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Charge distribution in nanostructured TiO2 photoanode determined by quantitative analysis of the band edge unpinning Dhritabrata Mandal, and Thomas W. Hamann ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.5b09200 • Publication Date (Web): 22 Dec 2015 Downloaded from http://pubs.acs.org on December 28, 2015
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ACS Applied Materials & Interfaces
Charge distribution in nanostructured TiO2 photoanode determined by quantitative analysis of the band edge unpinning Dhritabrata Mandal, Thomas W. Hamann* Department of Chemistry, Michigan State University, East Lansing, MI 48824 ABSTRACT: Conduction band (CB) edge position, trap state distribution and electron density are considered to be the most important properties of the mesoporous semiconductor photoanodes for detailed understanding of the various charge transfer processes associated with them. The electroactive surface states on these high surface area electrodes cause potential drop across the Helmholtz layer resulting in the unpinning of band edges. Herein, we present a spectroelectrochemical method that determines the magnitude of the CB unpinning and its effect on the overall electron distribution. The position of CB edge is determined from the band gap widening, also known as Burstein-Moss shift, observed under negative bias. Additionally, the spatial location of the trap states is also estimated. Trapped electrons are found to be distributed on the surface as well as in the bulk and with increasing negative potential bulk traps dominate the overall trap density.
KEYWORDS: Conduction band, TiO2, Dye Sensitized Solar Cells, trap state distribution, band edge unpinning, BursteinMoss shift
showed the necessity of considering the effect of this band edge unpinning while studying the electron transfer processes in DSSCs.8 However, due to the absence of any reliable method for quantitative analysis of the band edge shift, the magnitude of this shift was estimated indirectly in their study. Recently, we reported a straightforward spectroeletrochemical method to determine the conduction band edge from the apparent shift in the band gap transition, known as Burstein-Moss shift (BM shift), in response to an applied bias.9 This simultaneously established that the free conduction band electrons are the major absorbing species in Vis/NIR wavelength region. The extinction coefficient of free electrons, a necessary parameter for spectroelectrochemical studies of various charge transfer processes, was also determined.10 A very interesting phenomenon observed in this work was the upward shift or unpinning of the CB under negative bias which is generally ignored while studying the nanostructured photoanode and the charge transfer processes related to it. In this work, we have utilized spectroelectrochemical measurements to determine the magnitude of the band edge unpinning in the nanostructured TiO2 photoanode and its effect on the overall charge distribution. From these results, we are also able to accurately calculate the total trap state density and estimate the spatial location of the localized trap states in TiO2.
RESULTS AND DISCUSSION INTRODUCTION Mesoporous wide bandgap semiconductor electrodes have been widely studied for solar energy conversion, especially in the context of dye-sensitized solar cells (DSSC) and related systems.1,2 The conduction band (CB) edge position, trap state distribution and electron concentration are arguably the most important properties for detailed understanding of the various charge transfer processes associated with them.3 However, the efforts to determine the conduction band edge in the nanostructured semiconductor photoanode by Mott–Schottky analysis or from the photocurrent onset potential have failed due to their small dimensions and presence of large concentration of localized trapped electrons.4,5 Absence of any reliable method to determine the band energetics in nanostructured semiconductor photoanodes has also hindered an accurate determination of the distribution as well as the nature of the various trap states. During the early 1990s, Fitzmaurice et al. developed spectroeletrochemical methods to determine the conduction band edges in these porous semiconductor films.6 However, the nature of the absorbing species as well as the interpretation of their results have been the subject of continuing debate. Their model assumes that the conduction band edge does not change while raising the Fermi energy. However, high surface area mesoporous TiO2 films are known to have electroactive states on the surface which can cause potential drop across the Helmholtz layer resulting in the unpinning of band edges.7 Recently, Liu and Jennings et al. have
Due to good electronic connectivity throughout the TiO2 photoanode and the equipotential surrounding, the Fermi level, EF/q, within the semiconductor film can be considered to be equal to the applied potential, E.11 In this paper, E represents energy and E (= E/q) represents the electrochemical potential. Moving E towards more negative potentials fills the bottom energy states of the CB and inhibits the lowest energy inter-band transition. As a result, there is a blue shift of the band gap absorbance as shown in figure 1.12 The concentration of CB electrons (nCB) can be determined from the magnitude of this apparent band gap widening (∆EG) using following relation: ∆E G =
h 2 3nCB * 8meh π
2/3
(1)
where h is the Planck constant, meh* is the reduced effective mass of the charge carriers and nCB is the concentration of electrons in the CB. Once nCB is known, the conduction band edge energy, ECB, can be determined from the following equation: nCB = N CB exp
(E F − E CB ) kT
(2)
where NCB is the density of states (DOS) in the CB which is calculated by using the following equation,
m*kT N CB = 2 e 2 2πh
3/ 2
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(3)
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where ħ is the reduced Planck constant and me* is the effective mass of an electron. me* = 2.3me has been used in this study8 though a range of values are found in literature (1me to 10me).13–15 Due to the uncertainty in the effective mass of holes, mh*(= 1me and 0.8me), found in literature, mass of an electron is used as mh*.14,16 The variation of the calculated ECB due to this uncertainty of effective masses is small (± 42 meV) and this systematic error will not affect the calculation of the magnitude of the ECB shift which is the main interest of this paper.
Figure 1. Plot of absorbance of TiO2 under various applied potentials. Increasing negative potential moves the band gap absorption edge to higher energy. Our previous report showed a significant upward shift of ECB when the applied potential is increased to more negative values which was attributed to the potential drop across the Helmholtz layer.7,17,18 Change in the electric field of the Helmholtz layer occurs due to the accumulation of electrons in electrically active states on the surface or within close vicinity of the surface of mesoporous TiO2 films. In order to calculate the magnitude of the upward shift of conduction band, ∆ECB, an initial position of the conduction band, E*CB, needs to be determined. Figure 2 shows a plot of ∆EG determined as a function of E. A linear extrapolation of this plot to the intercept, corresponding to no bandgap shift, produced values of –1.17 V vs. SCE at pH 12.8 and –0.55 V at pH 2.0 for E*CB. The expected Nernstian shift of the conduction band with pH was observed, which can be expressed by:
E*CB / q = −0.435V(vs.SCE) − 0.058 × pH
(4)
This Nernstian behavior is well known for metal oxide semiconductors in aqueous electrolytes.19 Knowledge of the conduction band edge shift, ∆ECB/q (= E*CB/q − ECB/q), is required for accurate determination of the charge distribution by electrochemical methods. The magnitude of the conduction band edge shift as a function of the displacement of the Fermi level (applied potential) to the conduction band edge is also shown in figure 2.
Figure 2. Top: The position of the conduction band edge determined at pH 12.8 and 2.0. Bottom: Shift of the conduction band of TiO2 as a function of the displacement of the Fermi level with respect to the conduction band. The distribution of electrons in the nanostructured photoanode is generally measured by measuring its chemical capacitance, Cµ, which describes the change of electron density as a function of Fermi level and can be written as, 20 Cµ = q
dn dE
(5)
where n is the total electron density in the film. Considering the fact that nCB
