Influence of Doping Density on the Current− Voltage Characteristics of

J. Phys. Chem. C 2008, 112, 303-307

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Influence of Doping Density on the Current-Voltage Characteristics of p-Type Silicon in Dilute Hydrofluoric Acid T. L. S. L. Wijesinghe, S. Q. Li, and D. J. Blackwood* Department of Materials Science and Engineering, National UniVersity of Singapore, Block E3A, 7 Engineering DriVe 1, Singapore 117574 ReceiVed: August 31, 2007; In Final Form: October 16, 2007

The mechanism of p-type porous silicon formation in dilute hydrofluoric acid has been examined over a wide range of resistivities. The current-voltage curves show a negative potential shift as the resistivity of the silicon is reduced, a phenomenon that is explained in terms of a corresponding shift in the flat-band potential. Furthermore it is found that for all resistivities the flat-band potential is negative of the so called “Jps peak”, and an argument is presented that shows that this observation effectively disproves previous literature that has postulated that the “Jps peak” marks the transition between porous silicon formation and electropolishing. An observed decrease in the magnitude of the Jps peak for the two most heavily doped samples can be accounted for if the rate-determining step in PSi formation becomes the breaking of the Si-Si back-bonds, a process that should be potential dependent.

1. Introduction Anodic dissolution of silicon (Si) in hydrofluoric (HF) acid came to prominence when visible photoluminescence (PL) from porous silicon (PSi) at room temperature was observed in 1990.1-4 Current-voltage (IV) characteristics are particularly important in studying the electrochemical behavior of PSi formation, it being known that the relationship between anode current and potential varies with HF concentration, doping type, and doping concentration.2,5 A typical IV curve for p-type silicon (5.4 Ω cm) in 1% HF (+0.5 M NH4Cl) is shown in Figure 1, and this is usually divided into three regions.6-8 (i) Region I. The silicon is under inversion conditions, but because of the high overpotential for hydrogen evolution, very little current flows in this region. (ii) Region II. The current density starts to rise as a PSi layer is formed, and the silicon is found to etch with a dissolution valence of two.1,2 (iii) Region III. At high positive potentials, electropolishing occurs, and the silicon is found to etch with a dissolution valence of four.2,9 The band structures thought to be present at the silicon/ solutions interface in the three different regimes are shown schematically in the lower portion of Figure 1.10 The transition between region II (PSi formation) and region III (electropolishing) is marked by a peak in the current density. This point is usually given the symbol Jps [Note: For reasons that will be clear later in the text we have specifically avoided referring to Jps as the critical current density], with it being widely reported that PSi formation completely ceases once this current density is exceeded.1,5 Allongue et al.11 proposed that, in the mechanism of electrochemical anodization of silicon in hydrofluoric acid, first two holes are required to convert a Si-H bond to a Si-OH bond, and then either this is chemically replaced by a Si-F bond, yielding porous silicon, or further holes reach the surface * To whom correspondence should be addressed. Phone: +65-65166289. Fax: +65-67763604. E-mail: [email protected].

TABLE 1: Resistivities, Relevant Doping Densities, and Calculated Flat-Band Potentials (Vfb) of the p-Type Samples sample number 1 2 3 4 5 6

type p++ p++ p+ p p p

resistivity (Ω cm)

doping density (cm-3)

Vfb (mV vs SCE)

