当前位置:首页 >> 能源/化工 >>

Thin-Film Solar Cells Device Measurements and Analysis


PROGRESS IN PHOTOVOLTAICS: RESEARCH AND APPLICATIONS Prog. Photovolt: Res. Appl. 2004; 12:155–176 (DOI: 10.1002/pip.518)

Special Issue

Thin-Film Solar Cells: Device Measurements and Analysis
Steven S. Hegedus*,y and William N. Shafarman
Institute of Energy Conversion, University of Delaware, Newark, DE 19716-3820, USA

Characterization of amorphous Si, CdTe, and Cu(InGa)Se2-based thin-?lm solar cells is described with focus on the deviations in device behavior from standard device models. Quantum ef?ciency (QE), current–voltage (J–V), and admittance measurements are reviewed with regard to aspects of interpretation unique to the thin-?lm solar cells. In each case, methods are presented for characterizing parasitic effects common in these solar cells in order to identify loss mechanisms and reveal fundamental device properties. Differences between these thin-?lm solar cells and idealized devices are largely due to a high density of defect states in the absorbing layers and to parasitic losses due to the device structure and contacts. There is also commonly a voltage-dependent photocurrent collection which affects J–V and QE measurements. The voltage and light bias dependence of these measurements can be used to diagnose speci?c losses. Examples of how these losses impact the QE, J–V, and admittance characterization are shown for each type of solar cell. Copyright # 2004 John Wiley & Sons, Ltd.
key words: thin ?lm; amorphous Si; Cu(InGa)Se2; CdTe; quantum ef?ciency; admittance

INTRODUCTION
hin-?lm solar cells (TFSCs) have achieved ef?ciencies approaching 15–20%. Much of the progress has occurred by empirical processing improvements and in spite of a relatively poor understanding of the underlying mechanisms and electronic defects which control the device behavior. However, as each technology matures, a more complete picture of the device operation has emerged to enable both a better understanding of the devices and identi?cation of pathways to further improvements. In this article, differences between ideal crystalline solar cells and typical TFSCs will be identi?ed. It will be shown that the photovoltaic performance of present day a-Si, CdTe, and Cu(InGa)Se2-based devices have much in common, despite very different processing, device structures, and absorber properties. Experimental and analytical procedures will be described to characterize the quantum ef?ciency (QE), current–voltage (J–V), and admittance behavior. In each case, the approach will be based on eliminating parasitic effects common to the TFSCs in order to reveal the fundamental properties of the intrinsic junction and absorber. The objective of this article is to demonstrate methodology for analyzing TFSCs with examples from different devices rather than just to review previous work, so in many cases excellent work in the literature could not be cited.

T

*Correspondence to: Steven S. Hegedus, Institute of Energy Conversion, University of Delaware, Newark, DE 19716-3820, USA y E-mail: ssh@udel.edu Contract/grant sponsor: NREL; contract/grant number: ADJ-1-30630-12. Copyright # 2004 John Wiley & Sons, Ltd.

Received 2 September 2003

156

S. S. HEGEDUS AND W. N. SHAFARMAN

Solar cell operation, either crystalline or thin ?lm, can be described by identifying loss mechanisms. These can be divided into three categories. First are recombination losses which limit the open-circuit voltage VOC. Second are parasitic losses, such as series resistance, shunt conductance, and voltage-dependent current collection, which primarily impact the ?ll factor (FF), but can also reduce short circuit current JSC and VOC. Finally, there are optical losses which limit generation of carriers and, therefore, JSC. We focus on losses largely unique to TFSCs. Physical and electrical properties of TFSCs which cause them to have different losses from the standard ‘textbook’ crystalline Si (c-Si) cells include:
*

*

*

*

*

*

TFSC absorber layers have much higher absorption coef?cients than c-Si so a large fraction of the photogeneration occurs near the interface and in the high ?eld space charge region (SCR). This enables high currents, even with relatively small collection lengths; the semiconductor ?lms often have a range of shallow and deep defect levels or defect bands within the bandgap. These result from imperfect crystallinity or amorphous structure and from the use of low-cost materials and processes optimized for high throughput and low cost as much as for high device ef?ciency. This can create different recombination mechanisms than radiative band-to-band recombination commonly found in ideal crystalline semiconductor devices; poor minority carrier lifetime, due to the above factors, leads to increased reliance on the electric ?eld for suf?cient minority carrier collection rather than diffusion alone. This often results in voltage-dependent collection of light-generated current; TFSCs are heterojunction device structures with high densities of defect states at interfaces which can provide a path for interface recombination; the grain boundaries in polycrystalline Cu(InGa)Se2 and CdTe devices may act as high recombination surfaces or shunt paths. This leads to lateral ?eld nonuniformity and recombination varying in two dimensions; non-ohmic or blocking contacts can limit current at forward bias.

Devices to be studied here include a-Si p–i–n or n–i–p type cells, and polycrystalline CdTe/CdS and Cu(InGa)Se2/CdS p–n heterojunction cells. QE measurements will be used to determine optical losses, optical enhancements, and voltage-dependent photocurrent mechanisms. J–V measurements under standard test conditions will be shown and a systematic procedure to separate diode and parasitic effects will be presented. Standard C–V measurements often fail to provide much information on TFSC if they do not to yield a linear C?2–V relation, so we will describe other types of ac (admittance) measurements and analyses which do provide quantitative interpretation.

SAMPLES
The TFSC devices characterized here were made by a variety of methods and have a variety of device structures. Generically, there are two types of TFSC superstrate or substrate devices, as shown in Figure 1. Superstrate devices are made on a transparent substrate such as glass, so the light enters the absorber through the ?rst deposited layers. Substrate devices are typically made on opaque substrates such as metal foils or metallized

Figure 1. Typical superstrate (a) and substrate (b) TFSC con?gurations
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

THIN-FILM SOLAR CELL CHARACTERIZATION

157

glass and light enters the absorber through the last deposited layer. In this work, three types of TFSCs will be characterized. Most of them were fabricated at the Institute of Energy Conversion (IEC). Cu(InGa)Se2-based solar cells have a substrate device structure of glass/Mo/Cu(InGa)Se2/CdS/ZnO/ grid. The Cu(InGa)Se2 layers deposited by elemental thermal evaporation were 2–3 mm thick, and their bandgap could be varied from 1?0 to 1?7 eV by varying Ga/(In ? Ga). The CdTe based solar cells have a superstrate device structure of glass/SnO2/ CdS/CdTe/metal. The CdTe layers were deposited by several techniques by different groups and were 2–4 mm thick. The a-Si-based solar cells have a superstrate device structure of glass/SnO2/p-i-n/BR where the back re?ector (BR) is either metal or ZnO/metal. The a-Si layers were deposited by rf plasma chemical vapor deposition and were about 0?4 mm thick. The critical component of the TFSC is the absorber layer, where the photogeneration and most of the recombination occurs. Devices will be referred to by their absorber layer: Cu(InGa)Se2, CdTe, a-Si, or a-SiGe.

QUANTUM EFFICIENCY
Quantum ef?ciency (QE) measurements are valuable to characterize the photocurrent and are commonly used to determine the losses responsible for reducing the measured JSC from the maximum achievable photocurrent. Typical measurement equipment and techniques are described elsewhere.1 QE is a dimensionless parameter given by the number of electrons which exit the device per incident photon at each wavelength. The photocurrent is the integral over wavelength of the product of the measured external QE with the illumination spectrum, typically AM1?5 global for terrestrial solar cells. Thus, a good veri?cation of the QE measurement is that the current calculated by integrating the QE, measured with 0 V bias, with the AM1?5 spectrum agrees with JSC. Good agreement will typically be found in well-behaved devices such as crystalline Si solar cells, although signi?cant differences between the integrated QE and the photocurrent can occur in TFSCs when the collection depends on the intensity and spectrum of the incident illumination.2 Device losses measured by QE can be optical, due to the front re?ection and absorption in the window, transparent conductor, and other layers, or electronic, due to recombination losses in the absorber. Comparing the QE measured with different voltage bias is a powerful tool to separate electronic losses and optical losses since only the former should be affected by the applied bias. Figure 2 shows the QE for several high-ef?ciency TFSCs.3–5

Figure 2. QE of high ef?ciency TFSCs: (a) a-Si thin top cell of a triple junction with no back re?ector;2 (b) a-SiGe, bottom cell with graded bandgap and back re?ector;2 (c) CdTe;3 (d) Cu(InGa)Se2 with Ga/(In ? Ga) ? 0?3 and Eg ? 1?2 eV;4 (e) CuInSe24
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

158

S. S. HEGEDUS AND W. N. SHAFARMAN

The differences in shape and cut-off at long wavelengths are primarily related to the absorber bandgap. The shape and magnitude at short wavelengths is related to device structure and window layers. The TFSC is a multilayer optical stack, as illustrated in Figure 1. The light goes through several layers, including the TCO and emitter, before entering the absorber where the carrier generation occurs. The effect of these layers on reducing the amount of light available in the absorber can be numerically quanti?ed and the measured QE can be corrected for their in?uence. What remains, after accounting for all the other known losses, is the internal QE (QEINT), due only to the photogeneration and collection in the absorber. Sometimes QEINT is de?ned as just QE/(1-R) where R is the light re?ected from the solar cell. In that case, QEINT also includes window layer absorption losses. In this paper, we use the ?rst de?nition. Referring to Figure 1, impinging light ?rst encounters front surface re?ection from the air/glass/TCO/emitter or air/TCO/emitter interfaces, respectively. The transparent conducting oxide (TCO) may be SnO2, ZnO, ITO, or other materials, but they all have similar refractive indices, hence re?ective properties. There may also be an anti-re?ection layer on the front to reduce the air/glass or air/TCO re?ection. For analysis, these components of front-surface re?ection are grouped together as RF. In addition, substrate devices often have a metal grid on the thin TCO layer to provide low-resistance current collection. The grid shades a small fraction of the device thus reducing the active area and is accounted for by a wavelength-independent grid shadowing factor TG which is typically >0?95 for small-area devices, with TG ? 1 for gridless superstrate devices. Light can be absorbed in the TCO and emitter layers as well. In CdTe and Cu(InGa)Se2 devices, the emitter layer is typically CdS. In a-Si devices, the emitter is either an a-SiC or mc-Si p-layer. A common goal of all TFSC designs is to minimize emitter layer absorption by increasing its bandgap, decreasing its thickness or both. Most of the remaining light is absorbed in the absorber layer, generating the carriers which contribute to the photocurrent. Light that is not absorbed in the absorber layer impinges on the back contact where it is either absorbed and converted to heat or, as in the case of a-Si devices, partially re?ected back into the absorber. The fraction of incident light reaching the absorber layer is given by the product of the transmission through each of the front layers, or TF ?? ? TG ?1 ? RF ??? ?1 ? ATCO ??? ?1 ? AE ??? ?1?

where ATCO and AE are the absorption of the TCO (or TCO/glass) and emitter layer, respectively. Then the measured, or external, QE for a TFSC is QE?; V; I? ? TF ??QEINT ?; V; I???; V; I? ?2?

where ?(, V, I ) is a voltage-and-light-bias-dependent gain factor. QEINT, the internal collection, is dependent on the absorber layer’s absorption coef?cient , thickness d, and an effective minority carrier collection length. It also depends on the external variables of the applied voltage V, and bias light intensity I. QEINT decreases with increasing forward bias or increasing bias light intensity in most TFSCs, due to a reduction in ?eld and space charge width6,7 or due to series resistance effects.8,9 At suf?cient reverse bias QEINT reaches an optically limited maximum where there are no electronic losses, i.e., complete collection occurs, provided there is no light absorbed at the back contact. Optical enhancement, which commonly occurs in a-Si due to light trapping, is included in QEINT. ?(,V,I) describes photoconductive effects in which the ac chopped light used for the QE measurement is coupled with the stronger dc bias light. In most cases, ?(,V,I ) ? 1 unless the device is at far forward bias and/or has a spectrally ?ltered bias light spectrum. When ?(,V,I ) 6? 1 the measured QE should be referred to as the apparent QE (or AQE). In some cases this can be readily determined when the measured QE exceeds unity which violates energy conservation. QE curves for a Cu(InGa)Se2 TFSC at two different voltage biases, 0 and ?1 V, along with the most common losses, are shown in Figure 3.10 The losses are converted to equivalent photocurrent by integrating the re?ection, absorption or QE with the AM1?5 illumination spectrum and are listed in Table I. Losses 1–5 are optical and 6 is electronic. In practice, the magnitude of each of these losses will depend on details of the device design and optical properties of the speci?c layers. Optical absorption losses in the emitter and TCO layers are determined
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

THIN-FILM SOLAR CELL CHARACTERIZATION

159

Figure 3. Quantum ef?ciency at 0 V (lower solid curve) and ?1 V (upper solid curve) with optical losses for a Cu(InGa)Se2 solar cell in which the Cu(InGa)Se2 has Eg ? 1?12 eV; losses are identi?ed in Table I

from separate optical measurements on control samples of these layers which were deposited on glass substrates. Referring to their numbers in Figure 3, the losses include: 1. Shading from the collection grid used for some substrate devices. This is the only wavelength-independent optical loss; 2. Front-surface re?ection from the air/ZnO/CdS/CuInGaSe2 interfaces. For high-ef?ciency ‘champion’ devices, this is often minimized with an anti-re?ection layer. Typical re?ection from a superstrate TFSC device is slightly lower (8–10%) than from substrate devices, owing to the lower index of glass compared with TCOs; 3. Absorption in the TCO layer. Typically there is 1–5% absorption through the visible wavelengths which increases in the near IR region ( > 900 nm), due to free carrier absorption and at short wavelengths ( < 400 nm) approaching the TCO bandgap. Superstrate devices on glass/SnO2 have higher TCO absorption losses than substrate devices because the commonly used SnO2 has higher absorption losses than ZnO or ITO for a given sheet resistance. These cells also have absorption losses in the low-cost glass; 4. Absorption in the emitter layer. For CdS as in Figure 3, this becomes appreciable at wavelengths below $520 nm corresponding to the CdS bandgap 2?42 eV. The loss in QE for  < 500nm for most emitters is proportional to the layer thickness since electron–hole pairs generated in the emitter are not collected. Figure 3 shows a device with a $40-nm-thick CdS layer. In practice, the CdS layer is often thicker and the absorption loss greater; 5. Incomplete absorption in the absorber layer near the Cu(InGa)Se2 bandgap. Bandgap gradients, resulting from composition gradients in many Cu(InGa)Se2 and a-SiGe absorbers, also affect the steepness of the long-wavelength part of the QE curve. If the absorber is made thinner than 1/ g, where g is the absorption coef?cient just above the bandgap, this loss becomes signi?cant unless light trapping is employed;
Table I. Photocurrent loss due to the optical and collection losses for the Cu(InGa)Se2 TFSC in Figure 3. Jtot ? 42?8 mA/cm2 is the total photocurrent available for the AM1?5 spectrum for E > 1?12 eV
Region in Figure 3 1 2 3 4 5 6 Optical loss mechanism Shading from grid with 4% area coverage Re?ection from Cu(InGa)Se2/CdS/ZnO Absorption in ZnO Absorption in CdS Incomplete generation in Cu(InGa)Se2 Incomplete collection in Cu(InGa)Se2 ?J (mA/cm2) 1?7 3?8 1?9 1?1 1?9 1?0 ?J/Jtot (%) 4?0 8?9 4?5 2?5 4?4 2?3

Copyright # 2004 John Wiley & Sons, Ltd.

Prog. Photovolt: Res. Appl. 2004; 12:155–176

160

S. S. HEGEDUS AND W. N. SHAFARMAN

6. Incomplete collection of photogenerated carriers in the absorber. This is the only electrical loss factor and will be discussed below. At suf?cient reverse bias, in this case ?1V, all carriers are collected without any electrical losses. Generally the QE in a TFSC will increase with reverse bias. QE Voltage Bias Dependence Photocarrier collection proceeds differently in polycrystalline solar cells such as Cu(InGa)Se2 and CdTe than in a-Si based TFSC because transport in the former is limited only by minority carrier electrons in the p-type absorber layers, while in the latter carriers are generated in the intrinsic layer and transport is ambipolar. This particularly affects the analysis of the voltage bias dependence of QEINT because of the difference in ?eld pro?le and minority-carrier transport between the two types of devices. QEINT in Cu(InGa)Se2 and CdTe devices will be discussed ?rst. For unipolar absorbers such as CuInGaSe2 and CdTe, QEINT can be approximated7,11 by: QEINT ?; V? ? 1 ? exp?? ??W?V?? ??L ? 1 ?3?

