Constant amplitude driving of a radiofrequency excited plasmonic tunnel junction

Abstract

Constant-amplitude bias modulation over a broad range of microwave frequencies is a prerequisite for application in high-resolution spectroscopic techniques in a tunneling junction as e.g. electron spin resonance spectroscopy or optically detected paramagnetic resonance. Here, we present an optical method for determining the frequency-dependent magnitude of the transfer function of a dedicated high-frequency line integrated with a scanning probe microscope. The method relies on determining the energy cutoff of the plasmonic electroluminescence spectrum, which is linked to the energies of the electrons inelastically tunneling across the junction. We develop an easy-to-implement procedure for effective compensation of an RF line and determination of the transfer function magnitude in the GHz range. We test our method with conventional electronic calibration and find a perfect agreement.

Radio-frequency (RF) modulated bias in scanning tunneling microscopy (STM) opens the way for new kinds of spectroscopies with atomic resolution.^1–10 Operation in the frequency- and time-domain improves the temporal resolution of conventional STM which is usually limited by the small bandwidth of transimpedance amplifiers.² In addition, nuclear and electron spin resonance spectroscopy^3,11 can achieve energy resolution in the order of neV compared to conventional tunneling spectroscopies limited by thermal broadening of electronic states to several μeV at mK temperatures. Apart from spin resonance phenomena, the RF modulation of electric field in the tunnel junction permits access to many other physical phenomena relevant at the atomic scale, such as resonant Andreev reflections,^5,7 exciton dynamics,^10,12 or surface acoustic waves.^13,14 For detection of these transient phenomena with ultrafast temporal resolution, a detailed knowledge of the transfer function between a RF generator and the tunnel junction is needed.^10,15,16

The transfer function of an uncompensated RF line coupled to a tunneling junction in a cryogenic system typically has a complex dependence on the frequency, with a significantly variable attenuation in the GHz range. In order to obtain a harmonic driving with constant amplitude or a well-defined voltage pulse at the tunnel junction,^12,17 the output power of the RF generator has to be compensated for transfer function magnitude T(f). Vector network analyzer can be used to measure it on a wiring,^4,18 however in a working STM setup the characterization needs to be performed in-situ at the tunneling junction prior to each individual experiment. T(f) has been previously obtained by measuring rectification of the RF voltage on current-voltage nonlinearities,^18,19 and also by obtaining the instrumental impulse-response function using time-dependent intensity of plasmonic light generated by inelastically tunneling electrons.²⁰ The former method requires the presence of sharp I(V) nonlinearities such as spin excitation signals in magnetic adatoms, superconducting energy gap onsets or surface states in metal surfaces. The latter method is perfectly suited for tailoring short bias pulses in the ns range, but it is not very practical for generation of a constant-amplitude driving. In addition, both of the in-situ characterization methods need absolute amplitude calibration which can be time-demanding.

Here, we present an optical RF calibration method of the T(f) with a wide dynamic range that exploits the physical principle of the plasmonic electroluminescence occurring at the tunnel junction. In the STM, the nanocavity plasmon modes are excited by inelastically tunneling electrons which impose the limit on the highest energy of the detected photons. By measuring the energy distribution of the plasmonic response by optical spectroscopy and determining the high-energy cutoff of the plasmonic spectrum as a function of frequency we can evaluate the instrumental T(f) at the junction. Using an iterative procedure, we achieve an effective compensation of the transmitted intensity and constant-amplitude harmonic driving.

The experiments were carried out in an ultra-high vacuum Createc STM/AFM microscope with light detection capabilities at 8 K. The optical path from the tunnel junction to the detector consists of a hybrid achromatic lens (12 mm diameter, 15 mm focal length), two sapphire viewports in the cryostat shields, fused silica window and focusing lens outside the chamber. The refocused light is coupled to the bunch of optical 100 μm fibers formed into a slit termination inserted into Andor Kymera 328i spectrograph with Andor Newton DU920P BEX2-DD CCD camera. Three exchangeable gratings (150, 600 and 1200 gr./mm) are available. The majority of spectra were taken with 600 gr./mm grating enabling 1.2 nm spectral resolution and 130 nm range in our setup. This corresponds to 3.8 meV resolution at 2.0 eV (620 nm center wavelength) and 1.95–2.45 eV range.

