Terahertz near-field microscopy investigation of plasmons in 2D nanomaterials

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Universit`

a di Pisa

Dipartimento di Fisica

Terahertz near-field microscopy

investigation of plasmons in 2D nanomaterials

Candidato Fedor Getman

Relatore

Dr.ssa Miriam Serena Vitiello

Anno accademico 2016/2017

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Contents 2

1

Introduction

Electromagnetic radiation allows to perceive the world around us and communi-cate through it. Visible light is the most accessible part of the electromagnetic spectrum and emitters and detectors operating in this spectral have been devel-oped extensively in the last decades. Radio frequencies have been used for the first time more then a century ago to allow long range communication. Since then, the efficiency of receivers and sources has continuously improved, and the range of the electromagnetic spectrum to be explored simultaneously started to attract progressively more attention. By the end of the 20th century radio telescopes, x-ray scans, infrared visors and many other technologies based on the use of elec-tromagnetic radiation were developed. Terahertz (THz) radiation, loosely defined in the 30-300 µm wavelength, lies in the region of the electromagnetic spectrum located in the gap between visible light and radio frequencies. The energy of vibrational and rotational transitions of many atoms and molecules falls in this spectral range. This makes THz radiation spectroscopy an interesting tool to iden-tify atoms and molecules. This method of identification of complex chemicals can be also applied to airport security, where a non intrusive method of identification of illegal substances is required; or, in industry, to monitor production. Commonly used sources for THz radiation are Quantum Cascade Lasers (QCL) operating at cryogenic temperatures, but practically the most performing generators of THz frequency beams.

Microscopy in the Terahertz range appears unfeasible at the first glance. Diffrac-tion limit imposes that an optical microscope employing THz radiaDiffrac-tion would be unable to have a resolution lower then 0.61λ_n, with λ being the THz wavelength and n being the index of refraction. This means that details smaller then 100 µm cannot be easily unveiled. This limit holds for microscopes that use far field radiation. However, this limit can be overcome when using near field radiation. The purpose of this work has been to demonstrate a novel THz near field optical microscopy technique, based on the combination of a Scanning Near Field

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Mi-2

croscope (SNOM) by Neaspec GmbH and a QCL source. In our setup the QCL acts both as a source and a detector, exploiting the principles of laser self-mixing interferometry.

As an application of this novel instrument we probed 2D nanomaterials. In order to modulate the materials response to THz radiation, we fabricated field effect transistor devices (FETs). In this way, we were able to acquire SNOM scans while changing the carrier density in the FET active channel material.

This thesis is organized as follows:

• In Chapter 1 near-field techniques such as aperture and aperture-less mi-croscopy are introduced. Limits and advantages of each technique are dis-cussed, together with SNOM interferometric detection techniques. We present the self-mixing technique used in this work. In the last part of the chapter we briefly discuss FET devices and the properties of the materials employed as active channels for the FETs fabricated in this work.

• In Chapter 2 the experimental setup and the device fabrication procedure are described.

In the second part of the chapter we describe the optical measurement setup: the SNOM, the optical equipment, the THz source and the employed signal generators, filters and amplifiers. The alignment procedure is presented in details. We also describe the setup and the procedures for the electrical characterization of the devices.

• In Chapter 3 the main results are presented and discussed. For each de-vice, we provide Raman spectra, electrical characteristics, topography and Near-field scans acquired under THz illumination. The THz images are ob-tained for different charge density concentrations inside the devices. Various observed effects are highlighted and discussed.

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2

Principles of Terahertz

Microscopy

I will start this introductory chapter about near-field microscopy by describing the diffraction limit and the resolution of standard microscopy approaches.

2.1 Diffraction limit and standard microscopy

ap-proaches

It is conventional to assume that optical imaging cannot resolve objects that have a distance smaller then the employed wavelength. This is a diffraction phenomenon and it is due to the wave-like nature of electromagnetic radiation. A point source of light observed under a microscope produces a diffraction pattern due to finite size of the microscope lens. This pattern is a series of concentric circles and is called an Airy disk.

When two points that emit light are close to each other they produce two over-lapping Airy disks. The minimal distance between the two points that allows us to distinguish them can be defined as the one occurring when the central maximum of one Airy disk coincides with the first minimum of the other one. As shown in Fig-ure 2.1 this is known as Rayleight criterion and the maximum possible resolution for an instrument with a circular aperture is:

δDmin = 0.61

λ

nsinθ (2.1)

2.1.1 Microscopy approaches below optical resolution

According to the equation 2.1 the following approaches can be used to increase the resolution:

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2.1. Diffraction limit and standard microscopy approaches 4

Figure 2.1: The intensity curves for the radial distribution of the diffracted light for different distances between sources

• submerging everything in a liquid with a higher n(such as oil)

• using a light source with a decreased wavelength such as UV or X-rays • using electrons that have the de Broglie wavelength significantly smaller then

the visible light wavelength.

• employing fluorescent particles and specific activation mechanisms.

Unfortunately the listed approaches are usually invasive and have a high risk of damaging the sample.

X-ray microscopy makes it possible to resolve the atomic structure of crystalline materials up to 0.4 nm [32] and further depending on the unit cell. However, not all materials posses a crystalline structure. Additionally, for materials having a crystalline structure, this method does not allow dynamic studies.

On the other hand, electron microscopy does not require a crystal structure to work. An additional advantage is that electrons are charged particles and while producing lenses for high frequency radiation is complicated, electron beams can be focused with magnetic fields. The resolution of an electronic microscope is, in principle, determined only by the diffraction limit imposed by the de Broglie wavelength of electrons λ = h_p, but in practice limited by the quality of magnetic lenses. Electronic microscopes are routinely operated at a resolution of around 1nm.

High Resolution Transmission Electron Microscopy (HRTEM) can actually achieve sub atomic resolution but requires complicated sample preparations.

Other techniques that can be used only with specific types of samples are the ones that use fluorescence:

• Stimulated Emission Depletion (STED[2]) uses two subsequent light pulses. The first is a normal Gauss shaped pulse that excites a big diffraction limited

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area of the fluorescent dye. The second is a toroidally shaped pulse that depletes the dye by stimulated emission. The central hole in the second pulse is much smaller then the waist of the Gauss beam. As a result, by scanning the area we can obtain information from a patch of fluorescent molecules whose radius is below the diffraction limit for that wavelength. • Photo Activated Localization Microscopy (PALM[3]). In this technique

dif-ferent types of fluorescent molecules, resonant with difdif-ferent pumping fre-quencies, are used. The molecules belonging to each group are separated by more then a far-field resolvable distance. At a given time, only one type of fluorescent molecules is activated and, knowing that obtained image is gen-erated by a pinpoint source, we can compute its exact location. Doing this for each type of dye provides us with a complete map of the sample.

