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Contract No. DE-AC36-99-GO10337 

M.D. Kempe 

Prepared for the 31st IEEE Photovoltaics Specialists 

Conference and Exhibition 

Lake Buena Vista, Florida 

January 3–7, 2005 

February 2005 • NREL/CP-520-37390 

Control of Moisture Ingress 

into Photovoltaic Modules 
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CONTROL OF MOISTURE INGRESS INTO PHOTOVOLTAIC MODULES

Michael D. Kempe 

National Renewable Energy Laboratory

1617 Cole Boulevard, Golden CO 80401 

ABSTRACT 

During long-term exposure of photovoltaic modules to 

environmental stress, the ingress of water into the module 

is correlated with decreased performance. By using diffusivity measurements for water through encapsulants such 

as ethylene vinyl acetate (EVA), we have modeled moisture ingress using a finite-element analysis with atmospheric data from various locations such as Miami, Florida. 

This analysis shows that because of the high diffusivity of 

EVA, even an impermeable glass back-sheet alone is incapable of preventing significant moisture ingress from the 

edges for a 20-year lifecycle. This result has led us to 

investigate ways to protect module from the moisture 

through the use of different encapsulating chemistries and 

materials. 

INTRODUCTION

The ingress of moisture into photovoltaic (PV) modules has been correlated with increased failure rates, especially in hot and humid climates such as Miami, Florida. 

The first step toward understanding this failure mechanism 

is to determine how long it takes a module to approach 

equilibrium with the water in the external environment. To

do this, the diffusivity and water absorption capacity of 

ethylene vinyl acetate (EVA) was measured to obtain the 

necessary information to model water-ingress rates. This 

allowed one-dimensional (1-D) finite-element analysis to 

be performed using meteorological data to determine the 

transient water content within the module for the case of a 

breathable back-sheet and for a double-glass laminate. 

EXPERIMENTAL 

Diffusivity and solubility measurements

The transient water-vapor transmission rate (WVTR) 

through a 2.84-mm-thick EVA membrane was measured 

using a Mocon Permatron-W® 3/31. Passing dry nitrogen 

across both sides of the membrane dried the sample, and 

the measurement was started when liquid water was introduced to one side (see Fig. 1a). If one assumes that the 

diffusivity obeys Fick’s law (diffusivity is independent of 

concentration), then the transient WVTR can be described 

as: 

( ) ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

= + ∑ −

∞

=

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ −

1

2

2 2

( ) 1 2 1 n

l

Dn t

n S e

l

DC WVTR t

π

, (1) 

where D is the diffusivity, Cs is the saturation concentration, t is time, and l is the membrane thickness [1]. A 

small shift of ~80 s was needed for the time axis prior to 

fitting Eq. 1 to the data. The diffusivity is determined first 

by the time required to reach steady state, and then the 

water-saturation concentration is determined by the 

steady-state WVTR (see Fig. 1b). 

EVA Transient WVTR

(85 oC, 2.84 mm thick)

0

2

4

6

8

10

12

14

0 20 40 60 80 100 120 1

Time (min)

WVTR (10-8 g/cm2/s)

40

Measured

Calculated

(a) 

(b) 

1.0E-07

1.0E-06

1.0E-05

0.0027 0.0029 0.0031 0.0033 0.0035

1/Temperature (1/K)

Diffusivity (cm2/s)

0.0010

0.0100

0.1000

 Water Saturation 

 Concentration (g/cm3

)

∆HSol=0.17 eV

Csat,H O 2

Ea=0.40 eV

Diffusivity

Fig. 1. (a) Sample WVTR measurement used to measure diffusivity. The solid line was calculated using Eq. 1. (b) Plot of water 

diffusivity and solubility in EVA. 

The diffusivity and solubility for other polymeric materials was also measured to evaluate their potential use in 

PV modules (see Fig. 2). All of these materials (except for 

BRP-C, which contains considerable filler) were found to 

have a transient WVTR that was well described by Eq. 1, 

indicating that their diffusivity is Fickian. For BRP-C, the 

1 
diffusivity values are only effective diffusivities that are 

best applied at long times. 

1.0E-10

1.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-05

1.0E-04

0.0027 0.003 0.0033 0.0036

1/Temperature (1/K)

Diffusivity (c

m2/s)

GE RTV615

DC Sylgard 184

EVA

GSE

BRP-C

Tedlar

Mylar D (PET)

LCP

Aclar

Fig. 2. Diffusivity measurements for several polymers. 

