DE10259118B4 - Microscopy and Spectroscopy of Electromagnetic Near Fields of Thermal Origin - Google Patents

Abstract

Scanning probe microscope for the detection and spectral analysis of natural thermal electromagnetic near fields on a surface, comprising
A sharp electrically conductive scanning probe tip with a radius of curvature in the nanometer range,
A resonator connected to the scanning probe tip and
- Two connected in parallel with the resonator parallel amplifier whose signal outputs are connected to a correlator.

Description

thermal and quantum mechanical phenomena to lead in all dissipative media to fluctuations of electrical and magnetic polarizability and thereby fluctuating electromagnetic (EM) Fields. The fluctuation-dissipation theorem forms the basis for qualitative description of the relationships between the spectral Amplitudes of EM field fluctuations and generalized susceptibility matrix of the medium.

The theoretical expressions for nearby fluctuating EM fields (distance z) from a flat surface were derived in the work of ML Levin and SM Rytov ¹ . Thereafter, the material constants (dielectric and magnetic susceptibility) and the distance dependence are simply related to the spectral density of the fields (bilinear moments). We present the corresponding formulas in the simpler form of I. Dorofeyev ² and others. Thus, for the mean values of the components E _i , H _{j of} the spectral field density in the vicinity of a non-magnetic metal surface (at a distance z), the following relationships were found:

mit folgenden Bezeichnungen: ω, κ – Frequenz und Wellenvektor des EM-Feldes, σ₁-Leitfähigkeit und ε₁ = ε₁' + iε₁'', komplexe Dielektrizitätskonstante des Oberflächenmaterials, Θ – Plancksche Funktion,

Diese Formeln beinhalten sowohl die Wärmestrahlung nach dem klassischen Kirchhoff-Gesetz als auch die EM Nahfelder (evaneszente Felder). Die Messung der Wärmestrahlung im Fernfeld kz>>1 in allen Frequenzbereichen wird heute routinemäßig mit verschiedenen Techniken (Radar und Funkmessgeräte im RF und Mikrowellen Bereich, Wellenlänge unabhängige Wärmesensoren und Quantendetektoren bei höheren Frequenzen) durchgeführt. Als Messergebnis wird dabei die über einen makroskopischen Bereich gemittelte Temperatur ermittelt (Plancksche Strahlung).The corresponding expressions for a dielectric surface (low conductivity):

with the following designations: ω, κ - frequency and wave vector of the EM field, σ ₁ conductivity and ε ₁ = ε ₁ '+ iε ₁ ", complex dielectric constant of the surface material, Θ - Planck function,

These formulas include both the heat radiation according to the classical Kirchhoff law and the EM near fields (evanescent fields). The measurement of the heat radiation in the far field kz >> 1 in all frequency ranges is routinely carried out with various techniques (radar and radio measuring devices in the RF and microwave range, wavelength independent heat sensors and quantum detectors at higher frequencies). The measured temperature is the temperature averaged over a macroscopic range (Planck's radiation).

Further theoretical investigations of the EM near fields mainly focused on the energy dissipation ³ and energy transfer ⁴ between a surface and a nanoobject, as well as on detailed spectral properties ^{5 of} the near fields.

The prior art includes surface measurement methods based on reflection of high frequency signals ⁶ . Here, the generator signal is brought into the near field region with the help of a nanoscopic tip and the reflection is used for statements about the dielectric properties of the surface.

Physical basics the FNFM

• * Genauer auf den Term
  
  Da aber der Imaginärteil und der Realteil der Dielektrizitätskonstante durch die Kramers-Kroning Relation verbunden sind, kann gezeigt werden, dass auch in dem Term die gesamte Information über die Dielektrizitätskonstante enthalten ist.