2.1.2 Near-field approaches

Figure 2.2: SNOM types: (a) with aperture, (b) aperturless. Adapted from [9]

In the approaches described above we are unable to go beyond the diffraction limit. Indeed the relation δDmin = 0.61_nsinθλ holds only for the far field methods,

where the radiation source or the detector is situated far away from the observed object. Hence, it is possible to overcome it by bringing the source or the detector

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very close to the object, at a distance comparable to the radiation wavelength. Such an approach could be complicated to realize, due the usually considerable size of the source, cumbersome geometry of the setup or high vacuum requirements. These issues make it difficult to operate in close proximity of a delicate sample. To make use nevertheless of the evanescent fields near the surface of the illuminated object, a secondary element, able to funnel near field radiation, is required. In Scanning Near-field Optical Microscopy (SNOM) this element is a tip, metallic or dielectric, an optical fiber or a cantilever. The approaches using those elements are respectively called apertureless and aperture SNOM.

The aperture approach was first proposed in 1928 and suggested the use of a screen with a small aperture in it. It was first realized in 1972 by Ash and Nicholls [4], using a microwave source with a 3cm wavelength. The radiation transmitted through the subwavelength aperture is evanescent. In this way a sample underneath can be probed with a spot size comparable to the aperture size. This increases the resolution, that is now limited only by the aperture size, at the expense of a reduced signal trough the screen.

Since employing a large screen can cause damages to the sample, modern in-struments create the near field radiation spot using metal-coated optical fibers[5], as shown in Figure 2.2(a). As in the case of the metallic screen, decreasing the fiber aperture improves the resolution but lowers the transmission efficiency. Such a trade-off limits the actual resolution of an aperture type microscope to λ/10.

Apertureless SNOM exploits the enhanced field in the proximity of small and sharp objects, such as metallic or dielectric tip. The first working machines were made in 1994 by Zenhausern et al. [6] and by Inouye and Kawata [7]. The use of small tips allows a resolution up to 10nm [8] imposed by the radius of curvature of the tip termination.

Figure 2.3: Block diagram of an AFM operation a) and the diagram of an optical probe sensor [13].

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Micro-2.2. Tip Interaction Models 7

scope (AFM) as a base for the SNOM. An AFM is an instruments that maps the topography of a sample with the use of a sharp tip (probe). The tip is placed at the end of a flexible cantilever. In proximity of the sample surface the forces between the tip and the sample deflect the cantilever. The deflection of the cantilever can be measured with a laser, called the deflection laser, as shown in Figure 2.3 b). The probe is moved across the sample and using either the deflection of the can-tilever or the feedback signal required to keep the cancan-tilever at a constant position a topography map of the surface can be reconstructed. An AFM can operate in contact mode, which measures the height of each point of the surface with the tip is at rest, or in tapping mode which measures the height with the tip vibrating at a very high frequency. In ambient conditions, and close to the surface, the force between the tip and the sample can become attractive making the tip stick to its surface [14]. For this reason the tapping mode is more commonly used. The ability to bring a tip at subwavelength distances from the sample surface in a controlled manner and the freedom of movement across the surface made the AFM a prime candidate for integration of near-field microscopy.

Near filed microscopes using an AFM tip are called scattering-type SNOM (s-SNOM), since the tip scatters the impinging light in a near field spot is formed underneath the tip. The tip-sample interaction occurring in such a spot is scattered back by the tip to the detector and analyzed to obtain the image. In addition to this near filed contribution, the interaction with the sample creates in the far field also background reflections, carrying no information about near field radiation. Separation procedures, together with interaction models for tip and sample, will be discussed in the following.

2.2 Tip Interaction Models

The interaction between the tip and the sample is complex and there are several theoretical models, with different assumptions, simulating it. The most widely used are the models approximating the scanning tip to a dipole or a dipole plus a monopole. In the following we will describe this model, with the aim to clarify the physics of near field interaction.

The dipole model

The dipole model was the first to be developed and widely used. In the dipole model [10] the end of the tip is approximated as a sphere of polarizability α = 4πR3(−1)/(+2) inscribed in the tip apex as shown in Figure 2.4. In this picture,

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2.2. Tip Interaction Models 8

Figure 2.4: Dipole model with perpendicular (to the left) and horizontal (to the right) polar-izations

the incoming electric field E0 produces a dipole momentum p = αE0. An image

dipole is then formed on the sample surface p0 = βp. The image dipole interacts with the probe creating a secondary image dipole inside the tip, which in turn creates another mirror image on the sample. Infinite iterations give an infinite converging sum of image dipoles:

p = p0 inf X n=0 gn = p0 1 − g (2.2)

where g is the dipole coefficient after a double reflection, calculated in its two components considering the field produced by the a dipole distant 2D = 2(R + H) where R is the radius of our polarized sphere and H is the distance tip-surface. Equation 2.2 holds when the dipole is perpendicular to the surface as in Figure 2.4 a). The field generated by it will be E = _2πDp 3 and we can obtain gz:

gz =

βα

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In Figure 2.4 b) the dipole is parallel to the surface and it will generate a field E = _−4πDp 3, resulting in a dipole coefficient:

gx =

βα

32π(R + H)3 (2.4)

In the previous equations both β and α coefficients depend on materials charac-teristics only.

Due to its linearity the actual dipole would be a superposition of the perpen-dicular and parallel components, with a dominant perpenperpen-dicular component due to the elongated form of the tip. In the experiments, presented and discussed in the present work, we use a laser polarized along the tip, suppressing the creation of a horizontal dipole component.

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The monopole model

Figure 2.5

Graphical representation of the monopole model [9]. The monopole model is a more recent development

of the dipole model, that can better fit experimen-tal data, and requires additional parameters to be defined. In this case the tip is approximated by a conductive spheroid. Since we are interested in computing the electric field only close to the tip apex, we reduce the spheroid to a finite dipole p0 in

the apex region. p0 would produce the same field in

the apex as the one produced by the spheroid. This dipole is formed by two monopoles Q0 and −Q0 of

which only Q0, the closest to the apex, participate

in the near-field interaction. The interaction with the samples surface is approximated by the creation of a charge Qi closer to the apex and a

correspond-ing −Qi charge.

The interaction with the sample is solved by the mirror image method with a similar approach to the one used in the dipole model. As in the analyses of the dipole model we have a reflection factor β, which depends only on material characteristics: β =

−1

+1. Given β, the image charge Q 0

0 is obtained as:

Q0₀ = −βQ0. This image charge interacts back with

the tip, i.e. with the spheroid. We thus have a problem similar to a charge in the proximity of a conductive sphere. This problem can be solved by placing an imaginary point charge inside the sphere. Since in our case we do not have a sphere but an elongated spheroid, the solution to our problem can be found by taking the solution for a spherical tip and stretching it along the vertical axis. This leads to an image charge inside the spheroid in a shape of a line situated very close to the tip apex[11].

The resulting ratio η between the momentum of the first dipole and the image dipole is shown in Eq 2.5 obtained in [9]. η = β(2Lg − 2H − W0− R)ln 4L 4H+2W0+R 4Lln4L_R − β(4Lg − 4H − 3R)ln 4L 4H+2R (2.5) The higher number of parameters in equation 2.5: g being the factor of the

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2.3. Expansion in harmonics and background noise 11

induced charge compared to the original charge, β = ( − 1)/( + 1) being the reflection factor related to the dielectric constant , H, R and W0 being the

dis-tances shown in Figure 2.5 requires careful fitting procedures with experimental data, in order to calibrate the theoretical model.

