Patent Application
20150276795
This is the first application filed in respect of the present invention.
The present application relates generally to Atomic Force Microscopy (AFM), and more specifically to AFM techniques using correlated probe oscillation and probe-sample bias voltage to exploit asymmetric electrostatic force-bias curves.
Atomic Force Microscopy (AFM) is well known in the art for imaging nanoscale surface properties.
In the illustrated system, a sample 18 is mounted on a 3-axis support 20 (such as, for example a piezoelectric tube scanner), which is controlled by a set of 3 orthogonal position signals (Vx, Vy, Vz) from the electronic module 16. Using these position signals, the electronic module 16 can adjust the position of the sample 18 under the probe tip 4, for example to enable the probe tip 4 to interact with the sample surface 22 in a raster-scan pattern. Oscillatory motion of the cantilever 2 relative to the sample surface 22 can be excited, independently of the 3-axis support 20, by means of a cantilever drive signal, Vd, which is supplied to the piezoelectric element 6. Finally, a bias signal, Vb, may be used to apply a selected voltage difference between the AFM probe and the sample 18. In the example illustrated in
Cantilever deflection measurements provide information about the interactions between the probe tip 4 and sample surface 22. These interactions may arise from a variety of forces, such as mechanical, Van der Waals, magnetic, and electrostatic forces. Cantilever deflection measurements may be used for feedback to control the tip-sample separation and to measure and/or control signals related to a variety of surface properties. Deflection of the cantilever beam may be measured in a variety of ways. Some of the most common deflection detection methods include laser 8 beam deflection (illustrated in
AFM imaging is typically performed in either static mode or dynamic mode. In dynamic mode AFM, cantilever 2 is driven to oscillate, usually on or near its fundamental resonance frequency or a higher harmonic. The cantilever oscillation is typically driven by a piezoelectric element 6 (often referred to as a dither piezo), but it may be driven in a variety of other ways, including photothermal excitation. Tip-sample interactions are generally measured by changes in the cantilever dynamics induced during imaging. In static mode AFM, the cantilever 2 is not driven to oscillate, and tip-sample interactions are measured from the static cantilever deflection during imaging.
AFM is most commonly used to image surface topography, but may also be used to image a variety of other surface properties. Several AFM techniques measure surface electronic properties by applying a bias voltage, Vb, between the probe tip and the sample. For example, Electrostatic Force Microscopy (EFM) and Kelvin Probe Force Microscopy (KPFM, also known as surface voltage microscopy) involve the application of a bias voltage, Vb, and the detection of electrostatic force interactions between the tip and the sample. Both operate by measuring the changes in cantilever dynamics due to the electrostatic force arising from the relative potential difference between the tip and sample surface.
In EFM, a DC bias voltage, Vb, is applied across the tip and sample and the resulting cantilever dynamics are measured. Consequently, EFM images pertain to the local electrostatic force between the tip and sample.
In KPFM, an AC bias voltage is applied across the tip and sample and the resulting cantilever dynamics are measured. The component of cantilever oscillation corresponding to the AC bias oscillation frequency, ω/2π, is minimized using a feedback loop to apply a DC bias across the tip and sample corresponding to the local contact potential difference (CPD, approximately equal to the flat band voltage). Consequently, KPFM images pertain to the local CPD between the tip and sample.
In semiconductor analysis, it is frequently desirable to perform dopant profiling to locally map the type (p-type or n-type) and relative concentration of dopant in a sample. There are currently two methods to achieve this by AFM, both of which measure a property related to the local capacitance between the tip and the sample.
