A scanning probe microscope (SPM) brings a pointed probe close to a sample to detect the interaction between the probe and the sample (a tunnel current, an interactive force, or the like). The scanning probe microscope then feedback-controls the distance between the probe and the sample so as to keep the interaction constant. Moreover, the SPM scans the probe (or the sample) in the horizontal direction with the feedback control maintained. Thus, the probe (or the sample) moves up and down so as to trace recesses and protrusions on the sample. An image of the recesses and protrusions on the surface of the sample can be obtained by recording the track of the feedback scanning with respect to the horizontal position.
A known example of the SPM is an atomic force microscope (AFM). The AFM detects an interactive force acting between the probe and the sample. The AFM then feedback-controls the distance between the probe and the sample so as to keep the interactive force constant. The AFM uses a cantilever with a pointed probe provided at the tip thereof, as a force detector. When the probe is brought closer to the sample, the cantilever is displaced by the interactive force acting between the probe and the sample. This type of AFM configured to detect the interactive force based on the amount of displacement is called a contact mode AFM or a static mode AFM.
On the other hand, a type of AFM configured to mechanically excite the cantilever at a frequency close to the resonant frequency thereof is called a dynamic AFM. The dynamic AFM detects the interactive force acting between the probe and the sample, based on a variation in vibration amplitude, frequency, phase caused by the interactive force. AFMs detecting the interactive force using the amplitude, frequency, and phase are called an AM-AFM, an FM-AFM, and a PM-AFM, respectively.
The conventional dynamic mode AFM is disclosed in, for example, Japanese Patent Laid-Open No. 2004-226237. This document discloses an example of the FM-AFM.
FIG. 1 shows a general configuration of a dynamic mode AFM. An AFM 101 includes a cantilever 103, a sample stage 105, a scanner 107, and an excitation unit 109. The scanner 107 is, for example, a piezo actuator and moves a sample on the sample stage 105 in an X direction, a Y direction, and a Z direction to scan a sample and the cantilever 103 relative to each other. The excitation unit 109 is also, for example, a piezo actuator and excites the cantilever 103. For example, an amplifier configured to drive an actuator is omitted from FIG. 1.
An excitation and detection circuit 111 is configured to provide an excitation control function and a function to detect an interactive force. The excitation and detection circuit 111 applies an excitation signal to the excitation unit 109 to excite the cantilever 103. Furthermore, the excitation and detection circuit 111 detects, as the amount of the interaction between the probe and the sample, the amplitude, frequency, or phase of a displacement signal from the cantilever 103 detected by the sensor 113. The detected value is output to a feedback circuit 115 as a feedback signal and used to control the vertical position of the scanner 107. As a result, a feedback loop is formed which keeps the distance between the probe and the sample constant.
As described above, in the present specification, a circuit functioning as an excitation control circuit and an interaction detection circuit is referred to as the “excitation and detection circuit”. Several types of methods are available for implementing the excitation and detection circuit. The excitation and detection circuit can be roughly classified into an analog type and a digital type. The digital type is now mainly used because the specifications of the digital type can be flexibly changed and because the digital type can implement complicated signal processing.
FIG. 2 shows an example of an implemented excitation and detection circuit of a conventional digital type. The configuration in FIG. 2 corresponds to the AM-AFM and the PM-AFM and generates an excitation signal and detects an amplitude signal and a phase difference signal. The amplitude signal indicates the vibration amplitude of the cantilever. The phase difference signal indicates the difference in phase between the excitation signal for the cantilever and a displacement signal from the cantilever.
As shown in FIG. 2, an excitation and detection circuit 121 includes a DDS (Direct Digital Synthesizer) 123 and a lock-in amplifier 125. The DDS 123 corresponds to an excitation control circuit. The lock-in amplifier 125 corresponds to a detection circuit for the amplitude and phase difference.
In FIG. 2, the DDS 123 generates an excitation signal cos(2πft) that varies at an excitation frequency f. The DDS 123 holds sine-wave output values with respect to the phase, in the form of a lookup table. A sine wave signal is obtained by interpolating discreet values in the lookup table. The signal is not only output as the excitation signal for the cantilever but is also utilized as a reference signal for the lock-in amplifier 125 formed of a digital circuit.