2.3 Expansion in harmonics and background noise

The light scattered by a vibrating s-SNOM tip contain a strong contribution from the so called background scattering. Background scattering consists in the reflec-tions from optical elements, form the sample area outside the near-field zone and from parts of the tip not involved in the near-field interaction. This scattering is not useful since it brings no information about the near filed response of the sample and is considered noise to be suppressed. Unfortunately the background scattering constitutes the larger part of the back-scattered signal from the probing tip [63].

We note that if the tip oscillates with an amplitude comparable to the tip radius, the background variations, as a function of the tip-sample distance, are very small; this happens because the relative variation of the elongated part of the tip, mainly responsible for the background scattering, is very small. Over the same distances the evanescent fields, which mediate the near-field interaction, are modulated almost completely. The small oscillations of the probing tip required to separate the near-field from the background signal are usually obtained by vibrating it and bringing it in intermittent contact with the surface of the sample. The signal received u(t)from a SNOM tip is thus periodical and can be expressed with a Fourier series:

u(t) =

inf

X

n=inf

uneinΩt

Where Ω is the vibration frequency of the tip, t is time and un are Fourier

coefficients: un = 1 T Z T /2 −T /2 u(t)e−inΩtdt

For the reasons expressed above, the larger part of the background signal is con-tained in the first terms of the series; while the high non linearity in H of equation 2.3 translates in non negligible higher order harmonics in the Fourier transform. It is than possible to suppress the background contribution by demodulating the total signal at higher harmonics. Experiments have shown that at visible frequen-cies and at infrared frequenfrequen-cies the terms respectively |n| = 0, 1, 2 and |n| = 0, 1

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2.4. Detection methods in s-SNOM microscopy 12

are sufficient[63] to enable such a suppression. The following terms (|n| > 2and |n| > 3 respectively) give then the near-field signal. In this work, experimental near field signal is extracted from those higher harmonics. In the following, we call harmonics O0, O1, ..., O5 the coefficients n0, n1, ... n5 of the Fourier series of

the scattered signal.

2.4 Detection methods in s-SNOM microscopy

Tip-sample interaction can produce both an amplitude and a phase modulation of the backscattered near field signal. For this reason various methods to extract amplitude and/or phase have been developed in the last years. In the following, the most common ones for SNOM are described.

2.4.1 Homodyne detection

Figure 2.6

Homodyne detection setup.

Homodyne detection is a method that allows to acquire information on the phase of a signal by comparing it with a similar signal having a known phase. In optics, this is done by splitting the radiation emitted by a coherent source in two beams. The first beam moves with no obstacle on its way and is called local oscillator. The second beam interacts with the sample we want to study. Both signals are then mixed on a detector. The sample modifies the phase of the second beam, so that its presence can be detected as a modulation in amplitude, due to the interference.

This method can be used in combination with a SNOM as shown in Figure 2.6. Here, the reference beam is created via a mirror and a beam splitter. Unfortu-nately, the homodyne method is not sufficient for near-field imaging of samples

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providing weak optical contrasts. Homodyne detection gives reliable amplitude and phase values only when the reference beam has a much higher intensity with respect to the background. For samples with weak optical contrast this could not be verified, and the background could act as a reference with a point dependent phase and amplitude, hindering the detection of reliable near field amplitude and phase signals[9].

2.4.2 Heterodyne detection

Heterodyne detectors are based on interferometric principles similar to the ones employed in homodyne detectors. However, in hetorodyne schemes, the light used as reference is modulated in intensity by an Acoustical Optical Modulator (AOM). A setup that makes use of an AOM is shown in Figure 2.7. The AOM induced intensity modulation of the reference, produces a modulation of the interference between reference and near field at the frequency of the AOM. Interference at the detector is also caused by the tip oscillation. Interference with the modulated reference will than contain the standard tip frequency harmonics plus sidebands created by AOM modulations. The frequency shift between the main harmonic and the first sidebands is given by ∆ω = ±∆ where ∆ is the frequency of acoustic waves in AOM. When locking the detection to one AOM sideband of the tip oscillating frequency, we are thus isolating the interference contribution arising by the reference only, completely removing the background, that cannot have these sidebands.

Figure 2.7

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2.4.3 Pseudoheterodyne detection

A pseudoheterodyne scheme is similar to a heterodyne setup where a the modu-lation of the reference beam is introduced via a piezoelectric actuator shifting the mirror at the end of one of the arms of the interferometric setup. The scheme of such an approach is shown in Figure 2.8. Using demodulation techniques similar to the ones used in heterodyne detection[64] both the amplitude and phase of the scattered beam can be extracted.

In comparison to the heterodyne s-SNOM, the phase-modulation technique of the pseudoheterodyne setup offers the advantage of simple experimental realization and applicability in a broad spectral range. Furthermore, the vibrating mirror can be driven by piezoelectric actuators with kHz frequencies. The reference-near field interference signal is thus found in the sub-MHz range where it is possible to use slower detectors with respect to the ones required by the heterodyne technique.

Figure 2.8

Experimental setup for the interferometric detection of near-field and background scatterings from a s-SNOM probe employing a phase-modulated reference beam.

2.4.4 Our novel approach: self-mixing microscopy

Self-mixing interferometry is a measurement technique in which a laser beam is reflected back into the laser cavity. The reflected light and the generated light interfere inside the laser cavity, causing changes of the intercavity dynamics and the laser voltage. Those changes can be monitored and recorded by precise electrical instruments, and information about the targeted object and the laser itself can be extracted. Such a technique can be used for remote and contactless measurement of the vibration of a solid target. Self-mixing interferometry relies on the coherence

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properties of a laser beam, and on the high sensitivity of the coherent detection exploited in an interferometric setup, allowing to detect very small backscattered signal by a diffusing surface. In particular this surface can be the area directly underneath the vibrating tip of a s-SNOM probe.

Backscattered light no longer forms a parallel beam and an optical element able to collect it is commonly required. For this purpose a setup exploiting two lenses can be used, as shown in Figure 2.9. In the present thesis a similar setup, employing two parabolic mirrors instead of two lenses, is used.

Figure 2.9

A self-mixing s-SNOM setup that uses refraction to steer the radiation.

In the weak regime of self-coupling, when the perturbing field brings back into the laser cavity a fraction of the pre-existing field power, which lies between 10−8 and 10−2, the main phenomenon is amplitude (AM) and frequency (FM) modulation of the oscillating field. The weak coupling allows the use of a not reflective target. The condition for a good self-mixing signal is that the laser is single longitudinal mode and has low side-mode content, such as when it is biased well above threshold[16]. The self mixing process results in the power P inside the laser cavity deviating from the original power P0 as follows:

P = P0(1 + maF(φ)) (2.6)

where φ = 2ks is the optical shift due to the propagation to the target and back, k = 2πλ is the wavevector, s is the length of the optical path, F is a 2π periodic function depending on the coupling strength and m is the AM modulation index, that is expressed as [16]:

m = A−1/2(c/2s(γ − 1/τ )) (2.7) where τ is cavity decay time, A is the power attenuation and γ is the gain per unit of time of the active medium. When the emission time is much smaller then the cavity decay time (m 1) the F function can be approximated as a cosine function and the systems behaves as a common interferometer. For longer values we need to use the Lang and Kobayashi model[15]. The variables of the problem can be reduced to an adimensional parameter C which dictates F behavior [16]:

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C = (1 + α2)1/2A−1/2χs0/nlasLlas (2.8)

where χ is the fraction of the field that interacts with the principal laser mode, s0 is the target distance, nlasis the index of refraction inside the laser cavity, Llas

is the length of the laser cavity and α is the linewidth enhancement factor that depends on the stimulated emission G:

α = 2π

dnlas

dN

λ_dNdG

Figure 2.10

The intensity of the AM signal for various values of the parameter C. Adapted from [18].

