Mott—Schottky plot

The Mott-Schottky plot following from Eqs (4.5.12) and (4.5.14) is the relationship... 

Figure 7.5 Mott-Schottky plot for the depletion layer of an n-type semiconductor the flat-band potential Eft, is at 0.2 V. The data extrapolate to Eft, + kT / eo-...

Figure 8.4 Mott-Schottky plot for n-type SnC>2 for various donor concentrations (data taken from Ref. 5).

If VEB is increased, IEB increases and the current density at the electrode eventually becomes equal to JPS. It has been speculated that this first anodic current peak is associated with flat-band condition of the emitter-base junction. However, data of flat-band potential of a silicon electrode determined from Mott-Schottky plots show significant scatter, as shown in Fig. 10.3. However, from C-V measurement it can be concluded that all PS formation occurs under depletion conditions independent of type and density of doping of the Si electrode [Otl]. 

Fig. 10.2 Mott-Schottky plots of an n-type and a p-type silicon electrode in an electrolyte composed of 0.5 mol I"1 HF and 0.5 mol I-1 NH4CI. Dotted lines correspond to ND = l.l xlO15 cm" and NA=3.4xl015 cm-3.

Figure 5-47 shows the Mott-Schottky plot of n-type and p-type semiconductor electrodes of gallium phosphide in an acidic solution. The Mott-Schottl plot can be used to estimate the flat band potential and the effective Debye length I D. . The flat band potential of p-type electrode is more anodic (positive) than that of n-type electrode this difference in the flat band potential between the two types of the same semiconductor electrode is nearly equivalent to the band gap (2.3 eV) of the semiconductor (gallium phosphide). 

Fig. 6-47. Mott-Schottky plot of electrode capacity observed for n-type and p-type semiconductor electrodes of gallium phosphide in a 0.05 M sulfuric add solution. [From Meouning, 1969.]...

Fig. 5-61. Mott-Schottky plot of an n-type semiconductor electrode in presence of a surface state ib = flat band potential with the surface state fully vacant of positive charge Eft, - flat band potential with the surface state fully occupied by positive charge Q = maximum charge of the surface state e, = surface state level, s capacity of the surface state ( Ch ).

As the Fermi level reaches the surface state level, the interfacial capacity is determined by the capacity of the compact layer (the maximum capacity of the surface state) and remains constant in a range of potential where the Fermi level is pinned. A further increase in anodic polarization leads again to the capacity of the depletion layer in accordance with another Mott-Schottky plot parallel to the former plot as shown in Fig. 5-61. The flat band potential, which is obtained from the Mott-Schottlo plot, shifts in the anodic direction as a result of anodic charging of the siuface state. This shift of the flat band potential equals a change of potential of the compact layer, (Q /C = Q./Ch), due to the anodic charging of the surface state. 

Pig. 10-18. (a) PolarizatioD curves of anodic dissolution and (b) Mott-Schottky plots of an n-type semiconductor electrode of molybdenum selenide in the dark and in a photo-excited state in an acidic solution C = electrode capacity (iph) = anodic dissolution current immediately after photoexdtation (dashed curve) ipb = anodic dissolution current in a photostationary state (solid curve) luph) = flat band potential in a photostationary state. [From McEv( -Etman-Memming, 1985.]... 

Figure 11. Mott-Schottky plots of reciprocal square of differential capacitance of n-type TiO electrode in 0.5M HfSO, vs, electrode potential. (O) In the dark (O) under illumination as in Figure 10. Intercept at C = oo gives the value of the flat-band potential (19).

Figure 12. Mott-Schottky plots as in Figure 11 but for p-type GaP in 0.5M HgSO. Symbols have the same meaning as in Figure 11 (IQ).

Fig. 3.10 Mott-Schottky plot for n-type and p-type semiconductor of GaAs in AlCls/n-butylpyridinium chloride molten-salt electrolyte [79],...

The flat band potentials of a semiconductor can be determined from the photocurrent-potential relationship for small band bending [equation (4.2.1)], or derived from the intercept of Mott-Schottky plot [equation (4.2.2)] using following equations... 

