We present measurements of the low-temperature excess frequency noise of four niobium superconducting coplanar waveguide microresonators, with center strip widths s r ranging from 3 to 20 m. For a fixed internal power, we find that the frequency noise decreases rapidly with increasing center strip width, scaling as 1 / s r 1.6 . We show that this geometrical scaling is readily explained by a simple semiempirical model which assumes a surface distribution of independent two-level system fluctuators. These results allow the resonator geometry to be optimized for minimum noise. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2937855͔ Thin-film superconducting microresonators are of great interest for a number of applications ͑see Refs. 1-4 and references therein͒. Excess frequency noise is universally observed in these resonators 2,5,6 and is very likely caused by two-level systems ͑TLSs͒ in dielectric materials. 3,7 Indeed, the TLS hypothesis is supported by the observed dependence of the noise on resonator internal power 7,8 and temperature. 3 In a recent paper 4 ͑paper A hereafter͒, we presented measurements of the TLS-induced low-temperature frequency shifts of five niobium ͑T c = 9.2 K͒ coplanar waveguide ͑CPW͒ resonators with varying center strip widths s r . From the observed geometrical scaling of the frequency shifts ͑ϳ1 / s r ͒, we showed that the TLS must be located in a thin ͑few nanometer͒ layer on the surface of the CPW. In this letter, we propose a semiempirical TLS noise model that assumes this surface distribution, and we show that the model explains our measurements of the geometrical scaling of the noise.The device used for the experiment in this paper is exactly the same device used in paper A. In brief, the chip contains five CPW quarter-wavelength resonators ͑Z 0 Ϸ 50 ⍀, f r Ϸ 6 GHz͒ made by patterning a 120 nm thick Nb film deposited on a c-plane crystalline sapphire substrate. Each resonator is capacitively coupled to a common feedline, using a CPW coupler ͑coupling quality factor Q c ϳ 50 000͒ of length l c Х 200 m and with a common center-strip width of s c =3 m. The coupler is then widened into the resonator body, with a center-strip width of s r = 3, 5, 10, 20, or 50 m, and a length of l r ϳ 5 mm. The noise was measured using a standard IQ homodyne technique; 2,3 both the measurement setup and the analysis of the noise data are identical to our previous work. 7 The device is cooled in a dilution refrigerator to a base temperature of 55 mK. The fractional frequency noise spectra S ␦f ͑ ͒ / f r 2 of the five resonators were measured for microwave readout power P w in the range −61 to − 73 dBm; the −65 dBm spectra are shown in Fig. 1͑a͒. We clearly see that the noise has a common spectral shape but decreases as the center strip becomes wider. Unfortunately, the data for the lowest-noise ͑50 m͒ resonator are influenced by the noise floor of our cryogenic microwave amplifier, so we exclude this resonator from further discussion. The noise levels at = 2 kHz were retrieved from the n...