2.4.3 Atomic Force Microscope Lithography

Applying a negative potential to the AFM needle tip, while the silicon substrate is held grounded causes a negative electric field to be generated in the region. When the ambient is highly humid, a water meniscus forms between the AFM needle tip and the silicon substrate, shown in Figure 2.16.

Figure 2.16: Generation of a water meniscus between the AFM tip and silicon substrate after a negative voltage is applied.

The water meniscus, together with the high electric field, causes the water molecules to break up into oxyanions (H$^+$, OH$^-$, O$^-$) [198], [212]. The negatively charged oxyanions (mainly OH$^-$) are accelerated along the electric field lines towards the substrate, where they interact with the silicon to form silicon dioxide and byproducts. Since the introduction of the AFM as a lithographic tool by Day [40], countless other researchers have helped grow the technology into one of the most promising methods for localized oxidation of silicon [4], [57], [60], [63], [202]. The generated oxide can act as a mask for subsequent etching steps or as an insulating barrier for thin semiconductor film on insulator processes [55]. LON of graphene using AFM has also shown promise in growing oxide layers [224]. Graphene has recently been demonstrated to provide remarkable electronic properties and large effort is placed towards implementing graphene based fast electronic and optoelectronic devices [5]. A distinct advantage of AFM over STM is its ability to read back the actual topography of the generated pattern, while STM is unable to give the real height [198]. Over the years, empirical and analytical models have been suggested in order to predict how the semiconductor topography changes, when different voltages, pulse times, and tip velocities are applied to the AFM system [4], [6], [28], [38], [39], [84], [95], [192], [198]. LON with an AFM can be used in several operation modes: CM, NCM, and ICM, also known as TM.

2.4.3.1 Contact Mode Lithography

When LON is performed using AFM in contact mode, a small tip load is required, with a bias voltage variation of approximately 5 to 20V, and a typical tip speed from 0.1 to 10$\mu$m/s [212]. The applied force is an additional variable required for CM operation, and it ranges from 10 to 100mN [198]. The tip separation is zero, since the AFM needle is brought in contact with the sample surface. The electric field, generated due to the tip/sample interaction is in the order of 10$^7$V/cm.

The dependence of the applied force on the oxide height is independent of the applied voltage and is of the order of 0.01nm/nN [198]. The height is shown to vary linearly with voltage [73], with a limit of 0.4nm/V for low speeds, while having a logarithmic variation with respect to the probe speed [55]. The width of the generated oxide has a similar dependence on the experimental factors as those stated for the oxide height. The widths are relatively large due to the large size of the AFM needle tip used in CM [198].

In CM, the surface experiences both compressive forces due to the contact between the tip and sample, as well as shear forces, due to the lateral scanning motion of the needle tip across the sample surface [234]. Due to this direct interaction of the needle with the silicon surface, the needle tip tends to degrade and lose its hemispherical shape relatively quickly [197].

2.4.3.2 Intermittent Contact Mode Lithography

ICM lithography using an AFM, which is also known as TM and AC mode, is a dynamical mode, where the AFM needle tip is driven to oscillate at a frequency close to the resonant frequency of the cantilever (approximately 300kHz) [198]. The amplitude of this oscillation typically varies between 20 and 100nm [234] and the surface is struck by the needle tip at each oscillation. The main motivation behind ICM oxidation is to minimize the contact and lateral forces between the needle tip and the silicon surface, thereby increasing the process' reliability and needle lifetime [234].

The influence of bias voltage and tip speed on the heights of ICM-generated oxides is identical to the previously mentioned CM-generated oxides. Mainly, bias voltage has a linear influence, while pulse time has a logarithmic influence on the oxide height. However, using ICM over CM, the resolution is improved and the growth limit at low speeds is also improved to 0.25nm/V [55]. The oxide width is mainly governed by the shape of the needle tip, and for a hemispherical shape, the width-to-height ratio is approximately half of the needle tip diameter [198]. This can be understood by noting that the water meniscus which forms during the intermittent contact of the needle tip with the silicon surface limits the spread of the electric field. The water bridge provides the oxidizing ions and the spacial confinement required to pattern the silicon surface [198]. Since the meniscus shape is driven by the shape of the needle tip, it can be concluded that the tip shape is the main factor which determines the oxide width dimensions [55]. Several ICM versus CM comparative studies have observed that ICM lithography enjoys a higher aspect ratio, allowing for the generation of smaller oxide widths, and produces higher oxidation rates [53], [55], [209].

It was reported in [192] that, for oxides with heights of a few nm and pulse times below 10ms, the main driving agent for the growth rate is the generation of OH$^-$ ions. Only when the oxide is thick and the pulse time is in the 100ms range does ion diffusion and stress begin to play a role in the oxide growth rate [192], [198]. Thick oxides generated using an AFM, whose growth is driven by ion diffusion and stress, are beyond the scope of this work and will not be addressed in the LON modeling Section 3.4.

2.4.3.3 Non-Contact Mode Lithography

In 1998, Garcia et al. demonstrated that a process similar to ICM lithography can be used to generate oxide dots on a silicon surface [60]. The use of milliseconds pulsed voltages generates a water meniscus bridge even if the AFM needle tip does not directly strike the surface [133]. This is possible, when the bias voltage, applied between the AFM needle tip and the silicon surface is sufficiently large. The presence of the water meniscus and the high electric field is enough to cause localized oxidation to occur, therefore no direct contact between the needle tip and surface is required [133], [140]. Since no contact occurs, surface nanooxidation is easily reproducible and no degradation of the needle tip occurs, allowing for enhanced tip lifetimes and significantly reducing surface defects.

For NCM lithography, the needle tip is brought close to the silicon surface. An external voltage pulse is applied between the needle tip and the silicon substrate such that the needle tip is negatively charged with respect to the silicon substrate. The cantilever is then excited at its resonance frequency ($\sim$300kHz), similar to ICM operation. However, the cantilever is controled to oscillate with an amplitude of only a few nm and not 20 to 100nm, which is the case for ICM lithography. This allows for the cantilever to oscillate, but always remain above the silicon surface, thereby never striking it [28]. When the ambient humidity and bias voltage are sufficiently large, a water meniscus, such as the one described in the ICM section above and shown in Figure 2.16, is generated. The liquid bridge provides oxyanions (OH$^-$,O$^-$) needed to interact with the silicon in order to form SiO$_2$. In addition, it confines the lateral expansion of the patterned oxide, allowing for widths below those associated with CM- and ICM minima [28].

The procedure required in order to generate a single oxide nanodot using an AFM in NCM is laid out in [141]:

1- The AFM needle tip is oscillated above the sample surface, followed by the application of the bias voltage pulse.

2- The oscillator amplitude is reduced by the electrostatic interaction, which deflects the AFM needle tip position and modifies the AFM cantilever's resonant frequency.

3- The bias voltage is turned off; however, the AFM cantilever oscillation remain reduced due to the capillary force of the water meniscus.

4- Finally, the tip is lifted away from the water meniscus, allowing for its oscillations to return to their initial amplitude.

A well known drawback of NCM lithography is that the applied voltage in the feedback loop is off during silicon oxidation, resulting in the inability for the AFM needle to move during oxidation. Therefore, nanowires and continuous patterns cannot be generated with a single needle motion [198]. However, when pulses of the order of a few microseconds are introduced [120] and the lateral distance between pulses is smaller than the size of the individual nanodots [141], a SiO$_2$ nanowire can be generated.