GE RTV615 and DC Sylgard 184 are both polydimethyl 

silicones manufactured by General Electric and Dow Corning, respectively. GSE is an experimental film provided by

Global Solar. BRP-C is an experimental encapsulant from 

BRP Manufacturing. LCP is a liquid crystal polymer. 

It was found that EVA has a relatively high diffusivity

that is only exceeded by silicones. It should also be noted 

that the diffusivity of the different materials varies by orders of magnitude and that consequently the time for 

moisture ingress also varies by orders of magnitude. 

Determination of module exposure from meteorological data 

Meteorological data for Miami, Florida, for 2002 were 

obtained from Atlas Weather Services under a subcontract 

with the National Renewable Energy Laboratory (NREL). 

Data for Golden, Colorado, were measured at NREL. Because the Miami data did not include module temperature, 

this had to be estimated using heat-transfer equations, as 

outlined by Myers [2] The data from NREL included module temperature and were used to validate the heart transfer calculations and make slight modification to some of 

the model parameters for improved accuracy. 

The Miami data were obtained in 10-min increments, 

with occasional missing data points. When this occurred, 

the data were interpolated between adjacent points. For 

large sections of missing data, points were substituted 

from the previous day. 

RESULTS AND DISCUSSION 

Moisture ingress into a breathable back-sheet 

The moisture ingress through a breathable backsheet can be modeled as a one-dimensional (1-D) diffusion problem where the inner boundary (the PV device) is 

impermeable, the outer exposed surface is in equilibrium 

with the environment, and the elements at the interface 

between the EVA and the back-sheet are assumed to be 

in equilibrium (see Fig. 3). These assumptions were then 

used in a finite-element analysis. For each time step, the 

temperature of the module (along with the diffusivity and 

solubility) and the outer surface concentration are 

changed, and the implicit method is used to compute the 

concentration profile for the next time step. In this model, 

49 spatial elements were used for the back-sheet and 36 

spatial elements were used for the EVA layer. 

Back-Sheet

EVA

Glass

H2O

PV Device X=lEVA+lB

X=l

B

X=0

Back-Sheet

EVA

Glass

H2O

PV Device X=lEVA+lB

X=l

B

X=0

Fig. 3. Schematic of model used for a module with a 

breathable back-sheet. 

A module with a breathable back-sheet was modeled 

by starting with an initially dry EVA encapsulant (see Fig. 

4) with a thickness of 0.46-mm and a composite backsheet consisting of TedlarTM (0.038 mm) / polyethylene 

terepthalate (0.051-mm) / EVA (0.10-mm). Using an effective diffusivity and solubility for the composite backsheet, it takes approximately 24 to 36 h for the water content to reach equilibrium. 

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

01234567

Days

Concentration (g/c

m3

)

Module - Finite Element

Module - Simple WVTR

EVA Equilibrium Water Content

Fig. 4. Transient moisture content at the cell interface 

calculated using data from Miami, Florida, for 2002. The 

back-sheet was modeled using an effective diffusivity and 

solubility measured on a composite film of TedlarTM (0.038 

mm) / polyethyleneterepthalate (0.051 mm) / EVA (0.10 

mm). The EVA encapsulant was modeled as 0.46 mm 

thick. The simple WVTR line was modeled using Eq. 2. 

Rather than using a complicated finite-element analysis to determine the equilibration time, a simpler model 

equation can be assumed [3]: 

2 
[ ( ) ( ) B B B

E Sat E

E B Max C C l

C l

WVTR

dt

dC = 0 −

, .

, ], (2) 

where the subscripts Sat, B and E indicate conditions at 

saturation, in the back-sheet, and encapsulant, respectively, and WVTRB,Max is the rate with 100% and 0% relative humidity (RH) on opposite sides of the back-sheet. To

use this model, one assumes that the encapsulant diffusivity is much greater than the back-sheet diffusivity

(DE>>DB), that the concentration profile in the back-sheet 

is linear, and that the concentration in the encapsulant is 

independent of position. To use Eq. 2 with the meteorological data from Miami, one can simply estimate a small 

loss or gain of water for each time step. Figure 4 demonstrates that both methods produce qualitatively the same 

result, with the finite-element model predicting a small time 

lag. 

