Determination of Minority Carrier Diffusion Length in Silicon Wafers by

May 15, 1997 - The method is based on comparison of the limiting photocurrents ... may be determined with good accuracy in the cell Pt1/1 M NH4F/silic...
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J. Phys. Chem. B 1997, 101, 3961-3967

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Determination of Minority Carrier Diffusion Length in Silicon Wafers by a Dual Electrolyte Cell Sandro Cattarin* Istituto di Polarografia ed Elettrochimica PreparatiVa del C. N. R., Corso Stati Uniti 4, 35100 PadoVa, Italy

Laurence M. Peter School of Chemistry, UniVersity of Bath, Bath BA2 7AY, United Kingdom ReceiVed: NoVember 25, 1996; In Final Form: March 9, 1997X

The use of a cell with two electrolytic compartments for the determination of minority carrier diffusion length in silicon wafers is discussed. The method is based on comparison of the limiting photocurrents recorded at the front (illuminated) and back (dark) compartment under suitable polarization conditions. Results obtained in different polarization arrangements for n- and p-Si are compared and discussed. It is shown that the diffusion length of holes in n-Si may be determined with good accuracy in the cell Pt1/1 M NH4F/silicon/1 M NH4F/ Pt2 without application of metal contacts to the Si wafer.

1. Introduction The minority carrier diffusion length L is a parameter that greatly affects the performances of silicon material in most applications, notably in integrated circuits and solar cells.1 The assessment of this material property by the surface photovoltage (SPV) technique is well established1-4 and has become a standard ASTM test method.5 The method is based on the fact that under appropriate conditions the generation of a small constant photovoltage Usp requires a photon flux I, which is a linear function of 1/R (R being the optical absorption coefficient of the wavelength λ). The diffusion length L may be determined from the intercept of the straight line I vs 1/R at I ) 0.3 A variation of this method consists in measuring the wavelength dependent photocurrent in a solar cell based either on a p-n junction or on a semiconductor-electrolyte contact (SEC).1,6-8 In both cases a fairly complex apparatus is required, including monochromator and light detector to measure photon flux and reflectivity. As pointed out in recent papers,8-10 the SPV technique has some limitations: (1) it is suitable for determination of L values on the order of R-1 and suffers from increasing inaccuracy as L . R-1, namely, for L > 100 µm;9 (2) only a sample depth on the order of L + W = L can be probed (W, the space charge region width, being normally much smaller than L), and this is in many cases less than the sample thickness d; (3) the method is unsuitable for the characterization of large area samples, as typically required by solar cells, and does not allow fast surface mapping since the response has to be measured over a fairly large spectral region, at least in the near-infrared. Moreover, in the ASTM method the surface photovoltage Usp is detected using a conductive oxide glass top contact, which is not suitable for samples with irregular surfaces. Recently, Lehmann and Fo¨ll have proposed a photocurrent ratio method based on a dual electrolyte cell for the estimation of L at Si wafers.9-11 The wafer is inserted between two compartments containing HF electrolyte and connected to a potentiostat via an ohmic contact. The front interface is illuminated by a photon flux I0 (corrected for reflection losses) of visible monochromatic light, e.g. from a He-Ne laser. In a first experiment the front SEC polarized under depletion collects X

Abstract published in AdVance ACS Abstracts, April 15, 1997.