The most common technique used for semiconductor dopant profiling is scanning capacitance microscopy (SCM), which is described, for example, by J. R. Matey and J. Blanc, J. Appl. Phys. 47, 1437 (1985). SCM uses a resonant capacitance sensor to detect local differential capacitance, dC/dV. SCM is performed in contact mode (a static mode of AFM in which the probe tip is pressed into the sample surface and a constant cantilever deflection is maintained during imaging), and is particularly susceptible to tip wear. Because the resonant capacitance sensor has a sharp resonance peak, small changes to the tip-sample junction geometry can result in offset changes to the SCM image signal, dC/dV, scale and undesirable image artifacts. Accurate quantitative interpretation of SCM images tends to be difficult, and requires careful calibration and modeling. Therefore, when applied to semiconducting samples, SCM images are generally used to illustrate only the qualitative dopant profile of a sample surface, containing some information about both local mobile charge carrier type (n-type or p-type from the SCM signal phase) and relative concentration (from the SCM signal amplitude).
A second AFM technique for measuring surface properties related to capacitance has been proposed in Y. Martin, D. W. Abraham, and H. K. Wickramasinghe, Appl. Phys. Lett. 52, 1103 (1988)], that may also be applied to semiconductor dopant profiling. Unlike in SCM, this technique measures electrostatic force components and does not require a resonant capacitance sensor. Like in KPFM, an oscillating AC bias is applied across the tip and sample and the resulting cantilever dynamics are measured. In the implementation proposed by Martin et al., the component corresponding to twice the AC bias oscillation frequency, 2ω/2π, is measured. Images acquired by this implementation pertain to the spatial capacitance gradient, dC/dz, but stray capacitance effects result in low sensitivity.
A variation on the electrostatic force technique of Martin et al is described in U.S. Pat. No. 6,823,724 (Kobayashi et al.). In the technique of Kobayashi et al., the component corresponding to three times the AC bias oscillation frequency, 3ω/2π, is measured to reduce the effects of stray capacitance. Images acquired by this implementation, like in SCM, relate to the differential capacitance gradient, dC/dV.
An AFM technique that overcomes at least some limitations of the above-noted prior art would be desirable.
An aspect of the present invention provides a method of Atomic Force Microscopy (AFM). A first drive signal is generated for causing a periodic motion of a probe tip relative to a sample surface. The first drive signal has a known amplitude and frequency. A bias signal is generated for applying an electric potential to the probe tip relative to a potential at the sample surface. At least one component of the bias signal is oscillatory and correlated with the periodic motion of the probe tip. A response of the probe tip is detected and analyzed by a processor to infer information about a property of the sample surface.
Further features and advantages of the present invention will become apparent from the following detailed description, taken in combination with the appended drawings, in which:
It will be noted that throughout the appended drawings, like features are identified by like reference numerals.
The present technique provides an AFM technique that enables quantitative measurements of surface dopants of a semiconductor sample, by means of correlated probe motion and bias. In the following description, the present technique is described by way of representative embodiments in which the surface dopants of a semiconductor sample are determined from measurements of the electrostatic force interaction between an AFM probe and a semiconductor sample, and do not require an additional capacitance sensor.
The electrostatic force, Fes, between an AFM probe tip and a sample surface is given by the following formula:
where C is the tip-sample capacitance, z is the separation between the tip and the sample, and Ve is the effective potential difference across the junction. Ve is equal to the difference between the externally applied tip-sample potential, Vb, and the contact potential difference, VCPD (which relates to the tip and sample material work functions), Ve=Vb−VCPD. For simplicity, the effective potential difference, Ve, will be referred to herein as the tip-sample bias.
In general, the capacitance of a capacitor is a function of the spacing between electrodes. The capacitance of a metal-oxide-semiconductor (MOS, or equivalently, metal-insulator-semiconductor) capacitor is also a function of applied gate voltage due to band bending. The AFM tip-sample capacitance may then generally be considered a function of both the tip-sample separation, z, and the tip-sample bias, Ve; C(z, Ve). The electrostatic force between an AFM probe and a sample, using the appropriate tip-sample capacitance gradient, is therefore:
It is well known in the art that SCM generally operates based on the principle of a MOS capacitor. The conductive probe tip acts as the metal gate (which needn't actually be metal and is often degenerately doped silicon in MOS devices, but is generally referred to as “the metal” regardless), a surface oxide layer present on the conductor sample surface acts as the insulating oxide (or if no oxide layer is present, the tip-sample junction instead forms a Schottky contact), and the underlying semiconductor sample is contacted to bias the sample.