Moleküle) die komplexe Dielektrizitätskonstante eine der wichtigsten Charakteristiken des Oberflächenmaterials bleibt, dürfte durch diese Untersuchungen ein wesentlicher Beitrag für die Materialforschung entstehen. Zum Verdeutlichen der These ist in der 1 der typische Verlauf von Real- und Imaginärteil der Dielektrizitätskonstante in Umgebung zweier Resonanzfrequenzen eines Oszillators dargestellt (Bild aus J. D. Jackson, Klassische Elektrodynamik, Walter de Gruyter, Berlin-New York, 1983). Nur in der Umgebung der Resonanzabsorption ist der Imaginärteil groß und folglich sind die Nahfelder mit entsprechenden Frequenzen stark. Das gleiche gilt für Dipol-Relaxationen in vielen Materialien. Messungen der spektralen Nahfelddichte in verschiedenen Spektralbereichen ergeben dann ein Spektralbild, das charakteristisch für die chemische Zusammensetzung des Substrats unter der Spitze ist. Das Sensorsignal kann sowohl für die chemische Charakterisierung, lokale Temperaturmessung, sowie für die Abstandsregelung genutzt werden.However, the microscopic measurements of the fluctuating EM fields in the near range kz << 1 are likely to bring significant progress. If it were possible to determine the spectral energy density of the near fields locally (microscopically), it should also be possible to draw conclusions about the local dielectric constant as a result of the equations (1-6) ^* . As in the nanoscopic area (even for individual

• * Closer to the term
  
  However, since the imaginary part and the real part of the dielectric constant are connected by the Kramers-Kroning relation, it can be shown that also in the term all the information about the dielectric constant is included.

Molecules), the complex dielectric constant remains one of the most important characteristics of the surface material, these studies should be a major contribution to materials research. To clarify the thesis is in the 1 the typical course of real and imaginary part of the dielectric constant in the vicinity of two resonant frequencies of an oscillator shown (picture from JD Jackson, Classical Electrodynamics, Walter de Gruyter, Berlin-New York, 1983). Only in the vicinity of resonance absorption is the imaginary part large, and hence the near fields with corresponding frequencies are strong. The same goes for dipole relaxations in many materials. Measurements of the spectral near field density in different spectral ranges then give a spectral image that is characteristic of the chemical composition of the substrate below the tip. The sensor signal can be used for chemical characterization, local temperature measurement as well as for distance control.

In addition, as the theoretical studies ⁵ show, it should be possible, a number of subtle near-field effects on surfaces with EM-surface excitations to examine. Also immediately below the surface lying volumes with high dielectric losses should be found in the raster image. This would introduce a new kind of surface microscopy / spectroscopy - FNFM - Fluctuation Near Field Microscopy. So far, as far as known, no microscopic measurements were carried out of thermal near fields (in the nanometer range, kz << 1).

approach

The The aim is the direct measurement of fluctuating EM near fields with Help of extremely small sensors and use of the cross-correlation method to establish a new surface microscopy and spectroscopy. From measurement data in a certain spectral range, the frequency dependence of the permittivity be reconstructed and if necessary the surface material determined locally, or between different materials. Due to extremely small sensor dimensions (eg sharp SXM tips) the interaction zone (WW) is limited to the nanometer scale. As the most suitable model systems for this type of technology should biological macromolecules, Polymers, ferroelectrics, thin Films on metal surfaces and organic structures (eg monolayers, membranes) because of the relatively high imaginary part of the dielectric constant probably a higher one near field exhibit.

To clarify the physics of FNFM, comparison with a radio receiver is useful here. The tip in FNFM, as well as an antenna in the radio receiver, converts three-dimensional EM fields into a one-dimensional electrical signal. The signal is then processed in high-sensitivity electronics (eg, correlation receiver). The fundamental differences to radio wave reception lie in the geometry: the peak in FNFM has a very small effective length (l _eff of about 100 nm) and correspondingly low wave impedance Z _w ~ (l _eff / λ) ² . With radio reception, this would mean too weak a coupling to the field and, consequently, too low a signal amplitude. In FNFM geometry, two factors contribute which play no role in radio reception, greatly add to the signal amplification. First, near a surface the field strength grows drastically, e.g. Example, the z component of the E field according to the formula 4) as ~ 1 / z ³ . Secondly, the amplification of the electric field on sharp objects is considered, "lighting rod effect".

