEE Journal of Photovoltaics, vol. 3, 
no. 4, pp. 1184–1191, Oct. 2013, 
 https://doi.org/10.1109/JPHOTOV.2013.2270351.
5. H. Bashiri, M. A. Karami, and S. M. Nejad, ‘Hetero-
junction silicon solar cells performance optimi-
zation and sensitivity reduction to the interface 
defect states’ , Mater. Res. Express, vol. 4, no. 12, p. 
126308, Dec. 2017, 
 https://doi.org/10.1088/2053-1591/aa9c91.
6. M. Filipič, Z. C. Holman, F. Smole, S. D. Wolf, C. 
Ballif, and M. Topič, ‘Analysis of lateral transport 
through the inversion layer in amorphous silicon/
crystalline silicon heterojunction solar cells’ , J Appl 
Phys, vol. 114, no. 7, p. 074504, Aug. 2013, 
 https://doi.org/10.1063/1.4818709.
7. A. Kanevce and W. K. Metzger, ‘The role of amor-
phous silicon and tunneling in heterojunction 
with intrinsic thin layer (HIT) solar cells’ , Journal of 
Applied Physics, vol. 105, no. 9, pp. 094507–1, May 
2009, 
 https://doi.org/10.1063/1.3106642.
8. C. Messmer, M. Bivour, C. Luderer, L. Tutsch, J. 
Schon, and M. Hermle, ‘Influence of Interfacial Ox-
ides at TCO/Doped Si Thin Film Contacts on the 
Charge Carrier Transport of Passivating Contacts’ , 
IEEE J. Photovoltaics, vol. 10, no. 2, pp. 343–350, 
Mar. 2020, 
 https://doi.org/10.1109/JPHOTOV.2019.2957672.
9. P . Procel, G. Yang, O. Isabella, and M. Zeman, ‘The-
oretical evaluation of contact stack for high effi-
ciency IBC-SHJ solar cells’, Solar Energy Materials 
and Solar Cells, vol. 186, pp. 66–77, Nov. 2018, 
 https://doi.org/10.1016/j.solmat.2018.06.021.
10. P . Procel et al., ‘Opto-electrical modelling and op-
timization study of a novel IBC c-Si solar cell’ , Pro-
gress in Photovoltaics: Research and Applications, 
vol. 25, no. 6, pp. 452–469, Jun. 2017, 
 https://doi.org/10.1002/pip.2874.
11. P. Procel et al., ‘On the correlation between con-
tact resistivity and high efficiency in (IBC-) SHJ so-
lar cells’, 36th European Photovoltaic Solar Energy 
Conference and Exhibition, pp. 251–254, 2019.
12. Z. Shu, U. Das, J. Allen, R. Birkmire, and S. Hege-
dus, ‘Experimental and simulated analysis of front 
versus all-back-contact silicon heterojunction so-
lar cells: effect of interface and doped a-Si:H layer 
defects’ , Prog. Photovolt: Res. Appl., vol. 23, no. 1, 
pp. 78–93, Jan. 2015, 
 https://doi.org/10.1002/pip.2400.
13. R. Varache, J. P . Kleider, M. E. Gueunier-Farret, and 
L. Korte, ‘Silicon heterojunction solar cells: Opti-
mization of emitter and contact properties from 
analytical calculation and numerical simulation’, 
Materials Science and Engineering: B, vol. 178, no. 
9, pp. 593–598, May 2013, 
 https://doi.org/10.1016/j.mseb.2012.11.011.
14. M. Vukadinović, F. Smole, M. Topič, R. E. I. Schropp, 
and F. A. Rubinelli, ‘Transport in tunneling recom-
bination junctions: A combined computer simu-
lation study’ , Journal of Applied Physics, vol. 96, no. 
12, pp. 7289–7299, Dec. 2004, 
 https://doi.org/10.1063/1.1811375.
15. Synopsys, ‘Sentaurus
TM
 Device User Guide: Re-
lease Q-2019.12’ . 2019. [Online]. Available: http://
www.synopsys.com
16. J. Balent, F. Smole, M. Topic, and J. Krc, ‘Numerical 
Analysis of Selective ITO/a-Si:H Contacts in Het-
erojunction Silicon Solar Cells: Effect of Defect 
States in Doped a-Si:H Layers on Performance Pa-
rameters’ , IEEE J. Photovoltaics, pp. 1–14, 2021, 
 https://doi.org/10.1109/JPHOTOV.2021.3063019.
17. M. Bivour, S. Schröer, and M. Hermle, ‘Numeri-
cal Analysis of Electrical TCO / a-Si:H(p) Contact 
Properties for Silicon Heterojunction Solar Cells’, 
Energy Procedia, vol. 38, pp. 658–669, Dec. 2013, 
 https://doi.org/10.1016/j.egypro.2013.07.330.
