We present measurements of the nonlinear distortions of a traveling-wave silicon Mach-Zehnder modulator based on the carrier depletion effect. Spurious free dynamic range for second harmonic distortion of 82 dB·Hz(1/2) is seen, and 97 dB·Hz(2/3) is measured for intermodulation distortion. This measurement represents an improvement of 20 dB over the previous best result in silicon. We also show that the linearity of a silicon traveling wave Mach-Zehnder modulator can be improved by differentially driving it. These results suggest silicon may be a suitable platform for analog optical applications.