RF harmonic driving was produced by an arbitrary waveform generator Keysight 81160A for frequency below 500 MHz and by a continuous wave generator Keysight E8257D for frequencies up to 18 GHz. For the sub-GHz frequencies, the generator was coupled to a standard 50 Ω shielded bias wiring to the sample stage in STM using a bias-tee (Pasternack, PE1608) on the air side feedthrough. For GHz range, the continuous waveform was fed through a dedicated 50 Ω RF line consisting of two different cables. Inside the cryostat, a semi-rigid cable (COAX CO., Ltd. SC-086/50-SCN-CN, 2 m) is connecting the feedthrough with an in-vacuum SMA connector above the STM head. In the vacuum, the cable is attached to the outer envelope of the liquid nitrogen vessel for efficient thermalization. From the in-vacuum SMA connector a short (~10 cm) flexible cable (Teledyne Storm Flex 047), is used to deliver the RF power to the tip. This is achieved by an unshielded termination of the flexible cable (6 mm), which acts as the antenna emitting an RF signal absorbed by the tip, as shown in Fig. 1a. STM tip and antenna are strongly capacitively coupled allowing a high transmission efficiency compared to the standard STM wiring.^5,21–23 In a standard STM wiring, the T(f) is far from constant and typically very low (< 10⁻³) in the frequency range above 1 GHz. The antenna-coupled RF line partially overcomes these drawbacks but is limited by the geometry of the antenna and the cavity that cannot be optimized for lossless transmission in the broad frequency range 1–25 GHz. For our iterative compensation procedure, we use a custom software to simultaneously control the RF generator parameters, the Nanonis STM control electronics and to acquire the data from the CCD detector at the spectrograph.

Fig. 1.

(a) Scheme of the optical RF-STM setup with an antenna transmitting harmonic oscillations of the electrical field to the tip, which modulates the spectrum of the plasmon modes generated in the tunneling junction nanocavity. (b) Model of the dependence of the plasmon spectra intensity and high-energy cutoff on the static bias V ₀ without modulation (RF_OFF, blue curves) and with modulation (RF_ON, red spectrum, yellow curve) at the tunneling junction. The red-shaded area highlights the characteristic change in the high-energy cutoff, caused by the modulation averaging effect, weighted by an arcsine distribution (shown as black shaded area).

For the purpose of the calibration procedure a sharp tip and a sample are needed, both from metals with strong plasmonic response in the visible–NIR region such as silver, gold and copper.²⁵ In our measurements we used a clean Ag(111) sample and Ag-coated Pt-Ir tip. They are brought close to contact until a tunneling current starts to flow as a result of the applied bias voltage (V) (see Fig. 1a). A fraction of the inelastically tunneling electrons excite gap plasmon modes which rapidly decay as photons in the far field.²⁴ A spectral intensity profile of these photons is defined by the wavelength dependence of the dielectric function of the electrode materials,²⁶ by the tip geometry and tip-sample distances, which are shaping the geometry of the nanocavity.²⁷ However the most significant dependence of the plasmon spectrum stems from the applied bias voltage, which defines the range of the available inelastic tunneling channels and determines the quantum cutoff, the maximum energy that can a single tunneling electron transfer to the gap plasmon (i.e. h _max ≤ eV)²⁴ (see Fig. 1b). This h _max, is indicative of the maximum bias on the tunneling junction including the modulation and its energy can be precisely determined by measuring an optical spectrum cutoff with a sufficiently high resolution. The total resolution of the method will be limited mostly by stochastic noise in the spectra and the energy-time uncertainty. The upper range of the modulation frequencies detectable in this way is theoretically limited by the typical lifetimes of the gap plasmons, which are in the femtosecond range.²⁸ This permits to characterize the T(f) far in the region of several tens of GHz.^10,20 We note that the present method does not use the so-called overbias emission that produces spectral features well above the single electron energy (i.e. caused by multielectron inelastic electron processes).²⁹

For the cutoff detection we assume that the harmonic signal of frequency f, produced by the generator at amplitude A is transmitted to the tunnel junction without any distortion, but with attenuated amplitude A’ and phase shift Φ’. The energy cutoff h _max, corresponds to the maximum value of the time-dependent bias voltage:

$$h{v}_{\max }(f)=\max \left[V_0+A^{\prime }(f)\sin \left(2\pi ft+{\Phi }^{\prime }\right)\right]$$ (1)

The illustration in Fig. 1b shows the idealized plasmonic spectrum (blue, denoted as RF_OFF) for a static bias V₀, without modulation. Switching on the modulation results in a modified plasmon spectrum, corresponding to the RF_ON curve (red). This curve can be understood as a weighted average of plasmon at static biases in the interval (V ₀−A’, V ₀ +A’). The weight function (probability density function of the arcsine distribution centered around V ₀), is represented in Fig. 1b by the horizontal, black-shaded area. This function corresponds to the probability distribution of the bias over one sine modulation period and it peaks at its definition area limits (V ₀ ± A’), which gives rise to the new cutoff of the RF_ON plasmon at V ₀ + A’. Direct readout of A’(f) from the plasmon spectra allows to calculate the T(f) as A’(f) / A or as T _RF = 10 log(A’(f) / A) in dB.²¹ We determine the cutoff by finding a maximum in the second derivative of the spectra.

