Ultra stable tuning fork sensor for low-temperature near-field spectroscopy

Ultramicroscopy 90 (2002) 97–101

Ultra stable tuning fork sensor for low-temperature near-field spectroscopy A. Crottinia,*, J.L. Staehlia, B. Deveauda, X.L. Wangb, M. Ogurab a

Physics Department, Swiss Federal Institute of Technology Lausanne, CH-1015 Lausanne-EPFL, Switzerland b Electrotechnical Laboratory, 1-1-4 Umezono, Tzukuba, Ibaraki 305-8568, Japan Received in revised form 3 April 2001; accepted 26 September 2001

Abstract We report on a distance control system for low-temperature scanning near-field optical microscopy, based on quartz tuning fork as shear force sensor. By means of a particular tuning fork-optical fiber configuration, the sensor is electrically dithered by an applied alternate voltage, without any supplementary driving piezo, as done so far. The sensitivity in the approach direction is 0.2 nm, and quality factors up to 2850 have been reached. No electronic components are needed close to the sensor, allowing to employ it in a liquid He environment. The system is extremely compact and allows for several hours of stability at 5 K. r 2002 Elsevier Science B.V. All rights reserved.

Low-temperature near-field optical microscopy (LT-SNOM) [1] is a powerful tool in the experimental investigation of semiconducting materials, allowing to get an insight into the their optical properties with subwavelength spatial resolution [2]. This allows to study single nanostructures, namely quantum wires (QWRs) and quantum dots (QDs), and to isolate single features inside these structures: far-field inhomogenously broadened photoluminescence (PL) emission spectra reveal, when observed in the near-field (NF), a fine structure of a limited number of emission lines [3,4]. NF spectroscopy can therefore ‘‘zoom in’’ on a single semiconductor nanostructure, investigating the interaction between few photons and few excitons. In this respect, NF optical studies have allowed to directly map the local confining *Corresponding author.

potential for excitons in QWRs [5], to observe carrier diffusion and capture in QDs [6] and in QWRs [7]. The ideal condition of a system composed only by one photon, one exciton and the surrounding medium can be reached in PL spectroscopy only with very low intensity excitation measurements. This usually implies acquisition times of hours and requires therefore an experimental setup that is stable over such times. In this respect, LT-SNOM evidence its stability in setups where the whole system (distance control sensor, fiber, scanning piezos) is kept at low temperature by immersing it in a liquid or cold 4He gas environment. This increases the mechanical stability of the system, especially by minimizing scanning piezos drift deviations. Standard tuning fork-based SNOM distance controls [8] employ piezo elements to mechanically

0304-3991/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 9 9 1 ( 0 1 ) 0 0 1 4 4 - 9

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drive at resonance the oscillator composed by the fork and the fiber. Recently, Rychen et al. [9] successfully realized a ‘‘no piezo’’ tuning fork control for atomic force microscopy (AFM) working at low temperature in a He-bath cryostat. The main feature of their system is that the AFM tip is glued directly to one fork’s arm, and this ‘‘loaded’’ fork is electrically driven at resonance by an alternating voltage. Since the mass of the AFM tip is negligible compared to that of the fork, the perturbation to the mechanical properties of the oscillator is little and sharp resonances are still observed. No piezo is used to mechanically excite the fork to oscillate, resulting in a very compact system, with high stability and oscillator quality, and low joule heating due to power losses (less than 10 nW), allowing to work in He-liquid environment at temperatures below 2.2 K. The ideal situation is to extend this control to the case of LT-SNOM. In contrast to the AFM case, the difficulty is to load one arm of the fork with an optical fiber, whose mass is not negligible, without perturbing the oscillation properties of the tuning fork. The experimental goal is to have the loaded and the free prong of the fork dithering at the same frequency, thus taking advantage of the properties of a balanced couple of oscillators [10]. Here we show that, by choosing the right geometrical configuration for the fiber and the tuning fork, the system can still be electrically dithered by an applied alternate voltage, resulting in an excellent mechanical resonator, with quality (Q) factors up to 2850. The variation of the admittance across the fork contacts during the spatial scans is used as input in a negative feedback loop to keep constant the distance between the surface of the sample and the fiber tip. Our lowtemperature shear force distance control, which avoids standard electronics components (preamplifiers [8], compensating capacitor bridges [11]), is compact, stable over several hours and easy to implement. For the experiment we modified a generic commercial low-temperature scanning probe system (Oxford SXM), where a segmented piezo tube scanner allows for scanning along x, y and z directions. The total displacement at 5 K is 9 mm for x and y and 0.9 mm for z. The whole head has