If the gate bias applied to the “metal” of a MOS capacitor is varied within the accumulation, depletion and/or weak inversion regimes of a device (i.e. near the flatband and threshold voltages), the size of the space-charge region that forms in the semiconductor near the insulator interface will also vary. This variation of depletion-region width is the primary cause of bias-dependent variation of the MOS capacitor capacitance, C(V). (Equivalently, the metal can instead be held at ground and the semiconductor substrate can instead be biased appropriately. For simplicity, we will use the non-essential convention that the substrate be held at ground and gate bias applied to the metal.) This also results in an asymmetric electrostatic force between the tip and sample as a function of tip-sample bias, Ve, as will be discussed further below.
As the depletion region width increases with applied gate bias up to the threshold voltage (and exceeding it if deep depletion is possible, in the high frequency regime), the gate bias, Vg, is dropped across a larger effective electrode spacing and the MOS capacitor capacitance, C, decreases. The capacitance of a p-type MOS capacitor as a function of applied gate bias voltage therefore has a negative slope, dC/dV, for gate bias values below inversion. As may be seen in
It is an important concept to the interpretation of data arising from the present technique that the sign of dC/dV in the gate voltage range of interest (near the flatband and threshold voltages) is indicative of the type of mobile charge carriers present in a doped semiconductor sample. Consequently, the detection of the sign of dC/dV allows for the clear determination of mobile charge carrier type. The magnitude of dC/dV is indicative of the concentration of mobile charge carriers. High charge carrier concentrations allow smaller variations in depletion region width and therefore produce a lower dC/dV than low charge carrier concentrations. This information cannot be directly obtained from AFM techniques measuring surface electronic properties such as EFM and KPFM, and is crucial for semiconductor dopant profiling.
In the high frequency range (typically on the order of 1 MHz), an inversion layer cannot form in the absence of a source of minority charge carriers, and the MOS capacitance includes the deep depletion series component arising from the space-charge region in the semiconductor near the oxide interface. In the low frequency range (typically 5 to 100 Hz), an inversion layer of minority charge carriers forms above or below the threshold voltage for p-type and n-type substrates respectively, and the MOS capacitance returns to the oxide capacitance. Many commercially available AFM cantilevers have resonance frequencies on the order of 100 kHz, between the low and high frequency MOS regimes. In practice, confusion can arise in the low frequency range in the detection of dC/dV if the applied gate bias exceeds the threshold voltage and an inversion layer is allowed to form. It can therefore be desirable to run simultaneous KPFM (discussed further below) to maintain bias oscillations around the flat band voltage, in the monotonic portion of the curve, to minimize the risk of such confusion at low frequencies.
As may be seen in, extending the bias dependant change in capacitance (
If a sinusoidal oscillating bias is applied across a MOS SPM tip-sample junction within Regime A, the resulting attractive electrostatic force, Fes, between the tip and sample will oscillate as a function of time as illustrated in chart A. If the applied bias range intersects with the flatband voltage, VFB (approximately equal to the contact potential difference), as in Regimes B and C, the electrostatic force, Fes, will reach zero at these points
If the applied bias range extends into the portion of the electrostatic force that is decreased due to the MOS like behaviour of the tip-sample junction, as in Regimes C and D, less modulation of electrostatic force arises as a function of applied bias than would occur for the same geometry of a capacitor with two metal electrodes. If an oscillating applied bias represented by Regime C were applied across the same geometry of a capacitor with two metal electrodes, the resulting electrostatic force, Fes, as a function of time would oscillate sinusoidally with twice the applied AC bias frequency. The present technique takes advantage of the asymmetry in electrostatic force arising from the MOS behavior of the tip-sample junction. This technique is therefore suited for operating in any of Regimes A-C. The methodology is clarified in further discussion below.