Fig. 4.5 Mott-Schottky plot of n-Ti02 prepared at different temperatures. AC frequency 1000 Hz. Reprinted with permission from Ref. [47].

Where Vs is the potential value at the surface of the electrode. Then plotting the value of 1/Csc versus the applied potential E should yield a straight line whose intercept with the E axis represents the flat band potential, and the slope is used for the calculation of N, the charge carrier density in the semiconductor. A typical example of Mott-Schottky plot is given in Fig. 2 [7] in this graph, the extrapolated values of the fb potential are -1-0.8 V and —0.6 V vs. SCE for p-Si and n-Si respectively. 

Fig. 2 Mott-Schottky plots of n-type and p-type Si (5 2 cm) in NH4CIO.5 M -F HF0.5 M aqueous solution (after Ottow etal. [7]).

A more reliable method for the determination of the fb potential can be drawn from a thorough investigation of the complete impedance diagram equivalent to the space charge layer. In fact, the main difficulty encountered in the Mott-Schottky plot is the rather wide range potential for the C extrapolation, which necessarily lead to values where electrochemical reactions contribute to changing the surface properties of the substrate. Moreover, the expected linear relationship shows a significant deviation, which is explained... 

It follows from Eq. (19) that the dependence Csc(0sc) becomes a straight line in the coordinates (C 2, 5 ) the line thus obtained is called the Mott-Schottky plot. 

Straight lines plotted in the coordinates iph — < sc or iph —

depletion layer thickness Lsc on the potential. The straight line segments intersect at a single point. For materials studied in the works cited below, this point coincides, within 0.2 V, with the value of q>tb measured independently by the differential capacity technique. 

For later discussions, we also define a potential Us, which is a potential at which the inverse square of the differential capacitance l/C tends to zero as determined from the 1/C vs potential plot (Mott-Schottky plot). It is related to E in the following way ... 

Figure 3. Mott-Schottky plots for the illuminated (lll)-face of n-GaP (pH 12.9, modulation frequency 1 kHz). The anodic photocurrents flowing during measurements are shown in units of pAcm 2.

The experiments were performed with single crystal (111) p-Si electrodes with a resistivity of about 5.5 ohm cm non-aqueous electrolytes were used consisting of absolute methanol containing tetramethylammonium chloride (TMAC) or acetonitrile containing tetraethyl ammonium perchlorate (TEAP). The flat-band potentials or p-Si in the two electrolytes were determined from Mott-Schottky plots (in the dark) in the depletion range of the p-Si electrode, from open-circuit photopotential measurements, and from the values of electrode potential at which anodic photocurrent is first observed in n-type Si electrodes. These three methods all yielded consistent flat-band potential values for p-Si of + 0.05V (vs SCE)... 

Figure 4. Mott-Schottky plot of CSc from Figure 3...

Electroreflectance spectra were measured for n-CdSe in the liquid junction configuration, and variations of the lineshape as a function of potential were observed. As the potential was reduced below the flatband potential, the electroreflectance signals changed sign. The potential at which this change occurs correlates well with the turn-on potential for light-induced photocurrent and with the intercept of the Mott-Schottky plot. 

Figure 5 contains a summary of the Mott-Schottky plots obtained at 1 KHz and different electrolyte compositions ranging from 0.8 1 to 1.75 1 molar ratios. The intercepts were calculated from the least squares gradients taken in the voltage regions where faradaic processes are least significant, namely 2.0 to 0.6... 

The Mott-Schottky plot obtained experimentally for the Ag-modified Ti02 electrode, which satisfy the above requirements, differs from that for the initial electrode by the slope value, with an insignificant shift of the point obtained after extrapolating the plot to the electrode potential axis (Fig. 6.15). Since for the realization of such electrode system we have used a semiconductor characterized by the high concentration of ionized donors, under consideration of Mott-Schottky dependence it is worthwhile to take account of the Helmholtz layer capacity (CH) placed in series with the space charge capacity [100] ... 

---