Modeling study of mesh conductors and their electroluminescent devices

Bin Hu,1,a) Dapeng Li,2 Prakash Manandhar,2 Qinguo Fan,2 Dayalan Kasilingam,3

and Paul Calvert21Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755, USA2Department of Bioengineering, University of Massachusetts Dartmouth, North Dartmouth,Massachusetts 02747-2300, USA3Department of Electrical and Computer Engineering, University of Massachusetts Dartmouth,North Dartmouth, Massachusetts 02747-2300, USA

(Received 20 November 2014; accepted 10 February 2015; published online 18 February 2015)

Numerical models were established to correlate with the experimentally measured properties of

mesh conductors previously developed through a combined process of dip coating carbon

nanotubes and inkjet printing poly 3,4-ethylenedioxythiophene: poly styrene sulfonate. The

electroluminescent (EL) devices assembled with such mesh conductors as front electrodes were

modeled by commercially available finite element method software COMSOL Multiphysics. The

modeling results are in agreement with those from the experiments and suggest that an optimized

fiber arrangement is the key for further improving the performance of EL devices based on mesh

conductors. VC 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4913305]

Flexible optoelectronic devices such as light-emitting

diodes,1 photodetectors,2 and photovoltaic cells3,4 have

attracted much interest because of their resilience, low

weight, and lower cost. An important component of an opto-

electronic device is the transparent conductor. Indium tin ox-

ide (ITO) is widely used as a transparent conductor.

However, ITO has the drawbacks of being expensive and

fragile and therefore has limited use on flexible substrates.5

A substitute of ITO with similar performance but lower cost

and flexibility is needed. Transparent conductors have been

made using carbon nanotubes,6 metal nanowires,7 and gra-

phene.8–10 However, these mostly do not combine flexibility

with transparency and conductivity.

Electronic textiles have recently gained much attention

due to their inherently low stiffness. There is a strong interest

in flexible, lightweight, and wearable electronics.11–13

Textile based flexible solar cells,14–16 transistors,17–19 con-

ductive wires,13 stretchable electrochromic devices,20,21 and

supercapacitors11,22 have been demonstrated.

Previous studies in our group have integrated conductive

polymers and CNT into textiles to fabricate conducting

meshes,23,24 but both their conductivity and transparency are

still lower than ITO, except flexibility. In order to have a bet-

ter understanding of their optical and electrical properties,

both analytical modeling and finite element method compu-

tations (FEM) are used. Analytical expressions were devel-

oped to estimate the light transmittance of a mesh and

electrical surface resistivity. The surface resistivity obtained

from analytical expressions was also compared with FEM

studies.

An important trade-off of using mesh-conductors in

devices is balancing three factors: (1) light occluded by the

fibers in the mesh, (2) surface resistivity of the mesh, and (3)

higher luminous output around the mesh fibers. FEM was

also used to study the voltage and current density distribu-

tions in mesh conductor based EL devices. The experimental

and modeling results are discussed and compared in order to

design a better mesh conductor for improving transparency,

conductivity, and a better EL device with better luminance

performance.

The mesh conductors were prepared by following a

combined dip coating and inkjet printing process reported

previously.23,24 In brief, PET mesh fabrics 25 were sequen-

tially coated with CNT and PEDOT:PSS to form mesh con-

ductors that were used as the front electrode in EL devices.

Typical SEM images of such PET mesh conductors are

shown in Figs. 1(a) and 1(b). In the same way, nylon conduc-

tors were prepared and used as the back electrode, unless

otherwise indicated, in assembling the EL devices.

The architecture of our EL devices is shown in Fig. 1(c).

The device has a 4-layer structure with a phosphor layer

(ZnS:Cu,Cl: organic binder: 50:50) and a dielectric layer

(BaTiO3: organic binder: 50:50) sandwiched by the two con-

ductors. The back conductor was either conductive nylon

mesh or aluminum foil. The EL devices were assembled by

following the procedure reported previously in Refs. 23 and 24

and tested under ambient conditions using a Keithley 196 sys-

tem, HR4000 spectrometer, Tektronix oscilloscope 1001B,

Instron 5569, and Hirox KH-7700 digital microscope.

A cover factor (CF) model was established to predict the

light transmittance of mesh conductor, with the assumption

that pristine fibers or coated fibers completely block or

absorb light transmission through the fabrics, while the

spaces between fibers allow complete light transmission. The

transmittance of the mesh fabric and the mesh conductors

was then calculated based on such a cover factor model.

