Drift length

In the presence of an electric field the drift length is the mobility-lifetime product times the electric field A.mfp = prE [576]. With typical values of pz and E the mean free path usually exceeds by far the thickness of the solar cell, and virtually all photogenerated carriers can be collected. However, under certain operating conditions, field-free regions in the / -layer may exist, and the collection efficiency is decreased because the diffusion lengths of the carriers are much smaller than the thickness of the solar cell [11, 577]. 

Fig. 19.11 (a) Time of flight spectra of Ba 6p3/2 s 7=1 autoionization electrons. Peak 1, decay into the Ba+ 6s continuum peak 2, into the Ba+ 5d3/215/2 continua peak 3, into the Ba+ 6p1/2 continuum. The drift length was approximately 10 cm. The spectra were recorded with a gate width of 14 ns. (b) The same as (a) but with a drift length of approximately 45 cm and a gate width of 6 ns (from ref. 25). 

When an electric field was applied across the chamber some positrons annihilated prematurely, following field-induced drift to one of the electrodes. In this case the free-positron component of the lifetime spectrum was field dependent the maximum drift time, rmd, was given by the end-point of the lifetime spectrum and was due to thermalized positrons which had traversed the entire drift length l. The drift speed was then v+ = 1/rmd and the mobility could be found from... 

Figure 1 General diagram of a time-of-flight mass analyzer. R, repeller electrode G0, entry grid Gp acceleration grid, E, and E2, electric fields s0, distance to the midpoint of the first acceleration field sa and shaded circles, ion starting position closer to G0 sb and closed circles, ion starting position more distant from G() D, total drift length.

First, the drift current is calculated in the case of a constant electrical field, as one would expect for very thin bulk heterojunction solar cells. If the width W of the active layer is similar to the drift length of the carrier, the device will behave as a MIM junction, where the intrinsic semiconductor is fully depleted. The current is then determined by integrating the generation rate G = —dP/dx over the active layer, where P is the photon flux ... 

In most a-Si H solar cells, a built-in electric field (F) assists in the collection of photogenerated carriers, and efficient collection occurs as long as the drift length (/itF) is significantly larger than the film thickness. Crandall (1982) has shown that the transport in p-i-n cells can be charac-... 

In a drift dominated case the recombination probability depends on the mean drift length Wh/e = rih/eth/eF. If the mean drift length of one or both of the charge carriers is smaller than the device length d the recombination is significant. The saturated photocurrent density is given by [60],... 

Hence, measuring the drift time tD for a given drift length and given E yields an experimental value for K. For a given pressure (or particle density N) and temperature T of the buffer gas the ion mobility K is given by the collision cross section a by... 

Fig. 11a,b. Ion arrival time distributions of charge states +7 and -7 of the calcium-free protein calmodulin (T=300 K,p=4.9 torr, VD=90 V, drift length 4.5 cm). For +7 two distinctly different families of structures are present, one with larger cross sections (main peak) and one with smaller cross sections (shoulder to the left). The broad peak for -7 indicates an even distribution of structures with smaller and larger cross sections... 

Fig. 3.15 illustrates the point, and shows the mobility as a function of temperature according to Eq. (3.18) for constant measurement time. The actual mobility in a time-of-flight experiment is measured at constant drift length (the sample thickness) and is indicated by the dashed intersecting line, because the time of the experiment increases... 

If diffusion or drift lengths are low, the only way out is to change the layout of the cell in such a way that the local distance to the collecting contact falls within the possible transport path length. This guideline was followed in the CdTe-based ETA cell, where the local absorber thickness corresponded quite accurately to the estimated diffusion length. 

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