Minority charge carriers

Obviously, the recombination rate increases with decreasing transition time of the minority charge carriers. 

Figure 12. Energy diagram of a semiconductor/electrolyte interface showing photogeneration and loss mechanisms (via surface recombination and interfacial charge transfer for minority charge carriers). The surface concentration of minority...

In our approximation we start with relation (20) for the surface concentration of minority charge carriers and derive /pi, via formula (11). 

Since the magnitude and shape of this PMC peak depend on the rate constants of minority charge carriers, the PMC peak provides access to kinetic measurements. It is interest that the height as well as the shape of the PMC peak change with the frequency of light pulsing. This is shown... 

Figure 27. Minority charge carrier profiles near the semiconductor/electrolyte junction. calculated for a silicon interface at two different electrode potentials. Uf- -0.25 V and Uf= 5.0 V10 ((//= forward bias = t/ - Ufl>).

For a sufficiently large potential increase, the charge in the interphase finally corresponds to the minority charge carriers (Fig. 4.12D). The greater the width of the forbidden band eg, the broader is the potential range A f in which the space charge region has the character of a depletion layer, i.e. is formed by ionized impurity atoms. 

The photocurrent is cathodic or anodic depending on the sign of the minority charge carriers injected from the semiconductor electrode into the electrolyte, i.e. the n-semiconductor electrode behaves as a photoanode and... 

The band-gap excitation of semiconductor electrodes brings two practical problems for photoelectrochemical solar energy conversion (1) Most of the useful semiconductors have relatively wide band gaps, hence they can be excited only by ultraviolet radiation, whose proportion in the solar spectrum is rather low. (2) the photogenerated minority charge carriers in these semiconductors possess a high oxidative or reductive power to cause a rapid photocorrosion. 

JT depends on the number of generated electron-hole pairs, and it is limited by the minority charge carriers in the device, in this case, the electrons. Under this simplified assumption, Jr can be regarded as a constant if every electron-hole pair decayed by emitting light. When the thickness of Alq3 interlayer increases, fewer holes are injected into the NPB and thus, /h decreases, leading to an increase in 17, as can be seen in Equation 6.3. 

The existence of two types of mobile charge carriers in semiconductors enables us to distinguish between a majority charge carrier transferred from the electrode into the electrolyte and a minority charge carrier injected from the electrolyte into the electrode. Minority carrier injection causes significant reverse currents, but may also contribute to the total current under forward conditions. 

Holes, which initiate the dissolution process, are minority charge carriers in n-type electrodes. The concentration of holes nh is very low in n-type Si under equilibrium conditions. The hole concentration can be increased by illumination or by... 

For not too low doped samples (D W), however, the contribution of 1SCR is usually negligible. If the surface recombination velocity at the illuminated front is low, IBPC then only depends on sample thickness D, illumination intensity eP, and minority charge carrier diffusion length ID. 

As the polarization (the overvoltage t) ) increases of a redox reaction that requires the transport of minority charge carriers towards the electrode interface (anodic hole transfer at n-type and cathodic electron transfer at p-type electrodes), the transport overvoltage, t)t, increases from zero at low reaction currents to infinity at high reaction current at this condition the reaction current is controlled by the limiting diffusion current (iu.)tm or ip.um) of minority charge carriers as shown in Fig. 8-25. 

Fig. 8-26. Cathodic iiyectian of minority charge carriers (holes) followed by recomlmation of minority charge carriers (holes) with majority charge carriers in an n-type semiconductor electrode ipr - cathodic current of hole transfer at an interface - current of electron-...

For n-type semiconductor electrodes in which a redox reaction of cathodic hole iiyection reaches its quasi-equilibrium state at the electrode interface, the recombination current of iiqected holes (minority charge carriers) with electrons (minority charge carriers), w, is given by Eqn. 8-70 [Reineke-Memming, 1992] ... 

In this section, we have assumed that the limiting transport current of electrons or holes in semiconductor electrodes is much greater than the ion transfer current across the electrode interface. When the minority charge carrier transports charge... 

For n-type semiconductors (n p, and n An ), the quasi-Fermi level of electrons (Eqn. 10-3) approximately equals the original Fermi level (Eqn. 10-2) whereas, the quasi-Fermi level of holes (Eqn. 10-4) is lower than the original Fermi level (Eqn. 10-2) because the concentration of photoexcited holes, Ap , exceeds the concentration of holes, p, in the dark (p Ap ). In general, under the condition of photoexcitation, the quasi-Fermi level of mq ority charge carriers remains close to the original Fermi level but the quasi-Fermi level of minority charge carriers shifts away from the originEd Fermi level. 

It follows from Eqn. 10-13 that, if a 6sc is much larger than 1 (a 5sc 1, both a and being great), all the photoexcited minority charge carriers will be consumed in the interfacial reaction (ipb = e Iq ). In such a case, the photocurrent is constant at potentials away from the flat band potential as shown in Fig. 10-11 this figure plots the anodic ciirrent of photoexcited dissolution for a gallium arsenide electrode as a function of electrode potential. 

Eqiiation 10-14 indicates that if the diffusion length L of the minority charge carrier is much longer than the thickness 6sc of the space charge layer L sc), the photocurrent will be constant and independent of the electrode potential. 

On the other hand, if the diffusion length of the minority charge carrier is much shorter than the thickness of the space chaiige layer L sc), Eqn. 10-13 will yield Eqn. 10-15 ... 

Fig. 10-13. Anodic transfer of pho-toexdted boles (minority charge carrier) at an n>type semiconductor electrode E( -e 9o/e) = electrode potential E% (= — c /e) = potential of the valence band edge B02 (= - = equilibrium...

The potential, E, for the onset of the photoexdted reaction relative to the equilibrium electrode potential E of the same reaction can also be derived in a kinetics-based approach [Memming, 1987]. Here, we consider the transfer of anodic holes (minority charge carriers) at an n-type semiconductor electrode at which the hole transfer is in quasi-equilibrium then, the anodic reaction rate is controlled by the photogeneration and transport of holes in the n-type semiconductor electrode. The current of hole transport, has been given by Eqn. 8-71 as a function of polarization ( - ,) as shown in Eqn. 10-20 ... 

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