Numerical simulations were performed by COMSOL

Multiphysics software in the AC/DC electrostatics module to

determine the resistivity of mesh conductors and the electric

field and current density of the EL devices. The geometry of

the EL device was determined from SEM micrographs and

modeled with a single unit cell (Fig. 1(c)). The parameters

used for modeling the resistivity of PET mesh conductors

and their based EL devices are listed in Ref. 25.a)E-mail: bhu@umassd.edu

0003-6951/2015/106(7)/073302/5/$30.00 VC 2015 AIP Publishing LLC106, 073302-1

APPLIED PHYSICS LETTERS 106, 073302 (2015)

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Light transmittance of the mesh conductors is one of the

key factors that determine the luminance intensity of the EL

device. A CF model was developed to understand the corre-

lation between the open structure of textiles and their light

transmittance property, and to provide useful information on

textile structure design for maximized transparency.

Cover factor denotes the extent to which the area of a

fabric is covered by one set of threads. It is defined as the ra-

tio of the area covered by yarns to the total area of the fabric

and can be expressed by Eq. (1)

CF ¼ area covered by yarns

total area of the fabric

¼ d � pð Þ þ d � pð Þ � d2� �

p2¼ 2

d

p

� �� d

p

� �2

; (1)

where d is the diameter of fiber, while p is the fiber spacing

of fiber, respectively.

Fig. 2(a) shows the typical unit cell of a regular woven

structure, with d and p been marked.

We assume that the fibers block or absorb light com-

pletely. The light transmittance of mesh fabric can then be

expressed by Eq. (2)

T ¼ 1� CF ¼ 1� 2d

p

� �þ d

p

� �2

; (2)

where T stands for the light transmittance of the mesh fabric

and CF is the cover factor.

Equation (2) provides a convenient way of calculating

the transmittance of a given woven structure with known

fiber diameter and fiber spacing. For the mesh conductors,

Eq. (2) also applies since the CNT and PEDOT:PSS coatings

do not alter the woven structure of the mesh fabric. On the

other hand, the added thickness (1.3 lm according to Refs.

24 and 25) to fiber diameter and the reduced fiber spacing

due to the coatings ought to be taken into consideration.

Fig. 3 compares the experimentally measured light

transmittances with those calculated by Eq. (2) at different

inkjet printing cycles (note that the CNT coating causes a

negligible change in fiber diameter and fiber spacing). The

results from the model are in good agreement with the exper-

imental measurements. The fact that the model results are

slightly larger than the experimental results in the entire

range of the printing cycles is likely to be due to the addi-

tional light absorption of PEDOT:PSS coated on the fiber

surface.

According to Eq. (2), a smaller fiber diameter to fiber

spacing ratio results in a more transparent mesh. Thus,

reducing the fiber diameter, widening the fiber spacing or

combining both would be expected to enhance transmittance

of the mesh conductor.

FIG. 1. (a) and (b) SEM images of the

mesh conductor with fibers of 70 lm in

diameter and 210 lm in fiber spacing,

(c) configuration of the EL device

using the mesh conductor as the front

electrode.

FIG. 2. Unit cell of a woven structure. (a) d is the fiber diameter and p is the

fiber spacing, (b) resistance mesh-network model, and (c) network model for

calculation of surface resistivity.

FIG. 3. Comparison between light transmittances from the cover factor

model and those from experimental measurements for PET mesh (83-70PW)

with various printed coating thicknesses.

073302-2 Hu et al. Appl. Phys. Lett. 106, 073302 (2015)

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Besides transparency, surface resistivity of the mesh

conductor is another crucial factor that determines the over-

all performance of the EL devices. Circuit models used in

Refs. 26 and 27 can be used for analyzing mesh conductors.

Consider the unit-cell shown in Fig. 2(a). Each side of the

mesh is a PET monofilament covered with a thin coating of

conducting material. The resistance of a side of the square

mesh can be calculated as

Ra ¼qcp

tc2pd=2¼ qcp

tcpd(3)

where Ra is the resistance of each fiber in mesh square, qc is

the resistivity of the thin coating material, while tc is the

coating thickness and the resistances are networked as shown

in Fig. 2(b). The resistance of the network from nodes 1 to 2

in Fig. 2(c) can be calculated using Kirchhoff’s circuit

laws28 to obtain R ¼ Ra.25 Resistance can be converted to

surface resistivity by Eq. (4),29

R ¼ qt

L

W¼ RS

L

W; (4)

where R is effective resistance, Rs is effective surface resis-

tivity, q is the effective resistivity, and t is the effective

thickness, while L and W are the effective length and width

of the conductor. In the present case, L ¼ W ¼ 2p and t ¼ d.

Thus, Eqs. (3) and (4) reduce to Rs ¼ R ¼ Ra.

Table I reports a comparison of experimental results and

analytical modeling results from Eqs. (3) and (4) for various

fiber diameters and spacing. Coating thickness and resistivity

of coating materials are listed in Ref. 25. The analytical

model was found to give results close to experimental results.

Higher deviations were observed for larger fiber diameters.