0.001 0.003 0.015 0.15 2.0 5.4

8× 2 × 1019 3 × 1018 1 ×1017 7 × 1015 3 × 1015

-110 -75 -25 60 125 145

1019

to allow a SiO2 layer to form, resulting in electrochemical polishing. Although a number of variations on this etching mechanism have been proposed,2,12,13 the critical step in determining whether PSi formation or electrochemical polishing occurs remains a competition between the kinetics of the chemical dissolution of fluorinate terminal silicon atoms vs the rate of SiO2 formation. The value of Jps is often taken as being the transfer between these two processes. However, it is not exactly certain what is actually happening on the silicon’s surface at Jps, with it being described in terms of the current density at which either the electropolishing starts or an oxide film forms.14,15 Furthermore, the observation that the silicon’s dissolution valence gradually increases from two to four as the current density approaches Jps suggests that the switch between PSi formation and electropolishing is not sharp.14,16 Although the value of Jps is known to be a function of HF concentration, temperature, and the crystal orientation,8,16,17 it has been widely accepted to date that for p-type Si is independent of the resistivity (i.e., doping density).3,17 It has also been reported by Zhang that complete coverage by PSi can only be obtained in the exponential region at the beginning of region II; at potentials between the end of this exponential region and the Jps potential, i.e., the potential at which the Jps peak is observed, a porous layer will still form, but its surface coverage is no longer uniform.5 The present paper presents an investigation into the influence of donor density on the IV characteristics of p-type silicon in dilute hydrofluoric acid. The somewhat unexpected results are

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Figure 1. An IV curve for p-type silicon (5.4 Ω cm) in 1% HF + 0.5 M NH4Cl with, below, schematic diagrams of the interface band structure in the three different regimes, as proposed by Lehmann.6 (S.C. ) semiconductor; Sol. ) solution.)

Figure 2. IV curves for p-type silicon wafers of different resistivities in 1% HF + 0.5 M NH4Cl. All curves are after compensation for IR drop. The flat-band potential for each resistivity is given in parentheses.

explained in terms of the position of the flat-band potential and the influence of the applied field on the breaking of Si-Si backbonds. 2. Experimental Section Table 1 summarizes the p-type silicon samples used for this study. All samples were boron doped with (100) orientation and

had resistivities ranging from 10-3 to 5.4 Ω cm. Samples were first cleaved to around 1 cm × 1 cm; however, the surface area exposed to the solution was controlled to 0.017 cm2 by an O-ring attached to the polytetrafluoroethylene (PTFE) cell. Samples were cleaned in diluted HF, to remove the native oxide, just before being mounted in the cell and Ohmic contacts were made by applying GaIn eutectic on the back sides of the samples. A

p-Type Silicon in Dilute Hydrofluoric Acid

J. Phys. Chem. C, Vol. 112, No. 1, 2008 305 tion and electropolishing occurring in the accumulation region.20 This latter idea is consistent with the electrochemical mechanism of Allongue et al.,11 since under accumulation conditions one would expect the supply of holes to outstrip the chemical dissolution process. Therefore the switch between PSi formation and electropolishing can be expected to occur at, or just after, the flat-band potential, and it has been speculated that Jps coincides with the flat-band potential.6 The flat-band potential varies with pH, point of zero charge (pzc), and doping density; for the time being, any minor effects of surface states will be ignored. If one assumes that the pzc is independent of the silicon’s resistivity then for a given solution the relationship between flat-band potential and doping density should be given by21

Figure 3. Dependence of the current density of the Jps peak on wafer resistivity in 1% HF + 0.5 M NH4Cl.

Vfb ) VR -

[]

NA kT Ln q Nv

(1)

small surface area was found to give more reproducible IV curves; however, since areas close to the O-ring tend to show different pore-etching behavior from the center parts, it is recognized that the current density values measured from small areas may be less quantitative than those obtain from large area electrode. The IV curves were recorded using a standard three-electrode PTFE cell with a Si working electrode, a platinum mesh counter electrode, and a saturated calomel reference electrode (SCE). All potentials quoted in this paper are vs SCE. The reference electrode was furnished with a polyethylene luggin capillary with the tip positioned at around 5 mm distance from the working electrode. The anodizing solution was 1% HF + 0.5 M NH4F dissolved in a 1:1 mixture of H2O and ethanol. The samples were potentiodynamically polarized at a sweep rate of approximately 5 mV/s, using the potentiostat and sweep generator components of an ACM Instruments field machine. All the IV curves are displayed after IR compensation.

