Semiconductor carrier generation

Free-electron lasers have long enabled the generation of extremely intense, sub-picosecond TFlz pulses that have been used to characterize a wide variety of materials and ultrafast processes [43]. Due to their massive size and great expense, however, only a few research groups have been able to operate them. Other approaches to the generation of sub-picosecond TFlz pulses have therefore been sought, and one of the earliest and most successfid involved semiconducting materials. In a photoconductive semiconductor, carriers (for n-type material, electrons)... 

The simplest and most widely used model to explain the response of organic photovoltaic devices under illumination is a metal-insulaior-metal (MIM) tunnel diode [55] with asymmetrical work-function metal electrodes (see Fig. 15-10). In forward bias, holes from the high work-function metal and electrons from the low work-function metal are injected into the organic semiconductor thin film. Because of the asymmetry of the work-functions for the two different metals, forward bias currents are orders of magnitude larger than reverse bias currents at low voltages. The expansion of the current transport model described above to a carrier generation term was not taken into account until now. 

The Gartner model simulates charge collection by a potential-dependent space charge layer and considers diffusion into the space charge layer of charge carriers generated deep inside the semiconductor. The well-known Gartner formula for the photocurrent /ph is... 

Experimental evidence with very different semiconductors has shown that at semiconductor interfaces where limited surface recombination and a modest interfacial charge-transfer rate for charge carriers generate a peak... 

In polar semiconductors, carrier-mediated generation occurs in the form of transient depletion field screening (TDFS) depicted in Fig. 2.5 [30]. The driving force in (2.1) can be expressed by the sum of the Raman term and the nonlinear longitudinal polarization [10] ... 

Recall that the concept of Fermi quasilevels, suggested by Shockley (1950), can be introduced as follows. Under steady state photogeneration of charge carriers, a dynamic equilibrium arises in a semiconductor between generation and recombination of electron-hole pairs. As a result, certain steady state (but not equilibrium ) concentration values nj and p are established. The quasiequilibrium concentrations ng and pg are defined by the relations ng = n0 + A and Po = Po + Ap> and since photogeneration of carriers occurs in pairs, we have An = Ap = A. Let the following inequalities be satisfied ... 

Figure 28.3 The flatband potential of a semiconductor can be established by measuring the photopotential of the semiconductor as a function of illumination intensity. In the dark (left), the semiconductor Fermi level and the redox potential of the electrolyte are equal, providing an equilibrium condition. However, illumination of the semiconductor (right) generates charge carriers that separate the Fermi level and the redox potential. The difference in these two parameters is the observed photovoltage as shown for an n-CdS electrode immersed in a ferri/ferrocyanide electrolyte (bottom). The measured photovoltage is observed to saturate at the flatband potential. In this case, a value of -0.2 V vs. SCE is obtained. Note that the photovoltage response yields a linear functionality at low light intensity with saturation behavior occurring as the flatband potential is approached.

Illumination of the semiconductor leads to charge carrier generation p, which is enhanced by a carrier concentration Ap over the dark carrier concentration Po, for a given generation rate G and recombination rate U ... 

In the previous section, we described in detail the primary processes that give rise to photogenerated electrochemically active (and potentially electrochemically useful) charge carriers on illuminated semiconductor particles (reactions (9.1)-(9.4)). Thus, in this section, we will consider, from a predominantly electrochemical viewpoint, the thermodynamics and kinetics associated with the interfacial charge transfer processes that occur post-charge carrier generation (reactions (9.5)-(9.7)). 

Thus, it can be seen that a study of the steady state photoelectrochemistry of colloidal semiconductors with the ORDE can provide information relating to the energy distribution of the particle surface states, the photogenerated carrier density and the quantum efficiency of carrier generation. The next section describes how to obtain information pertaining to intraparticle charge carrier dynamics from a study of the behaviour of transient photocurrents at the ORDE. 

It is normally unnecessary for the electrochemist to be concerned with the mobility of carriers in most of the semiconductors whose properties have been studied, since the very low conductivity of "small polaron samples would normally preclude their measurement. However, a proviso must be entered here in the case of binary and, more especially, ternary samples. It may well be the case that the majority carriers in a particular material are indeed itinerant (i.e. have mobilities in excess of ca. 1 cm2 V 1s 1), but there is no guarantee that this will be true of the minority carriers generated by optical absorption. Thus, the oxide MnTi03 shows a marked optical charge transfer absorption from Mn(II) to Ti(IV), the latter being the CB. The resultant holes reside on localised sites in the Mn levels, presumably as local Mn(III) centres, and are comparatively immobile. The result is that there is... 

So far, the discussion has centered on the steady-state aspects of carrier generation and collection at semiconductor-electrolyte interfaces. As with their metal electrode... 

Figure 9.4 Recombination pathways of photogenerated charge carriers in an n-type semiconductor-based photoelectrochemical cell. The electron-hole pairs can recombine through a current density in the bulk of the semiconductor, the depletion region, or through defects (trap states) at the semiconductor/liquid interface, iss- Charges can also tunnel through the electric potential barrier near the surface, 4 or can transfer across the interface, The bold arrows indicate the favourable current processes in the operation of a photoelectrochemical cell. The hollow arrows indicate the processes that oppose the excess of charge carriers generated by light absorption.

Figure 10.1 Carrier generation under illumination arising at (a) the semiconductor/Uquid interface and (b) the semiconductor/dye sensitiser/liquid interface, shown for the case of an -type semiconductor.

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