A further numerical model was developed using

COMSOL Multiphysics (COMSOL Inc., Burlington, MA)

based on the real situation of the mesh conductor as the front

electrode in an EL device, i.e., the current flows from the top

surface of the front electrode and spread to the bottom.

Variation of the geometry of the mesh conductor was

achieved by this three dimensional FEM.

Four mesh conductors made from three types of PET

mesh fabrics were modeled and the specifications of the PET

mesh fabrics and the surface resistivity results from modeling

and experiments are shown in Table I. Models were estab-

lished in three dimensions with Al foil connecting with the

bottom surface of the mesh conductor. Resistance was calcu-

lated from the quotient values of voltage and integrated cur-

rent, and then converted into surface resistivity by Eq. (4).

As seen from Table I, the resistivity values from model-

ing are in excellent agreement with the experimental results

for the meshes with relatively small fiber spacing, i.e., 310 or

311 lm, regardless what coatings these meshes have on their

surface. Better agreement with experimental results were

obtained from FEM than from the analytical model as the an-

alytical model does not take into account the corner effects

where the mesh sides overlap in the unit-cell. In the FEM, a

relatively large difference between the modeled and the ex-

perimental measurement is only seen from the mesh that has

relatively large fiber spacing (i.e., 828 lm). Larger fiber

spacing results in a smaller contact area of mesh conductor

to the Al back electrode. (For PET 30-140PW, the experi-

mental resistivity is larger than the modeling might due to

the printing defects on the larger fiber surface. The PEDOT

does not cover entirely on the fiber.) The PET 83-70PW/

CNT/PEDOT has the lowest resistivity than any other mesh

conductors with the PEDOT coating only, which is due to

the higher conductivity of the combined CNT/PEDOT film.

All the four mesh conductors result in similar electric

potential distribution, although they have different surface

resistivity. A typical electrical potential distribution is shown

in Fig. 4 for the PET 83-70PW/CNT/PEDOT mesh conduc-

tor. This figure shows how we modeled the surface resistiv-

ity. The integrated surface current is obtained from the

bottom Al foil.

COMSOL Multiphysics was also used to examine the

current density and voltage distribution of the EL devices.

The 3D device model is built to study the relationship

between the real luminance intensity and the modeled cur-

rent density.

As shown in Fig. 1(c), four layers are involved in the

modeling of mesh conductor based EL devices. The mesh

TABLE I. Surface resistivity of different mesh conductors from modeling and experimental measurements.

Mesh conductor Fiber diameter d (lm) Fiber spacing p (lm)

Surface resistivity (X/sq)

Analytical model FEM Experimental

PET 30-140PW/PEDOT 140 828 362 526 639

PET 83-70PW/PEDOT 70 310 271 263 245

PET 83-70PW/CNT/PEDOT 70 310 163 158 147

PET 83-120PW/PEDOT 120 311 159 250 250

FIG. 4. Electrical potential distribution on PET 83-70PW/CNT/PEDOT

mesh conductor at 1 V DC voltage. The mesh conductor is attached to a

back Al electrode. 1 V DC voltage is applied at the top surface of mesh

conductor.

073302-3 Hu et al. Appl. Phys. Lett. 106, 073302 (2015)

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conductor is covered with a conformally coated CNT/

PEDOT film (gray color layer) and is top layer in the device.

The next blue layer is the phosphor light-emitting layer with

a thickness of 80 lm. The green layer is the 30 lm thick

dielectric layer, and the bottom layer is the back electrode.

Typical electrical potential and current density distribu-

tions of the modeled PET 83-70PW /CNT/PEDOT/Al EL de-

vice are shown in Figs. 5(a)–5(d). The current density and

potential are high at the interface between the fibers and the

phosphor layer (red domains in Fig. 5), but low in the central

open area of each unit cell (blue domains in Fig. 5). Such cur-

rent density distribution suggests that the light is generated at

the fiber-phosphor interface (red and yellow domains in phos-

phor layer) upon an applied voltage and travels through the

phosphor layer at some angles all the way up to the top surface,

as shown by the arrows in Fig. 5(d), and is emitted through the

central open area. Due to this light travel pathway, the thick-

ness of the phosphor layer also becomes an important factor

that determines the performance of such mesh conductor based

EL devices. The proportional relationship between applied

voltage and current density and the resulting luminance of the

EL devices with different configurations is shown in Ref. 25.

Fig. 6(a) shows the luminance intensity distribution

across one unit cell of the mesh conductor based EL device

measured with the Hirox KH-7700 microscope, while Fig.

6(b) shows the voltage and current density distribution across

one unit cell obtained from device modeling. The two white

lines that cross the two insets in Fig. 6 indicate exactly where

the luminance intensity measurements were taken and where

the modeled data was obtained, respectively. Both the meas-

ured luminance intensity (the red line in Fig. 6(a)) and the

modeled electrical potential and current density (Fig. 6(b))

have a “U” shape profile across the 240 lm width of the unit

cell. The highest luminance intensity is located at the edges

and the lowest the center of the unit sell. The experimental

data indicates that there is an approximately 38% luminance

intensity decrease from the edge to the center of the unit

(about 66 at the edges and 41 in the middle, Fig. 6(a)), while

the model shows an 88% difference between the current den-

sity at the edges (�2.8 A/m2) and that at the center (�0.3 A/

m2) (Fig. 6(b). Although virtually no light is generated in the

central area of a unit cell, as indicated by the model with a

very small current density (�0.3 A/m2), the light generated

from the fiber/phosphor layer is emitted through the central

open area due to scattering, as described above.

The comparison of Figs. 6(a) and 6(b) shows light emis-

sion is much more uniform than the current density. This

implies that the lateral transmission and scattering of light in

the phosphor is very important such that the light is emitted

as sketched in Figure 5(d).

The emitted light can be estimated approximately by the

light penetration depth into the phosphor layer. The optical

absorption coefficient of ZnS powders at 550 nm is around

6.36 cm�1.30,31 The penetration depth is around 1 mm

according to the Beer-Lambert law,

I ¼ I0 expð�axÞ; (5)

where I is the light intensity as the incident light (I0) travels

through the phosphor layer with an absorption coefficient of

a to a distance of x. A reduction in scattering and absorption

could give a more uniform light output. Another suggestion

is to replace the phosphor in the middle of the mesh cells

with a more transparent medium.

Increasing fiber spacing will lower the luminance inten-

sity of the center of the “U” shape profile. According to the

light attenuation rate in Figure 6(a), 600 lm fiber spacing

would result in zero luminance intensity, i.e., a dark spot at

the center. The mesh number that corresponds to 600 lm

fiber spacing is 15� 15 mesh/cm. In order to have a uniform

emission (intensity difference is less than 10%), the mesh

number must be higher than 61� 61 mesh/cm.

This model suggests that the light transparency of the

PET mesh conductors can be further enhanced with an

FIG. 5. Electrical potential distribution

of the PET 83-70PW/CNT/PEDOT/Al

EL device (a) and its cross-section (b)

at 100 VAC/3.5 KHz, current density

distribution of the PET 83-70PW/

CNT/PEDOT/Al EL device (c) and its

cross-section (d) at 100 VAC/3.5 KHz.

073302-4 Hu et al. Appl. Phys. Lett. 106, 073302 (2015)

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optimized mesh configuration, i.e., 39� 39 mesh/cm, woven

with PET monofilaments of 20 lm diameter (d) and at a

234 lm fiber spacing (p). According to the model and Eqs.

(1) and (2), such a mesh fabric offers 84.6% light transmit-

tance before dip coating with CNT and printing with

PEDOT:PSS and 81.6% after, both being much higher than

fabric used in this study (i.e., 60%) and comparable with that

of ITO/PET (i.e., �80%).

In conclusion, we have developed analytical and numer-

ical models that correlate well the light transmittance and

surface resistivity of the PET mesh conductors. The FEM

modeling was used to study the voltage and current density

distribution in the PET mesh conductor based EL devices.

Comparisons between the experimental and modeling results

suggest that optimizing the mesh structure is the key to fur-

ther improved transmittance of the mesh conductors and

therefore an EL device of uniform light emission. Reducing

the scattering in phosphor layer may also enhance the uni-

formity of light emission in these EL devices.

This work was supported by National Textile Center

(NTC, Blue Bell, PA) under the project of M08-MD07. The

authors thank Global Tungsten & Powders Corporation

(Towanda, PA) for providing phosphor powders and

Nanolab Inc. (Waltham, MA) for providing CNT and CNT

inks. The authors also thank Dr. Chen-Lu Yang in Advanced

Technology & Manufacturing Center (Fall River, MA) for

the SEM measurement.

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FIG. 6. Comparison of the experimental data (a) and modeled data (b) of a typical unit cell in the PET83-70PW/CNT/PEDOT/Al EL device. The red line in

(a) is the curve fitting of the experimentally measured intensity data, Eq. (4). The inset in (a) is an optical image of the unit cell in the PET83-70PW /CNT/

PEDOT/Al EL device driven at 200 VAC/3.5 KHz. The unit of the X coordinate is pixel and one pixel is equals to 3 lm in this case. The inset in (b) is the elec-

trical potential and current density distribution of the unit cell in the PET83-70PW/CNT/PEDOT/Al EL device model. The two white lines that cross the two

insets indicate exactly where the luminance intensity measurements were taken and where the modeled data was obtained, respectively.

073302-5 Hu et al. Appl. Phys. Lett. 106, 073302 (2015)

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