Integration of Eq. 2 (assuming a constant temperature 

and RH as will be justified in the next section) indicates 

that the equilibration follows an exponential decay and that 

the half-time (the time to reach half the equilibrium value) 

for this process is, 

B Max

Sat E E

WVTR

C l

,

,

2

τ 1 = 0.693 . (3) 

This equation suggests that for a back-sheet to have an 

equilibration half-time of 20 years, a WVTRB,Max of 10-4

(g/m2

/day) is necessary at 27oC. Because most backsheets used with PV devices have a WVTRB,Max that is 

typically greater than 10-1 (g/m2

/day), all these systems are 

at equilibrium. It is not until WVTRB,Max~10-6 (g/m2

/day) 

that one can neglect water permeation through a backsheet. 

Moisture ingress in double-glass laminates 

For the case where the back-sheet is an impermeable 

barrier (such as glass), water can still enter through the 

sides of the module. This process was modeled using a 1-

D explicit finite-element analysis consisting of 55 spatial 

elements using meteorological data for Miami, Florida, for 

2002 (see dotted lines in Fig. 5). The outer edge of the 

module was assumed to be at equilibrium with the surroundings, and because of symmetry the center of the 

module is modeled as an impermeable barrier. Ignoring 

the 2-D nature of the module is valid for short times (relative to the diffusion rate) or for long and narrow module 

shapes. 

In this 1-D model, an analytical solution can be obtained starting with an initially dry module if one assumes 

a constant temperature and external RH 

( ) ( ) ( ) ( )

∑

∞

=

⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎝

⎛ + −

⎥

⎦

⎤ ⎢

⎣

⎡ +

+ = +

0

2 1

2

2 2

2 1

sin

2 1

4 1 ,

m

l

D m t

s

S e l

m x

m

C

C x t C

π

π

π .

 (4) 

At distances greater than ~4 cm from the module edge, 

the seasonal fluctuations are damped out and Eq. 4 provides an accurate representation of the finite-element 

model when T=26.7o

C and RH=71% which correspond to 

an average temperature and an average water concentration. The high diffusivity of EVA allows for moisture to 

reach the center of a module with a width of 40 cm in 

about 2 years (see Fig. 5). 

0.0000

0.0004

0.0008

0.0012

0.0016

0 2 4 6 8 10 12 14 16 18 20

Distance from Edge (cm)

Dissolved Water (g/c

m3

)

Increasing

 Years

9 years

6 years

3 years

Fig. 5. Model of moisture ingress in double-glass laminate 

construction using EVA. Dotted lines are for the finiteelement model. Solid lines are for Eq. 4 using T=26.7o

C 

and RH=71%. 

This model demonstrates that by using environmental 

conditions of T=26.7o

C and RH=71%, one can approximate conditions of Miami, Florida, and obtain estimates for 

the time scale of moisture ingress. Evaluation and inspection of Eq. 4 indicates that the half-time for moisture ingress into the center of the module is given by

D

l

2

0.0947 2τ 1 = . (5) 

Therefore, to keep water out of the module center for 30 

years would require a module that is 3 to 4 times larger or 

a diffusivity that is more than 10 to 20 times smaller. For a 

square module, the prefactor for the equilibration time 

would be 0.0593 instead of 0.0947, indicating an approximately 38% increase in the water-ingress rate (see Table 

1). One should also consider that this model neglects 

moisture ingress due to diffusion along surfaces and 

through the junction box, or due to delamination and capillary action. Diffusion of water from the sides is significant 

over the lifetime of a module unless a module is a few

meters across. 

Encapsulant Material τ1/2

l=10 cm l=50 cm 

RTV615 Silicone 4 days 0.27 years 

EVA 0.35 years 8.8 years 

BRP-C 29 years 738 years 

Aclar 1,260 years 31,600 years 

Table 1. Time required for the center of a module with 

impermeable front and back-sheets to reach half of its 

equilibrium water content using different encapsulants. 

Data evaluated at 27o

C. 

3 
Table 1 shows the equilibration half-time for moisture 

ingress into a module with impermeable front- and backsheets. Because the diffusivities of the different materials 

vary by orders of magnitude, one can also see that the 

equilibration time for the low-diffusivity materials can be 

very long. In addition to the high cost of low-diffusivity

materials such as Aclar (polychlorotrifluorethylene) (which 

would keep a module completely dry for the lifetime of a 

module), there are also problems limiting their use associated with adhesion and with their high modulus. If the 

material delaminates under environmental exposure, water 

will enter a module extremely rapidly. One of the purposes of the encapsulant is to provide mechanical support 

to protect cells from breaking, but the high mechanical 

moduli of materials such as Aclar make them poor choices 

for encapsulants. 