where () is the absorption coef?cient, W(V) is the space-charge width, and L is the minority carrier diffusion length (all pertaining to the absorber). This approximation assumes that all carriers generated in the spacecharge region are collected without recombination loss and those generated in the neutral bulk diffuse to the depletion edge. It also assumes the absorber is relatively thick; d > 1/ g. A simple view is that carriers generated within one collection length W(V) ? L of the junction for polycrystalline materials are collected without recombination losses. In the limit of very short L, L ( 1, Equation (3) reduces to QE ? 1?exp[ ? W(V)] which is the expression for collection in the space-charge region. Since W(V) is a function of the applied voltage bias, QEINT and total light-generated current are, in general, voltage dependent, and the latter is referred to as JL(V ). Incomplete collection of minority carriers generated beyond L ? W(V) into the TFSC absorber layer can be a signi?cant loss mechanism. The effect of JL(V ) on J–V behavior increases with forward voltage and will be discussed below. Voltage-dependent collection is illustrated in Figure 3 by the increase in QE measured at ?1V compared with that measured at 0 V. For Cu(InGa)Se2, W(0 V) % 0?1-0?5 mm and L ’ 0.1–1 mm while for CdTe W(0V) ’ 2– 3 mm and L ’ 0.1–1 mm. Thus, the collection length at 0 V in Cu(InGa)Se2 is less than the typical thickness (2–3 mm), but in CdTe, it is comparable to or greater than the thickness of typical devices (2–4 mm), so CdTe may have more complete collection at long wavelengths, but also greater voltage dependence. The assumption in Equation (3) of complete collection from within W may not apply, such as in the case of low carrier density and large depletion width. Then Equation (3) would need to be scaled by exp[ ? t(V)/] where t(V) is the transit time of the electron drifting to the junction and  is the lifetime. This may be the case with CdTe devices. QEINT for a-Si p–i–n cells differs from the polycrystalline heterojunctions described above for three reasons. First, the photocarrier collection is primarily ?eld driven. There is no ?eld-free neutral region for diffusion-limited collection and no clearly de?ned depletion width W(V) from which it can be assumed that all generated carriers are collected. Second, collection of both holes and electrons must be considered, and recombination losses can be signi?cant for either. The concept of the limiting carrier is critical to understanding ambipolar photocurrent collection.12 The limiting carrier is the one which generates the smaller photocurrent and will have the smaller mobility-lifetime (m) product. The complexity of ambipolar transport requires considerable simpli?cation to develop an analytical model.12 Third, optical enhancement is typically employed to increase the pathlength of long-wavelength photons via light trapping. Because the limiting carrier typically changes from electrons at short wavelengths to holes at long wavelengths (for the case of light incident through the p-layer), it is not possible to derive a single analytical expression for the voltage dependence for a-Si solar cells valid at all wavelengths. The recombination mechanism for electrons, which determines the voltage dependence at short wavelengths, i.e., strongly absorbed light, is due to either back-diffusion into the p-layer (a p–i interface effect) or recombination while drifting across the i-layer (a bulk i-layer effect). The recombination mechanism for holes, which determines the voltage
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

THIN-FILM SOLAR CELL CHARACTERIZATION

161

dependence at long wavelengths, i.e., weakly absorbed light, is always due to recombination while drifting across the i-layer to the p-layer (a bulk i-layer effect). With considerable simpli?cation, the QEINT for a-Si devices is given by QEINT ?; V ? ? Ai ??c ?V ? The i-layer absorption Ai() is given as Ai ?? ? 1 ? exp?? ??m??d ? ?5? ?4?

where m is a wavelength-dependent enhancement factor due to scattering and light trapping which describes the increase in optical pathlength over that of a completely specular device with no back re?ector. The voltage dependent collection factor C(V ) depends on whether short- or long-wavelength collection is being considered.12 A model for JL(V ) under the assumption of a uniform ?eld gave, for weakly absorbed light where the hole is the limiting carrier:6,12 ? ? ?? c ?V ? ? X 1 ? exp X ?1 ?6? with X?   LC V 1? VFB d

?7?

Here LC is the collection drift length at zero bias given by LC ?0? ? E?0? ?  VFB d ?8?

m is for the holes (limiting carrier), E(0) is the average ?eld at 0 V bias, and VFB is the ?at-band voltage. Experimentally, VFB is the voltage where J(V ) ? JD(V ), or JL(V ) ? 0, and is typically $0?1 V greater than VOC. Additional terms accounting for nonuniform ?elds and diffusion contribution have been given, but are relatively minor.12 Determining LC at different wavelengths can help separate bulk and interface recombination.13 However, a single value obtained at long wavelengths is suf?cient to characterize the dominant collection in the i-layer under white light.14 The voltage dependence of QEINT(V,) has been used empirically to characterize collection problems in a variety of cases, including: Cu(InGa)Se2 devices with increasing bandgap5 or lower deposition temperature;15 a-Si devices due to impurity contamination in the i-layers;16 interface buffer layers;13,17,18 light degradation;19 and a-SiGe grading;20 and in CdTe devices due to interface recombination;21 photoconductive CdS;22 and Cu doping as a function of CdTe thickness.23 A useful method to characterize JL(V ) is to consider the wavelength dependence of the ratio of QE measurements at different voltage biases. For example, the ratio QE(?1 V)/QE(0 V) is shown in Figure 4 for 4 Cu(InGa)Se2 devices with increasing absorber layer bandgap. The increased voltage dependence at longer wavelengths indicates poor minority-carrier collection from the bulk of the absorber which becomes a more signi?cant loss in the devices as the bandgap increases. This is accompanied by indications of JL(V ) in J–V measurements, as discussed below. Figure 5 shows the QE voltage bias dependence as QE(?1 V)/QE(0 V) and QE(?0?5 V)/QE(0 V) for two a-Si p–i–n cells having similar VOC ($0?87 V) and JSC ( $15 mA/cm2) but very different values of FF. Cell A (FF ? 57%) has a large decrease in QE at long wavelengths with forward bias, suggesting poor collection of holes, since they have farther to drift compared with electrons. Cell B (FF ? 69%) shows a slight increase in bias dependence at shorter wavelengths, which is often associated with low electron lifetime, or low ?elds at the p–i interface allowing electron back-diffusion into the p-layer.16,19 Note that the ratio QE(?1 V)/QE(0 V) has less wavelength dependence than the ratio at 0?5 V, indicating that reduction in electric ?eld with forward bias is responsible for the photocurrent losses. Nevertheless, the cells show greater dependence of both QE ratios in the same wavelength region respectively. For example, the QE of
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

162

S. S. HEGEDUS AND W. N. SHAFARMAN

Figure 4. Reverse-bias QE ratio QE(?1 V)/QE(0 V) bias for four Cu(InGa)Se2 devices with different bandgap absorber layers

cell B has greater change with bias at short wavelengths for either ?1 V or ?0?5 V, indicating that the electron collection steadily decreases with decreasing electric ?eld. If the QE bias ratio is wavelength independent, it suggests a loss mechanism that affects all carriers equally, regardless of where in the device they were generated. Two such mechanisms occur at the heterojunction interface; interface recombination and a barrier due to heterojunction band-offsets. A third mechanism is related to the interaction between the equivalent series resistance and the operating bias point during the QE measurement.8,9 Specially fabricated solar cells having transparent back contacts allow for probing of the collection from either front or back. The measurements can be analyzed by simultaneously ?tting the data to the equations for collection with illumination from the front and back side, after making corrections for optical losses to

Figure 5. QE ratios for two a-Si devices at reverse (top) and forward (bottom) bias compared to 0V bias
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

THIN-FILM SOLAR CELL CHARACTERIZATION

163

determine QEINT for each case. This has been used to separate the ?eld-assisted and diffusion collection contributions for CuInSe224 and to compare hole- with electron-limited collection in a-Si devices.25 Bias light dependence of QE Standard J–V test conditions for solar cells use an illumination of $100 mW/cm2. In contrast, the monochromatic probe beam in a typical QE measurement will be 3–4 orders of magnitude weaker. In an idealized solar cell, these differences are irrelevant, since the response is assumed to be linear with input. Bias light will have negligible effect on devices with low trap density, but some TFSCs have nonlinear output due to trapping and photoconductivity.2 The effect of white bias light on the QE and collection in a-Si is due to an increase in the positive space charge from trapped charge,26,27 which changes the electric ?eld distribution and the regions with high or low drift-aided collection. Bias light can also affect polycrystalline heterojunction TFSCs, owing to photoconductive CdS changing the electric ?eld distribution in the absorber which in?uences the voltage-dependent collection.8,22 The bias light effects can be even greater for QE measurements under red or blue bias light.27 In general, to characterize the most relevant optical and collection effects in a device, the QE should be measured with white bias light and in the dark. Any signi?cant difference requires further investigation of the bias and spectral dependence. Optical enhancement In the case of highly absorbing direct bandgap layers such as Cu(InGa)Se2 and CdTe, most light is absorbed before it reaches the back contact, unless the absorber layer thickness is reduced suf?ciently that gd $1 which requires d < 1 mm. There is no need for light trapping and m ? 1. However, a signi?cant portion of the incident light is not absorbed in a single pass through the i-layer of a typical a-Si device. Therefore, textured substrates and re?ective back contacts are used to scatter the light and increase the pathlength. Long-wavelength light that reaches the back contact is re?ected back where it can make multiple passes to increase the probability for absorption leading to m > 1. Practical methods to use QE measurements to determine m have been presented.28,29 First, all other optical losses must be quanti?ed to determine TF and the optical absorption coef?cient of the a-Si i-layer must be determined. Then, the optically limited QE is measured at reverse bias. Thicker devices require greater reverse bias to achieve the same high electric ?eld and to assure that all photogenerated carriers are collected. Finally, the QE calculated from Equations (2) and (5) is ?t to the measured QE by adjusting m. Figure 6 shows the QE for three co-deposited p–i–n devices with d ? 0?39 mm, and m() derived from the

Figure 6. (a) QE at reverse bias and (b) optical enhancement, m(), of three a-Si devices with different TCOs. Device A had low texture SnO2 with an Al re?ector, B had high texture with Al, and C had high texture with an ZnO/Ag re?ector. Also shown in (a) is TF from Equation (2) using measured values for device C
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

164

S. S. HEGEDUS AND W. N. SHAFARMAN

?tting. One device (A) had minimal optical enhancement, m < 3, due to only lightly textured SnO2 and a lowre?ectivity Al back contact. Another device (B) was deposited on more textured SnO2, giving greater scattering and, hence, larger optical enhancement. A third device (C) had the more textured SnO2 substrate and also a highly re?ective back contact of ZnO/Ag. The JSC increased accordingly from 12?5 to 14?1 to 14?7 mA/ cm2.28 This device had m as high as 12, indicating ef?cient light trapping.

CURRENT–VOLTAGE ANALYSIS
Current-voltage (J–V) measurements under standard illumination conditions, 100 mW/cm2 AM1?5 spectrum at 25 C, are the most common tool for solar cell evaluation and characterization. Measurement equipment and standardized techniques are described elsewhere.1 Frequently, J–V characterization means determination of the basic parameters VOC, JSC, FF, and ef?ciency () which are determined by only three points on the J–V curve. While these parameters are well accepted indicators of solar cell performance and are particularly valuable for comparing and qualifying cells, there is a wealth of additional information that can be obtained by analyzing the entire J–V curve. This is particularly so if the dependence on light intensity and temperature is considered. With regard to characterizing J–V behavior, the most important difference between TFSCs and high-ef?ciency solar cells based on single c-Si or III–V materials is the prevalence of parasitic losses, in the TFSCs. Thus, for analysis of the J–V behavior to go beyond determining the basic parameters generally entails separation of the recombination losses from these other parasitic losses. The J–V behavior of a TFSC can be described by a general single exponential diode equation: h q i J ? J0 exp ?V ? RJ ? ? GV ? JL ?9? AkT for the case of constant JL. The series resistance R and shunt conductance G are lumped circuit model representations of the losses that occur in series or parallel with the primary diode, respectively. The diode current J0 is given by:   ?b J0 ? J00 exp ? ?10? AkT with the ideality factor A, barrier height ?b, and prefactor J00 dependent on the speci?c recombination mechanism that dominates the forward current J0. Combining Equations (9) and (10), for G ( JL/VOC, the open-circuit voltage is:   ?b AkT J00 ln ? Voc ? ?11? q q JL A speci?c objective in the characterization of J–V behavior of a solar cell is to determine the mechanism that limits VOC. Any of several different recombination paths could dominate the device behavior at VOC, including recombination currents in the space-charge or neutral regions of the absorber layer or at any of the critical interfaces, including the absorber/emitter interface or back contact in a Cu(InGa)Se2 or CdTe device or the p–i or n–i interfaces in an a-Si device. Each of these mechanisms can be expressed by the general diode model of Equations (9) and (10) and speci?c formulations of these equations for each case can be compared.11,30 Thus, experimental determination of these diode parameters is fundamental to determining the limiting behavior of these TFSCs. In practice, the recombination often may not ?t the textbook cases due to, for example, recombination through defect bands rather than discrete states or by tunneling or multistep processes. Many authors have presented models for some of these cases to explain speci?c observations such as the temperature or voltage dependence of the diode parameters that cannot be explained by the standard textbook formulations. These details will not be addressed in this article. The basic diode behavior and recombination mechanisms are the same for all the TFSCs. To illustrate this, it is helpful to look at the temperature dependence of VOC. Figure 7 shows VOC as a function of T for several
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

THIN-FILM SOLAR CELL CHARACTERIZATION

165

Figure 7. Temperature dependence of VOC for four TFSC devices with different absorber materials, in each case VOC ! Eg/q (absorber) as T ! 0

TFSCs, including a-Si, CdTe, and Cu(InGa)Se2 with two different bandgaps, with lines extrapolating each to T ? 0. In each case the line ?ts the data well with intercept VOC ! Eg/q as T ! 0, where Eg is the bandgap of the primary light–absorbing layer. Thus, experiments show that the barrier height is ?b ? Eg for these devices which indicates that the dominant recombination current occurs in the absorber layer. The measured temperature dependence of VOC justi?es writing the form of J0 as in Equation (10). Furthermore, for these TFSCs, the ideality factor of a well-behaved device is typically in the range 1?3 4 A 4 2. These results for ?b and A indicate that the solar cells operate with the diode current controlled by recombination through trap states in the space-charge region of the absorber layer. Typically this occurs in the few tenths of a micrometer closest to the junction in the absorber in a CdTe or Cu(InGa)Se2 solar cell or within the i-layer of an a-Si device. The variation in A between 1 and 2 depends on the energies of the deep defects that act as dominant trap states31 and its relatively small temperature dependence has been attributed to a distribution of traps32 or a tunneling contribution to the space-charge recombination current.33 As shown in Figure 7, measuring the temperature dependence of VOC enables ?b to be determined. To quantify the other terms which describe the recombination mechanism, A and J0, it is tempting to simply perform a least-squares ?t of the J–V data at a given temperature to Equation (9). However, this commonly leads to errors if it is not ?rst veri?ed that the J–V data are well-behaved in the sense that the basic diode model provides a complete description of the J–V data with R, G, and JL independent of voltage over the range in which the data is analyzed. In practice, R, G, A, JL and J00 can all be voltage and/or light dependent in TFSCs and these dependencies on extrinsic variables are a major source of complication in the analysis of TFSCs. Analysis procedure A practical procedure for verifying that the device is well-behaved and for determining the diode parameters is to use a set of four successive plots, each comparing data measured both in the dark and under white light illumination. In some cases, it is useful to make further comparison of data obtained at several illumination intensities. These plot types are: (a) A standard linear J–V curve. This should include suf?cient data in both the ?rst and third quadrants where non-ideal effects not described by Equation (9), such as current blocking behavior or light-to-dark crossover in forward voltage bias or breakdown in reverse bias, which are commonly observed in TFSCs. The next three plots are derived from these light and dark J–V curves. (b) A plot of the derivative g(V )  dJ/dV against V near JSC and in reverse bias where the derivative of the diode term in Equation (9) becomes negligible. If the shunt term is ohmic and JL is constant, g(V ) will be ?at with
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

166

S. S. HEGEDUS AND W. N. SHAFARMAN

the value in reverse bias equal to G. In practice, the slope of most J–V curves is very small in this range so there may be some noise in calculating the derivative, particularly under illumination. (c) The derivative r(J)  dV/dJ against (J ? JSC)?1 is plotted.34,35 From Equation (9) r ?J ?  dV AkT ?R? ?J ? JL ??1 dJ q ?12?

for the case when RG ( 1. So, a plot of r(J) against (J ? JL)?1 will yield a straight line with intercept R if JL is independent of voltage. With constant JL we can write JL ? JSC and more practically the data can be plotted against (J ? JSC)?1. A linear ?t to the data gives an intercept of R and a slope AkT/q from which A can be calculated. A correction can be made for the case in which G is not negligible by plotting (J ? JSC ? GV)?1 on the abscissa.35 For analysis of the dark J–V curve, JSC ? JL ? 0. (d) A semilogarithmic plot of J ? JSC against V-RJ using the value of R obtained from plot (c). A linear region over at least 1–2 orders of magnitude in current indicates a good ?t to the diode equation. The intercept then gives J0 and the slope in this case equals q/AkT so A can be calculated and compared with the value from plot (c). Again, a correction for G can be made, in this case by plotting J ? JSC ? GV on the ordinate. This set of plots is shown in Figure 8 for a typical Cu(InGa)Se2 cell with an ef?ciency of 15?5% and absorber layer bandgap Eg ? 1?2 eV. Figure 8(a) shows plot type (a) and appears consistent with Equation (9); that is,

Figure 8. Light and dark J–V characteristics for a well-behaved Cu(InGa)Se2 device: (a) standard J–V plot; (b) shunt characterization g(V); (c) r(J) with ?t used to determine R and A; (d) ln(J ? JSC) with ?t used to determine A and J0
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