In the real conditions, the V₀ is not time-invariant and therefore not simply equal to the preset bias voltage V_DC, but includes a component U(t), caused by noise originating from various sources, in particular from electrical noise, thermal broadening and other as detailed below. We can include this correction by rewriting (1) as:

$$h{v}_{\max }(f)=\max \left[V_{DC}+U(t)+A^{\prime }(f)\sin \left(2\pi ft+{\Phi }^{\prime }\right)\right]=V_{DC}+U_0+A^{\prime }(f)$$ (2)

In the determination of the frequency-dependent A’, we eliminate the offset by subtracting a reference value of V _DC + U ₀, obtained at A = 0, assuming that it remains constant in the range of evaluated frequencies.

Evolution of the actual shape of a typical plasmonic spectrum, obtained by a Ag-coated tip on Ag(111) sample, is demonstrated in Fig. 2a with 981 Hz modulation. The transmission through standard wiring at this frequency is expected to be almost ideal (near unity). The detected cutoff value is plotted as a function of the modulation amplitude in Fig. 2b and manifests good linearity over the entire range. Calculated T(f) in Fig. 2c indeed converges to unity for higher values of modulation A, due to the decrease of the relative error in T(f), caused mostly by the precision of the edge detection. Targeting an A’_T of 50 mV at the tunnel junction for the calibration of T(f) will therefore achieve a reasonable compensation accuracy (< 10%). Thus, for our specific generator maximum output 4950 mV, we would be able to reliably measure and compensate T(f) > 0.01.

Fig. 2.

(a) Reference plasmon cutoffs measured with V _DC = 2 V (blue curve) and f = 981 Hz modulation with amplitudes in the 10–300 mV range. Black dashed vertical lines mark the cutoff energies. Spectral resolution was 1.2 nm (or 4 meV at 620 nm), using a 600 gr./mm grating. A 11-point zero-order Savitzky-Golay filter was used for filtering of the spectra. (b) Test of the linearity between the amplitudes A’ derived from the plasmon spectra cutoffs and the applied modulation A. The values of A’ are compensated for the offset (at A = 0) (c) Transfer function magnitude (T) calculated from 10–300 mV lock-in modulation – data from (a).

In order to compensate the T(f) in the GHz range with sufficient precision for ESR measurements and alike, we apply two iterations as detailed in Fig. 3a–c. In the first step, we use a relatively large (~1.4 V) constant driving amplitude. Optical grating and bias voltage are chosen such that they provide a wide dynamic detection range (5–440 mV) for the RF-induced increase in the cutoff. After the first frequency sweep, the A’(f) is evaluated (see Fig. 3a), the T(f) is calculated as A’(f)/A. In a second frequency sweep, we seek a constant target amplitude (A’_T ) in the tunnel junction of 50 mV, and use therefore driving A(f) = 50 mV/T(f). With these parameters, a new A’(f) is measured. It can be seen in Fig.3b that the amplitude is still not perfectly compensated; therefore we recalculate again the T(f) as A’(f)/A(f). For a third frequency sweep, solely for the purpose of confirmation, we use this refined T(f) and create a new driving A(f) profile with a target amplitude of A’_T = 20 mV. The A’(f) measured in this final sweep (see Fig. 3c) is apparently well-compensated in the entire frequency range, with the exception of a few isolated deviations. The largest deviations from the target A’(f) (e.g. the dips at ~2 and 5.5 GHz) occur at frequencies with sharp minima in the T(f) (below the horizontal orange dashed line in Fig. 3d). These ‘dark’ bands cannot be effectively compensated due to the limited maximum driving power of the generator and the spurious thermal effects caused by excessive RF power dissipation within the microscope head and should be therefore avoided in the measurements. However, further improvement may be achievable by careful optimization of the entire RF setup.

Fig. 3.

(a) Effective amplitude A’(f) of the voltage at the tunnel junction measured as a function of frequency at constant driving amplitude 1414 mV. Black dashed line denotes the upper limit of the photon energy that can be measured with the spectrograph settings of 600 gr./nm grating and center wavelength 570 nm. Each point has been taken at constant tunneling current 3 nA, 2.0 V bias and averaging 2 s for each spectrum. (b) Effective amplitude A’(f) at the junction after first compensation of the RF driving with target amplitude 50 mV using values from (a). Each point was obtained with 5 nA, 2.0 V, 1.5 s and 600 gr./mm. (c) Effective amplitude A’(f) measured after second compensation using values from (b), with target amplitude 20 mV. Parameters were 5 nA, 3 s, 1200 gr./mm grating for each spectrum. (d) The transfer function magnitude (T) of the system calculated from the values in (c). The orange dashed line marks the lower limit of the T that can be compensated in the setup.

