8120
J. Phys. Chem. C 2007, 111, 8120-8127
Near-Surface Channel Impedance Measurements, Open-Circuit Impedance Spectra, and Differential Capacitance vs Potential Measurements of the Fermi Level Position at Si/ CH3CN Contacts Florian Gstrein, David J. Michalak, David W. Knapp, and Nathan S. Lewis* Beckman Institute and KaVli Nanoscience Institute, 210 Noyes Laboratory, 127-72, DiVision of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125 ReceiVed: September 22, 2006; In Final Form: December 15, 2006
Near-surface channel impedance measurements, open-circuit impedance spectra, and differential capacitance vs potential measurements have been used to determine the barrier height of liquid contacts formed with n-type and p-type Si electrodes. Barrier heights were measured as the redox potential, E(A/A-), of a metallocene-based, one-electron, outer-sphere, acceptor/donor (A/A-) pair was varied in CH3CN solvent. The barrier heights of p-Si(111) electrodes in contact with CH3CN-Me10Fc+/0 (where Me10Fc is decamethylferrocene) or CH3CN-CoCp2+/0 (where CoCp2 is cobaltocene) were 0.69 ( 0.1 and 1.1 ( 0.1 V respectively. In contrast, barrier heights for n-Si(111)/CH3CN-Me10Fc+/0 and n-Si(111)/CH3CN-CoCp2+/0 contacts were 0.66 ( 0.1 and 0.09 ( 0.01 V, respectively. These measurements indicate that the barrier heights closely track changes in the electrochemical potential of the contact, instead of being relatively invariant to changes in the Fermi level of the contacting phase, as is observed for Si/metal Schottky barriers. These measurements also demonstrate that the low effective surface recombination velocity, S, for silicon in contact with CoCp2+/0 is primarily the result of an accumulation layer rather than solely being due to a low density of surface electrical defects.
I. Introduction Semiconductor/liquid junctions offer a promising approach to the direct photoelectrolysis of water,1 providing an alternative to supplying photovoltaic-based electricity to an electrolysis unit.2 Among the potential advantages of direct photoelectrolysis are system integration of the energy production and storage functions, elimination of fixed costs associated with an inverter, grid, bus wiring, unfavorable scaling of the efficiency of electrolysis units at high input currents, and the ability to make massively parallel connections to a series of microscale absorber devices.2,3 However, to compete favorably on an efficiency basis with diffused p-n homojunctions, Fermi level pinning must be avoided at semiconductor/liquid interfaces.4 For example, Si/ metal contacts generally result in the equilibrium Fermi level, EF, being located at an energy of 0.4-0.9 eV from the bottom of the Si conduction band edge (EC).5 This pinning position, along with concomitant majority-carrier based thermionic emission currents at semiconductor/metal Schottky barriers, leads to only moderate (0.3-0.4 V) open-circuit voltages (Voc) under Air Mass 1.5 (AM 1.5) illumination of n-Si.6 This pinning position also typically produces low barrier, near-ohmic, or ohmic contacts on p-Si.5 In contrast, p-type Si/CH3CN-cobaltocene (CoCp2)+/0 contacts yield Voc values of 0.52-0.6 V under AM 1.5 conditions,7-10 comparable to the Voc values obtained under such conditions from diffused Si p-n homojunctions.11 We have previously suggested that the low surface recombination velocity, S, values ( |Vi|
Qs )
x
2qκ0 F(Vs) β
)
(7)
(x
Qn ) x2qNBLB
βVs - 1 +
( ) ni2
NB
2
)
eβVs - xβVs
(8)
where
The value of Qs was then used to calculate the built-in voltage. The charge necessary to reach inversion, Qi, can be calculated by integration of Poisson’s equation along with use of Gauss’ law to equate the field to the total charge at the surface5
Qi )
(
1 Eg - Vi 2 q
The second method21 allowed for an immediate calculation of Vs from Qn according to eq 8
(1)
where L denotes the separation between the highly doped source and drain contacts (1 mm for these devices), W is the width of the channel (8 mm), µmin is the mobility of minority carriers in the inversion layer (1000 cm2 V-1 s-1 for electrons in p-type Si),19,20 and Rch is the resistance of the channel as determined by the value of the low-frequency, in-phase impedance measured between the source and drain. Estimation of the equilibrium built-in voltage between the central channel region and the contacting liquid or ambient was performed using two different methods.17,21 In one method,17 the minority-carrier inversion layer charge, Qn, was added to the static charge needed to reach inversion, Qi. To obtain the total charge in the space-charge region, Qs, of the semiconductor:
Q s ≈ Qn + Qi
φb ) Vbi +
LB )
x
kBTκ0 q2NB
(9)
Both methods will only yield a meaningful built-in voltage value for cases of strong inversion. A minimum value of the minoritycarrier charge density necessary for strong inversion, Qn,i, can be estimated by substituting Vi for Vs in eq 8. The resulting value for Qn,i can then be used in eq 1 to calculate the value for Ri that yields the maximum channel resistance allowable for strong inversion. III. Results A. Current Density vs Potential Data. Figures 3 and 4 present the dark current density vs potential (J-E) profiles for the silicon/liquid contacts investigated. Although both p-Si/liquid contacts showed rectification, the p-Si(111)/CH3CN-Me10Fc+/0 contact displayed a larger reverse bias saturation current density than the p-Si(111)/CH3CN-CoCp2+/0 contact (Figure 3). This behavior is consistent with earlier studies which have shown that the open-circuit voltage of p-Si(100)/CH3CN contacts increases as the Nernstian potential of the solution decreases in the range -0.6 > E(A/A-) > 0.2 V vs SCE.10,22 Although n-Si(111)/CH3CN-Me10Fc+/0 contacts showed rectification (Figure 4), n-Si(111) CH3CN-CoCp2+/0 contacts exhibited Ohmic behavior (Figure 4), as expected for an accumulation layer with rapid electron-transfer kinetics. The behavior of these contacts is consistent with the hypothesis that the barrier height of the Si(111)/CH3CN contact is a strong function of E(A/A-) in this potential range.22 B. Differential Capacitance vs Potential Data. Figure 5 displays the differential capacitance vs potential data in the form of As2 Csc-2 vs E for the p-Si(111)/CH3CN-CoCp2+/0 and p-Si(111)/CH3CN-Me10Fc+/0 contacts, whereas Figure 6 displays
(6)
The value of Vs can then be numerically evaluated for each value of Qs. The voltage Vs is related to the built-in voltage, Vbi, and the barrier height, φb. For n-type electrodes, Vs ) -Vbi, while for p-type electrodes, Vs ) Vbi. The barrier height can then be calculated using eq 7, where Eg is the energy of the band gap (1.12 eV for Si).5
Figure 3. Representative current density vs potential (J-E) responses at 0.1 V s-1 for p-Si(111) electrodes in contact with CH3CN-CoCp2+/0 solution (black solid line) or CH3CN-Me10Fc+/0 solution (black dotted line), or for n-Si(111) electrodes in contact with CH3CN-Me10Fc+/0 solution (gray broken line). All measurements were performed in stirred solutions, under a N2(g) atmosphere, and in the dark.
8124 J. Phys. Chem. C, Vol. 111, No. 22, 2007
Figure 4. Representative current density vs potential (J-E) response at 0.05 V s-1 for an n-Si(111) electrode in a CH3CN-CoCp2+/0 solution. Measurements were performed in stirred solution, under a nitrogen gas atmosphere and in the dark. At E ) 0, the J-E curve is linear demonstrating that an ohmic contact has been formed. The anodic and cathodic currents at large voltage magnitudes are limited by masstransport of the redox species to the electrode surface.
Figure 5. Representative differential capacitance vs potential (Mott Schottky) plots for p-Si(111) electrodes in contact with either CH3CN-CoCp2+/0 (triangles) or CH3CN-Me10Fc+/0 (circles). All measurements were performed in stirred solution, under a N2(g) atmosphere in the dark.
Figure 6. Representative differential capacitance vs potential (Mott Schottky) plot for an n-Si(111) electrode in contact with a CH3CNMe10Fc+/0 solution. All measurements were performed in stirred solution, under a N2(g) atmosphere in the dark.
As2 Csc-2 vs E data for the n-Si(111)/CH3CN-Me10Fc+/0 contact. The As2 Csc-2 vs E data were well-fitted by a straight line with slopes that were within a factor of 1.5 of the dopant density of the sample measured using a standard 4-point probe technique.5 The resulting barrier heights, φb, were 1.13 ( 0.050, 0.69 ( 0.10, and 0.66 ( 0.10 V for the p-Si(111)/CH3CN-CoCp2+/0, p-Si(111)/CH3CN-Me10Fc+/0, and n-Si(111)/CH3CN-Me10-
Gstrein et al.
Figure 7. Representative Nyquist plots of the open-circuit frequency spectra for n-Si(111) and p-Si(111) electrodes in contact with a CH3CN-CoCp2+/0 solution. The black diamonds represent the data obtained for the n-Si(111) electrode, with the real impedance, Ζ′, axis and the imaginary, Ζ′′, axis on the bottom and right of the graph, respectively. The high-frequency data are characteristic of a single relaxation process, whereas the low-frequency data display a Warburg impedance, as expected for diffusion-limited transport of the redox species to the interface. The impedance values over the entire frequency range for the n-Si(111) electrodes are low, as expected for an ohmic contact. The concentrations of CoCp2+/0 were diluted by a factor of 2 and the stirring was stopped so that the diffusional profile could be observed easily at low frequency. The open squares represent the data obtained for the p-Si(111) electrode, with the real impedance, Z′, axis and the imaginary, Z′′, axis on the top and the left of the graph, respectively. The data in the frequency range from 100 kHz to 1 Hz are wellcharacterized by a single relaxation process, ascribable to the spacecharge region of the inversion layer. All measurements were performed in the dark under a N2(g) atmosphere.
Fc+/0 contacts, respectively. The barrier height value for p-Si(111) in contact with CoCp2+/0 contrasts with φb ) 0.2-0.4 V values that are that is observed for Au, Ni, Pt, and other metal contacts to p-type Si.5 The barrier height values for n-Si(111) and p-Si(111) in contact with CH3CN-Me10Fc+/0 demonstrate that the Fermi level is near midgap for these contacts. Differential capacitance data for the n-Si/CH3CN-CoCp2+/0 contact could not be reliably interpreted within a simple RC framework because the lack of rectification yielded no potential range over which the interface had a high faradaic resistance. C. Open-Circuit Frequency Spectra. Figure 7 shows a Nyquist plot (imaginary impedance, Z′′, vs real impedance, Z′) for the n-Si(111)/CH3CN-CoCp2+/0 and p-Si(111)/CH3CNCoCp2+/0 open-circuit frequency measurements. The lowfrequency region of the open-circuit frequency spectrum for the n-Si(111)/CH3CN-CoCp2+/0 contact was dominated by a Warburg-type (diffusion-limited) response. The high frequency (1100 kHz) response of the cell was in accord with a standard three-element circuit containing a resistor, Rs, in series with a parallel combination of a resistor, Rp, and capacitor, Cp. The differential capacitance value obtained by fitting this highfrequency region of the n-Si/CH3CN-CoCp2+/0 interface was 2.0 ( 0.6 µF cm-2. This value is too small for a Helmholtz capacitance18 but is in accord with expectations for an accumulation layer in Si. Performing the same impedance analysis at zero applied bias using a Pt working electrode produced a similar response, except that the high-frequency semicircle observed on the Nyquist plot (data not shown) was well-fitted by a capacitance value of 41 ( 7 µF cm-2, which is expected for the Helmholtz capacitance of this electrolyte solution.18
Fermi Level Position at Si/CH3CN Contacts
Figure 8. Bode plot for the n+-p-Si(111)-n+ devices in contact with various ambients: nitgrogen gas (black solid line), CH3CN-Me10Fc+/0 (gray solid line), 1 M LiClO4 in CH3CN (black broken line), and CH3CN-CoCp2+/0 (gray broken line). The low-frequency phase angle (lower graph) of approximately 45° for the CH3CN-Me10Fc+/0 contact (gray solid line) demonstrates that the current pathway between the n+-doped source and drain contacts was primarily through the solution rather than through the p-Si(111) channel. The impedance magnitude (upper graph) at low frequency can only be used to calculate an upper bound on the barrier height for this contact. Conversely, the devices displayed a low-frequency phase angle near 0° when contacted with either N2(g) (black solid line), CH3CN-LiClO4 (black broken line), or CH3CNCoCp2+/0 (gray broken line). This behavior demonstrates that the predominant current pathway for such systems was through the p-Si(111) channel region. Hence, for these contacts, the low-frequency impedance magnitudes can be used to calculate the barrier height.
The differential capacitance of the space-charge region, Csc, within a semiconductor is defined as the differential change in surface charge, Qs, with surface voltage, Vs
Csc ≡
dQs )( dVs
qβκ0 [pb,0(1 -e-βVs) + nb,0(eβVs - 1)] 2 F(Vs) (10)
x
Equation 10 holds for cases of accumulation, depletion, and inversion. The positive sign on the right-hand side of the equation is used for Vs > 0 and the negative sign is used for Vs < 0. Hence, the capacitance always has a positive value. The e(βV terms for the minority carriers should not be included for high-frequency measurements, for which the rates of recombination-generation or diffusion of minority carriers to the surface cannot follow the excitation signal.5 Using numerical methods, the value of Vs can be calculated from eq 10 for a given observed differential capacitance. The barrier height can then be calculated from eq 7. The open-circuit high-frequency parallel capacitance of 2.0 ( 0.6 µF cm-2 observed for the n-Si(111)/CH3CN-CoCp2+/0 interface leads to a barrier height of φb ) 0.091 ( 0.016 V. Open-circuit frequency spectra for p-Si(111)/CH3CN-CoCp2+/0 contacts (Figure 7) were also fitted to the same simple threeelement circuit containing Rs, Rp, and Cp. The resulting parallel capacitance value of 37 ( 2 nF cm-2 is reasonable for the differential capacitance of an inversion layer, and yields φb ) (0.87 ( 0.06) V. Multiple relaxation processes precluded a straightforward interpretation of the open-circuit frequency data for n-Si(111) and p-Si(111) contacts to the CH3CN-Me10Fc+/0 electrolyte. D. Channel Impedance Data. Channel impedance data were collected for n+-p-Si(111)-n+ devices exposed to various conditions. Figures 8 and 9 display Bode plots of the magnitude of the impedance vs frequency and of the phase angle vs frequency. These data are summarized in Table 1.
J. Phys. Chem. C, Vol. 111, No. 22, 2007 8125
Figure 9. Bode plot for a n+-p-Si(111)-n+ device in contact with either liquid CH3CN or CH3CN vapor for various lengths of time. The device was measured initially after bringing it into the nitrogen box (black solid line), and after longer exposures (black broken line, followed by the black dotted line) to CH3CN vapor above a solution reservoir. A measurement was also performed in contact with neat anhydrous CH3CN (gray solid line).
Samples in contact with N2(g) displayed a large lowfrequency resistance, characterized by a phase angle close to zero. This behavior demonstrates that the p-Si(111) channel is not under inversion in contact with N2(g) and current is forced through the rectifying n+-p contacts separating the source and drain. When in contact with pure CH3CN or CH3CN containing 1.0 M LiClO4, the low-frequency channel impedance displayed a low resistance. Contacting the devices with 1 mM CoCp2+/0 in 1.0 M LiClO4-CH3CN drove the low-frequency impedance to an even lower resistance, indicating that the surface had been driven further into inversion. Barrier-height values were numerically evaluated from the low-frequency resistance using eqs 1-7 for the first method (denoted as Vbi 1 in Table 1) and eqs 7-9 for the second method (denoted as Vbi 2 in Table 1). The two methods used to calculate the barrier height produced values within error of each other, and thus, the values obtained from the two methods were averaged together to yield a final barrier height estimate (Table 1). This procedure produced a value of φb ) 1.071 ( 0.014 V for the p-Si(111)/CH3CN-CoCp2+/0 contact, which is in very good agreement with the values obtained for this contact using the other methods (vide supra, Table 2). Contacting the n+-p-Si(111)-n+ device with 1 mM Me10Fc+/0 in 1.0 M LiClO4-CH3CN yielded a much larger low-frequency impedance and a nonzero phase angle (Figure 8), as expected for faradaic charge transfer into solution through the exposed source and drain contacts. Hence a value for the barrier height cannot be extracted from the channel impedance data for this contact. Instead, only an upper bound on the barrier height of 0.910 ( 0.006 V can be established from the channel impedance data. This upper bound is consistent with the value of φb ) 0.69 ( 0.10 V determined by Mott-Schottky analysis on the p-Si(111)/CH3CN-Me10Fc+/0 contact. Figure 9 displays the channel impedance spectra of the n+p-Si(111)-n+ device upon exposure to various amounts of liquid phase or vapor-phase CH3CN. The largest channel impedance was observed immediately after bringing the device into the dry box. The low-frequency channel resistance gradually decreased with time during exposure to CH3CN vapor above a solution reservoir. The lowest impedance values were obtained upon exposure of the device to neat liquid CH3CN. The decline in impedance could be reversed by pumping the device under vacuum for 20-30 min and performing a measurement immediately after bringing the device into a N2(g) atmosphere.
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TABLE 1: Channel Impedance Data for an n+-p-Si(111)-n+ Device contact
Rs,cha (Ohms)
Air/N2(g) CH3CN Only CH3CN-LiClO4 CH3CN-Me10Fc+/0 b CH3CN-CoCp2+/0 Inversion
3.2 ( 2.1 × 10 2.6 ( 1.3 × 103 2.7 ( 1.4 × 103 54 ( 9 × 103 640 ( 140 294 × 103 6
Qn (C cm-2)
Vbi 1 (V)
Vbi 2 (V)
φb (V)
5.7 ( 3.6 × 10-11 5.8 ( 2.9 × 10-8 6.5 ( 3.4 × 10-8
