5.5 Band alignment
5.5.2 Experimental reference values
The band edges determined through Eqs. 5.8 and 5.9 can directly be compared with experimen- tal values provided the latter are measured at pHPZC. In fact, band edges at semiconductor-
water interfaces show a Nernstian dependence on pH [240, 183, 241, 242], i.e. the band edges are shifted by 0.059 eV closer to the vacuum level as the pH is increased by one unit. However, while the pHPZCof a semiconductor immersed in an aqueous solution can be determined by
acid-base titration, the band offsets are not necessarily measured at the same value of pH. Therefore, in order to compare the calculated results with experiment, the conduction band edge measured at a given pH is shifted to its value at pHPZCthrough the following expression:
²SHE
c (PZC) = ²SHEc (pH) + (0.059eV) × (pHPZC− pH), (5.11)
where²SHEc (pH) is the conduction band edge at a given pH. In the following, Eq. 5.11 is
employed to shift conduction band edges measured at a given pH to their position at pHPZC,
prior to the comparison with their theoretical counterparts. We use experimental values for pHPZC. In order to identify reliable experimental results to be compared with our calculations,
the complex and rich literature of electrochemical measurements at semiconductor-water interfaces has been thoroughly investigated for each material.
For GaAs, the pHPZCwas determined to be ∼5.9 from measurements performed on powdered
material [243]. Benard and Handler [244] studied the capacitance-voltage behavior of n- and p-type GaAs on the (¯1¯1¯1) surface, and observed that the flat-band potentials of n- and p-type GaAs differed by ∼1.42 eV (i.e. the band gap), thus indicating that the band-edge positions are the same for both types of doping. Impedance measurements of (¯1¯1¯1) and (100) surfaces give²SHEc (PZC) = −1.22 eV [245, 246] and ²SHEc (PZC) = −1.19 eV [247], respectively. Photocur-
rent measurements on p-type GaAs with the (100) facet exposed in a 0.5 M H2SO4solution
give²SHEc (PZC) = −1.08 eV [248], in substantial agreement with the impedance experiments.
However, photoelectrochemical measurements of n-type GaAs with the (100) and (111) facets exposed in alkaline solutions provide the significantly different value of −0.78 eV for ²SHEc (PZC)
[249]. The latter agrees with the value of²SHEc (PZC) = −0.70 eV reported by Wrighton et al. [250]. The experimental large spread appears to be unresolved at present. Therefore, we consider in the present work the average value²SHEc (PZC) = −1.00 eV, which is expected to be
accurate within ±0.3 eV for GaAs.
For GaP, we have not been able to find any measurement of pHPZC. However, Butler and
Ginley [251] have shown that the pHPZC of semiconductors depends linearly upon their
electronegativity. By calculating the electronegativities of the compounds from those of the constituent atoms for both GaAs and GaP, and considering the pHPZC =5.9 for GaAs,
we infer a value of the pHPZC of 4.9 for GaP. From photoelectrochemical measurements of
n-type GaP at pH=0,²SHEc (PZC)= −1.42 eV [250]. This value is slightly different from that inferred from impedance measurements [²SHEc (PZC)= −1.30, −1.45 eV [252]]. Gomes and Cardon [253] summarized various electrochemical measurements on n- and p-type GaP
[247, 252, 250, 254, 255], and found that the conduction band edge of both types of GaP satisfied the expression²SHEc = −1.05 − 0.06 · pH (in eV). Furthermore, this expression appears to be independent of the exposed semiconductor surface. According to this expression,
²SHE
c (PZC)= −1.35 eV, and this value is used as our experimental reference for GaP. We estimate
an error of ±0.1 eV on the basis of the spread of the experimental data.