THIN-FILM SOLAR CELL CHARACTERIZATION

167

there is no indication of non-ideal parasitic effects. Plot type (b) in Figure 8(b) shows that g(V ) is ?at in reverse bias, and there is a small difference between the dark and illuminated results with G(dark) ? 0?05 mS cm?2 and G(light) ? 0?2 mS cm?2. Figure 8(c) shows plot type (c) for the same Cu(InGa)Se2 device with nearly identical linear results for the dark and illuminated cases. For each, the line gives R ? 0?2 /cm2 and A ? 1?4–1?5. Finally, plot type (d) in Figure 8(d) shows a linear region extending for $2 orders of magnitude in current with, again, good agreement between dark and illuminated data. The intercept for the dark data gives J0 ? 6 ? 10?7 mA/ cm?2 and the slope gives A ? 1?4, in agreement with the value obtained from Figure 8(c). Parasitic effects Figure 8 showed the well-behaved case with R, G, JL nearly independent of voltage and light intensity, as described by the basic diode equation. Deviations from this behavior are observed in different TFSCs and can be identi?ed by the plots described above. One common cause for deviation from the diode behavior illustrated above is a voltage–dependent current collection, JL(V ). The same analysis as above is shown in Figure 9 for a typical CdTe device. Again, there are no obvious deviations from the basic diode model evident in plot (a). However, in this case g(V ) plot (b) under illumination is voltage dependent over the entire range. The minimum value

Figure 9. Light and dark J–V characteristics for a typical CdTe device: (a) standard J–V plot; (b) shunt characterization g(V); (c) r(J) with ?t used to determine R and A for the dark data only; (d) ln(J ? JSC) with ?t used to determine A and J0 for the dark data only
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

168

S. S. HEGEDUS AND W. N. SHAFARMAN

of g(V ) would give an upper bound to the shunt of G(light) ? 0?4 mS cm?2 compared with the dark data for which the shunt term is neglible, G(dark) ? 0 mS cm?2. Similarly r(J) under illumination is not linear in Figure 9(c) with a discrepancy between the dark and illuminated data that increases with increasing (J ? JSC)?1. 1. The dark data in this case gives R ? 1?2  cm2 and A ? 1?7. Forcing a linear ?t to the light data shown in Figure 9(c) would give A ranging from 2?5 to 1?8, depending on the range of data included in the ?t. In general, an attempt to ?t a line to the data in a case with JL(V ) will overestimate, or at best give an upper bound to, the slope and A. Finally, in plot (d) of Figure 9, there is a large deviation in the current under illumination and the J–V data do not ?t the simple exponential form of Equation (1) so A and J0 cannot be reliably determined although it is well behaved in the dark. It is worth noting that this CdTe cell has relatively high FF ? 72?1%. Many other cells with lower FF have a much larger range of uncertainty in the analysis of A and J0. In general, there are several possible explanations for the behavior shown under illumination in Figure 9 as any of the parameters in the diode equation could be illumination dependent. This J–V behavior could be JL(V) caused by ?eld-dependent collection in the absorbing layer or a barrier to collection with barrier height changing as a function of voltage bias. These can be separated, as above, by the wavelength-and-voltagebias-dependent QE. Similarly, the difference in FF under blue and red light can be used to distinguish JL(V ) losses or to distinguish between p/i interface and i-layer recombination losses in an a-Si device. Generally the shunt term, which describes a path for current parallel to the main diode, is assumed to be ohmic, i.e., G is independent of V. A voltage-dependent shunt, G(V ) would affect light J–V measurements identically to JL(V ), but could be distinguished from JL(V ) because it would be expected to have the same effect on the dark data. Experience with many TFSCs has shown that voltage-dependent photocurrent collection is the most likely explanation when the dark J–V curve is well behaved, but the light photocurrent J–V curve deviates, as in Figure 9. It is useful to describe the light generated current as: JL ?V ? ? JL0 C ?V ? ?13?

to show explicitly the relation between the optically limited light generated current, JL0, and the collection function c(V ). This equation is analogous to Equation (4), and c(V ) can be the same function for QE and J–V analysis. As previously, JL0 can be measured by the current with far reverse bias (in practice ?0?5 to ?1 V is suf?cient in most cases). Then, a complete description of the light generated current can focus on determining c(V ) to quantify the mechanisms for losses due to incomplete collection. Several methods have been developed to experimentally determine c(V ), including the use of chopped ac measurement to separate light and dark currents36 and the difference of J–V measurements made at several different light intensities.37 In general, c(V ) will depend on some combination of ?eld-assisted collection and diffusion. The model for c(V ) in the case of a uniform ?eld presented in Equations (6–8) was applied to the J–V behavior of a-Si p–i–n solar cells.6,12,14 Along with the basic diode parameters in Equation (9), this form of the collection function provides a useful parametric description of the voltage-dependent collection in a-Si and a-SiGe devices.14 Another method which is sometimes used to determine diode parameters is to plot JSC on a logarithmic scale against VOC with measurements at different light intensities. This would give linear behavior with intercept J0 and slope q/(AkT), but only, again, for the well-behaved case of constant JL. In the case of voltage dependent JL(V ) or G(V), this method could also give erroneous results, overestimating A. One advantage to this method is that a series resistance correction can normally be ignored since it makes no contribution at VOC, since J ? 0, or at JSC, except in the case of an extremely large resistance. Other common parasitic effects that are observed in TFSCs include blocking behavior which can originate at a second junction in the device, such as a non-ohmic contact, or from an interface barrier that may block carrier collection in forward bias, as mentioned above. The latter situation could arise, for example, due to a step in the conduction band alignment at the p–n interface or the interface between the emitter and TCO layers. In some cases, blocking behavior is easily seen just from the J–V curves. However, a more de?nitive way to detect such behavior in forward bias is from the plot of r(J) against (J ? JSC)?1 as shown in Figure 10. The blocking behavior is apparent as an in?ection in the data as (J ? JSC)?1 decreases. In CdTe, this is commonly attributed to a blocking back contact. Because the blocking contact or other barrier may not necessarily be apparent in plot type (a), it is always necessary to characterize the derivative as in plot type (c). In the example
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

THIN-FILM SOLAR CELL CHARACTERIZATION

169

Figure 10. Plot of r(J) against (J ? JSC)?1 for a CdTe device, showing the effect of a blocking back contact for a case where the diode parameters R and A can still be determined

shown, the blocking behavior affects the J–V curve only in far forward bias. The parameters A and R can still be obtained from a linear ?t in Figure 10 and J0 from plot type (d). Then the characteristics of the blocking diode can be quantitatively extracted by subtracting the characteristics of the primary diode calculated from Equation (9) and a barrier height determined by doing this analysis as a function of temperature.38 In most cases, deviations from the behavior predicted by Equation (9) can be attributed to parasitic effects such as non-ohmic or blocking contributions in series or shunt-like effects is parallel with the primary diode. One other cause for non-ideal behavior is light-to-dark crossover which can be caused by photoconductive effects or a light-dependent barrier. In some cases with crossover, plots of type (a–d) may appear well behaved, although with different values of R, A, or Jo obtained between the dark and illuminated data. Other, more fundamental reasons for the inability to describe the data with Equation (9) include the contributions of more than one recombination mechanism or a bias-voltage-dependent diode quality factor.39 A ?nal effect that should be checked when characterizing J–V results to determine fundamental diode behavior is that the J–V curves are stable over time and the same for either J–V sweep direction, i.e., beginning in forward or reverse bias. Otherwise, the parameters determined from the analysis may not describe stable or equilibrium behavior of the device. The characterization described above in which the series resistance is obtained from the derivative r(J) with plot (c) determines a lumped resistance parameter that likely includes the sum of several contributions. Speci?cally, these may include spreading resistance through front or back electrodes, contact resistances, and through ?lm resistance in the active absorber, or emitter layers in the device. Some device structures incorporate a collection grid which can also contribute to the lumped resistance. Various methods to separate these contributions have been applied to TFSCs. In general, this can be done by fabricating devices with systematically varied geometries or lateral current paths on a single substrate with all vertical device layers identical. In particular, the device area can be varied to change the contact resistance contribution, and the lateral distance between devices and contacts can be varied to change the spreading resistance contributions.40,41 Such a technique was used to compare devices with ZnO or SnO2 contacts with the p-layer in a-Si devices. The ZnO/p contact gave lower VOC and FF, which was widely attributed to a barrier or contact resistance.42 R was determined as in plot (c) for cells with different path length in the ZnO or SnO2 and the contact resistance was determined by extrapolating to zero path-length. This analysis showed that the ZnO/p contact was ohmic with low resistance, contrary to standard assumptions. A similar problem was encountered in CuInSe2 devices which showed blocking behavior in forward bias, particularly at reduced temperature, that was generally attributed to a non-ohmic back contact. Specially constructed devices, with a gap in the Mo back contact enabled the voltage drop across the Mo/Cu(InGa)Se2 contact to be separated from the rest of the device.43 This showed that the blocking behavior did not occur at the back contact and it has since been attributed to the CdS/Cu(InGa)Se2 interface.44
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

170

S. S. HEGEDUS AND W. N. SHAFARMAN

ADMITTANCE CHARACTERIZATION
Admittance measurements, typically capacitance–voltage (C–V), are well established techniques to obtain free carrier densities, depletion widths, deep trap densities and potential barriers from the ac response of p–n junctions, including solar cells. Admittance measurements in TFSC are complicated by extraneous or parasitic factors such as contact or lateral series resistance effects, inductance at high frequency, neutral bulk capacitance and resistance in series with the junction, short-term instability or hysteresis due to thermal and bias cycling, and light intensity dependence due to trapping. It is the junction capacitance or conductance which contains information about the deep states, free carriers, diffusion voltage, etc. To extract signi?cant information, for example about the deep states, free carriers, or diffusion voltage, generally requires a circuit model approach to account for effects, including bulk and contact resistance, bulk capacitance, and inductance. Various circuit models have been proposed and applied to TFSC devices.45–48 A practical complication is that typically one does not know a priori what range of frequency and temperature are required to allow extraction of the given parameter (i.e., deep or shallow states, free carrier density, diffusion voltage) from the measured admittance, as discussed below. The standard analysis of an abrupt p–n junction assumes a uniform space-charge density created by a spatially uniform distribution of shallow ionized donors or acceptors. Analysis of the space charge electrostatics for this simple case is commonly found in many texts. It can be easily shown that C?V??2 ? q"N?W? 2?V ? VD ? ?14?

where C(V) is the capacitance per area, VD is the diffusion voltage, and N(W) is the net space charge density at the edge of the depletion width. When C?2 is plotted against V, a straight line is obtained whose slope is inversely related to N and whose intercept is VD. It is a common misconception that the intercept of C(V)?2 plotted against V is the built-in potential or barrier height VB ? ?b/q. The band bending or diffusion potential VD differs from built-in potential by the Fermi energy, qVB ? EF ? qVD. With c-Si, EF $kT, so VB and VD are numerically similar, but in TFSCs, EF can be 0?1–0?8 eV, leading to large differences between VB and VD. In most TFSCs, however, the simple ideal relationship in Equation (14) is rarely observed. It was realized in the early 1980s that capacitance was a valuable technique to characterize the deep states in the intrinsic layer in a-Si solar cells, but that new methods of measurement and analysis would be needed. In particular, a method called drive-level capacitance pro?ling (DLCP) was developed for TFSCs.49 An example of the failure of Equation (14) is shown in Figure 11 for two CdTe devices made by different processes, but both having $11% ef?ciency. This shows C?2 plotted against V measured at 100 kHz in the dark

Figure 11. Plot of C?2 against V for two differently fabricated CdTe devices in light and dark at 100 kHz
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

THIN-FILM SOLAR CELL CHARACTERIZATION

171

and light for each device. In the dark, neither yields a straight line, the intercept or slope of which are physically meaningful. Cell 1 has the classic shape of a p–i–n type device where the highly resistive i-layer is totally depleted. The curve is independent of voltage until forward biased near VD when the depletion region rapidly collapses leading to an increase in C. From the value of C at reverse bias, a CdTe layer thickness of 2?2 mm is calculated according to C ? "/W, with W assumed equal to the absorber layer thickness d. This agrees well with the thickness determined from growth rate and time. Most a-Si p–i–n devices have a dark C–V shape like CdTe Cell 1. Cell 2 in the dark has a varying slope implying a spatially varying N. It is not fully depleted even at ?2V, unlike Cell 1. With $1 sun light bias, the shapes of C?2 plotted against V change for both cells. The data for Cell 1 become more rounded but still do not yield a linear relation, while the data for Cell 2 have developed into a straight line from which the slope and intercept yield a space-charge density of 5 ? 1014 cm?3 and VD ? 0?56 V by ?tting to Equation (14). This value of N is consistent with values from 1–6 ? 1014 cm?3, as reported for a variety of CdTe TFSCs, typically measured in the dark. This relatively low value of free carriers identi?es one of the critical problems with CdTe technology, namely inability to dope the CdTe to a suf?ciently high carrier density. The increase in capacitance seen in Figure 11 with light bias is due to trapping of photogenerated charge at extraneous states within the bandgap. Thus, the calculated value of N does not represent a true free carrier or shallow dopant density, as often assumed in standard derivations. These extraneous states, common to most TFSCs, make analysis and interpretation of the C–V data very challenging. They cause the capacitance to vary with bias light intensity and spectrum, ac frequency, and temperature. However, these same sensitivities can be exploited to determine the trap density. There are many additional reasons why measurements and analyses of TFSC capacitance50,51 are more challenging and less straightforward than simply applying Equation (14). The root cause for the complications is often the presence of deep trapping states in the TFSC. Often not mentioned is the problem of hysteresis where the admittance is different for increasing voltage bias compared with decreasing voltage bias. This is typically due to incomplete charging or discharging of deep states when the voltage sweep up–down retrace time is less than the deep state response time, so the device is not at steady state during the measurement. One requirement is that the dielectric relaxation time  d ? " of the semiconductor must be less than the ac period !?1, otherwise the charge cannot move through the material to supply or empty the gap states. This is often overlooked in crystalline semiconductor C–V analysis because it is not a limitation in low-resitivity materials, but is necessary to consider with materials like a-Si or CdTe, especially at low measurement temperatures. In crystalline and polycrystalline devices, the capacitance is determined by the space-charge density at the edge of the depletion width N(W) since this is where the ac ?eld is modulating the space charge. Since W is a function of V, N(W) can be determined spatially by varying V. From Equation (14) dC?2 2 ? q"N?W? dV or N?W? ? C 3 q" dC dV !?1 ?16? ?15?

Then, a plot of N(W) against W(V) ? "/C(V) gives the net charge density pro?le across some portion of the absorber. This is often called the C–V pro?le method. It has been widely applied to both CdTe and Cu(InGa)Se2 TFSCs, but this is not a unique parameter to characterize the absorber, since N(W) gives the shallow carrier density jNA ? ND j plus the charge emitted from and captured at deep states which can empty and ?ll within the ac period. Since these rates depend on temperature and generation rate, N(W) will be a function of the ac frequency, light intensity and temperature. In a semiconductor with a large density of deep trap states, the concept of depletion edge between neutral space charge and bulk regions is not very helpful in understanding admittance measurements. More useful is a demarcation length XE which separates the material into a region between the junction and XE in which charge can not respond to the ac signal, and one beyond XE in which it can. This is illustrated in Figure 12 for a p-type
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

172

S. S. HEGEDUS AND W. N. SHAFARMAN

Figure 12. Band diagram of p-type semiconductor junction with a deep trap level ET and two measurement energies E!1 and E!2. Shaded areas represent variations in band bending and energy response, XE. due to the oscillating ac voltage. The equivalent circuit shows the junction (CJ and GJ) in series with the bulk (CB and GB)

absorber with a single trap level ET. XE depends on the energy distribution of the deep state density as well the measurement temperature, frequency and bias voltage. Trap occupancy is determined by the Fermi level. Hole traps above the Fermi level are assumed ?lled and those below empty, with the opposite for electron traps. In the presence of a modulating ac voltage VAC of frequency ! ? 2f, only states which can release their charge within the ac period will be able to contribute to the admittance. The cut-off energy dividing responsive from unresponsive states is E! ? kT ln   ! ?17?

