The open-loop gain of the unbuffered inverter decreases as power-supply voltage decreases. This decreases the closed-loop gain of the oscillator circuit. The value of Rs can be decreased to increase the closed-loop gain, while maintaining the power dissipation of the crystal within the maximum limit.
Rs and C2 form a low-pass filter and reduce spurious oscillations. Component values can be adjusted, based on the desired cutoff frequency.
C2 can be increased over C1 to increase the phase shift and help in start-up of the oscillator. Increasing C2 may affect the duty cycle of the output voltage.
At high frequency, phase shift due to Rs becomes significant. In this case, Rs can be replaced by a capacitor to reduce the phase shift.