Electron diffusion length

Photoelectrochemical techniques have been utilized to determine the minority (electron) diffusion length (L) and other electrical parameters of p-ZnTe [125] and p-type Cdi-jcZnjcTe alloys [126]. In the latter case, the results for a series of single crystals with free carrier concentration in the range 10 " -10 cm (L = 2-4 xm, constant Urbach s parameter at ca. 125 eV ) were considered encouraging for the production of optical and electro-optical devices based on heterojunctions of these alloys. 

Fig. 17.7 Current-voltage curves (a) and calculated electron diffusion lengths (b) from three DSSCs with Ti02 nanoparticles only, with 0.2 wt% pure semiconducting SWCNT, and with 0.2 wt% pure metallic SWCNT. L is the film thickness and Ln is the electron diffusion length.

The lifetime T and diffusion coefficient D of photoinjected electrons in DSC measured over five orders of magnitude of illumination intensity using IMVS and IMPS.56) fis proportional to the r m, indicating that the back reaction of electrons with I3 tnay be second order in electron density. On the other hand, D varied with C0 68, attributed to an exponential trap density distribution of the form Nt(E) <=< exp[ P(E - Ec)l(kBT) with 0.6. Since T and D vary with intensity in opposite senses, the calculated electron diffusion length L = (JD-z)m does not change linearly with the irradiance. 

Woodall et al.36 have analyzed the relationship between surface recombination velocity and the steady state band gap luminescence in GaAs. They calculate for 534nm excitation that a decrease in vs from 106cm/sec to 104cm/sec will triple the quantum efficiency at a 2.5Mm deep p-n junction if the hole diffusion length, Lp, is 3jim, and the electron diffusion length, L is 4/im. 

T o incorporate the reflections of electrons from the p+- i interface into the theory, consider the effect of the electron mirror on the photoconductivity of the i layer. It is assumed that the electrons are totally reflected back into the i layer when the internal electric fields are highest at Jd —> 0. The electrons are not reflected and back-diffusion exists when the internal fields are low at JT = 0 and = Jp. With the assumption that the electrons carry most of the current and that /d /, where /d is the electron diffusion length and / is the length of the i layer, the resistance of the i layer is... 

The technology of ETA cells is not yet mature, and future improvements in their efficiency can reasonably be expected. Modelling calculations (Taretto and Rau, 2005) indicate that 15% efficient CdTe ETA cells are possible even at electron diffusion lengths as low as 10 nm, provided that the built-in voltage is optimised to restrict recombination over the working bias range of the cell. If efficiency improvements of this order can be achieved and fabrication methods can be satisfactorily scaled up, ETA cells could offer a low-cost, stable alternative to traditional photovoltaic cells and dye-sensitised solar cells. 

A numerical simulation of this cell based on a one-dimensional model has been carried out by Ernst (2001), Grasso et al. (2002) and by Burgelman and Grasso (2004). In the work of Ernst and Grasso et al., the spectral response data could be simulated with reasonable accuracy using only a few adjustable parameters. These simulations confirm the electron diffusion length in the p-type CdTe films to be approximately 150 nm. The recombination centre density was found to be lO cm . These data indicate that the nanocrystalline CdTe films are of inferior quality than the material used in the conventional, planar CdTe solar cells, where diffusion lengths of 2 //m and defect densities of lO cm are typical. 

Peter L. M. and Wijayantha K. G. U. (1999), Intensity dependence of the electron diffusion length in dye-sensitised nanocrystalline TiOi photovoltaic cells ,... 

Peat R. and Peter L. M. (1987), Determination of the electron diffusion length in p-GaP by intensity-modulated photocurrent measurements with an electrolyte contact , Appl. Phys. Lett. 51, 328-330. 

Fig. 3. (a) Photocurrent-potential curves for p-GaP in 0.5moldm-3 H2S04 at the wavelengths shown (in nm). (b) Examples of the plots used to obtain values of the absorption coefficient a(A) and electron diffusion length L [eqn. (4)]. (c) Comparison of the absorption coefficients, obtained using eqn. (4) with the published absorption spectrum of GaP. (Reproduced with permission from ref. 8.)... 

In order to improve the photocurrent by increasing the electron diffusion length, mechanical compression of a binder-free film as a post-treatment is known to have a significant effect in efficiency improvement. Recently, an efficiency level close to 8% was obtained by Arakawa and co-workers based on our binder-free Ti02 coating technologies [25]. 

An improved solar harvesting efficiency compared with conventional sol-gel-derived Ti02 has been demonstrated [46]. In fact, the electron diffusion length is consistent with a collection efficiency for electrons close to 100%, even for thick nanotube films [47]. 

Fukai Y, Kondo Y, Mori S, Suzuki E (2007) Highly efficient dye-sensitized Sn02 solar cells having sufficient electron diffusion length. Electrochem Commun 9 1439-1443... 

Jennings JR, Li F, Wang Q (2010) Reliable determination of electron diffusion length and charge separation efficiency in dye-sensitized solar cells. J Phys Chem C 114 14665-14674... 

Fig. 5 Plots of distributed transport resistance (a), charge transfer resistance (b), electrode capacitance (c), and electron diffusion length (d) vs open-circuit photovoltage for a series of cells with average Ti02 layer thicknesses of 4 circles), 8 downward triangles), 14 squares), 16 upward triangles), and 18 pm diamonds). The dashed line in (a) is a fit with a slope of q/k T = 15.2 V , while the dashed line in (d) is just a guide to the eye. Adapted from [45] by courtesy of James Jennings and Qing Wang...

Jennings JR, Peter LM (2007) A reappraisal of the electron diffusion length in solid-state dye-sensitized solar cells. J Phys Chem C 111 16100-16104... 

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