In order to find the relationships underlying the FNFM, the in 2 assumed geometry. An extremely sharp scanning probe tip (eg, etched gold tip) is located in the near field of a substrate surface.

gegeben. Dabei ist j_ind(r,ω) = σE_ins(r,ω) die spektrale Stromdichte, die durch das innerhalb der Spitze hervorgerufene elektrische Feld E_ins(r, ω) induziert wird. Für eine scharfe Spitze, modelliert durch ein langes Ellipsoid mit Formfaktor h (h liegt zwischen 0 und 1/3) und Dielektrizitätskonstante ε_t = ε_t' + iε_t'', gilt E_ins(r, ω) ≈ (1/hε_t)E_z(r, ω). Für Metalle im Frequenzbereich von DC bis in Infrarot gilt ε_t ≈ ε_t'' = i4πσ/ω mit σ/ω >> 1. Damit ergibt sich für die MSL:

The energy exchange between the tip and the surface is dominated in this geometry by thermal fluctuating EM near fields ⁷ . The transferred surface power to peak power spectral power (MSL) is given by:

given. Here, j _ind (r, ω) = σE _ins (r, ω) is the spectral current density induced by the electric field E _ins (r, ω) induced within the peak. For a sharp peak modeled by a long ellipsoid with form factor h (h is between 0 and 1/3) and dielectric constant ε _t = ε _t '+ iε _t '', E _ins (r, ω) ≈ (1 / hε _t ) E _z (r, ω). For metals in the frequency range from DC to infrared ε _t ≈ ε _t '' = i4πσ / ω with σ / ω >> 1. This yields for the MSL:

As a possible input stage of the measuring arrangement, a tip is further considered to be connected directly to a resonator. Depending on the measurement frequency, the term resonator is understood to mean a resonant circuit, hollow resonator, dielectric resonator, etc. In the high-frequency range, the quasi-stationary approximation applies: Consequently, the input stage can be modeled by concentrated RCL elements, as shown in Figure 3. When the tip has good conductivity, the transferred power P ^{s → t is} largely absorbed in the resonator. More specifically, the real part of the resonator impedance ReZ _r is responsible for the losses. Finally, the conductivity σ in 8) occurs as the effective conductivity of the dissipative load of the tip / resonator system, and after integration over the volume ⁸ gives a factor Rz _r . Thus, the fluctuating near field of the surface induces voltage predominantly in the outer part l _{eff of} the tip, but the dissipation takes place in the resonator. The integration along the peak can be replaced by averaging over l _eff (d <l _eff << λ). This results in:

Formally, the tip / substrate coupling can be accomplished by connecting in parallel a resistor R _x and a current source i _x , as shown in FIG 4 shown, modeled. Here, the inherent noise of input stage of the amplifier is neglected. In practice, this is achieved by using low-noise preamplifiers connected in parallel and the following correlation processing ⁹ .

Applying the Nyquist theorem ¹⁰ to this circuit now yields for P ^{s → t} :

On the other hand, for the MSL P ^{t → s,} which is transferred from the resonator via the tip into the substrate, the Nyquist theorem is also valid:

1 / Z _r (ω) = 1 / R + i (wC - 1 / wL) and ReZ _r = R is the dissipative resistance with temperature T (the temperature resonator): Z _r (ω) is the impedance of the RLC circuit

The spectral density of the noise voltage ⟨u ² (ω)⟩ at the input of the amplifier results after a series of simple algebraic transformations:

Z (ω) here is the full impedance of the circuit:

Rp is the resistance of R _x and R in parallel, ω ₀ = (LC) ^-1/2 is the resonance frequency.

im Faktor A sind alle Konstanten gesammelt. Aus den Formelnsatz 9)–13) kann prinzipiell die gewünschte Abhängigkeit hergeleitet werden. Um zu transparenten geschlossenen Lösungen zu kommen werden noch folgende Näherungen genutzt: die Güte Q des Resonators ist in allen Fällen hoch genug, und gemessen wird über ein Frequenzbereich von ca. ω₀/Q in der Nähe der Resonanzfrequenz. Weiter wird angenommen, dass R << R_x. Das entspricht einem schwachen Signal der Spitze relativ zu dem Nyquist Rauschen des Resonators. Mit diesen Einschränkungen erhält man in der Nähe der Resonanzfrequenz ω₀:

The dependence of the measurement signal ⟨u ² (ω)⟩ on the physical parameters ΔT = T _s -T, d, ω and ε "/ | ε + 1 | ² , the unknown resistance _Rx (T, ε, ω) should be found. At this point, the equilibrium condition (at T _s = T should also P ^{t → s} = P ^{s → t} ) bear. In equilibrium follows from 9) and 10):

in factor A, all constants are collected. From the formula set 9) -13) can be derived in principle the desired dependence. In order to arrive at transparent closed solutions, the following approximations are used: the quality Q of the resonator is high enough in all cases, and measurement takes place over a frequency range of approximately ω ₀ / Q in the vicinity of the resonance frequency. It is further assumed that R << R _x . This corresponds to a weak peak signal relative to the Nyquist noise of the resonator. With these restrictions one obtains near the resonance frequency ω ₀ :

This formula now clearly represents the sought-after relationships. In the limiting case (d → ∞), when the peak is far from the surface, only the Nyquist noise of the resonator remains. When approaching, the second term in 14) increases in proportion to 1 / d ² , in parallel the position of the resonance maximum shifts to the lower frequencies. The form of frequency dependence is obviously (see formula 11) a Lorenz curve. In practice, it is appropriate to abstract the constant Nyquist term in formula 14) and to treat the term G (T, ε, ω, d) as the measurement result:

In the relation G (T, ε, ω, d), ε and T are the measured variables characteristic of the surface, ω and d the variables. To determine the local topography, surface temperature and loss factor ε '' / | ε + 1 | ² , different measurement scenarios are conceivable. For example, analogous to "constant-hight" and "constant-amplitude" measurements known from SPM technology, the topography could be excluded after two raster passes. Even more freedom is offered by the parallel measurement at several resonance modes when using hollow resonators. From a metrological point of view the measurement of the frequency shift with heterodyne techniques is often much more sensitive compared to amplitude measurements.

Practical realization

at the practical realization of the FNFM are essentially two Problems occurred. First, you need an extreme probe sharp and well conductive tip. Second, because the measurement signal is clear below the level of noise of a resonant mode are resonators with high quality and extremely low noise amplifier necessary.

Around to solve the first problem became an etching technique for production developed from tips of gold and silver with radii of curvature about 20 nm. This will be resolutions reached by a few tenths of nm. An improvement of the facility will radii of curvature below 10 nm. With the progress in nanotechnology are for a probe also solutions like single-electron transistor amplifier integrated in the sensor tip or Josephson contact sensors conceivable.

The two low-noise field effect transistors (HEMTs in our setup, connected in parallel directly to the resonator, 4 ) and subsequent noise suppression by means of correlation measurement methods allow a stable work on many samples and solve the second problem. The 5 shows the block circuit of the FNFM prototype, in which the signal processing takes place according to the concept described. The probe tip, the sample holder and the input stage of the electronics should be well shielded. The XYZ adjustment of the substrate holder via a Teflon rod which is mounted on the XYZ piezo. This isolates the substrate from interfering external fields. The pitch control works as in conventional scanning probe microscopes. When the signal at the output of the integrator reaches a predetermined target value, the control system's control circuit is activated. Further, the deviations from the target value are minimized by the distance control. The control signal is proportional to a convolution of the signal power of the band-limited input signal with the topographic profile of the surface. The information about the local temperature, dielectric constant and topography can be calculated as explained above.