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a photocurrent jf with a limiting value jfl = I0e ) j0 (e is the electron charge, unitary quantum efficiency is assumed) while the back interface floats at open circuit in contact with the HF electrolyte. In a subsequent experiment the front (illuminated) interface is left floating free while the back (dark) SEC collects a photocurrent jb with a limiting plateau value jbl. The ratio R ) jbl/j0 contains information on the recombination processes occurring in the second experiment and may allow estimation of the diffusion length L provided that the contribution of other recombination processes (e.g. at the surface) is known or may be estimated. Some ingenuous improvements of the method, including use of wavelengths with different penetration depths and collection of the generated carriers on one or both sides, allow depth profiling of the L parameter. The technique, dubbed ELYMAT (short for electrolytical metal tracer), has been developed into a practical tool for three-dimensional mapping of L (ref 11 and references therein). The dual electrolyte cell, used for the preparation of porous silicon layers,12-14 has been recently proposed as a convenient way of performing investigation and processing of semiconductor wafers in a bipolar geometry:15,16 the traditional metal contact to the semiconductor is replaced by a nonohmic electrolytic contact and the wafer exchanges currents of equal magnitude and opposite sign at the two interfaces. In the present paper we report and discuss the polarization curves that are obtained at Si wafers in the dual electrolyte cell operating in different polarization geometries. This approach shows how the state of polarization of the interfaces affects the processes of surface recombination and may contribute to the definition of optimal operating conditions for this kind of method. The possibility of estimating L at a bipolar electrode without metal contacts is discussed. 2. Experimental Section (100)-oriented silicon wafers (thickness 381 ( 25 µm) were purchased from Semimetrics Ltd. Reported experiments were made with n-Si and p-Si materials with similar resistivity (7.511 and 8-12 Ω‚cm, respectively). The wafers had different surface finishes on the two faces; unless otherwise stated, reported photoelectrochemical experiments were made illuminating the shiny surface, whereas the rough surface was © 1997 American Chemical Society

3962 J. Phys. Chem. B, Vol. 101, No. 20, 1997 used for the collecting contact (metallic or electrolytic). Some additional experiments in the transistor-like arrangement (vide infra) were performed with bipolished p-Si wafers from Wacker Chemie (thickness about 525 µm, resistivity 8-12 Ω‚cm). Prior to electrochemical experiments the electrodes were etched for 60 s in a 1:1 mixture of 40% HF/ethanol to remove the oxide layer, rinsed with distilled water, and blown dry in a nitrogen stream. Solutions were prepared from analytical grade commercial products (BDH, Aldrich, or Merck) and triply distilled water. NH4F solutions (1 M) were obtained by dilution of a semiconductor grade 12 M solution (BDH), adjusting the pH with H2SO4 and NH3. Some experiments were performed in a cell in the traditional three-electrode arrangement, using an SCE reference (to which potentials are referred) and a platinum counter electrode. nand p-Si samples, contacted with gallium-indium eutectic alloy, were mounted on mild steel strips and sealed with a PTFEcoated adhesive tape (Cole Parmer Instruments). A circular hole in the sealing tape exposed to the solution a surface varying typically from 0.38 to 0.60 cm2. Most experiments were carried out in a dual electrolyte geometry in the cell of Figure 1, made from plexiglass sheets. Platinum foils were inserted in the front (illuminated) and back (dark) compartment. A hole in the front foil allowed electrode illumination. In order to simplify the experimental work involving use of HF, two Pt wires were used as (pseudo)reference electrodes R1 and R2 in the two electrolyte compartments. The potential of the Pt electrode in 1 M NH4F was U = 0.15 ( 0.10 V vs SCE. The semiconductor wafer was clamped between the two compartments, exposing to each a geometric area of 0.90 cm2. The surface in contact with electrolyte was typically about 0.8 cm2. In all cases the front interface was illuminated by a photon flux I0 (corrected for reflection losses) of visible monochromatic light, e.g. from a light-emitting diode (LED). In analogy to experiments by Lehmann and Fo¨ll,9 the limiting photocurrent j0 observed for front collection of carriers was compared with the limiting photocurrent jbl collected at the back contact. Experiments were performed in different polarization conditions. The first corresponds to the arrangement used by Lehmann and Fo¨ll,9-10 shown in Figure 1a. Polarization was applied alternatively to the front and back interface in the standard threeelectrode mode. The second is the transistor-like polarization mode of Figure 1b, similar to that used in early work by Pleskov to investigate reactions at thin double-sided Ge electrodes.17,18 Experiments were performed with potentiostats (Hi-Tek Instruments, England), which offer a connection to the (floating) common of the circuitry, and a function generator (Hi-Tek PPRI). Electrochemical polarization was applied by connecting the Si wafer to the common points of both potentiostats (Figure 1b). The current flowing in each circuit was measured as the voltage drop over a resistance in series to the counter electrode, and the signal was detected by a PM8278 Philips XY dual pen recorder with floating inputs. This arrangement was preferred to the traditional measurement via the current followers since connection in parallel of the two operational amplifiers may result in measurement of unreliable currents in both circuits. The third arrangement, shown in Figure 1c, is based on a bipolar semiconductor electrode with two SECs.15,16 In this case electrochemical control was established in the (potentiostatic) four-electrode mode with a Schlumberger Technologies 1286 electrochemical interface, imposing the applied potential ∆U between R1 and R2 and using the two platinum foils as working and counter electrode (Figure 1c). The three geometries reported

Cattarin and Peter

Figure 1. Arrangements used for experiments with Si wafers in the dual electrolyte cell: (a, top) three-electrode mode applied alternatively to front side (1) and back side (2) collection of photogenerated carriers; (b, middle) polarization with two potentiostats in the transistor-like arrangement (for details see text and ref 18); (c, bottom) bipolar mode, polarization via the back electrolytic contact.

in Figure 1a-c will be referred to in the text as standard, transistor-like, and bipolar, in that order. Light-emitting diodes (LED) were used as light sources, and all reported experiments were performed under illumination with

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λ ) 650 nm. Monochromatic light intensities were measured with a calibrated silicon photodiode (SD112UV, Macam Photometrics). Reported photon fluxes are corrected for reflection losses. Photoelectrochemical experiments were performed with a conventional setup.19,20 3. Results 3.1. Preliminary Characterization of n-Si/Acidic Fluoride Interface. Literature current/voltage curves for n-Si (111) in 1 M NH4F (pH 4.7-5.3) show photocurrent onset at -0.48/0.50 V vs SCE.21,22 The latter values correspond within experimental accuracy to the flatband potential UFB determined for the same crystal orientation and pH in fluoride-containing aqueous solutions,23 i.e. UFB = Uon. The (photo)current/voltage curve recorded at n-Si (100) in 1 M NH4F, pH 4.5, under monochromatic light is illustrated in Figure 2. The onset of photocurrent occurs at Uon = -0.60 V vs SCE, close to the literature flatband value UFB = -0.57 V vs SCE determined for n-Si (100) in a similar medium.24 For simplicity we shall assume a flatband coincident with the photocurrent onset potential, UFB = -0.60 V vs SCE. The open circuit potential of the freshly etched electrode in 1 M NH4F is UOC = -0.49/ -0.46 V vs SCE. Hence, at open circuit in the dark the semiconductor will be under mild depletion.24 The dark current/voltage curve in Figure 2 shows a steep increase of the cathodic current on sweeping the potential from open circuit in a negative direction, due to proton reduction by conduction band electrons. On sweeping the electrode potential from open circuit toward positive (reverse) bias, the dark current turns anodic in sign and attains a limiting value on the order of 10 µA cm-2, which is much higher than observed in other media like acidic polyiodide, in which the limiting value remains well below 1 µA cm-2. The dark current is proportional to fluoride concentration and may be interpreted25 as an oxidation process controlled by a chemical reaction and proceeding via electron injection. The photocurrent increases rapidly at potentials positive to the onset, reaching a limiting value that corresponds, after correction for reflection losses (estimated to be around 23% for this wavelength, see ref 26), to a quantum efficiency Q = 1.95, close to a perfect photocurrent doubling. This finding, similar to results obtained in ref 22 for a similar medium and photon flux, may be interpreted as dissolution of divalent silicon, which then reacts with the solvent, producing hydrogen:22

hν f h+ + e-

electron-hole formation (1a)