where VR is a constant reference potential given by the flatband potential of the hypothetical wafer with NA ) Nv in the given environment, NA is the density of acceptors, Nv the effective density of energy levels in the valence band (Nv ) 1.04 × 1019 for Si at 298 K), k is Boltzmann’s constant, T is the temperature, and q is the fundamental charge. Equation 1 predicts that Vfb shifts negative with increasing donor concentration. Unfortunately, the determination of the flat-band potential for p-type silicon is a difficult exercise, with the Mott-Schottky technique yielding inconsistent values. To date, the most reliable data appears to be that of Ottow et al.,19 who by using highfrequency-resistrometry obtained flat-band potentials for p-type and n-type silicon (both of 5 Ω cm conductivity) that were consistent with one another according to the expected relation shown in eq 2

3. Results and Discussion

where ∆EG is the band gap of bulk silicon and ∆EC and ∆EV are the gaps between the Fermi level and the conduction and valence band edges, respectively. The value that Ottow et al. obtained for the flat-band potential of 5 Ω cm p-type silicon was +0.14 V SCE, and since these authors used the same etching conditions as in the present work, this value was used as a datum point to allow the VR of eq 1 to be calculated. In turn, eq 1 was then employed to estimate flat-band potentials for the six samples used in the present work, which are given in Table 1. When the flat-band potential values given in Table 1 are translated to the IV curves of Figure 2, it is clear that for each sample the flat-band potential is located prior to (i.e., negative of) the Jps potential. Therefore if oxide formation commencement occurs as soon as accumulation conditions are established and that this pathway leads to electropolishing then both of these processes must initiate prior to the Jps potential. That is at potentials negative of the flat-band potential only PSi formation occurs, but once positive of the flat-band potential, pore growth takes place alongside a certain amount of oxidation. This postulation is consistent both with the observation that the dissolution valence increases above two prior to reaching Jps2,16 and Zhang’s observation5 that complete coverage by PSi only occurs in an exponential region prior to the Jps potential. Unfortunately, the flat-band potentials estimated in the present work do not have sufficient accuracy to allow any meaningful correlation between them and the end of the exponential region to be determined; although it is cogitated here that these should

Figure 2 shows IR drop-corrected IV curves for the five different silicon wafers with resistivities from 10-3 to 5.4 Ω cm. It can be seen that the onset potentials for PSi formation and electropolishing both shift to more negative values as the specimen resistivity decreases; although for the three higher resistive samples (0.15, 2, and 5.4 Ω cm), the PSi onset potentials lie within a narrow range between -6 and 20 mV vs SCE. Gaspard et al.18 also reported a negative potential shift in the IV curve with increasing doping density and postulated that this resulted from variations in the potential drop across the Helmholtz layer. With a return to Figure 2, it can be seen that all p and p+ samples (ranging from 5.4 to 0.01 Ω cm) show similar Jps values, around 16 ( 1 mA/cm2; however, for the two least resistive samples, 0.003 and 0.001 Ω cm, Jps decreased to 9.5 and 6.8 mA/cm2, respectively. There appears to be no previous literature describing a change in Jps with p-type wafer resistivity; on the contrary, there are several reports that Jps is independent of the resistivity.3,6,17 However, it appears that these works did not investigate p++ silicon, and most previous studies on this material have been performed galvanostatically, rather than potentiostatically, due to problems associated with using reference electrodes in HF solutions. It has been argued by many authors that PSi formation occurs while the silicon is under depletion conditions, a view supported by flat-band potential (Vfb) measurements,19 with oxide forma-

Vfbp ) Vfbn + ∆EG - (∆EC - ∆EV)

(2)

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Figure 4. Schematic representation of the porous Si formation mechanism proposed by Allongue et al.11,22

Figure 5. Schematic representation of the dependence of PSi formation rate on applied potential.