The lock-in amplifier 125 is a two-phase digital lock-in amplifier. A displacement signal Acos(2πft+φ) from the cantilever is input to the lock-in amplifier 125. The excitation signal cos(2πft) is also input to the lock-in amplifier 125 as the reference signal as described above.
The reference signal is input to a 90° phase shift circuit (for example, a Hilbert conversion circuit) and a delay circuit, which then convert the signal into sin(2πft) and cos(2πft), respectively. These signals are converted into X=Acos(φ) and Y=Asin(φ), respectively, through a multiplication circuit and an LPF (Low Pass Filter). The multiplication circuit multiples each of the signals by the input displacement signal Acos(2πft+φ). The LPF removes high frequency components from the signals.
Then, a vector calculation circuit calculates the absolute value R and argument θ of a complex input X+jY. The absolute value R is (X2+Y2)1/2, and the argument θ is tan−1(Y/X). The absolute value R corresponds to the amplitude A of the displacement signal. The argument θ corresponds to the phase difference φ between the displacement signal and the excitation signal. Thus, R and θ are output as the amplitude signal A and the phase difference signal φ, respectively.
The configuration in FIG. 2 corresponds to an AM-AFM mode and a PM-AFM mode. In the AM-AFM mode, the amplitude signal A is output as a feedback signal and used for feedback control. The feedback control is performed such that the amplitude signal A equals a target amplitude. In the PM-ADM mode, the phase difference signal φ is output as a feedback signal and used for feedback control. In this case, the feedback control is performed such that the phase difference signal φ equals a target phase difference.
Now, the configuration of the excitation and detection circuit for the FM-AFM will be described with reference to FIG. 3 and FIG. 4. FIG. 3 is a diagram based on which the principle of the FM-AFM will be described, and illustrates the characteristics of amplitude and phase of the cantilever. In an upper graph in FIG. 3, the axis of abscissas indicates frequency, and the axis of ordinate indicates the amplitude of the cantilever. In a lower graph in FIG. 3, the axis of abscissas indicates the frequency, and the axis of ordinate indicates the difference in phase between the excitation signal for the cantilever and displacement signal from the cantilever.
As shown by a dotted line in the upper graph in FIG. 3, the resonant frequency f of the cantilever varies (shifts) as a result of the interaction between the cantilever and the sample. In FIG. 3, the amount of variation in resonant frequency is indicated by Δf. Furthermore, as shown in the lower graph, when the cantilever vibrates at the resonant frequency, the phase difference φ between the excitation signal and the displacement signal is 90°. Thus, the FM-AFM sets a target value for the phase difference φ to 90°, and controls the excitation signal such that the phase difference φ equals the target value. This excitation control is achieved by a phase locked loop (PLL) circuit and is such that even if the resonant frequency of the cantilever is varied by the interaction, the cantilever continues to vibrate at the resonant frequency. During this control, a variation in resonant frequency Δf is detected. Then, the feedback control is performed so as to keep the variation in resonant frequency Δf constant.
FIG. 4 shows an example of an implemented excitation and detection circuit corresponding to the FM-AFM. The excitation and detection circuit generates an excitation signal and detects a frequency signal. The frequency signal is indicative of a variation in the resonant frequency of the cantilever caused by the interaction between the cantilever and the sample as described above.
As shown in FIG. 4, an FM-AFM excitation and detection circuit 131 includes a proportional integral (PI) control circuit 137 in addition to a DDS 133 and a lock-in amplifier 135 (two-phase digital lock-in amplifier).
An excitation signal cos(2πft) output by the DDS 133 is input to the lock-in amplifier 135 as a reference signal. Furthermore, a displacement signal Acos(2πft+φ) from the cantilever is input to the lock-in amplifier 135. The lock-in amplifier 135 has a configuration similar to that of the lock-in amplifier 125 in FIG. 2 to output the phase difference φ between the excitation signal and the displacement signal. Here, the lock-in amplifier 135 functions as a multiplying phase comparator to perform phase comparison based on multiplication of the displacement signal.