Fig. 4 shows a full-range measurement demonstrating that a reasonable characterization of T(f) for our RF line is possible for large continuous frequency intervals between 500 MHz up to 16 GHz. In comparison, the transmission via standard wiring is very effective in the MHz range, but sharply deteriorates just below 1 GHz. However, strong compensation has not proven practical in the regions of T(f) below 2x10⁻³ (−27 dB), where the power dissipation leads to thermally induced movement of the tip with respect to the sample. The positions and depths of the T(f) minima are very sensitive to the actual position of the antenna with respect to the sample and the scanner within the scanning probe assembly. In our repeated measurements we have observed shifts of the T(f) minima by 100–300 MHz and also their complete disappearance upon macroscopical scanner movements. This can be attributed to the changes in the overall microscope head geometry which forms a very complex RF-cavity. Therefore, the calibration of the T(f) has to be performed prior to every particular experiment with RF driving. Optimization of the RF coupling to the tip-sample junction may decrease the number of minima in T(f). The geometry-dependent transmission in the microscope head also allows seeking an optimal T(f) shape at a particular frequency range by coarse scanner movements.

Fig. 4.

Transfer function magnitude (T) of the system in a broad range of frequencies measured using standard wiring of the STM (red points) and RF wiring with antenna near to the STM tip (black points). Every point has been obtained from plasmonic spectra taken during 3 s at 5 nA, 2 V, with 1200 gr./mm grating.

With our procedure, we were able to get a constant driving with a relative standard deviation of ~8%. The major factors causing the broadening of the cutoff in a real plasmonic spectrum are temperature (8 K corresponds to FWHM of 2.2 meV), spectral resolution of the spectrometer (1 nm corresponds to 3.2 meV error at 620 nm) and energy-time uncertainty (200 fs plasmon lifetime²⁸ corresponds to FWHM of 3.3 meV). The exact value of broadening caused by finite plasmon lifetime is unknown, but we did not observe any significant broadening in the range of tens of meV, in contrast to previous works.³⁰ Propagation of all errors mentioned above is suppressed when the reference value V _DC + U ₀ measured with a greater precision is subtracted from the h _max. Stochastic noise is therefore the main source of error in the cutoff evaluation.

Our data were obtained using a tip that yielded a typical intensity of 2–6⋅10⁵ photons per second at 2.5 V and 1 nA, which enabled fast collection of calibration spectra at each frequency value on the order of seconds when using the 1–10 nA tunneling current range. Therefore, calibration in 10 GHz wide range with 2 MHz step and each spectrum averaging time 2 seconds takes about 3 hours. Faster acquisition is possible by increasing the tunneling current yielding higher photon intensity provided that overbias emission is not hampering the cutoff evaluation. For the best signal-to-noise ratio and shortest acquisition time, a very steep cutoff at the photon energy corresponding to the bias V ₀+A’ and high derivative of the plasmon intensity between V ₀ and V ₀+A’ are desirable. For completeness, we have performed an additional simultaneous to compare our optical method to the conventionally used method that evaluates the T(f), based on a sharp feature in the tunneling spectroscopy,^18,19 in our case the surface state of Ag(111). The two methods show an excellent agreement in the measured range of frequencies (for details see the supplementary material). Finally, we have tested the optical calibration for current setpoints in the range 5–200 nA (resulting in Δz = 150 pm) and found no measurable differences in the T(f), inferring that typical variations in the tunneling distance will not alter the system RF characteristics.

In summary, we present a direct optical method for measuring the frequency-dependent transfer function of an RF-STM line. This method can be readily adapted to a wide range of instruments provided that they have optical access. The principle of the method does not require the presence of a sharp I(V) nonlinearity in the measured system. It is very robust against drift and intensity fluctuations and provides a wide dynamic range well above 1 eV due to the broad character of a typical gap plasmon spectrum. We demonstrated amplitude compensation in our RF-STM with antenna-tip capacitive coupling and constant-amplitude driving in the 1–18 GHz range. This method is particularly relevant for RF-phase fluorometry¹⁰ and for future application in optically detected electron paramagnetic resonance in STM. In addition, we envisage possible applications of this method in fields detached from scanning probe microscopy by using integrated light sources — e.g. on-chip metal-insulator-metal tunnel junctions — for calibration of RF driving amplitude on directly inaccessible devices.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.