coincide. Furthermore, it appears that Jps represents neither the onset of electropolishing nor that of oxide formation, as previously postulated in the literature, although perhaps it is the point at which a monolayer of oxide forms such that electropolishing becomes dominant over PSi formation. The trend in the location of the flat-band potential, i.e., a negative potential shift with increasing conductivity, will be mirrored by a corresponding negative shift in the potential at which the interface switches from inversion to depletion conditions allowing PSi formation to initiate (Figure 1). That is the shifting of the flat-band potential can also explain the observed shifts in the onset potentials for PSi formation (Figure 2). Although it is also possible that variations in the drop across the Helmholtz layer, as suggested by Gaspard et al.,18 and for the p+ and p++ samples tunneling, as suggested by Lehmann,6 play roles in the negative shift of the IV curves with increasing doping density. Another observation to be made from Figure 2 is the shift of Jps to lower current density values in the two most conductive samples; a dependency in the value of Jps upon the resistivity of p-type Si has not been previously reported. This dependence was both large and repeatable, so it cannot be blamed on experimental error. Figure 3 illustrates the dependence of the current density of the Jps peak on wafer resistivity. It can be seen that for the higher resistive samples (>0.01 Ω cm) Jps is a constant, at least within the experimental error of (1 mA/

cm2, but it decreases dramatically for the two most conductive samples: 0.003 and 0.001 Ω cm. A possible explanation for this effect can be obtained by studying the PSi formation mechanism originally proposed by Allongue et al.,11,22 which is schematically shown in Figure 4. The crucial part of the mechanism is whether the hydroxyl group can be replaced by a fluoride ion (step B), allowing sufficient polarization of the Si-Si back-bonds to break them and release the silicon atom (step C) before a third charge reaches that Si atom (step D). That is, electropolishing occurs when the current density reaching the silicon/electrolyte interface exceeds the capability of steps B and C to absorb it, thereby increasing the likelihood of additional charge reaching the surface silicon atoms to allow oxide formation prior to their dissolution. The value of this critical current density, Jcrit, will only depend on parameters that directly influence the rates of steps B and C. At first glance it appears that neither of these two steps is electrochemical in nature and thus should not depend on either the applied potential or the conductivity of the p-type wafer used. However, step C involves the breaking of the Si-Si back-bonds, the energetics of which can be expected to depend on the magnitude of the applied field across the electrochemical interface, i.e., the larger the field the more polarized the back-bonds and thus the easier it is to break them. It is thus proposed here that in the presence of a high field the rate of PSi formation is limited by the potential independent step B, such that Jcrit appears to be a constant. However, with a low field, or an opposing field, the PSi formation rate becomes limited by step C, such that it decreases and along with it the magnitude of Jcrit, i.e., less current density is required to exceed the capability of the PSi pathway to absorb it (Figure 5). Regardless of the exact meaning of the Jps peak, its magnitude is almost certainly directly proportional to Jcrit so changes in the former can be assumed to be caused by changes in the latter. From Figure 2 it can be seen that the Jps potential shifts negatively with increasing wafer conductivity, due to the shifting of the flat-band potential, which would cause a decrease in the rate of Step C, i.e., less polarization of the Si-Si back-bonds. It is proposed here that for the two p++ samples the applied field has become sufficiently weak that Jps (and Jcrit) occurs in a potential region where step C is still the rate-limiting step for PSi formation, hence its observed potential dependency and lower current density values (Figure 6). As yet it is uncertain if

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Figure 6. Dependence of the measured current density of the Jps peak against the potential at which it occurred on the silicon wafers of different resistivities in 1% HF + 0.5 M NH4Cl.

