Previous Up

Example: Mobility in ZnO

In this section we will present a few experimental results on the mobility in ZnO in order to illustrate the concepts of the previous sections. ZnO may not be one of the most commonly studied semiconductors, but it is a very interesting material. Because of its high bandgap it is transparent, and because it is easily doped n-type it can be made reasonable conducting. These two properties make it useful as transparent conducting front contact in solar cells.

The image below shows mobilty data with respect to the carrier concentration from a variety of sources. All of the films are polycristalline, most of them have been fabricated by sputtering or reactive evaporation. Note that the mobility in these films does not always follow the theoretical concepts and sometimes the authors explicitely claim transport processes that are different from the interpretations given here. Nevertheless, this collection of data may be useful to illustrate some processes that limit the mobiltiy and the range of their occurence.

Mobility vs. carrier density. Data (not exhaustive) from: full black squares: Uthanna, Optics Materials 19(4), p461 (2002), full black downward triangles: Subramanyam, Phys. Stat. Sol. 173(2), p425 (1999), open black circles: Subramanyam, Cryst. Res. Technol. 35(10), p1193 (2000), full blue squares and circles: Minami, Mat. Res. Bull. 25(8), (2000), open green squares: Nakada, Jap. J. Appl. Phys. 34(7A), p3623, (1995), open red circles: Nakada, Jap. J. Appl. Phys. 30(12A), p3344, (1991), open green circles: Haug, J. Vac. Sci. Technol. 19(1), p174, (2001) open stars: Agashe, J. Appl. Phys. 95(4), p. 1911, (2005) green diamonds: Steinhauser, PhD Thesis, Uni Neuchatel, (2009)

In particular we can distinguish several regions with respect to the carrier density:

For low carrier concentrations below approximately 10¹⁹ cm^-3 the mobiltiy is more or less constant. This is the regime of fully depleted grains, and the barrier at the grain boundaries decreases only slowly. Most of the data denoted by black symbols falls into this range.
The transition between full depletion and saturation of the trapping states at the grain boundaries is marked by a dip towards a mobility minimum.
For higher carrier concentrations between 10¹⁹ cm^-3 and 10²⁰ cm^-3 the gradual saturation of grain boundary traps results in increasing mobility. The region is more or less defined by the full blue squares which denote measurements in undoped ZnO. The curve that defines the upper limit in this regime yields a trap density of 5x10¹³ cm^-2.
For carrier concentrations above 10²⁰ cm^-3 the effect of scattering wihin the grains eventually takes over. The limiting curve given in red assumes ionized impurity scattering in a degenerately doped semiconductor with non-parabiloc effective mass according to the theory of Brooks, Herring and Dingle. The data represented by the full blue circles represent Al-doped ZnO deposited by sputtering.
The highest mobility values of doped samples have been obtained on ZnO films doped with boron by B₂H₆ (open green squares).

The figure shows that a substantial amount of data are quite below any of the outlined limits. Although not proven experimentally, I assume that in these samples most of the Al dopants are inactive. In order to substantiate this claim, I show a blown up region of the above diagram.

open green circles: Haug, J. Vac. Sci. Technol. 19(1), p174, (2001), open stars: Agashe, J. Appl. Phys. 95(4), p. 1911, (2005), all ZnO films have been sputtered from ceramic ZnO targets doped with Al₂O₃, colours correspond to the content of Al₂O₃ in the sputtering target: black: 0.5wt%, red: 1wt%, green: 2 wt%, blue: 4 wt%.

The data shown in the diagram have been measured on films that have been sputtered from ceramic targets with fixed aluminium concentrations. Neglecting the effects of preferential sputtering and Zinc loss which can occur during sputtering onto heated substrates, I think that is is meaninful to assume that the target concentration of aluminium is carried into the growing film; 1wt% should roughly yield 6.6x10²⁰ Al atoms per cm³. However, the measured carrier densities are significantly below these values. Assuming that the difference between the dopant concentration and the measured carrier density is present as inactive, neutral impurities, Erginsoy's simple formula for neutral impurity scattering would predict mobility limits as indicated by the continuous lines. Those limits are not really observed, but the four different dopant concentrations roughly fall into different areas of the graph.

Another piece of evidence comes from measurements of the thermo-power, or Seebeck coefficient. I do not present the theory here, but scattering at different types of impurity should result in clearly resolvable Seebeck characteristics [1]. I measured the thermopower for the samples denoted by the open green circles.

From the diagram shown above it appears that the neutral impurity scattering is dominant. Only towards higher carrier densities (mostly the black squares) there is a transition into the range of ionized impurity scattering. Note, that even in the sample with the highest carrier concentration only half the dopants are active.

[1] D. Young et.al., J. Vac. Sci. Technol. 18(6), 2978, (2000)

Previous Up