In order to take advantage of the asymmetric electrostatic force as a function of applied bias of a MOS tip-sample junction, the bias applied across the junction, Vb, should be phase and frequency locked to the AFM cantilever oscillatory motion, z. In other words, Vb and z should be both coherent and correlated. This allows p-type and n-type sample regions to be differentiated. As the tip-sample separation position, z, changes, the correlated tip-sample bias, Vb, also changes.
The tip-sample separation during oscillation can be described as:
z=z
0
+z
AC
where z0 is the steady state tip-sample separation and zAC is the oscillating component, given by:
z
AC
=A
c
e
i(ωt)
or
z
AC
=A
c sin(ωt)
Subsequently, Ac is the peak cantilever oscillation amplitude, and ω/2π is the oscillation frequency. We apply a tip-sample bias voltage:
V
b
=V
DC
+V
AC
where VDC is the DC component of the bias (including any correction for VCPD to the externally applied DC bias) and VAC is the oscillating component, given by:
V
AC
=A
V
e
i(ωt+φ)
or
V
AC
=A
V sin(ωt+φ)
where AV is the peak bias oscillation amplitude, and the oscillation occurs at the same frequency ω2π, with a phase shift of φ relative to zAC.
Aspects of the resulting AFM cantilever dynamics (such as oscillation amplitude, phase and frequency) can be measured and related to the probe-sample electrostatic force behaviour. Various embodiments of the present technique comprise determining an electrical property of the sample. In the case of a doped semiconducting sample, this electrical property pertains to the majority mobile charge carrier type and dopant concentration. However, the present technique is not limited to doped semiconducting samples. Depending on the nature of the sample under test, the electrical property analyzed by the present technique may pertain to any one or more of the contact potential difference, work function, polarizability, or relative permittivity of a sample.
As may be seen in
If a phase shift of π is used instead of zero between zAc and VAC, the correspondence between the doping type and the sign of the frequency shift simply exchanges (negative frequency shift arises for an n-type semiconducting sample and a positive frequency shift arises for a p-type sample). In both cases (phase shift of 0 and π), the work done by the electrostatic force in each region (I) and (II) is opposite in sign and equal in magnitude, resulting in zero net work (conservative interaction).
If the oscillating bias, VAC, is applied π/2 out of phase with the cantilever oscillation, zAC, as illustrated in
If the phase difference between the applied AC bias, VAC, and cantilever oscillation, zAC, is 3π/2 instead of π/2, the electrostatic force responses will be the opposite of those illustrated in
When the phase difference, φ, is 0 or π (or, more generally, an even multiple of π/2), the electrostatic interaction is conservative (as discussed above with reference to
When the phase difference, φ, is π/2 or 3π/2 (or more generally, an odd multiple of π/2), the electrostatic interaction is dissipative (as discussed above with reference to
As may be appreciated from
Several representative embodiments for implementing the present technique on an AFM system are described below. These embodiments include either open loop or closed loop control of the cantilever oscillation dynamics. The oscillating bias signals may be generated by either fixed or variable oscillators. Both open loop and closed loop embodiments of the present technique are possible. Open loop embodiments involve measuring the cantilever dynamic response to electrostatic force interactions with the sample surface while the cantilever oscillation is excited at a fixed drive frequency. Conversely, closed loop versions involve maintaining a constant cantilever oscillation amplitude, Ac, (or phase, φc) by varying either the cantilever drive signal, Vd, or the applied tip-sample bias voltage, Vb while the resonant frequency shift is tracked by a feedback loop. Additionally, various forms of KPFM can be performed during imaging to provide advantageous DC biases across the tip and sample. Alternative embodiments will also be discussed.
The fixed frequency oscillator signal is also supplied as a trigger for a signal/delay generator 28 used to generate an oscillating constant amplitude AC bias signal, VAc. This AC bias signal, VAC, may optionally be added to a DC offset bias VDC, which may be selected to tune the measurement response. The resulting bias signal, Vb=VAC VDC, is then supplied to the cantilever 2 to bias the probe tip 4. The measured amplitude and phase of the cantilever oscillation at each pixel of an AFM image can be used to extract dissipative and conservative probe-sample interactions at the corresponding location of the sample surface 22. The ratio between the amplitude and phase responses depends on the phase of the applied tip-sample bias signal, as described above with reference to
Alternatively, a PLL 26 with a variable frequency oscillator 24 can be used in conjunction with an amplitude controller feedback loop to produce the cantilever drive signal and measure changes in closed loop components (dissipation and/or frequency shift) of the deflection detector signal.