Jps would continue to depend on the doping density at higher HF concentrations, since as Jps increases with increasing HF concentration, as can be seen in the work of Zhang et al.,17 a larger field is required across the interface to obtain Jps. As a result it is less likely that step C will become rate determining, even for the most highly doped samples. 4. Conclusion The electrochemical characteristics of porous silicon formation on p, p+, and p++ in diluted HF have been examined. The IV curves show a negative potential shift as the resistivity of the silicon reduces, a phenomenon that has been explained in terms of a corresponding shift in the flat-band potential. Estimates of the flat-band potential suggest it is always, i.e., regardless of the doping density, located between the onset potential for PSi formation and the potential at which the familiar Jps peak occurs. The observation that the flat-band potential is always negative of the Jps peak implies that this peak does not represent the onset oxide formation and subsequent electropolishing as previously postulated in the literature. Instead, these are both thought to begin at a more negative potential, possibly at the end of the exponential stage of the IV curve. The negative shift in the IV curves also leads to a decrease in the magnitude of the Jps peak for the two most heavily doped samples. To explain this, it was proposed that the breaking of the Si-Si back-bonds is dependent on the magnitude of the applied field and that it can become the rate-determining step in PSi formation at sufficiently negative potentials (low fields). Once step C becomes rate limiting, any further negative shift in the applied potential will decrease the amount of the current density that the PSi formation process can consume, which in turn diminishes the magnitude of the Jps peak.

Acknowledgment. Financial support was provided by the Agency for Science, Technology and Research Project No. 42101008. References and Notes (1) Turner, D. R. J. Electrochem. Soc. 1958, 105, 402. (2) Memming, R.; Schwandt, G. Surf. Sci. 1966, 4, 109. (3) Meek, R. L. J. Electrochem. Soc. 1971, 118, 437. (4) Canham, L.T. Appl. Phys. Lett. 1990, 57, 1046. (5) Zhang, X. G. J. Electrochem. Soc. 2004, 151, C69. (6) Lehmann, V. Electrochemistry of Silicon: Instrumentation, Science, Materials and Applications; Wiler-VCH Verlag GmbH&Co.: Weinheim, 2002; pp 51-120. (7) Fo¨ll, H. Appl. Phys. A 1991, 53, 8. (8) Chazalviel, J.-N.; Etman, M.; Ozanam, F. J. Electroanal. Chem. 1991, 297, 533. (9) Monk, D. J.; Soane, D. S.; Howe, R. T. Thin Solid Films 1993, 232, 1. (10) Gerischer, H. Electrochim. Acta 1990, 35, 1677. (11) Allongue, P.; Kieling, V.; Gerischer, H. Electrochim. Acta 1995, 40, 1353. (12) Lehmann, V.; Go¨sele, U. AdV. Phys. Lett. 1991, 58, 856. (13) Hoffmann, P. M.; Vermeir, I. E.; Searson, P. C. J. Electrochem. Soc. 2000, 147, 2999. (14) Zhang, X. G. Electrochemistry of Silicon and Its Oxides; Kluwer Academic/Plenum Publishers: New York, 2001. (15) Gershinskii, A. E.; Mironova, L. V. SoV. Electrochem. 1990, 25, 1224. (16) Lehmann, V. J. Electrochem. Soc. 1993, 140, 2836. (17) Zhang, X. G.; Collins, S. D.; Smith, R. L. J. Electrochem. Soc. 1989, 136, 1561. (18) Gaspard, F.; Bsiesy, A.; Ligeon, M.; Muller, F.; Herino, R. J. Electrochem. Soc. 1989, 136, 10. (19) Ottow, S.; Popkirov, G. S.; Fo¨ll, H. J. Electroanal. Chem. 1998, 455, 29. (20) Ozanam, F.; da Fonseca, C.; Venkateswara, Rao, A.; Chazalviel, J.-N. Appl. Spectrosc. 1997, 51, 519. (21) Morrison, S. R. Electrochemistry at Semiconductor and Oxidized Metal Electrodes; Plenum Press: New York, 1980; Chapter 1. (22) Blackwood, D. J.; Zhang, Y. Electrochim. Acta 2003, 48, 623.