For GaN, pHPZC= 7 is inferred from an indirect estimate based on a model [256] used to fit the
measurements of Ref. [257]. Electrochemical capacitance measurements on n-type GaN give
²SHE
c (PZC)= −0.91 eV [241], in substantial agreement with earlier measurements of the same
group giving²SHEc (PZC)= −0.86 eV [183]. At variance, the interpolation of the values reported by Huygens and co-workers [242] lead to²SHEc (PZC)= −0.96 eV. Hence, we here adopt the average value of the reported data,²SHEc (PZC)= −0.91 eV. This value is expected to be accurate
within ±0.05 eV.
The pHPZCof CdS is reported to be 7.5 from measurements of the zeta potential on hydrous CdS
at various pH [258]. Numerous electrochemical measurements on CdS have been performed and very different values for the flat-band potential have been reported [259, 260, 261, 262, 263, 264, 265, 250]. In particular, it has been observed that the flat-band potential of CdS(0001) shifts drammatically when the measurements are performed on Cd and S surfaces [263]. In our work, the exposed face of CdS is (10¯10), a nonpolar surface with 1:1 ratio of Cd and S at the surface. Therefore, we consider as our experimental reference the average of the values measured for S and Cd surfaces in Ref. [263]. This leads to²SHEc (PZC)= −1.14 eV.
The pHPZC of ZnO is reported to lie in an interval between 8 and 10, depending on the
experimental setup [266]. Therefore, we considered the average value of 9 in this work. From capacitance-voltage measurements of n-type ZnO(11¯20) electrodes, we infer²SHEc (PZC)=
−0.46 eV [267, 268]. The experimental characterization of (0001) and (000¯1) surfaces did not show any significant difference, yielding²SHEc (PZC)= −0.41 eV in Ref. [269] and ²SHEc (PZC)=
−0.36 eV in Ref. [270]. We here adopt the average of the reported data, i.e. ²SHEc (PZC)= −0.41
eV. The adopted value is consistent within ±0.05 eV with all the available experimental data. A value of 4.3 for the pHPZCof SnO2has been reported in Refs. [251] and [271]. Photocurrent
measurements on n-type SnO2give²SHEc (PZC)= 0.11 eV [272], in accord with more recent elec-
trochemical experiments in Refs. [273] and [274], giving 0.15 and 0.16 eV for²SHEc (PZC), respec-
tively. Again, we here adopt the average value of the reported measurements,²SHEc (PZC)= 0.14 eV. With this assignment, all measurements are accounted for within ±0.03 eV.
As far as TiO2is concerned, the pHPZCis reported to lie in the interval ranging from 5.8 to
6.0 [251, 275], and to be independent of the crystal structure [275]. Thus, we set pHPZC =
5.9 for both rutile and anatase in this work. The literature of electrochemical measurements on rutile and anatase TiO2is extremely rich and the relative position of the band edges of
the two polymorphs is still debated [276]. However, electrochemical measurements for both types of TiO2agree within 0.1 eV or less, generally with the conduction band edge of a-TiO2
5.5. Band alignment
experimental results. Early measurements performed on rutile and anatase powders yield −0.36 and −0.40 eV, respectively [277]. We infer ²SHEc (PZC) values of −0.32 and −0.52 eV for
r-TiO2(001) and a-TiO2(101) from Ref. [278]. For rutile, a value of²SHEc (PZC)= −0.41 eV is
inferred from the pH-dependent band bending of TiO2(110) [279]. Values of −0.31 eV and
−0.39 eV for the same material have been reported in Refs. [280] and [272], respectively. For a-TiO2(101), Refs. [281] and [282] lead to²SHEc (PZC) at −0.41 and −0.36 eV, respectively. For the
purpose of this work, we take as reference for each material the average of the measured values. This gives²SHEc (PZC) = −0.36 eV for r-TiO2and −0.43 eV for a-TiO2. These values account for
all the experimental data within ±0.05 and ±0.09 eV, respectively.
The compilation of experimental²SHEc (PZC) used in this work is summarized in Table 5.10. Reference values for²SHEv (PZC) are achieved by adding the measured fundamental gap listed
in Table 5.7 to the pertinent²SHEc (PZC).