 Material τb 

(min) 

Membrane 

Thickness 

l (mm) (min/mm2)

Edge Seal 

Breakthrough 

Time for 

l=12.5 mm

RTV615 

PDMS 4.67 3.25 0.442 1.15 h 

EVA 3.6 0.457 17.2 2 days 

BRP-C 550 0.406 3,336 362 days 

Aclar 35 0.0229 66,740 20.3 yrs 

2 D l

K b τ

=

Table 2. Determination of break-through times for different edge-seal materials. 

The use of Aclar as an edge seal material is precludeed for the same reasons it cannot be used as an 

encapsulant. The BRP-C material, however, has potential 

as an edge seal because of its low-diffusivity. Even 

though its diffusivity is not Fickian, Eq. 6 can still be applied and an edge seal consisting of 12.5 mm of BRP-C 

should be able to exclude moisture for a year. If one were 

to replace the filler material with a desiccant, then the 

breakthrough time might be increased significantly. 

Edge Seals 

The effectiveness of edge-seal materials were determined by measuring the time required for significant 

amounts of moisture to begin permeating a membrane 

(see Fig. 6). This time (the breakthrough time τb) is related to the thickness and diffusivity of a membrane by CONCLUSIONS 

D

l

b K

2

τ = , (6) 

Because of the relatively high diffusion rate of water in 

EVA, even a module with a glass/glass construction will 

have significant moisture ingress over the lifetime of the 

module. The only way to prevent moisture ingress is with 

a true hermetic seal or by using a low-diffusivity edge seal 

containing a large amount of desiccant. Therefore, if a PV 

device is very sensitive to moisture, it may be more economical to focus on ways to reduce the corrosion processes that are enhanced by moisture ingress. 

where K is a material-dependent constant [4]. Because 

this is a 1-D diffusion process, similar to the permeation 

through an edge seal, the breakthrough time for a PV 

module can be determined by replacing l

2

 with the width of 

the edge seal (see Table 2). 

BRP-C

(T =25o

C l =0.406 mm)

0

2

4

6

8

10

12

14

0 5 10 15 20

Time (h)

WVTR (10-10 g/c

m2/s)

Breakthrough 

Time

REFERENCES 

 [1] J. Crank, “The Mathematics of Diffusion,” p. 50, Clarendon Press, Oxford (1975). 

[2] D. R. Myers, “Service Life Prediction of Organic Coatings, A Systems Approach,” Chapter 6, American Chemical Society, Oxford (1999). 

[3] M. Tencer, “Moisture Ingress into Nonhermetic Enclosures and Packages,” IEEE, 196-208 (1994). 

[4] D. R. Paul and D. R. Kemp, “The Diffusion Time Lag in 

Polymer Membranes Containing Adsorptive Fillers,” J. 

Polymer Sci.: Symposium No. 41, 79-93 (1973). 

Fig. 6. Transient WVTR profile for the BRP-C material 

indicating the breakthrough time. 

4 
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5a. CONTRACT NUMBER

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4. TITLE AND SUBTITLE

Control of Moisture Ingress into Photovoltaic Modules 

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NREL/CP-520-37390 

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PVB57201 

6. AUTHOR(S) 

M.D. Kempe 

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Golden, CO 80401-3393 

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14. ABSTRACT (Maximum 200 Words)

During long-term exposure of photovoltaic modules to environmental stress, the ingress of water into the module is 

correlated with decreased performance. By using diffusivity measurements for water through encapsulants such as 

ethylene vinyl acetate (EVA), we have modeled moisture ingress using a finite-element analysis with atmospheric 

data from various locations such as Miami, Florida. This analysis shows that because of the high diffusivity of EVA, 

even an impermeable glass back-sheet alone is incapable of preventing significant moisture ingress from the edges 

for a 20-year lifecycle. This result has led us to investigate ways to protect modules from moisture through the use of 

different encapsulating chemistries and materials. 

15. SUBJECT TERMS

PV; moisture ingress; module; diffusivity measurements; ethylene vinyl acetate (EVA); glass back-sheet; 

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