2.2 Characterization techniques
2.2.1 Scanning Tunnelling Microscopy
The STM technique is based on the quantum tunnelling effect. When two met- als are sandwiched between a thin insulating barrier and an electrical potential is applied, electrons should flow from one metal to the other according to the rules of classical physics only if the applied potential is higher than the barrier. Con- versely, quantum mechanics allow this process to happen even when the potential is lower than the barrier. In the particular case of the STM, an atomically sharp tip approaches an atomically flat surface, with a dielectric barrier in between. Usually this barrier is vacuum, but not only. It is also possible to measure in liquids[198], different gas atmospheres[199] or air [200]. If the distance between tip and sur- face is small enough (1-50 Å), their wave functions will overlap and therefore there is a finite probability of electron hopping between tip and sample, giving rise to quantum tunnelling, as shown in figure2.24. The critical factor which gives this microscope extremely high vertical resolution (of few hundredths of an angstrom) is that the tunnel current flow between tip and sample depends exponentially on
their relative distance. For a typical metal, the current will change by an order of magnitude for every Å in distance with an exponential decay as shown in equation
2.2. I ∼ e2κd, κ = r 2mφ ¯ h ≈ 0.5 p φ(eV )−1 (2.2)
The lateral resolution depends on the apex geometry and the electronic orbitals of the tip. Generally, the electrons of the tip are confined to a very narrow channel allowing real-space imaging down to atomic scale.
The tunnelling regime is characterized by three interdependent parameters: The tip-sample distance (typically 5-10 Å), the tunnelling current It(typically 0.01 - 10
nA) and the bias voltage Vt(typically 0.01 - 2V). Itand Vtare generally chosen to
set a tunnel resistance Rt=Vt/Itin the GΩ regime.
FIGURE 2.24: (a) Tunnelling process between the tip and sample
across a vacuum barrier of width d and height φ. (b) Schematic view of an STM.
A scanning tunnelling microscope is capable to collect topography and spec- troscopy data at local scales. In the topographic mode, the surface is mapped through the dependency of the tunnelling current, It, upon the tip-to-sample dis-
tance. In the spectroscopy mode, the Local Density of states (LDOS) of the material is extracted through measurements of the tunnelling conductance, as it is explained below. However, the measured Itcorresponds to a convolution of the LDOS of the
tip and the sample. To study intrinsic properties of the material, a tip with feature- less DOS and well-defined Fermi energy (Ef) surface, (ideally spherical) should be
used. The most common metals used for the tips are Au, W, Ir and PtIr.
Operation modes
To acquire topography images, two main modes are used. The first one is the so called constant-current imaging mode, which is the most used method to collect to- pographic maps. In this mode, It is kept constant by adjusting with the feedback
the tip vertical position during the scan. Since the tunnelling current integrates over all the states above or below the Fermi energy Ef (depending on the polarity
of the applied bias), the constant-current map represents a profile of constant inte- grated density of states (DOS). If the LDOS is homogeneous over the mapped area, this profile would correspond to a constant tip-to-sample distance, and therefore,
recording the height of the tip as a function of the (x,y) position a three-dimensional map of the surface is obtained.
The second mode is the so called constant-height mode. In this mode, the feedback loop is turned off and the the tip-sample distance is kept at a constant absolute value while mapping. The modulations in the Itare produced then by a change in
the tip-sample distance due to the surface corrugations. Therefore, recording the It
as a function of position will directly reflect surface topography. This mode allows faster scanning than the constant-current mode. However, it is limited to surface with corrugations in the angstrom regime to avoid tip collision with the surface.
Scanning Tunneling Spectroscopy
Besides obtaining surface topography images, the LDOS of the surface can be ob- tained by performing scanning tunnelling spectroscopy (STS). In this mode, the feedback loop is turned off and the distance between tip and sample is kept con- stant. Then a voltage sweep is performed and the tunnelling current as a function of bias voltage is recorded. The differential of this tunnelling current (dI/dV(V)) is proportional to the LDOS.
In first approach, the current between tip and sample can be expressed as I = constant·
Z
dω[f (ω − eV ) − f (ω)]Ntip(ω − eV )Nsample(ω, x) (2.3)
Where ω is the energy, f(ω) denotes the Fermi function, N(ω) is the DOS of tip and sample, and x denotes the lateral position of the tip. If a Ntipis considered constant
and taking the derivative with respect to the V, the local conductance is obtained:
G(V, x) = dI(V )
dV ∝
Z
d(ω)[−f0(ω − eV )]Nsample(ω, x) (2.4)
At T=0, f(ω) becomes a step function and then the conductance in eq.2.4becomes
G = dI
dV ∝ Nsample(eV, x) (2.5)
At higher temperatures, f’(ω) becomes broader and therefore the features in the DOS of the sample are smeared out. Therefore, by taking the derivative of the I(V) spectra with respect to the voltage, the LDOS of the material at a specific location is obtained with a good approximation, using this method.
