Electron-beam-induced current measurements with applied bias provide insight to locally resolved acceptor concentrations at p-n junctions

Electron-beam-induced current (EBIC) measurements have been employed for the investigation of the local electrical properties existing at various types of electrical junctions during the past decades. In the standard configuration, the device under investigation is analyzed under short-circuit conditions. Further insight into the function of the electrical junction can be obtained when applying a bias voltage. The present work gives insight into how EBIC measurements at applied bias can be conducted at the submicrometer level, at the example of CuInSe2 solar cells. From the EBIC profiles acquired across ZnO/CdS/CuInSe2/Mo stacks exhibiting p-n junctions with different net doping densities in the CuInSe2 layers, values for the width of the space-charge region, w, were extracted. For all net doping densities, these values decreased with increasing applied voltage. Assuming a linear relationship between w2 and the applied voltage, the resulting net doping densities agreed well with the ones obtained by means...

Electron-beam-induced current (EBIC) measurements have been employed for the investigation of the local electrical properties existing at various types of electrical junctions during the past decades. In the standard configuration, the device under investigation is analyzed under short-circuit conditions. Further insight into the function of the electrical junction can be obtained when applying a bias voltage. The present work gives insight into how EBIC measurements at applied bias can be conducted at the submicrometer level, at the example of CuInSe 2 solar cells. From the EBIC profiles acquired across ZnO/CdS/CuInSe 2 /Mo stacks exhibiting p-n junctions with different net doping densities in the CuInSe 2 layers, values for the width of the space-charge region, w, were extracted. For all net doping densities, these values decreased with increasing applied voltage. Assuming a linear relationship between w 2 and the applied voltage, the resulting net doping densities agreed well with the ones obtained by means of capacitance-voltage measurements. C  Electron-beam-induced current (EBIC) in a scanning electron microscope is established as a standard tool for analysis of local short-circuit current densities at electrical junctions. 1,2 When collecting the EBIC signals from a semiconductor device such as a single p-n junction solar cell, the analysis may be performed with the electron beam impinging on the front contact, 3,4 on the back contact, 5,6 or on the cross-section of the device. 7 Evaluation of EBIC data acquired on single p-n junction solar cells using these measurement geometries can deliver values for the width w of the space-charge region (SCR), the minority carrier diffusion length in the quasi-neutral part of the solar absorber, as well as the recombination velocities at the contacts and at the investigated surface of the specimen. [7][8][9][10] Most EBIC measurements at solar cells have been conducted under short-circuit condition, which does not correspond to the device operation under sun light. Therefore, further insight into the electrical properties of the device may be obtained when applying a bias voltage. 11 However, this approach may bring about background currents, superimposing the EBIC and being larger by several orders of magnitude (µA to mA vs. nA). There is a need for the lock-in amplification of the EBIC signal. 12 When evaluating the EBIC profiles across junctions of solar cells with p-n + characteristics (where the doping level of the n-type part of the junction is substantially higher than that of the p-type part) at various bias voltages, the width w of the SCR should decrease with increasing bias voltage V a according to 13 where ε, ε 0 , V b , e, and N A are the dielectric susceptibilities of the investigated material and the vacuum, the build-in potential of the junction, the elemental charge, and the net doping of the p-type part of the junction. Note that this equation is valid only assuming that the SCR is fully depleted, that the quasi-neutral region is indeed charge-neutral, and that N A is constant throughout the p-type part. These assumptions are generally not valid for real solar-cell devices.
The present work provides EBIC measurements with applied bias on CuInSe 2 thin-film solar cells. These devices consist of thin-film stacks with total thicknesses of only a few micrometers. Therefore, they pose a considerable challenge in terms of spatial resolution of the EBIC signals. Reports on EBIC measurements under short-circuit conditions performed on CuInSe 2 solar cells were published by several groups. 14-17 Only a few publications 18 dealt with EBIC at applied bias voltages, while EBIC signals across the p-n junction were evaluated only qualitatively, without extracting electrical parameters. The present work aims at modeling the acquired EBIC profiles across the p-n junction on cross-sectional samples, with the focus of obtaining values for the width of the SCR, w. The first objective is to give a proof of concept in terms of verifying the trend of decreasing w with increasing bias voltage V a , the second to extract values for the build-in potential V b and the net doping N A using Eq. (1), and to compare the N A values with corresponding measurements by means of capacitance-voltage profiling.
CuInSe 2 thin films were deposited on Mo-coated glass substrates by a three-stage coevaporation process. 19 The doping level in CuInSe 2 can be controlled by introducing different amounts of NaF into the layer, either as precursor prior to the deposition, or by a post-deposition treatment. In the present work, three different CuInSe 2 thin films were fabricated: -a Na-free CuInSe 2 layer, leading to a nominal net-doping level in CuInSe 2 of 10 14 cm −3 .
-one with an additional, 12 nm thick NaF layer deposited on the CuInSe2/Mo/glass stack, annealed at an elevated temperature, leading to a nominal net-doping level in CuInSe 2 of 10 15 cm −3 . -one with a 12 nm thick NaF precursor layer prior to the deposition of CuInSe 2 , leading to a nominal net-doping level in CuInSe 2 of 10 16 cm −3 .
Further details can be found in Ref. 20. Solar cells were completed by a CdS buffer layers via chemical bath deposition and by a i-ZnO/ZnO:Al bilayer via sputter-deposition. The photovoltaic performances of the three solar-cell with the different doping levels in the CuInSe 2 layers are given in Table I. Capacitance-voltage measurements were performed at room temperature using an HP4284 LCR-Meter and frequencies of 100 kHz. The capacitance values were calculated assuming a simply RC circuit.
