## Electrical characterization of sensors

This result is related to the electrical characterization of the mass sensors performed through the CMOS circuitry.

A complete electrical characterization of the sensor comprises the determination of operating input excitation and circuit polarization voltages, as well as the analysis of the readout signal in terms of voltage level, bandwidth, noise and stability.

Excitation voltages have been determined by simultaneously analysing the electrical readout signal and the optical image of the oscillating cantilever. The optimal combination of dc and ac excitation voltages will give a maximum on the resonance peak in the electrical readout signal.

Two main test criteria are used to prove that the electrical peak is not an artifact from the set-up: firstly resonance frequency should decrease linearly with the square power of the increasing dc voltage, secondly the electrical resonance peak should be almost coincident with the optically visible mechanical resonance of the cantilever. In order to quantify the mechanical frequency response of the cantilever and to get a more clear correlation to the electrical signal, a laser based readout system has been built.

This system allows acquiring an optical signal directly related to the vibration amplitude of the cantilever, simultaneously to the electrical signal. A detailed comparison between both signals shows a delay of the mechanical resonance with respect to the electrical peak, which can be attributed to the influence of the parasitic capacitances parallel to the cantilever-driver transducer.

The determination of the optimal polarization conditions are specially relevant when a voltage buffer amplifier is used. In this case, this condition is found by maximizing the ac level of the output readout electrical signal, obtained when the transducer is excited out of the resonance and only the capacitive current trough the static cantilever-driver capacitance is amplified by the CMOS circuitry.

Once the input excitation and polarization conditions are found, then the output signal characteristics can be analysed. From this analysis the following parameters are obtained:

- Resonance frequency as a function of the dc voltage (VDC). The natural resonance frequency of the cantilever can be determined by a linear fit of frequency values as a function of VDC2.

- Voltage amplitude of the readout signal and bandwidth. These parameter are used to quantify if the circuitry has been damaged by the postproces of transducer nanofabrication.

- Bandwidht and quality factor of the electrical resonat peak. This gives an idea of the parasitic capacitance parallel to the cantilever-driver.

- Absolute change and slope (dF/df) of the phase at the resonance. This parameter is realted to the Q-factor and to the mass sensitivity of the sensor. The larger the Q-factor, the larger the dF/df and the smaller the detectable change in frequency related to a measured change in phase.

- Noise and stability of the phase when the cantilever is excited at a constant frequency around the resonance. Both parameters will determine the minimum measurable change in the resonance frequency that can be detected through the corresponding change in phase detected when cantilever is excited at a constant frequency.

A complete electrical characterization of the sensor comprises the determination of operating input excitation and circuit polarization voltages, as well as the analysis of the readout signal in terms of voltage level, bandwidth, noise and stability.

Excitation voltages have been determined by simultaneously analysing the electrical readout signal and the optical image of the oscillating cantilever. The optimal combination of dc and ac excitation voltages will give a maximum on the resonance peak in the electrical readout signal.

Two main test criteria are used to prove that the electrical peak is not an artifact from the set-up: firstly resonance frequency should decrease linearly with the square power of the increasing dc voltage, secondly the electrical resonance peak should be almost coincident with the optically visible mechanical resonance of the cantilever. In order to quantify the mechanical frequency response of the cantilever and to get a more clear correlation to the electrical signal, a laser based readout system has been built.

This system allows acquiring an optical signal directly related to the vibration amplitude of the cantilever, simultaneously to the electrical signal. A detailed comparison between both signals shows a delay of the mechanical resonance with respect to the electrical peak, which can be attributed to the influence of the parasitic capacitances parallel to the cantilever-driver transducer.

The determination of the optimal polarization conditions are specially relevant when a voltage buffer amplifier is used. In this case, this condition is found by maximizing the ac level of the output readout electrical signal, obtained when the transducer is excited out of the resonance and only the capacitive current trough the static cantilever-driver capacitance is amplified by the CMOS circuitry.

Once the input excitation and polarization conditions are found, then the output signal characteristics can be analysed. From this analysis the following parameters are obtained:

- Resonance frequency as a function of the dc voltage (VDC). The natural resonance frequency of the cantilever can be determined by a linear fit of frequency values as a function of VDC2.

- Voltage amplitude of the readout signal and bandwidth. These parameter are used to quantify if the circuitry has been damaged by the postproces of transducer nanofabrication.

- Bandwidht and quality factor of the electrical resonat peak. This gives an idea of the parasitic capacitance parallel to the cantilever-driver.

- Absolute change and slope (dF/df) of the phase at the resonance. This parameter is realted to the Q-factor and to the mass sensitivity of the sensor. The larger the Q-factor, the larger the dF/df and the smaller the detectable change in frequency related to a measured change in phase.

- Noise and stability of the phase when the cantilever is excited at a constant frequency around the resonance. Both parameters will determine the minimum measurable change in the resonance frequency that can be detected through the corresponding change in phase detected when cantilever is excited at a constant frequency.