It should be noted that if the tip-sample applied bias, Vb, range is large enough that the cantilever 2 is driven in excess of the amplitude controller setpoint by electrostatic excitation, even a zero drive signal, Vd, may not reduce the cantilever oscillations to within the setpoint. In this case, a negative drive amplitude (corresponding to a π out of phase drive, related to active Q control) may be applied to compensate the cantilever oscillations and should be considered in data interpretation.
This embodiment is akin to conventional closed loop SCM techniques, and may yield high resolution measurements by maintaining an approximately constant sample probe volume. The amplitude of the AC applied bias at each pixel of an AFM image relates to the concentration of mobile charge carriers at the corresponding location of the sample surface 22. It should be noted that if the cantilever drive signal range is large enough such that the cantilever is driven in excess of the amplitude controller setpoint, even zero applied bias signal will not reduce the cantilever oscillations to within the setpoint. In this case, a negative applied bias signal amplitude (corresponding to a 180 degrees out of phase applied bias, again related to active Q control) may be applied to compensate the cantilever oscillations and must be considered in data interpretation.
In the embodiment of
Measurements pertaining to the technique can be performed in conjunction with CPD compensation by Kelvin Probe Force Microscopy (KPFM). This may improve operation by centering the applied bias in the regime of interest and allow quantitative characterization of semiconductor dopant concentration, and also allows measurement of the CPD minimum. The tip-sample CPD is not always negligible, but is generally ignored (or assumed constant across a sample) while performing SCM (despite the fact that this can lead to discrepancies in the relative amplitudes of p-type and n-type area SCM signals). Methods in accordance with the present technique can produce useful results when performed without CPD compensation. However, improved performance is possible with CPD compensation, which is therefore desirable.
It should be noted that while the electrostatic force is no longer parabolic about the CPD minimum due to the voltage dependent tip-sample capacitance gradient (arising from the MOS capacitance model), the steady-state electrostatic force will still be minimized near the flat band condition, approximately equal to the CPD minimum, where the effective tip-sample applied bias is zero.
Those skilled in the relevant art will recognise that several different KPFM configurations may be used in conjunction with the present technique. In principle, a variety of modulation frequencies are suitable for KPFM, but must be selected appropriately for the apparatus by considering measurement detection bandwidth. As is known in the art, frequency modulated (FM) KPFM is advantageous because it enables improved spatial resolution compared to amplitude modulated (AM) KPFM because the force gradient (relating to the cantilever oscillation frequency shift) decays faster than the force (relating to the cantilever oscillation amplitude). In double pass embodiments, KPFM may be performed during either the forward topography scan or the lifted backscan. While an extensive list will not be presented herein, two representative embodiments are described below, it being understood that alternate KPFM configurations may be used without departing from the intended scope of that attached claims.
In the embodiment of
Several variations on the instrument configurations developed herein are possible: for example, an embodiment can include an AM or FM KPFM loop for CPD compensation and a self excited, constant oscillator driven, or variable frequency oscillator driven cantilever drive signal or AC applied tip-sample bias.
Alternative embodiments could include: A torsional cantilever oscillation mode for lateral measurements with a sample electrode on or near the surface plane. A square wave applied tip-sample bias could be used instead of a sinusoid, for maximum changes in the electrostatic cantilever excitation (though this may also excite higher harmonics, depending on the transfer function). A modified KPFM technique could be implemented to set the applied bias with respect to the CPD (to measure, for example, in Regimes A, B or D instead of the general case of Regime C, as defined in
The embodiments of the invention described above are intended to be illustrative only. The scope of the invention is therefore intended to be limited solely by the scope of the appended claims.