18. S. Kirner et al., ‘The Influence of ITO Dopant Densi-
ty on J-V Characteristics of Silicon Heterojunction 
Solar Cells: Experiments and Simulations’ , Energy 
Procedia, vol. 77, pp. 725–732, Aug. 2015, 
 https://doi.org/10.1016/j.egypro.2015.07.103.
19. M. Mikolášek, ‘Silicon Heterojunction Solar Cells: 
The Key Role of Heterointerfaces and their Impact 
on the Performance’ , in Nanostructured Solar Cells, 
N. Das, Ed. InTech, 2017. 
 https://doi.org/10.5772/65020.
J. Balent et al.; Informacije Midem, Vol. 52, No. 2(2022), 129 – 142

141
20. L. Zhao, C. L. Zhou, H. L. Li, H. W. Diao, and W. J. 
Wang, ‘Role of the work function of transparent 
conductive oxide on the performance of amor-
phous/crystalline silicon heterojunction solar 
cells studied by computer simulation’, phys. stat. 
sol. (a), vol. 205, no. 5, pp. 1215–1221, May 2008, 
 https://doi.org/0.1002/pssa.200723276.
21. P. Procel et al., ‘The role of heterointerfaces and 
subgap energy states on transport mechanisms 
in silicon heterojunction solar cells’, Progress in 
Photovoltaics: Research and Applications, vol. 28, 
no. 9, pp. 935–945, Sep. 2020, 
 https://doi.org/0.1002/pip.3300.
22. J. Bullock et al., ‘Efficient silicon solar cells with 
dopant-free asymmetric heterocontacts’, Nature 
Energy, vol. 1, no. 3, p. 15031, Jan. 2016, 
 https://doi.org/10.1038/nenergy.2015.31.
23. R. Islam, P . Ramesh, Ju Hyung Nam, and K. C. Sar-
aswat, ‘Nickel oxide carrier selective contacts for 
silicon solar cells’ , Jun. 2015, pp. 1–4. 
 https://doi.org/10.1109/PVSC.2015.7355921.
24. M. Mews, A. Lemaire, and L. Korte, ‘Sputtered 
Tungsten Oxide as Hole Contact for Silicon Het-
erojunction Solar Cells’ , IEEE Journal of Photovolta-
ics, vol. 7, no. 5, pp. 1209–1215, Sep. 2017, 
 https://doi.org/10.1109/JPHOTOV.2017.2714193.
25. D. Sacchetto et al., ‘ITO/MoOx/a-Si:H(i) Hole-Se-
lective Contacts for Silicon Heterojunction Solar 
Cells: Degradation Mechanisms and Cell Integra-
tion’ , IEEE Journal of Photovoltaics, vol. 7, no. 6, pp. 
1584–1590, Nov. 2017, 
 https://doi.org/10.1109/JPHOTOV.2017.2756066.
26. Y. Wan et al., ‘Magnesium Fluoride Electron-Se-
lective Contacts for Crystalline Silicon Solar Cells’ , 
ACS Applied Materials & Interfaces, vol. 8, no. 23, 
pp. 14671–14677, Jun. 2016, 
 https://doi.org/10.1021/acsami.6b03599.
27. W. Yoon et al., ‘Hole-selective molybdenum oxide 
as a full-area rear contact to crystalline p-type Si 
solar cells’ , Japanese Journal of Applied Physics, vol. 
56, no. 8S2, p. 08MB18, Aug. 2017, 
 https://doi.org/10.7567/JJAP .56.08MB18.
28. J. Krč, S. Franc, and T. Marko, ‘One-dimensional 
semi-coherent optical model for thin film solar 
cells with rough interfaces’ , in Informacije MIDEM 
32, Ljubljana, 2002, vol. 2002.
29. Z. Lokar et al., ‘Coupled modelling approach for 
optimization of bifacial silicon heterojunction so-
lar cells with multi-scale interface textures’ , Optics 
Express, vol. 27, no. 20, p. A1554, Sep. 2019, 
 https://doi.org/10.1364/OE.27.0A1554.
30. A. Richter, S. W. Glunz, F. Werner, J. Schmidt, and 
A. Cuevas, ‘Improved quantitative description of 
Auger recombination in crystalline silicon’, Phys. 
Rev. B, vol. 86, no. 16, p. 165202, Oct. 2012, 
 https://doi.org/10.1103/PhysRevB.86.165202.
31. S. Olibet, E. Vallat, and C. Ballif, ‘Model for a-Si:H/C-
Si interface recombination based on the ampho-
teric nature of silicon dangling bonds’, Physical 
Review B, vol. 76, Jul. 2007, 
 https://doi.org/10.1103/PhysRevB.76.035326.
32. D. Schroeder, Modelling of Interface Carrier Trans-
port for Device Simulation. Vienna: Springer Vien-
na, 1994. 
 https://doi.org/10.1007/978-3-7091-6644-4.
33. K. Horio and H. Yanai, ‘Numerical modeling of het-
erojunctions including the thermionic emission 
mechanism at the heterojunction interface’, IEEE 
Trans. Electron Devices, vol. 37, no. 4, pp. 1093–
1098, Apr. 1990, 
 https://doi.org/10.1109/16.52447.
34. F. Jiménez-Molinos, F. Gámiz, A. Palma, P. Car-
tujo, and J. A. López-Villanueva, ‘Direct and trap-
assisted elastic tunneling through ultrathin gate 
oxides’ , Journal of Applied Physics, vol. 91, no. 8, pp. 
5116–5124, Apr. 2002, 
 https://doi.org/10.1063/1.1461062.
35. A. Palma, A. Godoy, J. A. Jiménez-Tejada, J. E. 
Carceller, and J. A. López-Villanueva, ‘Quantum 
two-dimensional calculation of time constants of 
random telegraph signals in metal-oxide–semi-
conductor structures’ , Phys. Rev. B, vol. 56, no. 15, 
pp. 9565–9574, Oct. 1997, 
 https://doi.org/10.1103/PhysRevB.56.9565.
36. A. Fell et al., ‘Input Parameters for the Simulation 
of Silicon Solar Cells in 2014’ , IEEE Journal of Photo-
voltaics, vol. 5, no. 4, pp. 1250–1263, Jul. 2015, 
 https://doi.org/10.1109/JPHOTOV.2015.2430016.
37. M. Baudrit and C. Algora, ‘Tunnel Diode Modeling, 
Including Nonlocal Trap-Assisted Tunneling: A Fo-
cus on III–V Multijunction Solar Cell Simulation’, 
IEEE Transactions on Electron Devices, vol. 57, no. 
10, pp. 2564–2571, Oct. 2010, 
 https://doi.org/10.1109/TED.2010.2061771.
38. MeiKei Ieong, P. M. Solomon, S. E. Laux, H.-S. P. 
Wong, and D. Chidambarrao, ‘Comparison of 
raised and Schottky source/drain MOSFETs us-
ing a novel tunneling contact model’ , in Interna-
tional Electron Devices Meeting 1998. Technical Di-
gest (Cat. No.98CH36217), San Francisco, CA, USA, 
1998, pp. 733–736. 
 https://doi.org/10.1109/IEDM.1998.746461.
39. E. O. Kane, ‘Theory of Tunneling’ , Journal of Applied 
Physics, vol. 32, no. 1, pp. 83–91, Jan. 1961, 
 https://doi.org/10.1063/1.1735965.
40. A. Klein et al., ‘Transparent Conducting Oxides for 
Photovoltaics: Manipulation of Fermi Level, Work 
Function and Energy Band Alignment’ , Materials, 
vol. 3, no. 11, pp. 4892–4914, Nov. 2010, 
 https://doi.org/10.3390/ma3114892.
41. E. Fortunato, D. Ginley, H. Hosono, and D. C. Paine, 
‘Transparent Conducting Oxides for Photovol-
J. Balent et al.; Informacije Midem, Vol. 52, No. 2(2022), 129 – 142

142
taics’ , MRS Bull., vol. 32, no. 3, pp. 242–247, Mar. 
2007, 
 https://doi.org/10.1557/mrs2007.29.
42. M. A. Green, E. D. Dunlop, J. Hohl‐Ebinger, M. 
Yoshita, N. Kopidakis, and A. W. Y. Ho‐Baillie, ‘Solar 
cell efficiency tables (Version 55)’ , Progress in Pho-
tovoltaics: Research and Applications, vol. 28, no. 1, 
pp. 3–15, Jan. 2020, 
 https://doi.org/10.1002/pip.3228.
43. M. Filipic, F. Smole, and M. Topic, ‘Optimization of 
interdigitated back contact geometry in silicon 
heterojunction solar cell’ , in Numerical Simulation 
of Optoelectronic Devices, 2014, Palma de Mallor-
ca, Sep. 2014, pp. 161–162. 
 https://doi.org/10.1109/NUSOD.2014.6935406.
44. L. Gupta, A. Mansingh, and P . K. Srivastava, ‘Band 
gap narrowing and the band structure of tin-
doped indium oxide films’, Thin Solid Films, vol. 
176, no. 1, pp. 33–44, Sep. 1989, 
 https://doi.org/10.1016/0040-6090(89)90361-1.
45. F. Fuchs and F. Bechstedt, ‘Indium-oxide poly-
morphs from first principles: Quasiparticle elec-
tronic states’ , Phys. Rev. B, vol. 77, no. 15, p. 155107, 
Apr. 2008, 
 https://doi.org/10.1103/PhysRevB.77.155107.
Arrived: 11. 03. 2022
Accepted: 08. 07. 2022
J. Balent et al.; Informacije Midem, Vol. 52, No. 2(2022), 129 – 142
Copyright © 2022 by the Authors. 
This is an open access article dis-
tributed under the Creative Com-
mons Attribution  (CC BY) License (https://creativecom-
mons.org/licenses/by/4.0/), which permits unrestricted 
use, distribution, and reproduction in any medium, 
provided the original work is properly cited.