Here  is the attempt-to-escape frequency (phonon frequency), of the order of 1013 rad/s. For traps to respond to the ac signal, they must be shallower than E!. In Figure 12, E!1 represents a measurement condition where either T is too low or ! is too high for charge to respond. E!2 represents measurements at higher T and/or lower ! such that hole traps at ET can respond to the ac signal. For the case of a continuous trap distribution as in a-Si, XE is where E! ? EF. The region between the junction and XE behaves like an insulator, or space-charge region, of thickness XE where traps are empty since ET < EF. Far beyond XE, trap states can respond much more rapidly than the ac cycle, so their charging and discharging can be described by the bulk capacitance CB ? "/(d-XE) and conductance GB ? /(d-XE). Around XE, states respond in approximately the same time as the ac period and therefore contribute to the ac capacitance CAC (out-of-phase signal) and conductance GAC (in-phase signal). There will be a static, or dc capacitance and conductance associated with response at XE as well. Thus, the admittance YJ of the junction region at XE is YJ ? ?GDC ? GAC ?!?? ? i!?CDC ? CAC ?!?? ? GJ ? i!CJ ?18?

where GDC ? J(V)/AkT is the dynamic conductance of the diode current, and CDC ? "/L0 is the static or dc capacitance at XE due to the charge screening length L0. The correct series-parallel circuit model must be used to extract these parameters from measurements.45,47,48 Equation (18) represents the case for junction capacitance and conductance in parallel. The total admittance of the device should include the parallel combination of bulk
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

THIN-FILM SOLAR CELL CHARACTERIZATION

173

elements CB and GB in series with the junction elements as in Figure 12. In general, the parameter of greatest interest in characterizing deep states in highly resistive material such as a-Si or CdTe is CJ while in lower resistivity material such as Cu(InGa)Se2, both CJ and GJ can contain information about the trapping states.52 To ensure correct admittance measurements, the dissipation D ? G/(!C) of the net circuit should be monitored. D increases exponentially with increasing T or V since dc current through the conductance will dominate and effectively short out the capacitance, leading to incorrect values with very low phase angle. In general, D should be < 5–10, depending on the measurement circuit. A completely general treatment of CJ yields   EE ?1 CJ ? " XE ? " E ?19?

where EE and E are the ?eld and charge density at XE.49 In the case of an exponential density of midgap states, Equation (19) reduces to " CJ ? ?20? X E ? L0 where L0 is the Debye screening length related to the midgap state density g0.53 This formulation describes the two capacitors in series, and predicts that the capacitance should depend on T and f through E!. Figure 13 shows C measured on an a-SiGe p–i–n cell over a range of temperatures at one frequency and over a range of frequencies at two temperatures plotted as a function of E!, determined by Equation (17). The data show a single capacitance response curve due to the dependence of the deep state response on E!, not on T and f individually. The solid line is the ?t to this data, using the procedure described elsewhere.53 Three regions are indicated in Figure 13. Region I is the ‘freeze-out’ region where no charge can respond since E! < EF, and the capacitance is "/d. The increase in Region II is due to the deep state response and the peak value of the capacitance occurs for suf?ciently low f, high T, or forward bias that XE ? 0 hence CJ ? "/L0 according to Equation (20). The density of states at the Fermi level g0 ? 3 ? 1017 cm?3eV?1 can be readily obtained from this peak value. The fall-off in C in Region III occurs because the junction capacitance, now constant at "/L0, is shunted by the increasing current conduction through the junction diode term GDC, as seen in the equivalent circuit. This example shows how obtaining information about deep traps from the measured capacitance requires understanding the TFSC device as a circuit to account for parasitic elements, and then making measurements in the right temperature and frequency space for the states to respond. It also shows that admittance measurements must be performed at a

Figure 13. Plot of C against E! for a-SiGe p–i–n TFSC measured at 1 kHz with T varied from 0 to 140 C and at 40 or 110 C with f varied from 0?1 to 100 kHz. The solid line shows a ?t to the data53
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

174

S. S. HEGEDUS AND W. N. SHAFARMAN

range of voltage, frequency and temperature to identify the region where the desired parameter determines C or G. For example, to obtain the absorber thickness from d ? "/C(V) the entire absorber should be depleted (V < 0) and f should be high enough and/or T low enough that E! < EF. To obtain the maximum sensitivity to deep states, the entire absorber should not be depleted (V 5 0) and f should be low enough and/or T should be high enough that E! > EF. Equation (19) is also the basis for DLCP which has been applied to characterize the spatial and energetic distribution of defects in TFSC. In DLCP, the ac voltage amplitude VAC is varied along with the dc bias voltage VDC.49 Drive level capacitance has been applied to study Ge defects in a-SiGe,53 Cu doping in CdTe54 and defects in Cu(InGa)Se2 as a function of relative Ga content,55 all obtained in a TFSC device con?guration.

CONCLUSIONS
Many of the methods developed for characterization of crystalline semiconductor solar cells either do not apply or must be modi?ed for valid application to TFSCs. The primary reasons are a high density of trapping and recombination states, which is related to the polycrystalline and amorphous materials, and parasitic losses, which can be related to the deep states and also to the device structure and contacts. One must always be wary when analyzing data from TFSCs that the actual properties being sought are not masked or in?uenced by the many possible losses or non-idealities which occur in these devices. Various methods have been presented for the characterization of QE, J–V, and admittance measurements of TFSCs that identify and, in some cases, correct for these extrinsic effects and enable analysis of the intrinsic junction behavior. These methods have contributed to the remarkable improvements in the performance and fundamental understanding of a-Si, CdTe, and Cu(InGa)Se2 solar cells.

Acknowledgements We would like to thank all of our colleagues who have helped us understand the pitfalls and caveats in analyzing TFSCs, especially Jim Phillips. We thank the staff of IEC for having made the devices and measurements from which much of this work was derived. This work was supported in part by NREL under subcontract ADJ-130630-12.

REFERENCES
1. Emery K. Measurement and characterization of solar cells and modules. In Handbook of Photovoltaic Science and Engineering, Luque A, Hegedus S (eds). Wiley: Chichester, 2003; Chap. 16. 2. Dalal V, Rothwarf A. Comment on ‘A simple measurement of absolute solar cell ef?ciency’. Journal of Applied Physics 1979; 50: 2980–2981. 3. Yang J, Banarjee A, Glatfelter T, Sugiyama S, Guha S. Recent progress in amorphous silicon alloy leading to 13% stable ef?ciency. Proceedings of the 26th IEEE Photovoltaic Specialists Conference 1997; 563–568. 4. Wu X, Dhere R, Yan Y. High ef?ciency polycrystalline CdTe thin ?lm solar cells with oxygenated amorphous CdS window layer. Proceedings of the 29th IEEE Photovoltaic Specialists Conference 2002; 531–534. 5. Shafarman W, Klenk R, McCandless B. Device and material characterization of Cu(InGa)Se2 solar cells with increasing bandgap. Journal of Applied Physics 1996; 79: 7324–7328. 6. Crandall R. Modelling of thin ?lm solar cells: uniform ?eld approximation. Journal of Applied Physics 1983; 54: 7176–7186. 7. Liu X, Sites J. Solar-cell collection ef?ciency and its variation with voltage. Journal of Applied Physics 1994; 75: 577–581. 8. Phillips J, Roy M. Resistive and photoconductive effects in spectral response measurements. Proceedings of the 20th IEEE Photovoltaic Specialists Conference 1998; 1614–1616. 9. Sites J, Tavakolian H, Sasala R. Analysis of apparent quantum ef?ciency. Solar Cells 1990; 29: 39–48.
Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:155–176