mit einer Standartabweichung σ_s = g(τ)(Δω T)^–1/2. Hier ist T die Integrationszeit, τ die Zeitverschiebung. Von besonderem Interesse ist der Wert g(0), der nach dem Wiener-Khinchine-Theorem¹¹ die Signalleistung darstellt. Aus (16) ist ersichtlich, dass für bandbegrenztes weißes Rauschen der Wert g(0) und die Bandbreite Δω des Bandpasses ausreichen, um alle statistischen Aussagen zu treffen und die volle Messung der Kreuzkorrelationsfunktion keine zusätzliche Information ergibt. Damit kann die technisch aufwendige Realisierung eines Vollkorrelators auf einfacheres System bestehend aus Mischer und Integrator reduziert werden.The correlator in the setup is for noise suppression and forms at the output a signal which is proportional to the power of the correlated input signal component. For band-limited white noise, sensor signal S (t), the preamplifier noise of the two preamplifiers R ₁ (t) and R ₂ (t) are all uncorrelated and have an average of 0. Thus, the approximation of the correlation function Γ (τ, T ) with the time of the correlation function

with a standard deviation σ _s = g (τ) (Δω T) ^-1/2 . Here T is the integration time, τ the time shift. Of particular interest is the value g (0), which according to the Wiener-Khinchine Theorem ^{11 represents} the signal power. From (16) it can be seen that for band-limited white noise, the value g (0) and the band width Δω of the bandpass are sufficient to make all statistical statements and full measurement of the cross-correlation function gives no additional information. Thus, the technically complex realization of a full correlator can be reduced to a simpler system consisting of mixer and integrator.

At the The current state of the art covers the arrangement described above a frequency range of EM nearfields up to several tens of GHz. This limits the applications to substrates with high dielectric Losses in this frequency range. These include ferroelectrics, macromolecular Substances, free molecules with low rotation frequencies, some glasses, etc.

A much wider area of application would be the detection of EM near fields in THz infrared and optical frequency ranges. Here are the great number of characteristic molecular and atomic vibration frequencies well known from Raman, infrared, and microwave spectroscopy and cataloged. The extension of FNFM to these frequency bands is likely to be accessible with advances in nanotechnology.

The above consideration was related to the detection of the electric field E _z . The detection of the magnetic field H _z is possible by modification of the sensor. What is needed is a magnetic field sensor with dimensions in the nanometer range.

• 1. Anwendung als sensitiven Sensor für Nachweis von gasförmigen Molekülen. Freie Moleküle besitzen Rotations-Resonanzen mit Frequenzen im Mikrowellenbereich. Folglich, wenn in der direkten Umgebung der Spitze entsprechende Moleküle vorkommen, steigt das Ausgangssignal für bestimmte Frequenzen an.
• 2. Erfassung von charakteristischen Spinaufspaltungsfrequenzen in der Probe durch Anlegen eines äußeren Magnetfeldes (Zeeman-Effekt) mit hoher räumlichen Auflösung. Die durch thermische Anregungen induzierten Übergänge zwischen aufgespalteten Spinniveaus werden zu verstärkten EM-Fluktuationen mit charakteristischen Spinspaltungsfrequenzen führen und im FNFM Spektrumbild ein Ausstoß (mit einer Breite von ca. reziproker Spin-Relaxationszeit) hervorruffen. Die Lage der Ausstoßensfrequenz lässt sich mit der Magnetfeldstärke steuern und leicht in den HF Bereich umsetzen. Damit wäre eine Alternative zum Spinresonanz Verfahren mit Auflösung in Nanometerbereich etabliert.

Other possible uses of the FNFM method include:

• 1. Application as a sensitive sensor for detection of gaseous molecules. Free molecules have rotational resonances with frequencies in the microwave range. Thus, if molecules are present in the immediate vicinity of the tip, the output will rise for certain frequencies.
• 2. Detection of characteristic spin-splitting frequencies in the sample by applying an external magnetic field (Zeeman effect) with high spatial resolution. Thermal-induced transitions between split-spin levels will lead to increased EM fluctuations with characteristic spin-cleavage frequencies and cause ejection (with a width of approximately reciprocal spin-relaxation time) in the FNFM spectrum image. The position of the ejection frequency can be controlled with the magnetic field strength and easily converted into the HF range. Thus, an alternative to the spin resonance method with resolution in the nanometer range would be established.