The form of the function F (φ) of self-mixing signals for different values of C is shown in Figure 2.10. Various regimes can be identified:

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2.5. Major applications of near-field s-SNOM microscopy: plasmonics 17

• C < 0.1, very weak coupling regime. As mentioned before, F (φ) assumes a form similar to a sine/cosine function typical of a Michelson interferometer. • C = 0.1 − 1, weak coupling regime. The form becomes progressively more

distorted and asymmetrical.

• C = 1 − 4.6, moderate coupling regime. A single switching appears and the function F (φ) becomes two valued. This regime can be developed without incurring in the ambiguity as the switching indicates the polarity, downward for increasing φ and upward for decreasing φ.

• C > 4.6 strong coupling regime. The form becomes erratic with more then one switching per period. This erratic regime allows the waveform to jump at different values of switching. The behavior becomes one of multi-stability and chaos and the setup is no longer useful for measurement purposes, but can be used for chaos generators [17].

In the originally proposed configuration the signal is read from a photodiode placed at the rear end of the laser cavity. Another configuration, the one used in this work, have the signal detected by monitoring the voltage across the device[19]. Due to the long cavities length of the cavities employed in the present work (2mm) on the order of 1mm), and the low values of α [20] it is believed that QCLs operate in the weak coupling regime C < 1. The numerical and experimental study [21] show the stability of self-mixing setups employing a QCL. Furthermore, with the increase of the optical feedback the QCL do not experience erratic phenomena, such as incoherent collapse or mode-hoping, but maintains a single longitudinal mode, making them suitable for the purposes of this work.

2.5 Major applications of near-field s-SNOM

mi-croscopy: plasmonics

Plasmonics studies the interactions of plasmons, collective electron density oscu-lations, in analogy to photons as quanta of light oscillations. Plasmons along with excitons are typical collective effects of systems of interacting electrons. They are present in every type of crystal and are among the most studied many-body effects on the band structure. A propagating particle, consisting of coupled oscilla-tions of electron density and electromagnetic radiation, is called a surface plasmon polariton.

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2.5. Major applications of near-field s-SNOM microscopy: plasmonics 18

2.5.1 Surface Plasmon Polaritons

Surface plasmons are electromagnetic waves which propagate at the surface be-tween two mediums having different dielectric constants. Surface plasmons can be coupled with light even in sub-wavelength regions; and it is therefore very appeal-ing to use near-field microscopy to explore and unveil their propagation behavior. Let’s assume an infinite flat interface between two semi-infinite media, a metal and a dielectric. In our experiments the dielectric medium is air. The interface is the x,y plane as shown in Figure 2.11. We assume that 1 = 1 − ω_p2/ω2 is the dielectric function of the metal ( ωp being the characteristic plasma frequency

of the metal) and that 2 is the dielectric function of the dielectric (frequency independent). We want to find the conditions under which the electromagnetic excitation is propagating along the surface z = 0 only, meaning that the fields decay both in z > 0 and z < 0.

Figure 2.11: Schematic representation of two semi-infinite media in contact with each other for the study of surface plasmon modes on the contact surface[1].

Due to symmetry considerations, we impose that our plasmon is propagating along the x direction. Our plasmon changes the local charge density at the surface, so that a z component of the electric field is generated. The fields can be written

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2.5. Major applications of near-field s-SNOM microscopy: plasmonics 19 as:          E1(x, y, z, t) = (E1x, 0, E1z)ei(q1x−ωt)e+k1z z < 0 B1(x, y, z, t) = (0, B1y, 0)ei(q1x−ωt)e+k1z E2(x, y, z, t) = (E2x, 0, E2z)ei(q2x−ωt)e−k2z z > 0 B2(x, y, z, t) = (0, B2y, 0)ei(q2x−ωt)e−k2z (2.9)

Here 1 and 2 refers to quantities being inside the metal and dielectric media respectively, q1 and q2 are real propagation wavenumbers and k1 and k2 are real

positive quantities representing the exponential decay of the fields away from the interface.

The Maxwell equations must be fulfilled. In our simple model we have no ex-ternal sources:

∇ · (iEi) = 0 ∇ · B = 0

(2.10) ∇ × (Ei) = −1_c∂B_∂ti ∇ × (Bi) = E1_c∂B_∂ti

In previous equations the index i runs from 1 to 2, indicating metal and dielec-tric, respectively.

Boundary conditions must be satisfied, first by imposing that electric and mag-netic fields parallel to the interface are equal in the two materials:

E1x = E2x, B1y = B2y, q1 = q2.

We can bring our equations Eq.2.9 to a more useful form:          E1(x, y, z, t) = (E1x, 0, E1z)ei(q1x−ωt)e+k1z z < 0 B1(x, y, z, t) = (0, B1y, 0)ei(q1x−ωt)e+k1z E2(x, y, z, t) = (E2x, 0, E2z)ei(q2x−ωt)e−k2z z > 0 B2(x, y, z, t) = (0, B2y, 0)ei(q2x−ωt)e−k2z (2.11)

Boundary conditions require also that perpendicular field should be continuous: 1E1 = 2E2 (2.12)

Substituting Eq. 2.11 in Eq. 2.10 we obtain: (

iqEx+ k1Ez1 = 0

iqEx− k2Ez2= 0

(2.13) Combining with Eq.2.12 we obtain the condition for the existence of a surface plasmon mode:

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2.6. Device architectures of the present thesis work: bidimensional field effect transistors 20 1 k1 + 2 k2 = 0 (2.14)

Considering the first equation of Eq.2.10, taking the rotor of both members, and substituting the magnetic field from the second Eq.2.10, and the identity ∇ × (∇ × A) = ∇(∇ · A) − ∇2_{A we obtain:} ∇ × ∇ × Ei = − i c2E¨i =⇒ ∇ 2_E i = i c2E¨i

The last equation, applied to the electric fields in Eq.2.11 gives: q2 = k₁2+ i

c2ω

2 _(2.15)

Multiplying the first of the above equations by 1/2_i, taking into account Eq.2.14 and subtracting the equation with i = 1 from the one with i = 2, we achieve the dispersion relation for surface plasmons:

q2 = ω 2 c2 12 1+ 2 (2.16) In the case of the metal-dielectric interface, q(ω) assumes real values for fre-quencies in the interval [0 < ω < ωs] (both numerator and denominator are

nega-tive) and in the interval [ω > ωp] (both numerator and denominator are positive.

