The measured or effective lifetime consists of the bulk lifetime and the surface lifetime, via:
\(\cfrac{1}{\tau_{eff}} = \cfrac{1}{\tau_{bulk}} + \cfrac{1}{\tau_{surface}}\)
That‘s why the surface properties, especially the surface recombination velocity S, has a huge influence on the measured lifetime. This can be used to investigate the surface properties of a sample. Thermal silicon oxide or SiNx are often used to passivate the surface of Cz- , Fz- or mc-Si, which means that the surface recombination velocity is minimized strongly. The homogeneity of this passivation layer can be investigated by lifetime measurements. The aim is to measure the homogeneity of a passivation layer with a high resolution.
With MDPmap, MDPingot or MDPinline it is possible to investigate the homogeneity of a passivation layer with a very high resolution (only limited by the diffusion length of the carriers), which is exemplary shown in figure 1. Especially in high quality material with a high bulk lifetime the surface recombination is very dominant, so that every difference in a lifetime map has its origin in passivation inhomogeneity.
By a measurement with different wavelength or different sample thickness even a good estimation of the surface recombination velocity can be made. If the sample quality is very high as in FZ-Si the surface recombination velocity can be determined from the measured lifetime by assuming that the bulk lifetime is only dependent on the Auger recombination.
MDPmap, MDPingot or MDPinline enables to measure the homogeneity of a passivation layer with a very high resolution even inline. With this an optimization of the passivation process is possible.
To approximate the bulk lifetime from the measured lifetime on unpassivated bricks, the following equation is used:
\(\tau_{eff, \lambda} = \cfrac{\tau_{bulk}}{1-\alpha ^2L^2} \Biggl \lfloor 1-\alpha L\cfrac{\alpha L + \frac{SL}{D} coth \frac{\alpha d}{2}}{1 L + \frac{SL}{D} coth \frac{d}{2 L}} \Biggr]\)
With d - sample thickness
α - 1/penetration depth
α = a/s (s – skin depth of the microwave; a – empiric factor, which was determined from comparison with passivated wafers from the same bricks)
L – diffusion length
D – diffusion coefficient
S – surface recombination velocity for as cut surface (S = 2.0e+5)
For further information please read:
[1] J. Schmidt, Thesis, Universität Hannover, 1998
Fig. 1: Example of an oxide passivated Cz-Si wafer with a gradient in the oxide thickness
Related Solutions and Industries: Epitaxial Layers & Thin Films, Photovoltaic, Research and Development
