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Verification of Phototransistor Model for Cu(In,Ga)Se2 Solar Cells

Thomas Ott, Francillina Schonberger, Thomas Walter, Dimitrios Hariskos,Oliver Kiowski, Oliver Salomon, Raymund Schaffler

PII: S0040-6090(14)00903-1DOI: doi: 10.1016/j.tsf.2014.09.025Reference: TSF 33714

To appear in: Thin Solid Films

Please cite this article as: Thomas Ott, Francillina Schonberger, Thomas Walter,Dimitrios Hariskos, Oliver Kiowski, Oliver Salomon, Raymund Schaffler, Verificationof Phototransistor Model for Cu(In,Ga)Se2 Solar Cells, Thin Solid Films (2014), doi:10.1016/j.tsf.2014.09.025

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Verification of Phototransistor Model for Cu(In,Ga)Se2 Solar Cells

Thomas Ott1, Francillina Schönberger

1, Thomas Walter

1, Dimitrios Hariskos

2, Oliver Kiowski

2,

Oliver Salomon2 and Raymund Schäffler

3

1University of Applied Sciences Ulm, Albert-Einstein-Allee 55, 89081 Ulm, Germany

2Zentrum für Sonnenenergie- und Wasserstoff-Forschung Baden Württemberg, Industriestr. 6, 70565

Stuttgart, Germany 3Manz CIGS Technology GmbH, Alfred-Leikam-Str.25, 74523 Schwäbisch Hall, Germany

Corresponding author: th.ott@hs-ulm.de

Key: JMGC2

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Verification of Phototransistor Model for Cu(In,Ga)Se2 Solar Cells

Thomas Ott1, Francillina Schönberger

1, Thomas Walter

1, Dimitrios Hariskos

2, Oliver Kiowski

2,

Oliver Salomon2 and Raymund Schäffler

3

1University of Applied Sciences Ulm, Albert-Einstein-Allee 55, 89081 Ulm, Germany

2Zentrum für Sonnenenergie- und Wasserstoff-Forschung Baden Württemberg, Industriestr. 6, 70565

Stuttgart, Germany 3Manz CIGS Technology GmbH, Alfred-Leikam-Str.25, 74523 Schwäbisch Hall, Germany

Corresponding author: th.ott@hs-ulm.de

ABSTRACT

Previous studies of Cu(In,Ga)Se2 thin film solar cells showed that the long term stability critically

depends on the bias across the junction. As a result of a dark anneal the current-voltage (IV)-

characteristics in the dark showed a blocking behavior with increasing anneal time. In the final stage

the device exhibits an open circuit voltage (Voc) which is independent from the illumination

intensity, a crossover of the dark and illuminated IV-characteristics and Voc saturation for decreasing

temperatures. These characteristics also occur in the initial state prior to the endurance test, however,

at low temperature (<200 K) measurements. We suggested a phototransistor model to explain the

observed characteristics. The prerequisite of this model is the existence of a Schottky barrier at the

back contact. In this contribution more insights into this phototransistor model and its experimental

verification will be given and discussed. Finally we suggest how to avoid the effects of the back

barrier with the help of a CuGaSe2 layer at the back of the absorber and a Ga gradient through the

absorber. These measures will be verified with simulations and compared to measurements on co-

evaporated devices.

1. Introduction

With a record efficiency close to 21 % on laboratory scale devices [1,2] Cu(In,Ga)Se2 passes

multicrystalline Si and consolidates its position as the most promising thin-film technology for the

future. Besides efficiency, the long term stability is a crucial issue for the competitiveness of a solar

cell technology. Previous studies investigated the long term stability of Cu(In,Ga)Se2 solar cells

which can be evaluated by accelerated aging as a result of a dark anneal at elevated temperatures.

From measured parameter drifts activation energies were determined for life time predictions. After

test times exceeding 3000 h the device current-voltage (IV)-characteristic changes. A blocking

behavior of the forward current in the dark occurs, the open circuit voltage (Voc) is independent from

the illumination intensity and a crossover of the dark and illuminated IV-characteristic is visible [3].

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These correspond to measurements in the initial state for Cu(In,Ga)Se2 solar cells at low

temperatures [4,5]. Previous studies suggested a “Phototransistor model” to explain adequately this

behavior [6]. This contribution explains this Phototransistor model in more detail involving a

Schottky barrier at the back contact. A band diagram of a Cu(In,Ga)Se2 solar cell based on the

suggested model is shown in Fig. 1. Furthermore, it will be demonstrated that the barrier height of

the Schottky diode can be extracted from temperature dependent Voc measurements. Finally different

ways to overcome this phototransistor effect will be presented and discussed. Measurements will be

compared to simulations.

2. Experimental Details

Fig. 2 a) shows the IV-characteristic of a Cu(In,Ga)Se2 solar cell in the initial state deposited by

multistage co-evaporation. The device was measured at 300 K and 90 K at 1 sun (1000 W/m²) with

different intensity filters from 0 (dark) to 100 % (1000 W/m²) illumination intensity. An optistat

DN2-V from oxford instruments was used to cool down the cells and the IV-characteristic was

detected with an Agilent 4155C semiconductor parameter analyzer. At room temperature the device

shows a “normal” solar cell behaviour. No crossover of the dark and illuminated IV-characteristic,

the Voc depends on the illumination intensity and no blocking of the forward current in the dark. For

90 K the behaviour changes, a blocking behavior of the forward current in the dark occurs, the Voc

is independent from the illumination intensity and a crossover of the dark and illuminated IV-

characteristics is obvious. The Voc versus temperature characteristic of this device is shown in Fig. 2

b). At higher temperatures the Voc depends on the illumination intensity and shows a linear

behaviour. At lower temperatures the different curves coincide with a lower temperature coefficient.

An extrapolation from higher temperatures to 0 K leads to the band gap energy. Using the low

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temperature behaviour shown in Fig.2 b) a determination of the Schottky barrier height at the back

contact is possible from this characteristic. This will be presented and discussed in the next section.

In order to support the phototransistor model, a device structure with a Schottky back barrier was

implemented in SCAPS1D (solar cell capacitance simulator in 1 dimension) version 3.2.01 [7]. The

key simulation parameters are listed in Table 1. Our standard model for a Cu(In,Ga)Se2 solar cell

was used and only a Schottky barrier at the back contact was added. The important parameter in this

context is the barrier height (ϕB) measured from the hole Fermi level to the valence band edge at the

back contact (see Fig.1).

3. Results and Discussion

The key for the phototransistor model is a Schottky barrier at the back contact as defined above.

Fig. 1 shows the simulated band diagram of a Cu(In,Ga)Se2 solar cell with a Schottky barrier height

of 250 meV at room temperature. The band diagram can be interpreted as a phototransistor with a n-

ZnO emitter, a p-Cu(In,Ga)Se2 base and a Schottky collector. The barrier leads to a depletion of

holes at the back contact with a second space charge region due to the Schottky barrier. Injected

electrons with a sufficient diffusion length are collected in the space charge region of the Schottky

diode. These collected electrons are responsible for the diode current in the dark as a hole current is

blocked by the Schottky diode. Under illumination photo generated holes are concentrated between

the two space charge regions compensating the negative charge, thus lowering the potential barrier.

Due to the lowering of the barrier the injection of electrons is enhanced. Modulating the illumination

intensity therefore modulates the diode current. The photo current therefore acts as a base current

and so the base current (absorber) modulates the current from the collector (Mo) to the emitter

(ZnO).

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In the initial state, this behavior is observable only for low temperatures. Our previous

contributions showed that after accelerated ageing at elevated temperatures under certain conditions

the phototransistor behavior already occurs at room temperature [8]. The height of the Schottky

barrier is the key parameter determining at which temperature the device changes its normal solar

cell characteristic to a phototransistor like characteristic. To support this assumption, it is necessary

to determine the barrier height.

Figure 3 shows the schematic current diagram of a Cu(In,Ga)Se2 solar cell in the phototransistor

state. With the help of this diagram it is possible to derive an equation determining the barrier height

at low temperatures. For the analytical calculations the following assumptions and simplifications

were taken into account (it should be noted that all of these assumptions count for the analytical

derivation. In the simulation presented below the complete set of semiconductor and transport

equations were considered and solved):

The photo generated electrons are all driven to the ZnO

There is no recombination in the space charge region; i.e. injection of electrons is assumed

(common base current gain) is constant (the Early effect is not considered)

The hole emission current -ICh across the back barrier (an electron flow from left to right in Figure 3

is counted positive) is governed by the Schottky barrier and the voltage drop VBC across this back

barrier.

1exp0

kT

qVII BC

ChC (1)

where IC0 is the saturation current of the Schottky junction, q the unit electronic charge, k the

Boltzmann constant and T the temperature. The electron emission current IEe across the principal

barrier is determined by the voltage drop VBE:

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1exp0

kT

qVII BE

EeE (2)

where IE0 is the saturation current of the principal junction. A part of this current recombines with

photogenerated holes, the rest of the current is injected to the back contact and collected by the

electric field of the Schottky contact. This current is determined by the common-base current gain α

[9]. Parameters such as electron diffusion length or base width influence the gain . For Voc

conditions the current at both sides of the device have to be zero, leading to:

ePhEe II (3)

ePhChEe III (4)

Voc is the sum of the voltage drops across the main junction and the Schottky barrier:

BCBEoc VVV (5)

Combining equation (1) and (4), equation (2) and (3), dissolving to VBC and VBE leads with equation

(5) to:

1ln1ln

00 C

Phe

E

Pheoc

I

I

I

I

q

kTV

(6)

For high temperatures IC0 >> αIPhe. Thus equation (6) can be simplified to

1ln

0E

Phe

ocI

I

q

kTV (7)

which corresponds to the well known equation for the open circuit voltage. For the low temperature

regime (IC0 << αIPhe and IE0 << IPhe) where the device can be considered as a phototransistor,

equation (6) can be simplified to

0

0lnE

C

ocI

I

q

kTV

(8)

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Equation (8) shows that the photocurrent has no influence on the Voc. The Voc is independent from

the illumination intensity. With the equations:

kTII B

CC exp000 (9)

kT

EII

g

EE exp000 (10)

where Eg is the band gap of Cu(In,Ga)Se2, IE00 and IC00 are pre- factors of the saturation current for

the principal and Schottky junction, the following equation can be derived for the low temperature

regime:

Coo

EooBg

ocI

I

q

kT

q

EV

ln (11)

For 0 K Voc extrapolates to the band gap energy reduced by the Schottky barrier height ϕB.

From the Voc versus temperature characteristic an extrapolation from higher temperatures and low

temperatures lead to the band gap energy and the above mentioned value (band gap energy reduced

by barrier height equation (11)). The value for the height of the back barrier is the delta between

these two points extrapolated to 0 K and can be determined directly from the Voc versus temperature

characteristic. Measurements of a Cu(In,Ga)Se2 device in the initial state in Fig.2 b) lead to a ϕB of

250 meV for this solar cell. The simulated Voc versus temperature characteristic of a Cu(In,Ga)Se2

standard device with a barrier at the back contact of 250 meV is shown in Fig.4 b). As can be seen

from a comparison of Fig.2 b) and Fig.4 b) a good agreement between measurements and

simulations could be obtained also with respect to the intensity dependence of Voc. Furthermore, the

temperature where the temperature gradient of the curves becomes lower and the characteristics of

the different illumination intensities coincide is in good agreement between measurement and

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simulation. Fig.4 a) shows the simulated IV-characteristic for a Cu(In,Ga)Se2 solar cell with a barrier

at the back contact of 250 meV for different illumination intensities at room temperature and at a

low temperature of 150 K. At room temperature a solar cell characteristic is visible, whereas for the

low temperature the characteristic looks like a set of characteristic curves of a phototransistor. The

simulations again fit well to the measurement results in Fig.2 a). Simulations (parameter table II)

showed that for a barrier height of round about 330 meV the performance of Cu(In,Ga)Se2 at room

temperature is affected due to a slight crossover of the dark and illuminated IV-characteristic.

Based on the considerations discussed above, it is evident that injection of electrons to the back

contact leads to a lowering of Voc. In order to reduce this effect, barriers for this electron injection

can be introduced at the back contact.

In a first approach a thin CuGaSe2 layer with a thickness of 80nm is introduced at the back

contact. Due to a band gap of 1.68 eV and under the assumption that the band offset predominantly

occurs in the conduction band a barrier for the electron injection is present at the back contact. Fig. 5

a) shows the simulated temperature dependence of Voc for a device with an 80 nm CuGaSe2 layer

between the Mo and the Cu(In,Ga)Se2. Compared to the device with a homogeneous bandgap the

saturation of Voc occurs at a significant lower temperature.

In a second approach a Ga/(In+Ga) gradient through the Cu(In,Ga)Se2 is inserted into the

simulated device. This approach is similar to the first approach, however, the band gap increases

linearly from the heterojunction (1.2 eV) to the back contact (1.4 eV) resulting in a barrier for

injected electrons. This device structure is also included in the simulations of Fig. 5 a). Again this

saturation of Voc occurs at a much lower temperature as compared to the homogeneous device.

However, it should be noted that the extrapolated value at 0 K appears to be independent from this

band gap grading, only depending on the barrier height at the back contact. Such a band gap grading

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is an inherent property of sequential processes [10]. Therefore, such phototransistor effects with

respect to the Voc saturation occur at much lower temperatures.

Figure 5 b) shows the conduction bands in the reference state, with a Ga gradient and a

CuGaSe2 layer at the back contact. Compared to the reference an electron barrier occur for the other

two states. This avoids the phototransistor effect. So the temperature at which the gradient of the

Voc(T)-characteristic starts to decrease shifts to lower temperatures.

4. Conclusions

In this contribution it could be shown that the phototransistor model can explain the behavior of

Cu(In,Ga)Se2 solar cells with a Schottky diode at the back contact for low temperatures. The

properties of this phototransistor include a crossover of the dark and illuminated IV-characteristics, a

blocking of the forward current and the Voc independence from the illumination intensity. From the

temperature dependence of Voc at low temperatures the barrier height at the back contact can be

extracted as deduced and verified from simulations. Furthermore, it has been pointed out that a

CuGaSe2 layer at the back contact or a graded band gap can shift the observed and simulated Voc

saturation to lower temperatures.

5. Acknowledgements

This work has been supported by German Federal Ministry for the Environment, Nature

Conservation and Nuclear Safety.

6. References

[1] P. Jackson, D. Hariskos, R. Wuerz, W. Wischmann, M. Powalla, Compositional investigation

of potassium doped Cu(In,Ga)Se2 solar cells with efficiencies up to 20.8 %, Phys. Status

Solidi (RRL) 8 (2014) 219-222.

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[2] M. Nakamura, N. Yoneyama, K. Horiguchi, Y. Iwata, K. Yamaguchi, H. Sugimoto, T. Kato,

Recent R&D Progress in Solar Frontier’s Small-sized Cu(In,Ga)Se2 Solar Cells, Proc. of 40th

IEEE PVSEC (2014), to be published.

[3] T. Ott, T. Walter, D. Hariskos, O. Kiowski, R. Schäffler, Accelerated Aging and Contact

Degradation of CIGS Solar Cells, IEEE J. of Photovolt. 3 (2013) 514-519.

[4] T. Eisenbarth, R. Caballero, M. Nichterwitz, C. A. Kaufmann, H. W. Schock, T. Unold,

Characterization of metastabilities in Cu(In,Ga)Se2 thin film solar cells by capacitance and

current- voltage spectroscopy, J. Appl. Phys. 110 (2011) 094506.

[5] T. Eisenbarth, T. Unold, R. Caballero, C. Kaufmann, H. W. Schock, Interpretation of

admittance, capacitance-voltage, and current-voltage signatures in Cu(In,Ga)Se2 thin film

solar cells, J. Appl. Phys. 107 (2010) 034509.

[6] T. Ott, T. Walter, T. Unold, Phototransistor effects in Cu(In,Ga)Se2 solar cells, Thin-Solid

Films 535 (2013) 275-278.

[7] M. Burgelmann, P. Nollet, S. Degrave, Modelling polycrystalline semiconductor solar cells,

Thin-Solid Films 361-362 (2000) 527-532.

[8] T. Ott, F. Schönberger, T. Walter, D. Hariskos, O. Kiowski, R. Schäffler, Long term

endurance test and contact degradation of CIGS solar cells, Proc. of SPIE 8825 (2013)

88250J.

[9] S.M. Sze, K.K. Ng, Physics of Semiconductor Devices, third ed., WILEY-Interscience, New

Jersey, 2007.

[10] F. R. Runai, F. Schwäble, T. Walter, A. Fidler, S. Gorse, T. Hahn, I. Kötschau,

Imaging and performance of CIGS thin film modules, Proc. of 37th

IEEE PVSEC (2011)

3399-3403.

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Table 1

Simulation Parameters

Parameter CIGSe2 CdS i-ZnO

d (µm) 2 0.1 0.08

(eV) 4.5 4.45 4.55

Eg (eV) 1.18 2.45 3.4

ɛr 10 10 10

NC (cm-³) 2*10

18 2*10

18 4*10

18

NV (cm-³) 2*10

18 1.5*10

19 9*10

18

μn (cm2/V s) 1000 50 50

μp (cm2/V s) 20 20 20

NA/D (cm-³) 8*10

14 (A) 1*10

15 (D) 5*10

17 (D)

Fig.1: Band diagram of a Cu(In,Ga)Se2 solar cell with a Schottky barrier of 500 meV at the back

contact.

Fig.2: a) shows a measured IV-characteristic for a Cu(In,Ga)Se2 device at temperatures of 300 K

and 90 K, for different illumination intensities. b) shows the corresponding Voc(T)-characteristic also

for different illumination intensities.

Fig.3: Schematic current diagram of a Cu(In,Ga)Se2 solar cell with a Schottky barrier in the

phototransistor state.

Fig.4: Simulated IV-characteristic for different illumination intensities at temperatures for 300 K

and 150K in a). A standard parameter set was used with a Schottky barrier at the back of 250 meV.

Corresponding Voc(T)-characteristic for different illumination intensities.

Fig.5: a) Simulated Voc(T)-characteristic. With a standard parameter set (ref), a CuGaSe2 layer

(Eg=1.68 eV) added at the back contact (CuGaSe2) and Ga/(In+Ga) gradient through the absorber

(1.18 eV 1.38 eV) increasing to the back contact (Ga lin. grad.). Every set was simulated with a

Schottky barrier at the back contact of 250 meV. Left figure b) shows the three different conduction

bands.

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Figure 1

Figure 2

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.5 1 1.5 2

ener

gy

in

eV

x in µm

Ec(eV)

Ef(eV)

Ev(eV)

ϕB

Cu(In,Ga)Se2

-50

0

50

100

150

0 0.2 0.4 0.6 0.8 1 1.2 1.4

curr

ent

den

sity

in

mA

/cm

²

voltage in V

1000W/m² 300K

500W/m² 300K

dark 300K

1000W/m² 90K

500W/m² 90K

dark 90K

a)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 100 200 300 400

Voc

in V

temprature in K

1000W/m²

500W/m²

100W/m²

10W/m²

ϕB

b)

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Figure 3

Figure 4

-50

0

50

100

150

0 0.5 1

curr

ent

den

sity

in

mA

/cm

²

voltage in V

1000W/m² 300K

500W/m² 300K

dark 300K

1000W/m² 150K

500W/m² 150K

dark 150K

a)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 100 200 300 400

Voc

in V

temperature in K

1000W/m²

500W/m²

100W/m²

10W/m²

ϕB

b)

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Fig.5

0

0.2

0.4

0.6

0.8

1

0 100 200 300 400

Voc

in V

temperature in K

ref. ɸB = 250 meV

CuGaSe2 ɸB = 250meV

Ga lin. Grad ɸB = 250 meV

a)

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.5 1 1.5 2 2.5

ener

gy

in

eV

x in µm

ref Ec

CuGaSe2 Ec

Ga lin. Grad Ec

Ef

b)

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Highlights

Phototransistor model explain behavior of Cu(In,Ga)Se2 solar cells(low temperature)

Main part of the phototransistor model is a Schottky barrier at the back contact

From Voc(T)-characteristic the barrier height at the back contact can be extracted

CuGaSe2 layer at the back contact prevent a phototransistor behavior

Graded band gap (absorber) prevent a phototransistor behavior