Most STS experiments use the so called current-imaging tunneling spectroscopy (CITS) firstly introduced by Hamers et al. in 1986 [201]. A CITS image consists of a regular matrix of points distributed over the surface. The tip scans over the surface with a fixed tunnelling resistance Rt=Vt/It, recording the topographic profiles. At each
point of the CITS array, the scan is frozen and the feedback turned off. With the tip (x,y,z) position frozen, the voltage is swept to measure I(V) (or dI/dV curves with a lock-in amplifier). After the sweep, the bias voltage is set back to Vtand the
scanning resumed. At the end of the experiment, a topographic image obtained at Vtand simultaneously obtained spectroscopic images reconstructed from the I(V)
any value, specially V = 0V . In that case, G(0V ) is called the Zero Bias Conductance (ZBC), which is related to the number states available in the vicinity of the Fermi level.
STM protocol measurement
STM measurements were performed in Prof. Christoph Renner’s group, under the supervision of Dr. Ivan Maggio-Aprile at the University of Geneva (Switzerland). I could perform these measurements thanks to two stays (May-July 2015 and May- July 2016) that were carried out during my PhD funded by the Spanish Ministry of Economy. A schematic diagram of the experimental setup and a picture of the microscope employed is shown in figure2.25.
Tip holder and piezoelectric tube
Sample holder and X-Y large positioning
system
a)
b)
FIGURE2.25: (a) Schematic representation of an STM imaging pro-
cess (taken from [202]). (b) Microscope used in all the experiments at the University of Geneva.
The setup consist of a home-made STM controlled by a Nanonis SPM controller. Sample and tip holders are electrically isolated, and are located in a copper Faraday box hanging with a spring from another Faraday box on top a granite table. This configuration minimizes mechanical and electrical noise to a background noise of ∼ 200 fA. The tip holder is connected to the feedback system explained above. Tip motion is controlled by a piezoelectric tube with a working range of 20µm x 20µm in the XY direction and 3µm in the Z component. Tip is grounded while the bias voltage is applied to the sample, which is firmly attached and electrically contacted to the holder with conductive silver paste. With this configuration, when applying a positive (negative) bias voltage V to the sample, electrons tunnel preferentially from the tip into unoccupied (occupied) sample states [202]. Additionally, this STM system has an optical microscope attached to facilitate the location of the tip onto specific areas within the sample.
For all the experiments shown in this Thesis, the same measurement conditions were used. A Vbias = 800mV and a set-point current It = 200pAwere used. To-
pography images were acquired in a constant-current mode and spectroscopic data were acquired according to the CITS method explained above [201]. Figure2.26(a) shows a typical topography image in a 8 nm La0.8Sr0.2MnO3 film. A stair-like ter-
races morphology is observed. The white line in the map corresponds to the profile in the figure2.26(b), where 1 u.c. (∼ 0.4nm) steps are found.
a)
b)
0 50 100 150 200 250 300 -0.4 -0.2 0.0 0.2 0.4 0.6 Z (nm) Profile (nm) 1 u.c. steps (~0.4 nm)FIGURE2.26: (a) 800x800 nm2topography image obtained for a 8
nm LSMO sample at 800 mV and 200 pA. Stair-like terraces are ob- served. White line indicates the region where the profile in (b) was
extracted.
For the spectroscopic measurements, the CITS method was used. The feedback in the Itis turned off and Vbiasis varied from −800 to 800 mV to acquire It(V) curves.
Figure2.27(a) shows the typical I-V curve obtained in the same film, whereas (b) shows the so called conductance curve, G(V). This G(V) is obtained through the nu- merical derivative of the I(V) data.
-300 -200 -100 0 100 200 300 -20 -10 0 10 20 I (pA) Sample Bias (mV) -300 -200 -100 0 100 200 300 0.00 0.05 0.10 0.15 ZBC (nS) Sample Bias (mV)
a)
b)
FIGURE2.27: (a) Typical shape of an I-V curve obtained in LSMO
thin films. (b) Conductance curve (G(V)) obtained by numerical derivative of the I-V in image a).
The CITS image is composed of a regular array of pixels, in which an I(V) was ac- quired with the feedback turned off. At each pixel of the image, the system corrects the Z position of the tip to meet the setpoint conditions (800 mV, 200 pA). This correction motion is used to acquire a topography image at the same time that the spectroscopy is performed. This Z image is very useful for a fine correlation of the spectroscopic and real-space features. Figure2.28(a) shows roughly the same topography as in figure 2.26, but with less resolution due to the decrease of the number of pixels of the image2.
Figure 2.28(b) shows the ZBC map of the region. At each pixel, the numerical derivative of the I-V curve is calculated and then evaluated at V = 0V , i.e., G(0) is the ZBC. Homogeneous conduction along the area is obtained, with small jumps at the edge of the terrace. For a matter of clarity, figure2.28(c) shows the histogram of the ZBC map. These diagrams and the ZBC values will be the main tool used in
2Typically, STS experiments were done in a grid of 128 pixels x 128 pixels. At each pixel, 3-10 IV
curves were averaged. Each I-V curve was acquired in 500 ms, which means that one single STS map is acquired in 6-12 hours, depending on the conditions
0.000 0.02 0.04 0.06 0.08 20 40 60 80 100 120 140 Counts ZBC (nS)
a)
b)
c)
FIGURE 2.28: a) Topography image obtained during the STS mea-
surement. b) ZBC map of the region The map has been obtained by calculating the numerical derivative of the I-V curves acquired at each pixel of the image. Then, the G(0) value is plotted for each
pixel. c) Histogram of the ZBC of image b).
the discussion presented in chapter4in relation to the tunnel spectroscopic study of high resistances areas induced by RS effect.