A phase difference φ generated by the lock-in amplifier 135 is input to a PI control circuit 137. The PI control circuit 137 controls an output 2πΔfT (reference character T denotes a sampling period for input and output signals) such that the input phase difference φ equals a target value φ0. The output 2πΔfT is input to the DDS 133 to vary the frequency f of an output signal (excitation signal) cos(2πft) of the DDS 133. The frequency f varies around the free-running frequency f0 (an oscillation frequency obtained when the input is 0) of the DDS by Δf.
In the configuration in FIG. 4, the DDS 133, the lock-in amplifier 135, and the PI control circuit 137 form the phase locked loop (PLL) circuit. The PI control circuit 137 functions as a loop filter for the PLL circuit. The PLL circuit varies the value of the frequency f of the excitation signal so that the frequency of the displacement signal equals that of the excitation signal, that is, f=f0+Δf. Thus, an output value from the PI control circuit 137 is proportional to a variation in the frequency of the displacement signal. Thus, the output value from the PI control circuit 137 is output as the frequency signal.
Furthermore, the difference in phase between the displacement signal and the excitation signal can be adjusted by varying the target value φ0 for the PI control circuit 137. As described with reference to FIG. 3, the FM-AFM sets the target phase difference to 90°. Thus, the phase difference φ is kept at 90°, and the cantilever vibrates at the resonant frequency. Even if the resonant frequency of the cantilever is varied by the interaction between the cantilever and the sample, the cantilever continues to vibrate at the resonant frequency. The frequency signal has a value indicative of a variation (shift) Δf in the resonant frequency of the cantilever. The frequency signal is used for feedback control.
The conventional AFM excitation and detection circuit has been described. There is still room to improve of the conventional circuit configuration as described below.
In the conventional technique illustrated in FIG. 2, the lock-in amplifier functions as a multiplying phase comparator and internally compares the excitation signal with the displacement signal by multiplication. This leads to generation of an unwanted harmonic component. More specifically, an output from the multiplication circuit in the lock-in amplifier contains a component of the difference in frequency between input signals and a component of the sum of the frequencies of the input signals. The sum component corresponds to the unwanted harmonic component. The harmonic component cannot completely be removed even by the LPF arranged after the lock-in amplifier. Such a residual harmonic component may not only distort an output waveform but also affect the feedback control as described below.
The AFM forms a feedback loop for control of the probe-sample distance, and the excitation and detection circuit is present in the feedback loop as shown in FIG. 1. A signal in which the harmonic component is mixed in the lock-in amplifier is used in the feedback loop. In this case, a feedback gain needs to be limited to a small value in order to avoid oscillation at the frequency of the harmonic component. This conventionally constitutes a factor preventing quick and stable feedback control from being achieved.
In the FM-AFM circuit configuration shown in FIG. 4, as is the case with the circuit in FIG. 2, the lock-in amplifier functions as a multiplying phase comparator, leading to generation of an unwanted harmonic component. In particular, in the FM-AFM, the harmonic component not only limits the feedback gain but also works against the PLL circuit. This will be described below.
In the FM-AFM configuration shown in FIG. 4, the lock-in amplifier is a part of the PLL circuit. Thus, the lock-in amplifier (multiplying phase comparator) generates an unwanted harmonic component in the loop in the PLL circuit. The harmonic component cannot completely be removed even by the LPF arranged after the lock-in amplifier. In particular, the LPF is present in the loop in the PLL and is thus subject to another restriction; the LPF cannot be designed independently of the response characteristics of the PLL. Thus, removal of the harmonic component in the FM-AFM is more difficult than in the AM-AFM and the PM-AFM. Because of the residual harmonic component, an increase in the gain of the PLL causes the PLL circuit to oscillate at the frequency of the residual harmonic component. Thus, in the conventional technique, the gain of the PLL is limited, preventing the frequency from being detected quickly and stably.
As described above, in the FM-AFM, disadvantageously, the harmonic component limits not only the feedback gain of the whole AFM but also the gain of the PLL.