Si(0) + h+ f Si(I)

hole capture

(1b)

Si(I) f Si(II) + e-

electron injection

(1c)

Si(II) + 2H+ f Si(IV) + H2

H2 evolution

(1d)

Within experimental accuracy, the photocurrent is proportional to the photon flux up to the explored current density limit of about 1 mA‚cm-2. The (photo)current/voltage curve recorded at the rough face of n-Si in the above conditions closely resembles the curve in Figure 2: the dark current is similar and the limiting photocurrent value is higher by 10-13%, corresponding to lower reflectivity losses at a less shiny surface. Hence, recombination losses are remarkably similar for the two faces, indicating a low density of recombination centers at the rough face. Possibly, the latter was not damaged in depth and the surface defects were rapidly etched away by the fluoride electrolyte.

Figure 2. (Photo)current/potential curve in 1 M NH4F, pH 4.5, for n-Si electrode with metal back contact: under illumination (solid line a) and in the dark (dashed line). Line b shows a typical curve recorded collecting the photocurrent at the dark (back) interface in experiments in standard geometry. Illumination conditions: photon flux I0 ) 4.8 × 1014 s-1 cm-2; photocurrent for unit quantum efficiency j0 = 77 µA cm-2.

3.2. Experiments with n-Si. Some experiments were performed in the standard geometry used by Lehmann and Fo¨ll.9,10 In the first series of experiments the interface in the dark was left floating free and the illuminated interface was polarized under reverse bias (front collection). These experimental conditions were equivalent (apart from the change of reference electrode) to the three-electrode mode described in the previous section, and indeed the current-potential curves showed a limiting photocurrent j0 equal to that observed in Figure 2 (line a). In a second series of experiments the illuminated interface was left floating free and the back interface was polarized under reverse bias (back collection). In these conditions the photogenerated carriers either recombine at the front surface (with a given surface recombination rate) or diffuse to the back contact with a bulk recombination rate defined by L. For n-Si samples jbl was typically jbl = 0.10j0 to 0.15j0 (Figure 2, line b). R ) jbl/j0 may be used in principle to estimate L provided that the surface recombination rate is known or, as assumed by Lehmann and Fo¨ll,9-11 negligible. The latter assumption does not apply to our system, as shown in the following. Experiments in transistor-like geometry (experimental setup of Figure 1b) were performed polarizing the dark electrode interface under depletion in the potential region in which an anodic limiting current flows (U ) 2.0 V vs Pt). The potential of the illuminated side was scanned over the range U ) 1.5 to -2.5 V vs Pt, namely, from depletion to accumulation, recording and comparing the currents flowing at the two interfaces (Figure 3). The curve showing the current collected at the front side (Figure 3a) resembles that of Figure 2a, with a limiting photocurrent proportional to light intensity. The photocurrent collected at the back contact (Figure 3b) depends on the potential applied at the front interface: it is very small in the potential range of the photocurrent plateau; it increases slowly on moving the electrode potential toward the open circuit value (reaching at the latter point a typical value in the range of 0.10j0); it increases steeply when the potential is swept negative to flatband toward accumulation, reaching a plateau limiting value jbl in the potential region where a large cathodic current of hydrogen evolution flows at the front interface. Figure 4 shows a typical current-voltage curve recorded at n-Si in the polarization arrangement of Figure 1c (bipolar

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Figure 5. (a) Curve showing the variation of the ratio R ) jbl/j0 in experiments of the type shown in Figure 3, as a function of the front collected photocurrent density j0; (b) curve showing the similar ratio observed in the experiments of Figure 4. Figure 3. (Photo)current/potential curve in 1 M NH4F, pH 4.5, for n-Si electrode in the transistor-like arrangement of Figure 1b. The back (dark) interface is polarized under reverse bias at the constant potential U ) 2.0 V, and the potential of the front (illuminated) interface is scanned from 1.5 to -2.5 V vs Pt. The currents flowing at the front and back interfaces are recorded in part a and b, respectively. Illumination conditions: photon flux I0 = 1.11 × 1015 s-1 cm-2; photocurrent for unit quantum efficiency j0 = 178 µA cm-2.

