Metodología y elementos didácticos empleados

6.3 Nanopillar array force measurements

There is scope to optimise the design of NV based nanomechanical sensors due to the unique way in which it is stress within the diamond is sensed, not the deection of a mechanical element. This allows for the sensor part of a nanomechanical sensing device to be spatially separated from the sample being sensed. Many sensors can be employed simultaneously since the only required information is the uorescence signal from the NV− _{centres. These two exibilities led to the idea of sensing forces}

using a nanopillar array, as this was the simplest concept that could explore these capabilities.

The nanopillar force sensor has an NV located at the base of the nanopillar, which can be prepared into an array of nanopillars and combined with wide-eld imaging. These arrays can provide parallel force measurements from each nanopillar allowing for spatial mapping of forces at very high spatial density. Each nanopillar has an NV at the base which is sensitive to the bending forces within the pillar. This bending is generated from a force acting at the tip of the pillar. Knowing both the placement of the NV within the base of the pillar, and the geometry of the pillar enable the force exerted at the tip of the nanopillar to be reconstructed.

If an array of nanopillars is used, then the information from multiple pillars can be combined to generate a vector force map. Four pillars are used to generate a superpixel that can project the force onto a 2D map. Obviously, these techniques are more suited to wideeld techniques and not single site microscopy as the re- quired number of NV centres required to generate a useful sized map would make single site microscopy slow and cumbersome. Ideally these arrays would be placed underneath a cell and its movement recorded, the traction forces exerted by cells give information about how that cell can move. This is particularly important for high mobility cells like some cancers cells and can provide information to target their treatment. Other techniques that use the deection of nanopillar arrays have been demonstrated but the nanopillar deections are usually measured optically and so the periodicity and deection of the nanopillars are diraction limited [177], for sensitive measurements the deection of the nanopillar tip must be relatively large compared to the diraction limit. These requirements put an upper limit on the spatial sensitivity (periodicity) and the force sensitivity of the device.

To create a spatial map of the applied force in wide-eld, the nanopillars could be arranged in a array with spacing so that the diraction limited spot of adja- cent nanopillars does not overlap (spacing ≥ 250 nm). Each nanopillar at posi-

2b)h ~Fi,j · ~ξi,j/I for the (+) upper and (-) lower spin branches. The dot product

of _F~_{i,j ·} ~_{ξi,j/I is the projection of the applied force F}~_{ij on the NV position} ~_ξi,j

within the nanopillar. If the position of the NV centre within the nanopillar is previously determined, most likely from applying a known force and measuring the spin-response, then the local force _F~_{i,j can be determined. Since only the scalar}

projection of the local force onto the NV coordinates in that nanopillar is measured, the vector of the force is not known. However, the spin response of neighbour- ing nanopillars can be combined into a super-pixel (I, J) using the neighbour-

ing spin resonance shifts _∆~_f±

IJ = ∆f ± 2I−1,2J−1,∆f ± 2I,2J−1,∆f ± 2I−1,2J,∆f ± 2I,2J T and a corresponding position of neighbouring NVs within their respective nanopillars

ΞIJ =

~

ξ2I−1,2J−1, ~ξ2I,2J−1, ~ξ2I−1,2J, ~ξ2I,2J T

, as shown in gure 6.1. The in plane estimate of the super-pixel force is then _F~_{IJ =} I/h

a±2b Ξ T IJΞIJ −1 ΞT IJ∆~f ± IJ. It would

be practical to choose only one of the spin-resonance branches (+ or -) either by taking advantage of some inherent stress or an applied magnetic eld to identify the spin-resonances. The intrinsic stress in nanostructures is often non-zero [178]. Applying a small bias eld to separate the strain split branches does not eect the spin-mechanical response as show in gure 4.5(a). Assuming that the mag- netic eld is kept constant throughout the experiment, its eect to the shift of the spin-resonance can simply be subtracted. Alternatively, both resonances can be recorded and their spin response can be post processed by comparing to neighbour- ing nanopillars. To determine the vector of the total super-pixel force _F~_{IJ across}

the super-pixel some extra information is required, because _F~_{IJ is really just a col-}

lection of scalar values that represent the projection of a local force onto a known NV location. If it is assumed that the magnitude of the force is constant across the super-pixel than the vector force can be extracted. Alternatively, if the local force direction is expected to be constant across the super-pixel then the magnitude of each component can be extracted. Even with the restriction of these approximations the high density of information from such an array would still provide an insightful force map. Uniquely, the AC dependence of the spin-mechanical interaction due to an applied time-varying force can be extracted from this array using pulsed ODMR techniques (spin-echo, CPMG, XY-8, etc.) and wide-eld microscopy. The pulsed sequence can be used as a lter function to sample only signals of certain frequency bands [108]. This ltering eect could be useful to see wide-eld frequency shifts of the nanopillars due to some external perturbation from the sample, for exam- ple a change in damping coecient. The frequency of the thermal vibration of the nanopillar is far from the sensing band of the NV−_{centre. The rst order vibration}

6.3. NANOPILLAR ARRAY FORCE MEASUREMENTS

Figure 6.1: (a) Nanopillar array with cell of interest placed on tips of nanopillar array. Optical access is from beneath and microwaves are applied from a nearby stripline. (b) The red NV centres at the base of the nanopillars give a force mea- surements Fij performed at each nanopillar.(c) Four force measurements (orange

square) are combined to create force vectors super-pixelsFIJ. (d) Simulation of the

expected PL signal from the nanopillar array.

of a free cantilever in one-dimension is given as f1 = 3.516_L2 q

EI ρA

1

2π ∼ 1GHz, for the

dimensions of this example nanopillar 1GHz1/(Tmin

AC )∼100MHz the maximum

frequency the NV spin can practically measure. Any AC sensing with these pillars will be far from the resonant case, unlike the situations discussed in sections6.4 and

6.5.

This array can be manufactured with existing diamond etching techniques using a top down approach of e-beam lithography (EBL) followed by reactive ion-etching (RIE) [15, 172] and high precision nitrogen implantation [179, 180, 181, 182, 183]. Ion implantation can have poor z accuracy due to large stopping distance straggle

but quite good lateral (x, y) accuracy. Conversely, delta-doping techniques [179,184]

have very goodz accuracy but little control over the lateral position of the nitrogen

placement. Either method could be used and both have trade-os. Initially a delta- doped layer grown in at a depth equal to the nanopillar height followed by EBL and RIE nanopillar creation would be the simplest manufacturing avenue to pursue. The delta-doped density can be tuned to provide an average of one NV per nanopillar in a random position [15]. The non-optimal placement of the NV centres within the

base of the nanopillar means that only a portion of the nanopillars will be optimally useful with well placed NVs. This will give a poorer force sensitivity for small forces and imaging.