EBIC analyses were conducted using a Zeiss UltraPlus scanning electron microscope, equipped with a beam blanker and an EBIC amplifier by point electronic GmbH. For these analyses, crosssectional specimens of the CuInSe 2 solar cells given in Table I were fractured. For each doping level, 3 specimens were measured. The EBIC signals were recorded by means of the acquisition and evaluation software DIPS (point electronic GmbH), which also controls the applied bias voltage. In order to avoid high-injection conditions, 21 beam currents of only few pA for the impinging electron beam were used. The beam energies were kept small at 3-7 kV, for best spatial resolutions. The frequency of the beam blanker was chosen between 10 and 40 kHz, for sample areas of 4-9 mm 2 . The time constant of the lock-in amplifier was 3 ms, i.e., about three times smaller than the frequency of the beam blanker. For each pixel, a dwell-time of 1.1 ms was selected. As a result, the amplified EBIC signal was integrated across about 3 pixels. The gain was about 7x10 4 . The SEM and the EBIC images were recorded on areas of 250x25 pixels. It was found that for values outside a certain range of bias voltages, the EBIC profiles exhibited shapes with very large SCR widths and increased diffusion lengths, which were not able to be described by the model outlined below and persisted also after changing the bias voltage back to a different value. For the 10 15 and 10 16 cm −3 samples, this range was about -0.1 to 0.4 V, for the 10 14 cm −3 sample about -0.05 to 0.15 V. This behavior can be attributed to a persistent irradiation effect, as outlined by Kniese et al., 16 which is more pronounced for the solar cell with a considerably low doping level (10 14 cm −3 ) in the CuInSe 2 layer.
The EBIC simulations were conducted based on the one-dimensional, analytical model proposed by Donolato. 7 It is assumed that the EBIC signals do not vary substantially parallel to the p-n junction but only perpendicular to it. The EBIC value I(a) measured when the electron beam impinges on the solar-cell cross-section at position a can be regarded as the convolution of generation profile g(x, a) and the collection function f c (x), where x is the position of generation of electron-hole pairs upon electron irradiation: (2) Note that g(x, a) and f c (x) are generally not independent. 22 Still, for the sake of simplicity, we assume independency in order to be able to apply Eq. (2) for the simulation of the EBIC profiles. The generation profile g(x, a) can be approximated by an empirical expression. 15 The collection function f c (x) was divided into three parts (where x = 0 is set to the CdS/CuInSe 2 interface): -for all x within the SCR (of width w), f c (x) is assumed to be 1 -for the CdS/ZnO buffer/window region, f c (x) = exp(-|x|/L p ) (L p is the diffusion length of holes in the CdS/ZnO region) -for the quasi-neutral region in the CuInSe 2 absorber layer, where L n and D n are the diffusion length and diffusion constant of the electrons in the CuInSe 2 absorber layer, S Mo is the recombination velocity at the Mo back contact, and x Mo and x SCR are the positions of the Mo back contact and the edge of the SCR. In order to fit the simulated to the experimental EBIC profiles, w (equivalent to x SCR ), x Mo , L p , L n , and D n are used as parameters (where w and L n exhibit the largest impact).
An exemplary EBIC measurement and the simulation of the acquired EBIC profile are given in Fig. 1, where a SEM image ( Fig. 1(a)), an EBIC image ( Fig. 1(b)), and an extracted EBIC profile across the ZnO/CdS/CuInSe 2 /Mo/glass stack is presented, along with the corresponding simulated EBIC signal (Fig. 1(c)). Note that all EBIC profiles acquired on the three solar-cell samples listed in Table I at various bias voltages are provided in Ref. 23.
The squares of the widths of the SCR, w 2 , were plotted as a function of the applied bias, V a , for the three investigated solar-cell samples (Fig. 2). Indeed, decreasing widths of the SCR with increasing applied bias for all three solar-cell samples were found, which is according to Eq. (1). Therefore, the first objective of the present work was achieved.
In addition, the dependencies of w 2 vs. V a were fitted using a linear function and ε r = 13.6 (Ref. 24), in order to determine the build-in potentials. It is clear from Figs. 2(a)-2(c) that the values of w 2 vs. V a do not exhibit a linear relationship for the complete voltage range. However, a linear relationship is assumed in order to extract values for V b and N A , which are given in Table II. This is justified since the R 2 values 25 for the three linear fits range from 0.65 to 0.90, i.e., they are closer to 1 than to 0.
The extracted V b values are slightly smaller than those calculated by 26 The results from capacitance-voltage measurements on the same identical solar cells are given in Fig. 3. In the Mott-Schottky plots ( Fig. 3(a)), the capacitance C is related to the applied voltage V a via C −2 = 2(V b -V a )/(ε r ε 0 eN A ). This is, N A and V b were determined by a linear fit of C −2 (V a ) and represented in Table II. The net doping densities in Fig. 3(b) were calculated by derivation of the Mott-Schottky plots in Fig. 3(a). Since with varying applied bias voltage, the edge of the SCR in the CuInSe 2 absorber layer shifts basically from close to the Mo back contact (for large negative V a ) to close to the CdS buffer layer (for large positive V a ), Fig. 3(b) can be interpreted in terms of a spatial doping distribution perpendicular to the p-n junction. Apparently, the net doping densities N A are not constant across the CuInSe 2 absorber layer. Nevertheless, the values obtained by EBIC and C-V measurements are in good agreement (Table II).
It should be noted that the determination of the net doping densities N A from EBIC measurements by use of Eq. (1) can by no means replace capacitance-voltage analysis as standard technique TABLE II. Values for the build-in potential V b and the net doping N A , determined from EBIC measurements, capacitancevoltage analysis, as well as by use of Eq. (3). We note that the nominal doping level is to be considered as order of magnitude.