Figure 4. (Photo)current/potential curves recorded in the bipolar geometry of Figure 1c with n-Si. The indicated potential difference is applied between R1 and R2. Same illumination conditions as in the experiment reported in Figure 3.

geometry). Sample and illuminating conditions were the same as those used in Figure 3. Under application of a positive potential difference an anodic photocurrent is observed, which gradually increases with the bias up to a limiting value close to that of Figure 3. The lower slope of the curve in Figure 4 as compared to Figure 3 is due to the fact that part of the applied voltage is used to negatively bias the back interface, at which the same current (with opposite sign) must flow.15 The cathodic photocurrent that appears in Figure 4 under application of a negative bias was not observed in similar experiments with InP.15,16 The reason is that in InP and in most other semiconductors light-generated minority carriers have a diffusion

length much shorter than the wafer thickness and they do not reach the back surface, so that no photocurrent is observed at bipolar electrodes upon illumination of the (front) interface under direct bias. Conversely, when diffusion lengths of holes are comparable with the wafer thickness, as in our n-Si samples, the photogenerated holes can reach the back surface, where they are collected by the reaction of Si dissolution (mechanism 1a1d); due to the peculiar arrangement, a cathodic current is detected in Figure 4. Figure 5 illustrates the ratio R ) jbl/j0 as a function of the front current density j0. For experiments in the transistor-like geometry (Figure 5a) the ratio is constant at R = 0.71 ( 0.02 above j0 = 100 µA cm-2 and shows a limited decrease below the latter value. Experiments with three samples from the same wafer gave R values in the range 0.68-0.75. A more pronounced dependence of R on j0 is observed in the bipolar geometry (Figure 5b): a limiting R value is only attained at j0 > 350 µA‚cm-2, but markedly lower values are obtained at the lowest explored light power. In the latter conditions on the basis of eq 3 (vide infra) L will be underestimated. 3.3. Preliminary Characterization of p-Si/Acidic Fluoride Interface. Figure 6 shows the (photo)current/voltage curve recorded at p-Si (100) under the same conditions used in Figure 2. The open circuit potential was in this case UOC = -0.46/ -0.44 V vs SCE. The flatband potential for p-Si may be estimated on the basis of the value adopted for n-Si (UFB = -0.60 V vs SCE), assuming (i) a bandgap of 1.12 eV;27 (ii) equal (or similar) band edges for n- and p-Si; (iii) a distance between band edges and Fermi level of about 0.2 eV for both materials calculated on the basis of typical literature data;27 and (iv) a resulting distance between Fermi levels of 0.65-0.70 eV.24 Hence, the flatband for p-Si may be estimated as UFB = +0.10 V vs SCE, close to the literature value UFB = +0.16 V vs SCE obtained for p-Si in 0.1% HF.24 It may be concluded that at open circuit the p-Si/1 M NH4F interface will be under fairly strong depletion conditions. The characteristic in the dark shows a steep increase of the anodic current of electrode dissolution under direct (positive) bias and very small cathodic currents under reverse (negative) bias. The limiting photocurrent value

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Figure 6. (Photo)current/potential curve in 1 M NH4F, pH 4.5, for p-Si electrode with metal back contact: under illumination (solid line a) and in the dark (dashed line). Line b shows a typical curve recorded collecting the photocurrent at the dark (back) interface in experiments in standard geometry. Same illumination conditions of Figure 2.