In the particular case of the surface between a metal and a dielectric, with dielectric functions 1 = 1 −

ω2p

ω2and 2 = d, Eq.2.16 becomes:

q2 = w 2 c2 d ω2_{− ω}2 p (d+ 1)ω2− ωp2 (2.17) This equation can be solved in terms of q giving us a dispersion curve shown in Figure 2.12

2.6 Device architectures of the present thesis work:

bidimensional field effect transistors

The field effect transistor (FET) is a device that employs the field effect to control its electrical behavior. The conductivity between the drain and source electrodes is modulated by an internal electrical field, which is generated by the voltage difference between a gate electrode and the active channel of the device. This modulation of conductance is called field effect.

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2.6. Device architectures of the present thesis work: bidimensional field effect

transistors 21

Figure 2.12

Dispersion curve of the surface plasmon polariton at the interface between a metal and a dielectric. The dashed line denotes the dielectric light line [1].

The change in conductance is caused by the applied field, that alters the energy levels available to electrons in the transistor material. In a metal, the density of electrons that respond to applied fields is so large that an external electric field can penetrate only a very short distance inside the material. However, in a semi-conductor the lower density of electrons (or holes) that can respond to an applied field is sufficiently small, allowing the field to penetrate quite far into the material. This field penetration alters the conductivity of the semiconductor and thus the electrical current across it.

A FET device consists of an active channel through which charge carriers, electrons or holes, flow. The source and the drain are respectively defined as the injection and the collection electrode of the current. Source and drain terminal conductors are connected to the semiconductor through ohmic contacts. The third electrode of a FET is the gate defined as the terminal that, when electrically biased, modulates the channel conductivity. The MOSFET (metaloxidesemiconductor field-effect transistor) employs an insulator (typically SiO2) between the gate and

the body. The device behaves essentially as a parallel plate capacitor, where the gate and semiconductor act as plates. The schematics of a MOSFET are shown in Figure 2.13. The conductivity of the channel is a function of the potential applied across the gate and source terminals.

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transistors 22

Figure 2.13

Schematic diagram of a top gated MOSFET[34].

voltage between them VSD. The voltage between gate and drain is called VG and

the current leaving the gate is IG. IG should be zero for a dielectric insulator that

did not undergo a breakdown.

In this work, we use a back gated MOSFET, that differs from a top gated MOSFET in the position of the gate electrode, as shown in Figure 2.14.

Applying a voltage to the gate electrode causes the charge carriers to accumu-late in the channel above the gate. The density of the charge carriers depends on the sign and magnitude of the voltage. The current-voltage characteristics of the MOSFET are calculated assuming that the variation in the electric field due to VSD is much smaller than the variation in the field due to VG. This assumption is

justified as the thickness of the gate insulator is of the order of nanometers, while the channel length is of the order of micrometers[36].

For lower VSD, the ISD follows an ohmic behavior which can be described by:

ISD =

W

LµF ECi(VG− V t)VSD

Where L is the length of the channel, W is the width of the channel, µF E is

the field effect mobility, Ci is the capacitance of the insulating layer, and Vtis the

threshold voltage.

At higher VSD the charge density becomes very low in the region in proximity

of the drain contact. Increasing the gate voltage still results in higher currents, as the gate voltage controls the density in the conductive channel. However, the

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transistors 23

Figure 2.14

Schematic diagram of a back gated MOSFET[35].

current is no longer dependent on VSD and saturates. The value of VSD above

which saturation occurs is known as pinch-off voltage. The saturation current can be described by [36]:

ISD =

W

LµF ECi(VG− V t)

2

An example of FET IV curve is shown in Figure 2.15. In this thesis we will work in the linear region of the FET IV curve, that for our devices means applying drain voltages never exceeding 1mV.

For a 2D channel, we can also compute the surface concentrations of holes and electrons, that are of interest for this work, since they should be probed by THz light. Those concentrations are expressed in terms of the surface potential, as follows using equilibrium statistics:

ps= Naexp(−φ/Vth)

(2.18) ns = npoexp(φ/Vth)

where Na is the shallow acceptor density in the p-type semiconductor, npo is

the equilibrium concentration of the minority carriers (electrons) in the bulk, Vth

is the thermal voltage and φ is the potential distribution in the semiconductor. The potential distribution φ is a solution of the Poisson’s equations:

d2φ r = −

q(ps+ ns− Na)

s

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transistors 24

Figure 2.15

Theoretical output characteristics of a FET [35].

In the general case, the set of equations 2.18 and 2.19 do not have an analytical solution. However, a relation can be derived for the electric field Esat the

insulator-semiconductor interface and the total charge Qs = −sFsas function of the surface

potential φs obtained [37]. This dependence is shown in Figure 2.16.

At the flat-band condition (V=VF B and φs = 0) the surface charge is equal

to zero. In accumulation condition (V < VF B), the surface charge is positive;

in depletion and inversion condition (V > VF B), the surface charge is negative.

In accumulation (when φs is much greater then Vth) and in strong inversion, the

mobile sheet charge density is proportional to exp[φs/(2Vth)]. In depletion and

weak inversion, the depletion charge is dominant and its sheet density varies as φ1/2s .

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2.7. Materials employed in the present thesis 25

Figure 2.16

Normalized total semiconductor charge per unit area versus normalized surface potential [37].

2.7 Materials employed in the present thesis

2.7.1 Tin Selenide SnSe

Tin selenide (SnSe), a representative of layered IVVI chalcogenides, is an attractive binary p-type semi-conductor material with a wide range of potential applications, such as memory switching devices[38], infrared optoelectronic devices[39], and an-ode materials with improved lithium-ion diffusivity[40].

Bulk SnSe presents a direct band gap of 1.30 eV and an indirect band gap of 0.90 eV, this offers a great potential for applications in the fields of photovoltaics and optoelectronics [41]. Recently, ultralow thermal conductivity and a high ther-moelectric figure of merit have been found in SnSe bulk crystals [43], which also gives them prospects regarding applications in thermoelectric energy conversion.

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Figure 2.17

Morphology of synthetic SnSe [26].

Layered SnSe has an orthorhombic crystal structure, which can be regarded as a distorted NaCl structure, with atoms arranged in two adjacent double lay-ers of selenium and tin, forming a planar bilayer (BL) structure that is held together by weak van der Waals interactions, as shown in Figure 2.17. Unlike their bulk form, 2D SnSe nanostructures are expected to present a tunable band gap [44], high photosensitivity and rapid photosensitivity [44]. These effects are due to the large specific surface to volume ratio and to the quantum confine-ment effects arising in nanostructures, affecting their electronic and optical prop-erties. Furthermore, the 2D material structures, and the possibility to explore ?????????????????????????????????????????? of this material as for graphene, are compatible with modern micro and nano-fabrication techniques and can be easily inserted into complex structures for various electronic and optoelectronic applications [45].

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2.7.2 Tin Diselenide SnSe

2

As a new 2D semiconducting material, SnSe2 has a crystal configuration similar

to the one present in MoS2. In such a configuration the Sn layer is sandwiched

between two Se layers to form a stable three-layer structure [54] as shown in Figure 2.18. Experiments on SnSe2 FETs indicated that the current cannot be

completely turned off due to the high electron density in SnSe2 layers. SnSe2

shows a carrier density of 1018_cm3 _{in the bulk [}₅₅_{], compared with the 10}16_cm3

density in MoS2 [56] and the 1015cm3 value for black phosphorus[57], two recently

emerged nanomaterials of interest for photonic and electronic applications.

Figure 2.18

Structural model of a layered SnSe2 [54].

The crystal structure of SnSe2 belongs to the hexagonal space group P3m1.

It is a van der Waals material with 1T structure. Within each layer, every six Se atoms are located at the corners of an octahedron and feature an inversion symmetry with respect to the central Sn atom.

High drive current FETs have been made from thick (84 nm) SnSe2 flakes [58].

Thinner SnSe2 flakes combined with other 2D materials, such as WSe2 [59], and

black phosphorus [60], have been adopted in tunneling devices, which showed pro-nounced negative differential resistance (with BP and WSe2) or good subthreshold

swing (with WSe2). SnSe2 flakes have also been used as high performance

photode-tectors [61][62] Despite these efforts in utilizing SnSe2, most of its basic electronic

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2.7.3 Black phosphorous doped with selenium BP

Black phosphorous (BP), the most stable allotrope of the phosphorus element, was first discovered by Bridgman [49] in 1914 and obtained from ordinary white phos-phorous. It has individual layers with puckered honeycomb structure, as shown in Figure 2.19(a). The side and top views of BP are presented in Figure 2.19(b)-(d). The crystal structure of BP is orthorhombic with Cmca Space Group. The prim-itive cell is made of four atoms with intra layer bonds having a covalent nature and inter layer interactions resulting from van der Waals forces.

Figure 2.19

(a) Puckered honeycomb layers of black phosphorous, (b), (c), and (d) side and top view of black phosphorus [50] [52].

Atomically thin black phosphorous, a novel 2D semiconductor material, is ex-pected as a good candidate for high-performance photodetectors. First, few-layer BP FETs exhibited high on/off ratios of 105 and hole mobility of 1000 cm2 V1 s1 [47] Second, BP has a thickness-dependent direct bandgap from 0.3 eV for bulk to 1.5 eV for the monolayer[47]. The band structure and hence photo-electronic property of this 2D material can be easily changed with doping, as shown in ex-periments done with Se-doped BP photodetector[51].

Furthermore, few-layers thick black phosphorus is transparent to radiation po-larized along the axis x, shown in Figure 2.19(d) (zigzag direction), and absorbs radiation polarized along the axis y, shown in Figure 2.19(d) (armchair direction), within a wide range of electromagnetic frequencies, including part of visible light

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and infrared light. This anisotropy is also present in thermal and electrical char-acteristics: along the armchair direction BP presents high hole mobility and poor thermal conductivity, and the situation is reversed along the zigzag direction. For this reason we can identify the armchair direction as the electrical transport di-rection, and the zigzag direction as the heat transport direction.

The synthesized Se-doped BP crystals exhibit uniform doping and high crys-tallinity. Field effect transistors based on mechanically exfoliated few-layer Se-doped BP possess excellent electronic properties with on/off current ratio of 105

and hole mobility of 561 cm2V1s1 at ambient temperature. More significantly, the external quantum efficiency and the responsivity of 2D BP photodetectors have been improved to be 15.33 AW1_{and 2993 % with the introduction of selenium}

dop-ing. This is a 20-fold enhancement in responsivity with respect to the pristine BP [51]. Furthermore BP provides a highly anisotropic band structure which makes this material extremely appealing for emerging specific effects ”from scratch”.

In this work only Se-doped black phosphorus so that in the following we will indicate it only as black phosphorus.

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3

Methods and

Experimental setup

3.1 Fabrication

The fabrication of transistors with nano-metric precision requires high-tech equip-ment and a workspace clean from air particles such as dust. For the fabrication of our devices we employed the facilities of Laboratorio NEST - National Enter-prise for nanoScience and nanoTechnology such as a ZEISS electron microscope, a Sistec evaporator, wet benches and a reactive ion etching chamber. See following sections for detailed explanations of the aforementioned machines and processes. Most of the fabrication was done inside the NEST’s cleanroom, with the exclusion of final steps, such as wire bonding performed outside the clean room on ready to test devices.

In order to produce our field effect transistors (FETs), the following steps are required:

• Choose a suitable substrate and clean it properly.

• Evaporate the metal for the back gate electrode on the bottom part of the device.

• Draw a reference grid on the upper part of the device for precision lithogra-phy.

• Deposit thin layers of the desired material on the upper part of the device. • Cover the upper part of the device with a polymer and engrave the desired

pattern of the mask for source and drain electrodes on it, using electron beam lithography (EBL).

• Evaporate a metal sequence of chromium and gold on the engraved mask to create source and drain contacts.

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3.1. Fabrication 31

• Mount and connect the device to a chip to allow the interface with laboratory electronics.

In this work we call ”device” a single transistor on top of the substrate cut from a silicon wafer, and we call ”sample” such a substrate, that can have multiple devices on it, all made of the same 2D nanomaterial.

3.1.1 Substrate preparation

The fabrication of our devices starts by selecting and cleaning the substrate on which they will be build. We choose prime grade silicon wafer p-doped with boron and made by Siegert Wafer. The silicon must be doped in order to act as a back gate. The Si-Wafer is thick 279 ± 25µm and the upper part is covered with 300 ± 15nm of SiO2 oxide.

We mechanically clean the bottom part of the Si-wafer to make sure that the internal layer of doped silicon is exposed. Then we chemically clean the wafer at the wet bench: the wafer is dipped for 3 minutes in semiconductor grade acetone (ACE), then for 40 seconds in Isopropylalcohol (IPA). The sample is then dried under a N2 flux. The back gate electrode can now be fabricated by evaporating

on the bottom part of the wafer 10nm of chrome and followed by 100nm of gold. After that a reference grid of markers (5nm of chrome and 25 nm of gold) is imprinted on it, with the same procedure we use for fabrication of the source and drain electrode.

The specific details of the procedure will be explained in the following sections. As explained in the next section, flakes are randomly deposited on the substrate surface after mechanical exfoliation, and the grid of markers is necessary as a reference system for fabricating electrodes precisely on top of the flakes.

3.1.2 Mechanical exfoliation

After preparing the silicon substrate we prepare the 2D materials. The same pro-cedures were followed for the three investigated materials: SnSe, SnSe2 and black

phosphorous. We took a grain of the selected bulk material and pressed it on a sheet of high quality scotch tape leaving a very small (few millimeters wide) footprint behind. After that the bulk is returned into the storage. The footprint left on the tape is an extremely thin sheet of bulk material required for the FET. In order to reduce even further the thickness of the material crystals the tape is folded, making sure the sheet of the material is in contact on both sides with the tape, and then slowly opened. The interlayer cohesion forces in the material

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3.1. Fabrication 32

are weaker then the adhesion to the tape. For this reason the material layers are separated in two blocks, and one of two halves has a thickness that is lower then then half of the original thickness of the material.

This procedure was repeated 10 times resulting in a distribution of thin flakes of material on the tape. To transfer the exfoliated flakes on the substrate, the silicon sample is pressed on top of a selected part of the tape and then slowly peeled off. A portion of the flakes from the tape remains attached to the substrate. During this process some glue from the tape is also transfered to the substrate, hence the sample has to undergo the same cleaning procedures described in subsection 3.1.1.

Figure 3.1

Exfoliated flakes of SnSe2 on a SiO2 substrate. a) a cluster of SnSe2 flakes. b) a

marker that form the reference grid. c) a cluster of flakes inside a 200x200 write field defined by markers at the four corners that is good for device fabrication.

Now the transfer is complete and we can observe the sample in an optical mi-croscope. We are able to see different flakes, their color and their position with respect to the markers. From the flake color it is possible to roughly estimate the

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3.1. Fabrication 33

thickness of the flake, since the color variations between the flakes are caused by light interference. The light reflected by the upper surface of the flake and the light reflected by the bottom part of the flake interfere with each other. For a given thickness light with a determined wavelength form a destructive interfer-ence. For thin enough flakes this effect is not negligible and it is expressed in the suppression of a part of the reflected spectrum. Such an effect results in a dif-ference of flake color. Exfoliated flakes of different colors can be seen in Figure 3.1.

3.1.3 SEM image acquisition

The sample with flakes on it is then placed in the vacuum chamber of a scanning electron microscope (SEM). SEM produces images by scanning the surface of the sample with a focused beam of electrons. Scattered and secondary electrons are recorded by a detector. Due to the short de Broglie wavelength of electrons, the spatial resolution of such a microscope can reach nanometers. Unlike the trans-mission electron microscope (TEM), SEM does not require samples to be treated with metal coating before exposure. We are thus able to put our freshly produced device inside the vacuum chamber and start acquiring images without any delay. This is important for thin reactive materials that exposed to air oxidation degrade within days. An example of such a material is the black phosphorus used in this work.

The employed SEM is Ultra Plus by ZEISS, shown in Figure 3.2. Two detectors are present on the SEM for the scattered electrons from the sample.

1. A backscatter electron detector that collects high energy electrons from the beam that scatter from the sample

2. A secondary electron detector that collects low-energy (< 50 eV) secondary electrons that are ejected from the k-shell of the specimen atoms by inelastic scattering interactions with beam electrons. Secondary electrons originate from a superficial layer of the material that is only few nanometers thick, and are useful for the characterization of the sample surface [31].

When the electron beam is turned on, the chamber must be always in vacuum. The imaging process consists in focusing the beam on a spot of the sample, col-lecting the scattered electrons and uploading the value of the measured charge as a pixel. This process is repeated for all pixels forming an image. Thus the resolu-tion is determined by the quality of the focusing of the electron beam and by the precision of the scanning coils that control the position of the electron beam. We have two ways of changing the point of interaction between the electron beam and

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3.1. Fabrication 34

Figure 3.2

Scanning electron microscope Ultra Plus by ZEISS used in this work.

the sample: we can mechanically move the stage on which the sample is mounted or we can control the current of the scanning coils that deflect the electron beam. The latter is more precise, but can move the electron beam only up to a certain degree. For this reason mechanical positioning of the stage is used for large move-ments (of the order of millimeters or centimeters), like changing the zone we want to investigate, and the scanning coils for small movements during the acquisition of a single image. The focusing is done manually and is a crucial step for a good imaging.

The SEM is controlled via the software ELPHY MultiBeam. It allows to move the stage, set the electron beam parameters, focus on the sample and execute pro-cedures for image acquisition. For imaging we use electron accelerated by a 5kV voltage and an interferometric stage. The specifics of the interferometric stage are described in section 3.1.5. A very precise stage is important since, after aligning software coordinates to the coordinates of existing markers, we can acquire images containing the coordinate information, and move the beam across the sample with high precision. A map of images can be created, with each acquired image contain-ing 4 markers for alignment correction needed in lithographic processes described in section 3.1.5. An example of an image with a black phosphorus flake surrounded

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3.1. Fabrication 35

by markers can be seen in Figure 3.3

Figure 3.3

a) SEM image of a substrate with black phosphorus flakes (circled in red and magnified in b)) surrounded by 4 markers (circled in green and magnified in c)).

After the aligned imaging the sample is extracted from SEM and covered with PMMA-polymer. This polymer has a double effect of protecting the flakes from degradation and acting as resist for the later writing e-beam exposition (see sub-section 3.1.5). The polymer used is ARP 679.04. The covering process involves depositing the polymer on the sample surface, putting the sample in a spinner, spinning it at 4000 rpm to achieve uniform polymer thickness of 270nm and finally baking it on a hot plate at 120◦C. After this procedure the sample can be safely stored in a vacuum chamber (10−5mbar) while the ”design” of transistor is per-formed.

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3.1. Fabrication 36

Figure 3.4: Computer-aided design (CAD) of SnSe2 FETs we used in this work. Different

elements of the CAD are marked with different colors that are exposed at different times. The orange color denotes the marker grid already present on the substrate. The green and blue structures denote the source and drain contacts near the flakes and the bonding pads. The red color denotes markers that will be used for alignment correction during the lithographic process.

3.1.4 CAD ”design” of the transistor

Once we have acquired SEM images of our flakes we can design the transistors that incorporates them as active channels. We use ELPHY MultiBeam software to design the computer-aided design (CAD) of our device. This is the same software was used to interact with our SEM Ultra Plus to avoid any compatibility issue. On the base of optical acquisition and SEM images acquisition we individuate thin flakes. An example of a possible black phosphorus flake candidate is shown in Figure 3.3. The source and drain contacts are drawn on top of the flake, having the SEM image as a background for the CAD. Contacts are as wide as the flake and they overlap with it for at least 0.5µm. The typical width of the contact near the flake is slightly larger then the flake width and typically reaches several µm.

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3.1. Fabrication 37

The contacts get thicker as they approach the bonding pads. Bondings pads in our case are squares 150x150 µm wide that will be used to contact the device to a larger chip through aluminum wires. The position of the pads and contacts can’t be chosen randomly, and we have to take into account the complications of the fabrication process. Elements are arranged in a way that minimizes the possibility of incidents that could compromise our devices. Furthermore, we have to keep in mind the future THz measurements with the SNOM. For signal acquisition SNOM uses a very delicate tip similar to an atomic force microscope (AFM) tip. Such a tip must have enough clearance to move around the sample without hitting anything and being damaged. The precautions that have been taken to ensure the best possible result are:

• Bonding pads situated far away from the flakes and at least 100µm from other pads. The reasons for this are, first, that the bonding process is manual and can damage objects near the pad; secondly that the bonding pads are exposed to a 10kV electron beam during the process of writing. A 10kV electron beam is less precise then the 20kV one used for source and drain contacts, and may cause unwanted exposure of the resist.

• Sharp angles should be avoided in the device design, since a difficult geometry could compromise the detachment of the evaporated gold not sticking to the substrate.

• The position of the bonding pads and of the wires, that will be attached in the future, should permit the movement of the SNOM tip during the measurements on THz frequencies. The tip of our SNOM and the cantilever, to which the tip is attached, is positioned very close to the surface and must be able to move around the sample. Bonding wires reach a certain height above the sample surface, and moving the tip near them could break it or disturb the signal.

Due to all those constraints we can make less then 10 FETs on a wafer, among which only some will be electrically connected to the chip during a single SNOM measurement session. After the measurements, the bonding process can be re-peated and different devices connected from the same sample to the same chip. In Figure 3.4 we can see a complete CAD of a prototypical device.

3.1.5 Electronic beam lithography

After the CAD is completed, we return to the SEM, insert our PMMA-polymer covered sample and begin the writing process. In such a process, the polymer is exposed to the electronic beam for a right amount of time, with the geometry

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3.1. Fabrication 38

drawn in the CAD. Exposed areas can be removed later in a chemical way, by dissolution in a specific developer. The exposure time is the time needed for the electron beam to create chain scission inside the polymer, and has been determined experimentally. To achieve the correspondence between the geometry in the CAD and the physical position of the flakes on the substrate, it is crucial to set the microscope parameters properly. It is needed to:

• Set the microscope in such a way that the coordinates of our CAD match the positions of the original markers.

• Focus properly the beam on the surface of the sample. This procedure must be done close to the area of interest, since the presence of small tilting of the sample will make the e-beam out of focus in the region of interest. However, to avoid unwanted exposure of the sample, focus is performed avoiding the region of interest.

• Measure the current of the beam, in order to calculate the correct exposition time.

• Calibrate the deflection of the e-beam by the scanning coils, to be certain that it moves correctly inside the field of writing (the so called ”writefield”). When the procedure is compete the e-beam starts ”writing” on the sample. Source and drain terminals are exposed with the minimal possible aperture of 10 µm and a 20kV electron accelerating voltage. With those parameters and a correct alignment procedure, the precision of the lithography can reach 5nm.

An explanation of the movements inside the SEM is needed to understand the next step. The sample is mounted on a stage that can move mechanically and its horizontal position is determined with the help of two laser interferometers. During the writing and the imaging processes the magnetic fields produced by scanning coils move the e-beam across an area, the writefield. In our case, we used an area of 200 × 200µm for contacts and 1 × 1mm for the bonding pads. The movement of the e-beam across the writefield is much more precise than the mechanical movements of the stage. Such a movement has to be calibrated, via a writefield alignment procedure that can be realized using the four markers present in each writefiled. The SEM beam is deflected from the center of the writefield to the expected positions of the four markers, where four zoomed images of them are taken. The operator visually analyzes the SEM images acquired in this way, and, in case the marker is not central to the image, the operator indicates to the machine the real position of the markers. This generates correction parameters

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3.1. Fabrication 39

for beam deflection, that can be implemented to have an aligned writefield. The four markers employed in this procedure are shown in red in Figure 3.4. After this procedure the exposure can take place.

To expose the bonding pads we set the e-beam to have an aperture of 60µm and a voltage of 10kV. The focusing of the beam and measurements of the total current must be repeated for the new aperture and voltage, in the same way as described above.

After the contacts and the pads for all devices are exposed, we can extract the sample from the SEM chamber.

3.1.6 Reactive ion etching

After the exposition to the e-beam we need to create the mask, by chemical dis-solution of part of the polymer in the developer AR 600.56 for 3 minutes. Since we employ a positive resist, only the exposed the PMMA-polymer is dissolved by it, and not exposed PMMA-polymer remains on the substrate. To ensure that the metallic terminals adhere to the sample surface, this surface must be as clean as possible. After being rinsed in Isopropyl alcohol, the sample is dried with com-pressed N2 and undergoes a reactive-ion etching cleaning (RIE).

The sample is thus placed in a chamber between two metallic plates, acting as electrodes to perform the RIE process. Air is pumped out of the chamber until a vacuum of 10−5 mbar is reached. Etching gas (oxygen) enters the chamber, then the high voltage plates turn it into plasma and sample is bombarded by plasma ions. The bombardment of charged ions removes organic dirt from the sample. The quantity of oxygen, the duration of the process and the ionizing etching voltage have to be set carefully to remove all the unwanted material, while not damaging the exposed parts of the flake and the remaining PMMA-polymer. At the end of the process we extract the sample from the chamber and move it into the evaporator as fast as we can. The fabrication is done inside a clean room and the chance of a dust particle setting on the sample is extremely low. However, water vapor from the air can condense on it, compromising the quality of the subsequent steps.

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3.1. Fabrication 40

3.1.7 Evaporation

Figure 3.5: a) Exfoliated flakes, b) covered with resist. c) resist exposed during the EBL, d) developed, e) Cr and Au are evaporated on top, f) excess metal are removed during the Lift off.

The evaporator is an instrument that evaporates on the surface of a loaded sample a thin film of de-sired metal, or a sequence of thin metal layers, in a controlled way. To achieve clean and con-trolled layers, the process is performed in a vac-uum chamber, where both sample and metals are loaded. The sample is placed upside down on a stage, situated in the upper part of the chamber, with the flakes facing downwards. Four crucibles with specific metals are sitting on the bottom of the chamber. Those metals are heated and evapo-rated with a high current passing through the cru-cible, and the evaporated metal is uniformly de-posited on the sample and on a vibrating quartz crystal. The vibration frequency of the crys-tal changes with the thickness of the material de-posited on it, so that the frequency measurement can be used, after calibration, as a thickness measure-ment.

For the fabrication of our contacts we have chosen to evaporate 10nm of chromium and 100nm of gold on the top of our sample. Chromium is used to provide a bet-ter adhesion[22] between gold and the sample. Gold is used as the main material for current conduction as it has a very low resistivity and does not oxidate by reacting with atmospheric gases. The evaporated metal covers both the parts of the sample still covered by PMMA-polymer and the parts where the exposed PMMA-polymer was washed away by the developer. The thicknesses of various materials are wisely chosen so that the resist is thicker than the deposited metals. Since evaporation is non conformal but directional, the layer of chrome and gold covering the flake and SiO2 is

not in contact with the layer of chrome and gold cov-ering the PMMA-polymer. Thanks to the absence of structural contact, the two layers can be separated by a process called lift-off.

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3.1. Fabrication 41

3.1.8 Lift-off

To remove the layer of metal on top of the PMMA-polymer we submerge our sample in a liquid that dissolves the aforementioned polymer. In our case we use acetone. To be sure that the acetone has time to infiltrate under the whole layer of gold and dissolve all the remaining PMMA-polymer, the sample is left submerged for 3 hours. Without removing the sample from acetone bath, we flux it with acetone through a syringe. The acetone flow peels away all the superfluous gold and chromium, so that only the designed circuit remains attached to the substrate. The last step is the cleaning of the sample, by dipping it in IPA for 40 seconds. After this step we have a sample with working FETs that can be measured if connected to a proper electronic measurement setup.

3.1.9 Atomic Layer Deposition

Figure 3.6: Variation of signal intensity (blue line) with the distance between the SNOM tip and sample [23]

Samples containing SnSe and SnSe2 are already completed and we only need

to bond them to a chip. However, black phosphorus is reactive to air. If exposed to atmosphere, such a device has a lifetime of several days, which is not enough to perform our SNOM measurements. Furthermore, working with a device that deteriorates and changes its optical and electric characteristics during the exper-iment is unfeasible. To solve this problem we have to isolate our flake from the atmosphere, while allowing the optical interaction with the SNOM. Fortunately the near-field produced by the SNOM has a sizable depth extension and is able to acquire the signal through a transparent material if it is of the order of 5−10 nanometers. We thus covered our black phosphorus transistor with 10nm of Al2O3,