Influence of Surface Recombination on Charge Carrier Kinetics in

Organic Bulk Heterojunction Solar Cells with Nickel Oxide

Interlayers - Supplemental Material

Scot Wheeler,1 Florent Deledalle,1 Nurlan Tokmoldin,1 Thomas

Kirchartz,2, 3, ∗ Jenny Nelson,4 and James R. Durrant1, †

1Department of Chemistry and Centre for Plastic Electronics,

Imperial College London, South Kensington Campus, SW7 2AZ London, U.K

2IEK5-Photovoltaics, Forschungszentrum Julich, 52425 Julich, Germany

3Faculty of Engineering and CENIDE, University of Duisburg-Essen,

Carl-Benz-Str. 199, 47057 Duisburg, Germany

4Department of Physics and Centre for Plastic Electronics,

Imperial College London, South Kensington Campus, SW7 2AZ London, UK

(Dated: August 6, 2015)

∗ t.kirchartz@fz-juelich.de† j.durrant@imperial.ac.uk

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FIG. 1. Short circuit current density JSC (circles) for treated (blue) and untreated (red) NiO

devices as a function of light intensity, and linearity of JSC as a function of light intensity.

A. Supplemental Material

In figure 1, JSC as a function of light intensity appears linear for both devices up to a

light intensity of 200 %. In the untreated NiO device, at light intensities above 200 %,

JSC versus light intensity is observed to be deviating from linearity, more so than for the

O2 plasma treated device. This indicates that recombination with a greater than linear

charge density dependence is occurring at short circuit. As VBI is smaller in the untreated

device, the internal field at short circuit driving charge extraction is less. In this case, non-

geminate recombination could begin to compete more with the extraction of charge. This

is unlikely to be an effect of surface recombination as it is believed to be linearly dependent

on the minority charge carrier density, and would therefore not cause a non-linearity in the

short-circuit current with light intensity.

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FIG. 2. a) Charge carrier lifetime as a function of open-circuit voltage for O2 plasma treated (blue)

and untreated (red) NiO. b) Simulation

FIG. 3. Comparison of experimental and simulated ideality factors as a function of open-circuit

voltage for O2 plasma treated (blue) and untreated (red) NiO.

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FIG. 4. a) Experimental and simulated charge carrier density as a function of open-circuit voltage

for O2 plasma treated (blue) and untreated (red) NiO. b) Experimental and simulated charge

carrier lifetime as a function of open-circuit voltage for O2 plasma treated (blue) and untreated

(red) NiO.

FIG. 5. Work function of ITO and NiO as measured by Kelvin Prove as a function of time while

exposed to air.

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FIG. 6. Simulation of VOC vs light intensity, taken to high light intensity to show the expected

plateaux effect for this system

FIG. 7. Simulation of JV curve for untreated NiO device, with poor electrode alignment, with

varying majority surface recombination velocity Smaj (left) and minority surface recombination

Smin (right)

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FIG. 8. Simulation of the open-circuit voltage of the untreated NiO device with poor electrode

alignment, as a function of Smaj and Smin.

FIG. 9. Simulated band diagrams for the untreated NiO device with poor electrode alignment and

low minority surface recombination velocity Smin at 3 different voltages across the JV curve, as

labeled in figure 7.

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B. Effect of reduced surface recombination velocity

Both Smaj and Smin are predicted to cause S-shaped JV curves when very small, as seen in

figure 7. In the case of Smaj, as described by Wagenpfahl et al.,[? ] a low Smaj restricts

extraction of majority carriers out of the device. This leads to a build-up of space charge

in the device, lowering the VOC. In the case of a low Smin, restricting surface recombination

of minority carriers causes them to accumulate at the electrode around open-circuit. In

the case of electrons at the anode, this causes the conduction band and the Fermi-level to

come closer together. At open-circuit, by definition the Fermi-level is flat; this forces the

conduction band to bend down. At voltages just less than VOC where charges still need to

be extracted, there is additional bulk recombination losses as electrons now have to diffuse

against the electric field over a barrier to get collected at the cathode. The simulated band

diagrams can be seen in figure 9.

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C. Derivations

nid =q

kT

dVOC

d ln (φ)=

q

kT

dVOC

d ln (R)

R =n

τn=

n0

δτ∆n0

exp(qVOC

mkT

)exp

(− qVOC

ϑkT

)ln (R) = ln

(n0

δτ∆n0

)+qVOC

kT

(1

m+

1

ϑ

)d ln (R)

dVOC

=qVOC

kT

(1

m+

1

ϑ

)1

nid

=1

m+

1

ϑ

At VOC no external current flows, therefore Jgen = Jloss

Jgen ≈ JSC = Jloss = edn

τn= ed

n0 exp(qVOC

mkT

)δτ∆n0 exp

(− qVOC

ϑkT

)δJSCτ∆n0

edn0

=exp

(qVOC

mkT

)exp

(− qVOC

ϑkT

)ln

(δJSCτ∆n0

edn0

)=qVOC

kT

(1

m+

1

ϑ

)VOC

(1

m+

1

ϑ

)=kT

qln

(δJSCτ∆n0

edn0

)

As δ = mϑ

+ 1

VOC =mkT

qδln

(δJSCτ∆n0

edn0

)

D. Simulation Equations

Three coupled equations are solved, these are the Poisson equation,

∆ϕ = −ρε

(1)

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where ϕ is the electrical potential, ρ the space charge and ε the dielectric constant; the

continuity equations for electron and holes

∂Jn∂x

= −q [Gopt (x)−R (x, n, p)] (2)

∂Jp∂x

= q [Gopt (x)−R (x, n, p)] (3)

where Gopt (x) is the optical generation rate, R (x, n, p) is the recombination rate and q is the

charge. The current densities for electrons Jn and holes Jp are driven by drift and diffusion

are

Jn = q

(nµnF +Dn

∂n

∂x

)(4)

Jp = q

(pµpF −Dp

∂p

∂x

)(5)

where the diffusion constants are given by the Einstein relation Dn,p = µn,pkBT/q, n and p

are electron and hole concentrations, µn,p the electron and hole mobilities, F is the electric

field, kB is the Boltzmann constant and T is the temperature. The boundary conditions for

the currents at both contacts are

Jn (0) = qSnf [n (0)− n0 (0)] (6a)

Jp (0) = qSpf [p (0)− p0 (0)] (6b)

Jn (d) = qSnb [n (d)− n0 (d)] (6c)

Jp (d) = qSpb [p (d)− p0 (d)] (6d)

where Snf,b is the surface recombination velocity for electrons at the front and back, respec-

tively, while Spf,b is the same but for holes.

The bulk recombination term is a sum of direct recombination and trap assisted recombi-

nation R = Rdirect+Rtrap. The direct recombination rate is calculated according to Langevin

theory[? ] such that

Rdirect = βDR

(np− n2

i

)(7)

where βDR is a coefficient for free carrier recombination and ni is the intrinsic carrier concen-

tration, given by ni =√NCNV exp (−qEg/2kBT ) where NC and NV are the effective density

of states of the conduction and valence band. The trap assisted recombination rate is given

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by the tail recombination model as previously described[? ] The complete equation for the

recombination rate RCBT via conduction-band states is given by.

RCBT =

∫ EC

EV

NCBT (E) ηR (E) dE (8)

=

∫ EC

EV

NC0exp

(E − EC

EUC

)np− n2

i

(n+NCexp [(E − EC) /kT ]) /β−p + (p+NVexp [(EC − E) /kT ]) /β0

n

dE (9)

where NC0 is the density of tail states per energy interval at the conduction-band edge and

β−p and β0n are capture rate coefficients. An equivalent expression defines the recombination

rate RVBT via valence-band tail states, and the total recombination rate is the sum of the

two.

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