observed under negative bias corresponds, after considering reflection, to a quantum yield Q = 1, as expected for a process of proton reduction occurring with little recombination losses. The (photo)current/voltage curve recorded at the rough face of p-Si under the same conditions closely resembles the curve in Figure 6, the main differences being an increase of the limiting photocurrent by 10-13% (an effect to be interpreted as for n-Si) and a larger dark current probably due to the incomplete blocking behavior of a less perfect surface. 3.4. Experiments with p-Si in Different Geometries. Experiments of back collection in the standard geometry give jbl = 0.18j0 to 0.21j0 (Figure 6, line b). To better elucidate the dependence of this result on the polarization conditions of the illuminated interface, experiments were done in the transistorlike geometry (Figure 7). The dark interface was polarized at U ) -2.0 V vs Pt, in the potential region in which a cathodic limiting photocurrent flows. The potential of the illuminated side was swept from -1.5 to 1.0 V vs Pt, namely, from strong depletion conditions to a potential beyond the first peak observed in the current/voltage curve of anodic dissolution of Si in fluoride media20-23 (note: the broad shape and the shift toward positive potentials of the maximum of the dissolution peak in Figure 7a are due to a large iR drop). In the negative potential domain the front collected photocurrent jf attains the limiting value j0 ) I0e and the back collected photocurrent is negligible. On sweeping the potential in a positive direction, jf starts decreasing (positive to -1.0 V vs Pt), and soon after jb starts increasing, reaching its maximum jbm when the total current at the front interface is zero, namely, around open circuit conditions. On sweeping the potential of the front interface further positive, the relevant photocurrent rapidly drops to zero, whereas the dark current sharply increases due to electrodissolution with formation of porous silicon.23 By contrast with the behavior observed at n-Si (Figure 3), the back photocurrent rapidly drops to zero when the front interface is swept from open circuit toward direct bias (Figure 7b), and it remains very small over the region of front potentials leading to anodic dissolution, up to and beyond the current peak. (Photo)current/voltage curves recorded with a p-Si wafer in the bipolar arrangement are presented in Figure 8. The limiting photocurrent j0 recorded under negative bias is the same as that obtained with an electrode with metal contact, as shown, for example, by comparison with the photocurrent in Figure7a collected under the same photon flux. The curve of Figure 8 shows blocking behavior under application of a direct (positive)

Figure 7. (Photo)current/potential curve in 1 M NH4F, pH 4.5, for p-Si electrode in the transistor-like arrangement of Figure 1b. The back (dark) interface is polarized under reverse bias at a constant potential U ) -2.0 V, and the potential of the front (illuminated) interface is scanned from 1.0 to -1.5 V vs Pt. The currents flowing at the front and back interfaces are recorded in part a and b, respectively. Illumination conditions: photon flux I0 = 9.4 × 1014 s-1 cm-2; photocurrent for unit quantum efficiency j0 = 151 µA cm-2.

Figure 8. (Photo)current/potential curves recorded in the bipolar geometry of Figure 1c with p-Si. The indicated potential difference is applied between R1 and R2. Same illumination conditions as in the experiment reported in Figure 7.

bias in the dark and only a small anodic photocurrent. The ratio R ) jbl/j0 is markedly lower than the maximum value R ) jbm/j0 obtained in the experiments in transistor-like geometry, in which jbm is attained around open circuit conditions. Extensive surface recombination appears to occur in these experiments of back collection in the bipolar geometry, which force the illuminated interface into dissolution. 4. Discussion According to ref 10, if charge carriers are generated in a thin layer at the front interface of a Si wafer in the dual electrolyte cell, and negligible recombination occurs at either interface

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during experiments of charge collection, the relation holds

R ) jbl/j0 ) R2L2/[(R2L2 - 1) cosh(x/L)]

(2)

(where R ) penetration depth; L ) diffusion length; x ) sample thickness). If R2L2 . 1, a condition valid for visible light, and L > 20 µm, the relation simplifies and L may be estimated as

L = x/[arccosh(1/R)]

(3)

For eq 3 to be valid, jbl and j0 must correspond to electrode processes with equal quantum yield Q. The simplest case is that of photocurrents at p-Si material, in which photogenerated electrons perform proton reduction with constant Q = 1 up to fairly large current densities, where bubbles may partially block the surface. At n-Si the photogenerated holes are collected by a reaction of Si dissolution, whose apparent Q may vary somewhat in the region of porous silicon formation, both as a function of the (photo)current density and as the result of formation of the antireflection properties of the porous layer.20,28 However, equal Q values may be assumed provided that measurements are taken on fresh surfaces and that jbl and j0 have values in the same range, which was indeed our case. The experiments performed at n-Si in the transistor-like arrangement of Figure 1b show that the photocurrent collected at the back (dark) interface attains a limiting value jbl = 0.71j0. Inserting the sample thickness of 381 µm in eq 3, one obtains L = 435 µm. When the front interface is under open circuit conditions, the back collected photocurrent jbl is much lower, typically jbl = 0.10j0 to 0.15j0, corresponding to values obtained in the experiments in standard geometry (Figure 2b): inserting the associated R in eq 3, one obtains L ) 127-147 µm, considerably below the previous estimation. This would indicate that the standard geometry does not provide reliable results in the case of n-Si. The in situ electropolishing treatment performed by Lehmann and Fo¨ll prior to experiments,9-11 not possible in our cell, may actually improve the results. However, the curves of Figure 3 were recorded at bipolished samples accurately etched a few minutes before the experiments, and cathodic polarization of the illuminated interface seems indeed necessary to get the highest jbl values, namely, low surface recombination and reliable L. The likely reason is that recombination at the illuminated interface of n-Si is active at open circuit and becomes negligible only in the presence of a space charge due to accumulation of electrons, which creates a field screening the photogenerated minority carriers from surface recombination centers. Hence, determination of R in this arrangement will be less sensitive to surface conditions than in the standard operation mode. The curve in Figure 5a shows that, in the explored range of photon fluxes, measurements at n-Si in the transistor-like arrangement give a limiting constant value of R above a minimum photon flux (corresponding to a front collected photocurrent j0 of about 100 µA‚cm-2). The reason for the (limited) decrease of R in the range of low j0 is not clear and may be tentatively attributed to recombination processes that are comparatively more important at low photon fluxes; at higher fluxes the recombination centers might be filled. The R decrease in the range of low photon fluxes is more substantial in the bipolar geometry (Figure 5b). The likely reason is that polarization of the front interface is controlled in this case by the current density. At low photon fluxes experiments of back collection are performed with the front interface under mild cathodic polarization, and extensive surface recombination occurs (compare experiments in transistor-like geometry, Figure 3). On increasing the photon flux and the current, a stronger

cathodic polarization is imposed on the front interface, recombination decreases for the same reasons discussed in the case of the transistor-like arrangement, and R approaches the same limiting value. Considering now p-Si, in the standard current ratio method the photocurrent is collected at the back contact while the front contact is at open circuit.9,10 As shown in Figure 7b, under this condition jb attains its maximum jbm but not a limiting plateau value like, for example, in Figure 3. The value of diffusion length that is obtained inserting R ) jbm/j0 = 0.20 in eq 3 is L = 230 µm (x ) 525 µm) and is probably underestimated. In the bipolar arrangement only a small limiting photocurrent is observed on applying a positive bias between the metal electrodes (Figure 8). This behavior may be understood by considering the recordings in the transistor-like geometry (Figure 7): on sweeping the potential of the front interface from open circuit in a positive direction, a small anodic current causes a drop of the back collected photocurrent jb to very low values; jb stays negligible over the region of anodic dissolution up to and beyond the first peak. It must be concluded that whenever the illuminated interface is polarized in the region of porous silicon formation, the photogenerated carriers undergo rapid recombination. This problem, already addressed in earlier literature,29 is discussed in more detail in another paper,30 which describes the use of transistor-like geometry to study electron injection phenomena during silicon dissolution. 5. Conclusions In summary, comparison of results obtained in different polarization geometries shows that the procedure of evaluating L on the basis of R ) jbl/j0 is subject to limitations. For the case of p-Si, the traditional geometry9 probably underestimates Ln. Lehmann and Fo¨ll found a rather marked dependence of the measured diffusion length L on the photon flux, which they attributed entirely to the dependence of L on minority carrier concentration.9 Actually, the observation may originate partially from a surface recombination phenomenon which is comparatively less important at large photon fluxes. Our results indicate that the technique is more suitable to determine relative values of L in maps than real absolute values. More reliable results can be expected in the mode consisting in carrier generation by a penetrating infrared light and collection at both interfaces polarized under depletion.11 This is a particular case of the transistor-like geometry, and in the given polarization conditions surface recombination should be low at both interfaces. The bipolar geometry is unsuitable since when the illuminated interface is forced into dissolution most of the photogenerated carriers readily recombine. For n-Si, the limiting back current value jbl is achieved only when the illuminated interface is polarized under accumulation in the regime of hydrogen evolution. Hence, a reliable estimate of R (and Lp) may be obtained with the transistor-like arrangement, whereas in the standard measurement (with the illuminated interface at open circuit) R will be affected considerably by surface recombination; neglecting it will cause L to be underestimated. For n-Si, a convenient alternative is offered by the bipolar arrangement, in which the traditional metal contact is replaced by an electrolytic contact: using a fairly large photon flux, the same limiting value of R is obtained as in the transistorlike geometry. The bipolar method, clean and nondestructive, therefore seems indicated for quality control at early stages of photovoltaic cell preparation, especially in the case of polycrystalline silicon wafers for which traditional contacts suffer from sample fragility.11

Minority Carrier Diffusion Length Acknowledgment. This work was performed during a visit by S. Cattarin to Bath University, supported by a study visit award of the Royal Society, London, which is gratefully acknowledged. References and Notes (1) Fahrenbruch, A. L.; Bube, R. H. Fundamentals of Solar Cells; Academic Press: New York, 1983; p 90, and references therein. (2) Goodman, A. M. J. Appl. Phys. 1961, 32, 2550. (3) Wang, E. Y.; Baraona, C. R.; Brandhorst, H. W., Jr. J. Electrochem. Soc. 1974, 121, 973. (4) Micheels, R. H.; Rauh, R. D. J. Electrochem. Soc. 1984, 131, 217. (5) ASTM F 391-78, 1979, Annual Book of ASTM Standards; American Society for Testing and Materials: Philadelphia, 1979; Part 43, p 770. (6) Stokes, E. D.; Chu, T. L. Appl. Phys. Lett. 1977, 30, 425. (7) Etcheberry, A.; Etman, M.; Fotouhi, B.; Gautron, J.; Sculfort, J.L.; Lemasson, P. J. Appl. Phys. 1982, 53, 8867. (8) Bastide, S.; Vedel, J.; Lincot, D.; Le, Q. N.; Sarti, D. J. Electrochem. Soc. 1995, 142, 1024. (9) Lehmann, V.; Fo¨ll, H. J. Electrochem. Soc. 1988, 135, 2831. (10) Fo¨ll, H. Appl. Phys. A 1991, 53, 8. (11) (a) Carstensen, J.; Lippik, W.; Fo¨ll, H. In Semiconductor Silicon/ 1994; Huff, H., Bergholz, W., Sumino, K., Eds. Electrochem. Soc. Proc. Vol. 94-10; 1994, p 1105. b) Carstensen, J.; Lippik, W., Liebert, S.; Ko¨ster, S.; Fo¨ll, H. In Analytical Techniques for Semiconductor Materials and Process Characterization II; Kolbesen, B. O., Claeys, C.. Stallhofer, P., Eds.; Electrochem. Soc. Proc. Vol. 95-30; 1995; p 83.

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