THIN-FILM SOLAR CELL CHARACTERIZATION

175

10. Shafarman W, Stolt L. Cu(InGa)Se2 solar cells. In Handbook of Photovoltaic Science and Engineering, Luque A, Hegedus S (eds). Wiley: Chichester UK, 2003; Chap. 13. 11. Fahrenbruch A, Bube R. Fundamentals of Solar Cells. Academic Press: New York, 1983; 231–234. 12. Misiakos K, Lindholm F. Analytical and numerical modeling of amorphous silicon pi–n solar cells. Journal of Applied Physics 1988; 64: 383–393. 13. Arya R, Catalano A, Oswald R. Amorphous silicon p–i–n solar cells with graded interface. Applied Physics Letters 1986; 49: 1089–1091. 14. Hegedus S. Current voltage analysis of a-Si and a-SiGe solar cells including voltage dependent photocurrent collection. Progress in Photovoltaics Research and Applications 1997; 5: 151–168. 15. Shafarman W, Zhu J. Material Research Society Symposium Proceedings 2001; 668: H2.3. 16. Dalal V, Leonard M, Booker J, Vaseashta A, Hegedus S. Quantum ef?ciency of amorphous alloy solar cells. Proceedings of the 18th IEEE Photovoltaic Specialist Conference 1985; 837–841. 17. Rocheleau R, Hegedus S, Buchanan W, Tullman R. Effects of impurities on ?lm quality and device performance in a-Si:H deposited by photo-assisted CVD. Proceedings of the 19th IEEE Photovoltaic Specialists Conference 1987; 699– 704. 18. Banerjee A, Xu X, Yang J, Guha S. Carrier collection losses in amorphous silicon and amorphous silicon-germanium alloy solar cells. Applied Physics Letters 1995; 67: 2975–2977. 19. Fortmann C, Fischer D. Mobility, recombination kinetics, and solar cell performance. Proceedings of the 23rd IEEE Photovoltaic Specialists Conference 1993; 966–970. 20. Hegedus S, Buchanan W. Understanding graded a-SiGe solar cells using bifacial photocurrent collection. Proceedings of the 23rd IEEE Photovoltaic Specialists Conference 1993; 991–994. 21. Sudharsanan R, Rohatgi A. Investigation of metalorganic chemical vapor deposition grown CdTe/CdS solar cells. Solar Cells 1991; 31: 143–150. ¨ 22. Agostinelli G, Batzner D, Dunlop E. Apparent quantum ef?ciency in CdTe solar cells. Proceedings of the 17th European Photovoltaic Solar Energy Conference 2001; 1254–1257. 23. Toyama T, Suzuki T, Gotoh M. Reduction of infrared response of CdS/CdTe thin-?lm solar cell with decreased thickness of photovoltaic active layer. Solar Energy Materials and Solar Cells 2001; 67: 41–47. 24. Phillips J. Determination of diffusion length from bi-facial spectral response. Proceedings of the 20th IEEE Photovoltaic Specialists Conference 1990; 782–786. 25. Crandall R, Sadlon K, Kalina J, Delahoy A. Direct measurement of mobility–lifetime product of holes and electrons in an amorphous silicon p–i–n cell. Material Research Society Symposium Proceedings 1989; 149: 423–427. 26. Hegedus S, Lin H, Moore A. Light induced degradation in amorphous silicon studied by surface photovoltage technique: a comparison of lifetime vs. space charge effects. Journal of Applied Physics 1988; 64: 1215–1219. 27. Chatterjee P, McElhenry P, Fonash S. In?uence of illumination conditions on the spectral response of amorphous silicon Schottky barrier structures. Journal of Applied Physics 1990; 67: 3803–3809. 28. Hegedus S, Kaplan R. Analysis of quantum ef?ciency and optical enhancement in amorphous Si p–i–n solar cells. Progress in Photovoltaics Research and Applications 2002; 10: 257–269. 29. Lechner P, Geyer R, Schade H. Detailed accounting for quantum ef?ciency and optical losses in a-Si:H based solar cells. Proceedings of the 28th IEEE Photovoltaic Specialists Conference 2000; 861. 30. Phillips J, Birkmire R, McCandless B. Polycrystalline heterojunction solar cells. Physica Status Solidi (b) 1996; 194: 31. 31. Sah C, Noyce R, Shockley W. Carrier generation and recombination in P–N junctions and P–N junction characteristics. Proceedings of the Institution of Radio Engineers 1957; 45: 1228. 32. Walter T, Menner R, Koble CH, Schock H. Characterization and junction performance of highly ef?cient ZnO/CdS/ CuInSe2 solar cells. Proceedings of the 12th European Photovoltaic Solar Energy Conference 1994; 1755–1758. 33. Rau U. Tunneling-enhanced recombination in Cu(In,Ga)Se2 heterojunction solar cells. Applied Physics Letters 1999; 74: 111. 34. Swartz G. Computer model of amorphous silicon solar cell. Journal of Applied Physics 1982; 53: 712. 35. Sites J, Mauk P. Diode quality factor determination for Solar Cells. Solar Cells 1987; 27: 411. 36. Eron M, Rothwarf A. Effects of a voltage-dependent light-generated current on solar cell measurements: CuInSe2/ Cd(Zn)S. Applied Physics Letters 1984; 44: 131. 37. Phillips J, Titus J, Hoffmann D. Determining the voltage dependence of the light current in CuInSe2 solar cells. Proceedings of the 26th IEEE Photovoltaic Specialists Conference 1997; 463. 38. Roy M, Damaskinos S, Phillips J. The diode current mechanism in CuInSe2/CdS Heterojunctions. Proceedings of the 28th IEEE Photovoltaic Specialists Conference 1988; 1618.

Copyright # 2004 John Wiley & Sons, Ltd.

Prog. Photovolt: Res. Appl. 2004; 12:155–176

176

S. S. HEGEDUS AND W. N. SHAFARMAN

39. Lyakas M, Zaharia R, Eizenberg M. Analysis of nonideal Schottky and p–n junction diodes—extraction of parameters from I–V plots. Journal of Applied Physics 1995; 78: 5481. 40. Meier M, Schroder D. Contact resistance: its measurement and relative importance to power loss in a solar cell. IEEE Transactions on Electron Devices 1984; ED-31: 647. 41. Schade H, Smith Z. Contact resistance measurements for hydrogenated amorphous silicon solar cell structures. Journal of Applied Physics 1986; 59: 1682. 42. Hegedus S, Kaplan R, Ganguly G, Wood G. Characterization of the SnO2/p and ZnO/p contact resistance and junction properties in a-Si p–i–n solar cells and modules. Proceedings of the 28th IEEE Photovoltaic Specialists Conference 2000; 728. 43. Shafarman W, Phillips J. Direct current–voltage measurements of the Mo/CuInSe2 contact on operating solar cells. Proceedings of the 25th IEEE Photovoltaic Specialists Conference 1996; 917. 44. Eisgruber I, Granata J, Sites J. Blue-photon modi?cation of nonstandard diode barrier in CuInSe2 solar cells. Solar Energy Materials and Solar Cells 1998; 53: 367. 45. Losee D. Admittance spectroscopy of impurity levels in Schottky barriers. Journal of Applied Physics 1975; 46: 2204– 2214. 46. Snell A, Mackenzie K, Le Comber P, Spear W. The interpretation of capacitance and conductance measurements on metal–amorphous silicon barriers. Philosophical Magazine B 1979; 40: 1–15. 47. Viktorovitch P, Moddel G. Interpretation of the conductance and capacitance frequency dependence of hydrogenated amorphous silicon Schottky barrier diodes. Journal of Applied Physics 1980; 51: 4847–4854. 48. Sco?eld J. Effects of series resistance and inductance on solar cell admittance measurements. Solar Energy Materials and Solar Cells 1995; 37: 217–226. 49. Michelson C, Gelatos A, Cohen J. Drive-level capacitance pro?ling: its application to determining gap state densities in hydrogenated silicon ?lms. Applied Physics Letters 1985; 47: 412–414. 50. Eron M. Steady-state and transient capacitance of a p–n junction in the presence of high density of deep levels. Journal of Applied Physics 1985; 58: 1064–1066. 51. Mauk P, Tavakolian H, Sites J. Interpretation of thin-?lm polycrystalline solar cell capacitance. IEEE Transactions on Electron Devices 1990; 37: 422–427. ¨ 52. Walter T, Herberholz R, Muller C, Schock H. Determination of defect distributions from admittance measurements and application to Cu(In,Ga)Se2 based heterojunctions. Journal of Applied Physics 1996; 80: 4411–4420. 53. Hegedus S, Fagen E. Midgap states in a-Si:H and a-SiGe:H p–i–n solar cells and Schottky junctions by capacitance techniques. Journal of Applied Physics 1992; 71: 5941–5951. 54. Gilmore A, Kaydanov V, Ohno T. Treatment effects on deep levels in CdTe based solar cells. Proceedings of the 29th IEEE Photovoltaic Specialists Conference 2002; 604–607. 55. Heath J, Cohen D, Shafarman W. Distinguishing metastable changes in bulk CIGS defect densities from interface effects. Thin Solid Films 2003; 431–432: 426.

Copyright # 2004 John Wiley & Sons, Ltd.

Prog. Photovolt: Res. Appl. 2004; 12:155–176


相关文章:
...and Stability of Thin Film Solar Cells_4
Barrier Coatings and Stability of Thin Film Solar Cells 4th Quarterly Report...There are three types of cells on test, a bare device with a CSU ...
...Time for Co-vaporation CIGS Solar Cells
thin film solar cells due to its high absorption...It is known that the EDS analysis is sensitive ...Regardless of grain sizes, all CIGS devices have...
solar cells
3 A solar cell is an electrical device that converts the energy of light directly into electricity by the photovoltaic effect, so we also call it ...
模板0902114001李四
thin film solar cells Abstract This thesis first ... solar cell, and gives a comprehensive analysis....solar cell device research, materials, structure, ...
附5. 1002114001张三 论文模板 (1)
thin film solar cells Abstract This thesis first ... solar cell, and gives a comprehensive analysis....solar cell device research, materials, structure, ...
本科论文模板
thin film solar cells Abstract This thesis first ... solar cell, and gives a comprehensive analysis....solar cell device research, materials, structure, ...
2015年最新大学毕业论文-模板-范文_图文
thin film solar cells Abstract This thesis first ... solar cell, and gives a comprehensive analysis....solar cell device research, materials, structure, ...
本科毕业论文_有机薄膜太阳能电池的研究进展
thin film solar cells Abstract This thesis first ... solar cell, and gives a comprehensive analysis....solar cell device research, materials, structure, ...
太阳能电池发展综述
of several kind of solar cells such as crystalline silicon solar cells, thin film solar cells.based on this analysis, a conclusion was drawed that thin...
Solar Cell
solar cell is the device that through the photoelectric effect or ... working in the photoelectric effect of film type solar cell is the ...
更多相关标签: