**Understanding the Physics of CdS-based PV: Band Diagram, Interfaces,
and Nonuniformities**

V. G. Karpov, D. Shvydka, J. Drayton, L. Cooray, and A. D. Compaan

Department of Physics and Astronomy, University of Toledo, Toledo, OH
43606, <vkarpov@physics.utoledo.edu>

#### ABSTRACT

Our recent discovery of piezo-PV coupling together with other indicative
evidence suggest an adequate band diagram for CdS based thin-film PV.
The proposed model is solved analytically leading to numerous
predictions that include lack of the carrier collection from CdS, buffer
layer effects, and others. This understanding points at new pathways for
device improvement.

**1. Objectives**

The research is aimed at better understanding the major polycrystalline
thin-film PV, CdTe and CIGS with the goal of device improvement through
understanding its physics.

**2. Technical Approach**

The approach is based on the analysis of indicative device facts and
focused experiments. The devices are described in the terms of band
diagrams that depend on film interfaces and are affected by structure
nonuniformities. Analytical modeling of J-V characteristics was verified
by numerical simulations, and model predictions were tested against a
variety of experimental results.

**3. Results and Accomplishments**

*3.1 New observation: piezo-photovoltaic coupling*

![](media/image1.wmf)

Fig. 1. Pressure effect on Voc and Jsc in CdTe based PV.

This recent observationError: Reference source not found attributes the
pressure related effects (Fig. 1) to the well-known strong piezo-
(pyro-) electricity of CdS. The implications include strong electric
field across the CdS layer and the depletion width exceeding CdS
thickness. The piezo-related electric potential difference across the
CdS layer can be as large as \~ 0.5 V. The CdS grains become electric
dipoles whose energetically favorable orientation is against the
photovoltaic electric field thus corresponding to the case (b) of Fig.
2, MIS type of PV. We continue working on this topic.

![](media/image2.wmf)

Fig. 2. AMPS simulated J-V curves corresponding to different band
diagrams: p-n junction (a) and MIS (b). Solid and dashed lines show
light and dark JV. The case (b) dark curve is laying flat on the voltage
axis for this particular choice of parameters. Because both (a) and (b)
are consistent with the experiment (within the data variability), this
J-V curve modeling appears not indicative.

*3.2 J-V modeling and other indicative facts*

While J-V fitting has become a major test for device modeling, it is
often inconclusive, since comparable fits can be obtained with
strikingly different models (Fig.2). Additional indicative facts include
(1) CdS related piezo-effect.[^1] (2) MIS nature of the device allowing
the reach-through band bending in CdTe caused by a proper \'metal\' on
the other side of CdS.[^2] (3) Buffer layers of certain morphology (for
example, sputtered) strongly increasing Voc while other chemically
equivalent layers (such as CVD) do not cause this effect;Error:
Reference source not found (4) Absence of carrier collection from
CdS;[^3] (5) Negative QE under the blue illumination for devices with
thick CdS.[^4] (6) Light and dark J-V crossing and, in some cases, flat
dark J-Vs in the forward bias.[^5]

*3.3 Device Model*

Our model consistent with the above facts is shown in Fig. 3. Here we
ignore backfield effects. The positive interfacial charge density
corresponding to the seagull singularity in the conduction band diagram
can originate from the piezo-effect. Each of the components, CdS and
absorber layers, is characterized by the standard diode equations
including the corresponding photocurrents (J~L~) and saturation currents
(J~S~). This model was solved analytically[^6] in the approximation of
two-dimensional electron charge density (*σ*) accumulated in the seagull
region (based on the sharp Boltzmann's distribution),

$$J = J_{S1} + J_{L1} - \frac{J_{L2} + J_{S2} + J_{L1} + J_{S1}}{1 + \left( \frac{J_{S2}}{J_{S1}} \right)\text{exp}(\frac{\text{qV}}{\text{kT}})} - J_{R}$$

![](media/image3.wmf){width="3.0in" height="1.875in"}Fig. 3. Band
diagram of CdS based thin-film PV. Grey shaded area represents the
electron density *σ* accumulated in the narrow proximity of conduction
band cusp.

where the recombination current *J~R~* is relatively small and
proportional to *σ* ; its analytical expression is omitted here. This
result predicts all the facts listed in Sec. 3.1 above. In addition, it
predicts the ratio of shunt over series resistances
$\frac{R_{\text{sh}}}{R_{s}} \approx \left( \frac{J_{L2}}{J_{L1}} \right)^{2}\text{\textasciitilde}\text{100}$,
in the ballpark of the typical values for both CIGS[^7] and CdTe[^8]
based PV (although they can be affected by shunting and backfield
effects). Also, it quantitatively describes the dark to light J-V
crossing and voltage dependence of recombination rate *J~R~(V).*
Finally, our model can account for the hopping transport, especially
important with thin CdS.

We verified our analytical results by numerical simulations with the
AMPS parameters from Ref.[^9] To simulate the interfacial charges we
added two artificial narrow layers[^10] (thickness of 0.1*l*~1~)
containing very high concentrations of shallow donors (for the positive
charge) and acceptors (for the negative charge): good agreement was
obtained.

*3.2 Practical Issues*

Several practical opportunities suggested by our new understanding
include (i) substrate and buffer layer surface morphology as a factor
that through the internal stress can affect the voltage distribution and
related device parameters; (ii) a possibility to affect the device
parameters by conducting the deposition and/or subsequent treatments
under the light or external bias (through changing the orientation of
CdS grain electric dipoles).

We note that reorienting the CdS dipole does not require the grain
rotation. The predominantly Cd or S terminations determine the locations
of the positive and negative faces of the grain. Therefore, it only
takes a single atomic layer to diffuse along the grain to electrically
reverse its orientation. This predicts the reorientation process to be
practically achievable and dependent on the grain boundary morphology.
CdCl2 treatments known in the CdTe technology or similar can create the
required favorable conditions.

Our most recent work[^11] on CdCl~2~ treatments under electric field
does show significant differences between samples treated under
different biases.

*3.2 Nonuniformity and other device physics work*

Superimposed on the above understanding are the effects of nonuniformity
that can originate from the fluctuations in the CdS transparency
(fluctuations in J~S1~) and back barrier. Our AFM study of the back
barrier nonuniformity has revealed significant lateral fluctuations in
the local transversal currents.[^12] We have started systematically
using the PSPICE software to model the nonuniformity loss in both
laboratory scale cells and integrated large area modules.[^13]

**4. Conclusions**

Based on the discovered piezo-PV coupling and other indicative evidence
we have proposed a new model of CdS based PV that explains a large
number of facts and predicts new ways in device improvement.

## ACKNOWLEDGEMENTS

This work was partially supported by the NREL Grant No.
RXL-5--44205--01.

## REFERENCES

[^1]: D. Shvydka et. al., Appl. Phys. Lett. **87**,123505 (2005)

[^2]: Y. Roussillon et. al., Appl. Phys. Lett. **85**, 3617 (2004); C.
    S. Ferekides et. al., This Meeting Proceedings

[^3]: Handbook of Photovoltaic Science and Engineering, Edited by A.
    Lique and S. Hegedus, Wiley 2003

[^4]: S. Hegedus, S. Hegedus, private communication and

    National CdTe R\\&D Team Meeting Minutes, Editors P. V.

    Meyers and H. S. Ullal, NREL Golden, CO, January 27-28 (2000),
    Appendix 12.

[^5]: B. Tetali, et. al., in 29th IEEE, New Orleans, LA, 2002, p. 600;
    T. J. McMahon and A. L. Fahrenbruch, in 26th IEEE PVSC, Anaheim,
    1997, p. 539

[^6]: L. Cooray and V. G. Karpov, submitted for publication.

[^7]: D. Liao, A. Rockett, 28^th^ IEEE PVSC (Alaska2000) p. 446.

[^8]: X. Li, et. al., J. Vac. Sci. Technol. A 17, p. 805 (1999). 

[^9]: M. Gloeckler, A. L. Fahrenbruch, and J. R. Sites, 3rd World
    Conference on Photovoltaic Energy Conversion, Osaka, Japan, 11-18
    May 2003, p. 2P-D52.

[^10]: We are grateful to A. L. Fahrenbruch who suggested this
    technique.

[^11]: D. Shvydka, J. Drayton, A. D. Compaan, unpublished.

[^12]: D. Shvydka, V. Parikh, V. G. Karpov, and A. D. Compaan, MRS Proc.
    Vol. 865, paper F12.2.1 (2005).

[^13]: D. Shvydka,V.G. Karpov, Phys.Rev. **B 71**,115314 (2005).

    ### **MAJOR FY 2005 PUBLICATIONS**

    In addition to Refs. 1, 6, 12, and 13, we note

    V.G. Karpov, D. Shvydka, and Y. Roussillon, "*[Physics of CdTe
    Photovoltaics: From Front to
    Back](http://www.mrs.org/members/proceedings/spring2005/f/F10_1.pdf)",*
    MRS 2005, Vol. 865, paper F10.1.

    V. G. Karpov, Diana Shvydka, and Y. Roussillon, "*Physical modes of
    thin-film PV degradation"* 31st IEEE PVSC, (2005), p. 437