literature

• ¹ ML Levin and SM Rytov, Theory of equilibrium thermal fluctuation in electrodynamics, (Science Publish., Moscow, 1967)
• ² I. Dorofeyev, H. Fuchs, B. Gotsmann, and J. Jersch, Damping of a moving particle near a wall relativistic approach, Phys. Rev. Lett. To be published
• ³ IA Dorofeyevy: "Energy dissipation rate of a sample-induced thermal fluctuation field in the tip of a sample microscope", J. Phys. D: Appl. Phys. 31, pp. 600-601 (1998)
• ⁴ AI Volokitin and BNJ Persson, Radiative heat transfer between nanostructures, Phys. Rev. B63, 205404
• ⁵ R. Carminati and JJ Greffet, Near-Field Effects at Spatial Coherence of Thermal Sources, Phys. Rev. Lett. 82 (1999) 1660; AV Shchegrov, K. Joulian, R. Carminati, and JJ Greffet, Near-Field Spectral Effects to Electromagnetic Surface Exitations, Phys. Rev. Lett. 85 (2000) 1548
• ⁶ M. Tabib-Azara, R. Ciocan, G. ponchak and SR Leclair: "Transient thermography using evanescent microwave microscope", Rev. Sci. Instrum. 70, pp. 3387-3390 (1999)
• ⁷ JP. Mulet, K. Joulain, R. Carminati, and JJ Greffet, Appl. Phys. Lett. 78, 2931 (2001)
• ⁸ JD Jackson, Classical Electrodynamics, 2 Edition, Chapter 6.9, New York, 1975
• ⁹ M. Sampietro, L. Fasoli, and G. Ferrari, Spectrum Analyzer with Noise Reduction by Correlation Technique on Two Channels, Rev. Sci. Instrum. 70, (1999), 2520
• ¹⁰ O. Zinke, H. Brunswig, High Frequency Technology 2, Springer, Berlin 1999
• ¹¹ HD Lüke, Signal Transmission (Textbook), Springer-Verlag, 1992

Claims (14)

Scanning probe microscope for detection and spectral Analysis of natural thermal electromagnetic near fields on a surface, comprising - a sharp electrically conductive scanning probe tip with a radius of curvature in the nanometer range, - one Resonator connected to the scanning probe tip and - two with the resonator connected in parallel amplifier whose signal outputs connected to a correlator. Scanning probe microscope according to claim 1, characterized in that that used as raster probe tip a sharp etched metal tip becomes. Scanning probe microscope according to claim 1, characterized in that that a sharp etched tungsten tip steams as a scanning probe tip used with silver and / or gold. Scanning probe microscope according to claim 1, characterized in that that a coaxial tip is used as scanning probe tip. Method for the detection and spectral analysis of natural thermal electromagnetic near fields on a surface (FNFM) using a scanning probe microscope according to one of claims 1 to 4, characterized in that - the energy of the natural thermal electromagnetic near fields at a surface with a sharp electrically conductive scanning probe tip is derived with a radius of curvature in the nanometer range, - the energy derived from the tip is absorbed in the connected resonator, - the output signal of Resonator is passed to two connected in parallel with the resonator parallel amplifier, and - the two output signals of the parallel-connected amplifier are fed to a correlator. Method according to claim 5, characterized in that that by using a cross-correlation method, the noise the preamp repressed becomes. Method according to one of the preceding claims, characterized characterized in that the amplified FNFM signal in a narrow bandwidth near the resonance frequency of the Resonator is measured. Method according to one of the preceding claims, characterized characterized in that FNFM with one of the known SXM methods (AFM, STM, SNOM et al.) Combined and used. Use of the method according to claims 5 to 8 for determining the local chemical composition of a surface the spectral analysis of the FNFM signal. Use of the method according to one of claims 5 to 8 for determining the chemical composition of gaseous substances near of the sensor by the spectral analysis of rotational resonances. Use of the method according to one of claims 5 to 8 for determining the local spin relaxation and the local magnetic Properties of the sample, which is in an external magnetic field. Use of the method according to one of claims 5 to 8 for determining the local temperature with nanometer resolution. Use of the method according to one of claims 5 to 8 for measuring the dielectric properties of a surface. Use of the method according to one of claims 5 to 8 for the investigation of hidden and no-noise material noise Particles.