been inserted into a 4He-bath optical cryostat. Temperatures between 5 and 300 K can be achieved by pumping out the liquid He from a reservoir through a needle valve into the SNOM chamber. Helium is heated after the needle valve by an electrical heater. Constant gas flux (50 l/h), pressure (60 mbars, typically), and regulation of the heater current allow for temperatures stable within 0.1 K for several hours. The whole system is mounted on a massive optical table residing on pumped air pillows (resonance frequency of about 0.5 Hz), leading to an uncoupling of the system from external vibrations. We equipped our scanning probe system with a setup comprised essentially by a commercially available quartz tuning fork (standard frequency 215 Hz at room temperature), a 125 mm diameter optical fiber and a rigid holder. The tuning fork is mounted parallel to the x–y scan plan (Fig. 1). The end part of the optical fiber is glued to one prong of the tuning fork, and the fiber is also anchored, two centimeters far from the tip, to the rigid holder. The vibrational motion of the sensor is therefore parallel to the surface of the sample. The tuning fork is driven by a sinusoidal voltage from a function generator (Hewlett Packard 33120A), reduced by a factor of 200 with a voltage divider, allowing a typical excitation amplitude of 1–10 mV, which corresponds to a tip oscillation amplitude less than 1 nm [11]. The current through the tuning fork is directly measured at the current input of a lock-in amplifier (Stanford SR830), synchronous to the excitation frequency. Since the measured current is directly proportional to the mechanical tip amplitude, which depends on the tip-surface distance via shear-forces [8], a closedloop (negative feedback) based on the current amplitude realizes an active control for the sampletip distance (Fig. 1). In Fig. 2 we plot the values of the measured current amplitudes as a function of excitation frequency for different tip-surface distances at 5 K, when the feedback is off. At distances larger than 12 nm the admittance shows a pronounced maximum at a frequency f0 close to 33.535 kHz, the measured low-temperature resonance frequency of our free, unloaded fork. The Q factor, defined as f0 =Df ; where Df is the full width at half maximum (FWHM) of the resonance,

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6 4

Distance tip-sample (nm)

8

10

10 8 6 4 0

10 20 Z distance (nm)

Current at max. (nA)

Current (nA)

10

z =12 nm z = 6 nm z = 1 nm

Current at max (nA)

Fig. 1. Left: scheme of the shear-force detection. The fork-fiber ensemble is electrically forced to oscillate by an alternating voltage. The electrical current through the fork serves as negative feedback signal, on which the z-piezo depends to keep the distance constant. Right: picture of our sensor.

8 6 4

Q

2

=2850

max

33.40

33.50 33.60 33.70 Frequency (KHz)

Fig. 2. Amplitude of the current, in phase with the excitation voltage, through the fork pads as a function of excitation frequency, at tip-surface distances of 12, 6, and 1 nm. The distances are derived from the voltage applied to z-piezo. Inset: plot of the current amplitude at resonance during the approach onto a nominally flat GaAs surface.

amounts to 2850. Decreasing the tip-surface distance, decreases the resonance amplitude, while its width increases. A typical approach curve (inset of Fig. 2) on a nominally flat GaAs surface shows an averaged decrease of the measured amplitude of current of 0.54 nA/nm. This, considering a noise of 0.1 nA, as determined when the tip is far from the surface, gives a signal-to-noise ratio (SNR) equal to 60, and therefore a sensitivity along the approaching axis of 0.2 nm. The proportionality dependence between Q and the amplitude of current (Fig. 3a) is a clear fingerprint that the

(a)

1200 1600 2000 2400 Q factor

Feedback off

7 6 5

0

(b)

5

10 Time (min)

15

Fig. 3. (a) In the tip-surface approach, the amplitude of current is proportional to quality (Q) factor, indicating the presence of viscous dragging forces acting onto the tip. (b) The distance between the tip and the surface, as derived from the value of the current amplitude at resonance (Fig. 2), remains constant over several minutes. The feedback electronics is switched off during measurements.

damping of the oscillator while approaching the surface is due to viscous forces acting onto the tip [8]. To test the mechanical stability of the whole sensor, we have checked the amplitude of the current when the feedback control is off. A remarkable stability (Fig. 3b) is evidenced: when the tip is positioned at 6 nm from the surface, the distance, as derived from the value of the measured current, is constant within 15% of its value over several minutes. This value concerns the overall stability of the experimental setup (sample holder, scanning piezos, etc.), and the stability of

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the sensor itself should therefore be better than stated above. It is also clear that an even longer stability is achieved once the feedback electronics is switched on, thus allowing to perform long acquisition measurements, as will be shown at the end of this letter. The critical parameter in our fiber-tuning fork configuration is the ratio R; given by the distance H (Fig. 4a) between the fork’s basis and the point where the fiber is glued to, and the total length L of the prong. The Q-factor for the experimental value of the current through the fork at 5 K, as a function of R; is depicted in the plot of Fig. 4b (dotted line). The highest Q value is obtained for R ¼ 0:6; while the system does not resonate if the fork is glued to the extremities of the prong. This can be theoretically explained within the classical theory of vibrating beams [12]. We determine the fundamental frequency of a vibrating lever employing the Rayleigh method, which consists in equating the strain energy of the prong when the deformation uðz; tÞ is at maximum, to the kinetic energy when the deformation is zero. This frequency reads [12] as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u RL   u G IðzÞ q2 uðz; tÞ=qz2 2 dz 0 t o ¼ RL ð1Þ  2 0 SðzÞPðzÞ quðz; tÞ=qt dz

Fig. 4. (a) When a voltage is applied, the fork prongs bend and a displacement uðzÞ from equilibrium is produced. Our tuning fork prongs are 4 mm long (L), 0.6 mm thick (S) and 0.4 mm wide (P). (b) Experimental Q values for different H=L ratios R (solid line with dots). A resonance is observed only for R between 0.4 and 0.8. The result of the theoretical model are shown (dashed line).

and it is coupled to the equation q2 uðz; tÞ=qz2 ¼ Mðz; tÞ=½GIðzÞ:

ð2Þ

In Eqs. (1) and (2), S and P are the characteristic dimensions of the prong, M the external moment acting onto the considered section, I the crosssectional moment of inertia, G the quartz value for the Young modulus. I; S; and P are function of z; depending on the point of the prong where the fiber is glued to (through the coefficient R defined above), and reflecting therefore the profile in Fig. 4a. At low temperature the rigidity of the glue is such that the added fiber has to be considered in its inertial and elastic properties. We have numerically evaluated o as a function of R; using the dimensions for our tuning fork (Fig. 4a) and of the optical fiber (from the tip to the support), and compared it to the frequency o0 of the free vibrating prong. The quantity o0 =jo  o0 j; which gives the relative detuning between the two oscillators and estimates the upper value of Q; is plotted dashed in Fig. 4b and accounts for the observed maximum at R ¼ 0:6: The main features of our LT-SNOM in terms of long time stability are here demonstrated in the case of high spatial and spectral resolution PL measurements of GaAs/AlGaAs V-groove QWRs [13] at 5 K. The sample is far-field excited (10 W/ cm2) by the 2.4 eV line of an Ar+ laser and the luminescence is collected, scanning over the sample, via an uncoated fiber and detected with a photomultiplier tube. Taking advantage of an optical resolution of 200 nm (FWHM of the intensity profile in the inset of Fig. 5a), we show that the emission originates from a series of boxes aligned along the wire axis (Fig. 5a). The light emission from one single box (arrow in Fig. 5a) is dispersed by a double monochromator (0.08 meV spectral resolution) and detected by a cooled CCD camera. The spectral emission at the same excitation power density shows a large number of peaks, centered at 1.645 eV, over a spectral window of 7 meV (FWHM). Once the excitation power is decreased by three decades to 0.01 W/cm2, the emission reveals the presence of a limited number of homogeneous peaks (B0.1 meV FWHM, Fig. 5b). To obtain this spectrum, we position the tip at a distance of 4 nm from the surface of the

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suitable for low-temperature SNOM. Its high stability makes it possible to perform measurements with acquisition times over several hours.

Acknowledgements We are grateful to J.D. Ganie" re, J. Rychen, C. Lienau and K. Karrai for stimulating discussions. One of us (A.C.) acknowledges financial support from Fond National Suisse de la Recherche Scientifique, contract no. 2000-055817.98.

References

Fig. 5. (a) Intensity map of the QWR PL emission. Inset: Spatial profile of the light emission and shear force topography along the line marked by an arrow: FWHM of the intensity peak is 200 nm. (b) Spectrally resolved emission from a zone of the wire (arrow in a) for two excitation power densities.

sample and perform the acquisition over 1 h. The rate of collected photons per spectral emission line is in this case less than 0.1 photons/s. The observed emissions are due to localized excitons recombining in the QWR. It is possible therefore to study the intrinsic one-dimensional properties of excitons in the homogeneous regime [14]. In conclusion, we have presented here a new configuration for fiber-tuning fork sensor assembly, which, limiting to a minimum mechanical and electrical components, is particularly

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