Verification of Rate Constant Estimates at n-Si / Methyl Viologen (MeOH) Interfaces
Robert C. Rossi  June 22, 1998

To ensure the validity of recent results obtained in our laboratory, I was asked to attempt to reproduce those results based only on the information provided in the paper we published on the topic:

A. M. Fajardo, N. S. Lewis, Journal Of Physical Chemistry B 101, 11136-11151 (1997).

My own research is in silicon photoelectrochemistry, but does not involve the use of viologens nor impedance measurements. Thus my approach to these aspects of the experiments described in the paper above were essentially those of a novice, and I let the text of the paper guide me where specific details were given but made my own choices with regard to everything else. As a result, the cell configuration, calculation methodologies, and even the impedance equipment I used differed from those used by the paper's author. My results, however, are in very reasonable agreement with those presented in the paper, at least for the one redox couple I utilized in my experiments. Those results are presented here in appreciable detail.

 After running through the entire experimental process with two test electrodes, the following four electrodes were prepared from a test-grade P-doped n-Si wafer:
Electrode Identifier RCRPS3 RCRPS4 RCRPS5 RCRPS6
Exposed Area (cm2) 1.538 1.022 1.556 1.563
This wafer's conductivity was measured with a four-point probe and found to be 5.54±0.08 ohm•cm, indicative of a dopant density (ND) of 8.1±0.1 x 1014 cm-3.

 A 20 mM solution of dehydrated methyl viologen dichloride in dehydrated methanol containing 1 M LiCl was prepared in a nitrogen-purged flush box. A cyclic voltammogram of this solution showed two waves, as expected for methyl viologen. The half-wave potential of the first wave was found to be roughly -450 mV vs. SCE. Bulk electrolysis of the solution using a counterelectrode held in a separate cell separated from the working solution by a vicor frit was used to form the radical cation form of methyl viologen, mv+•;. After passing -28.94 Coulumbs of charge (the ideally expected amount) at -200 mV vs. the cell potential, the solution potential was measured to be -413 mV vs. SCE. Passing an additional 4.92 Coulombs of charge compensated for side reactions and loss of the radical to traces of oxygen and brought the solution potential to -450 mV vs. SCE, indicative of a 1:1 solution of mv2+ / mv+•;. At this point a small amount of methanol was added to the open cell to compensate for the loss of solvent to evaporation.

 The four electrodes described above were each etched for 30 seconds in fresh 48%wt HF(aq) (Mallinckrodt AR grade) and rinsed with 17.8 Mohm·cm Nanopure water. They were then dried under filtered, rapidly-flowing nitrogen and transferred immediately into the antechamber of the nitrogen flush box where the experiment was being carried out. After the 30 minutes required to cycle the antechamber, the electrodes were brought into the flushbox and the following steps performed on each of them individually:
1) The electrode was submerged for a minimum of two minutes in a 0.2 M solution of ferrocenium tetrafluoroborate in methanol.
2) The electrode was placed into the cell and cycled at 50 mV/sec between +500 and -100 mV vs. the cell potential (as measured with a Pt wire electrode) under ambient illumination for a minimum of 20 minutes. The current-voltage characteristics of the electrodes were recorded between +500 and -200 mV vs. the cell potential at 50 mV/sec at the beginning and end of the cycle time.
3) Limiting anodic and cathodic current densities were measured at a 0.755 cm2 Pt electrode placed in the cell and potted with epoxy in a manned similar to that used for the Si electrode.
4) The room was darkened completely, and the current-voltage characteristics of the dark junction were measured between +500 and -300 mV vs. the cell potential, scanning at 50 mV/sec.
5) The electrode capacitance was measured using a 10 mV AC bias superimposed on a DC bias incremented from 0 to +800 mV vs. the cell potential at 50 mV intervals. At each DC bias, the electrode impedance was measured at 20 frequencies logarithmically distributed between 1 and 100 kHz. The integration time for each impedance measurement was 10 seconds. Other impedance analyzer settings were left at the manufacturer's defaults as set in the CorrWare (Win 95 32-bit ver. 2) software package used to control the instrument.
6) Step 4 was repeated following the impedance analyses.
7) The lights were turned back on and the electrode's current-voltage characteristics again recorded between +500 and -200 mV vs. cell at 50 mV/sec.

 The potentiostat used was a Solartron 1287; the impedance analyzer a Solartron 1260. The counterelectrode was a Pt ribbon, 6mm wide and 26 mm long, the in-cell reference a 4 mm Pt wire. The solution was stirred with a large stirbar fast enough that a slight vortex formed in the cell but not so fast that this vortex was unstable.

 The data obtained from these experiments is tabulated in detail at the bottom of this page. The rate constants extracted from this data are presented here:
Experimental Electron Transfer Rate Constants as Measured by Impedance Analysis 
at a methyl viologen (++/+•; 10mM : 10 mM in MeOH) / n-Si Junction at 25°C
Electrode Efb 
[V vs. cell]
Diode Quality 
Factor (A)
ket (Float A) 
ket (Mixed A) 
ket (A = 1) 
RCRPS3 -0.29 1.41 2 x 10-18 6 x 10-17 9.5 x 10-18
RCRPS4 -0.27 1.32 3 x 10-18 3.5 x 10-17 8 x 10-18
RCRPS5 -0.30 1.21 1 x 10-17 1 x 10-16 3.4 x 10-17
RCRPS6 -0.34 1.16 3 x 10-17 2 x 10-16 7 x 10-17
The flatband potentials (Efb) were derived by fitting the experimental impedance data to the Mott-Schottky equation as adapted to apply to this experiment:
The rate constants (ket) were extracted from the following equations:
Because the observed diode quality factors extracted from the dark J-V data were not exactly one, it was unclear how to extract the rate constants from these results. To allow for differences of opinion on this issue, three different approaches were used:
1) The diode quality factor was allowed to float in both the J-V fit (A2) and the correction to flatband (A1), giving the smallest ket estimates.
2) The diode quality factor (A2) was allowed to float in the J-V fit but set to A1 = 1 in the flatband correction, giving the largest ket estimates.
3) The diode quality factors (A1 and A2) were both forced to one in calculating ket, yielding a different (and somewhat questionable) y-intercept (b) value. This gave intermediate ket esitmates.

The more fundamental data leading to the results presented above is presented in the following spreadsheets, stored in Microsoft Excel 5.0 (IBM or Macintosh) format:

Dark JV Data:

Mott-Schottky Data: