kinetic processes taking place at the surface is shown in
Figure 2.3: Schematic display of the ideal growth mode. (a) Equilibrium growth and (b) non-quilibrium growth
Many factors might be responsible for the layer-plus-island growth, such as the lattice mismatch between the substrate and the deposited film and alternatively, the symmetry or orientation of the overlayers with respect to the substrate. Addi-tionally, if the microscopic kinetic processes taking place at the surface is taken into account, the substrate topology can be found to have much influence on the growth mode. The possible kinetic processes taking place at the surface is shown in Fig.
2.4.
Figure 2.4: The possible kinetic processes taking place at the surface.
2.2 Magnetic hysteresis loop
August 14, 2009
2.2. Magnetic hysteresis loop 14
[!ht]
Figure 2.5: An example of hysteresis loop. The magnetization at zero external field is the remenance. The external field at zero net magnetization is called the coercive field and coercivity.
Hysteresis loop is one of the most distinctive experimental facts of ferromag-netism. An example is shown in Fig. 2.5. Loops like this are obtained by applying to the sample a cyclic magnetic field H and by recording the ensuing change of the magnetization M along the field, where M is defined as the average magnetic mo-ment per unit volume. Hysteresis loops may be of many different shapes, thus it’s important to get some parameters to characterize the loop properties. Two quanti-ties of particular importance are the remanent magnetization or remanence, Mr, and the coercive field or coercivity, Hc. As indicated in Fig. 2.5, remanence represents the magnetization obtained by applying a magnetic field and then removing it, and coercivity is the field needed to bring the remanence to zero. Unlike remanence, the coercive field spans an very wide interval, from less than 1 A/m to more than 106 A/m, in different specimens. The shape of a hysteresis loop strongly depends on not only the intrinsic properties of the specimen but also the external factors such as the measurement method, the specimen geometry etc.. Therefore, we have to make sure that the loops are measured in the same process, specimen geometry etc before comparing their results. The variety of the hysteresis loop shape is the di-rect consequence of the variety of possible magnetic domain structure. The primary mechanisms of the hysteresis loop are magnetization rotation and wall motion. In general, wall motion can occur in low field, and magnetization rotation needs strong applied field to overcome the energy barrier.
2.3. Quantun well effect 15
Figure 2.6: Examples of hysteresis loops measured in (a) easy and (b) hard axis.
2.3 Quantun well effect
Quantum well effect was clearly discussed in systems of thin film [48–55]. The
”well” confines electron to layer with lower inner potential and quantizes the moen-tumand energy perpendicular to the layers. The coresponding underyling is spin dependent owing to the spin dependence of the inner potential in ferromagnets, Namely, these quantized states become spin polarizes. As the system dimensions reduce, there is an increased locationlizationand overlap of electronic wave func-tions, and consequently, an increase in electron correlation. Thus, low-diemesional systems offer a convenient platform for experimenting with many body effects. To exame the descret states from confined electrons in space by a potential well, an elementary example can be found in general quantun mechenics textbooks. Here comes a simple model.
Assume there is an electron confined in an 1-D box, the allowed wave vector k for stationary states , or quantum well states, are determined by the fitting in geometry, that standing waves exsist with
k = nπ d
where n is an interger quantum number and d is the width of box or the film
August 14, 2009
2.3. Quantun well effect 16 thickness. The energy levels are given by
E = ~2k2 2m = ~2
2m(nπ d )2
where m is the mass of a free electron, and the wave functions of the electron in different states are
ψ(z) ∝ sin(nπz d )
Although the basic phisics is similar, energy levels in atoms or molecules are generally not reffer to as quantum well state. When the quantum well effects elec-tronic and magnetic properties were discussed, The most important dorminant is the quantum well state at the Fermi-level. The density of states at the Fermi-level triggers electronic phase transitions, such as superconductivity,charge density waves, ferromagnetism, antiferomagnetism and electrical and thermal transport.
Chapter 3
Experimental Apparatus
3.1 Multi-functional UHV systems
The thickness of the deposited layer we made is about only few monolayer, that any nano-scale unexpected deposition, or, pollution will contribute unknown effect to our measurement, or kill the weak micro-phenomenon we want to observe. For example, Lieberman discovered the pollution will result in magnetic dead layer in 1969 [56,57], and Hope found that only 0.08 mono layer CO falls on Co/Cu(110) will also change the easy axis [58]. For the purpose to avoid the sample surface being polluted, an ultra high vacuum (< 10−10 torr) is basically recommend. The other way, we can also sketch the pollution rate with respect to the base pressure by the dynamics of gas.
We know the frequency of the gas atoms collide the sample surface is r = nva
4
where the root mean square velocity of a gas molecular of mass m under Kelvin degree T is
vrms2 = 3kBT m
17
3.1. Multi-functional UHV systems 18 where and the mean velocity of gas is
va = vrms
Combine these into idea gas formulation P = nkBT
We can get
r = P
√2πkBmT
Substituting, making this formula more readily useful by expressing P in torr and merging all convetion factors into a constant. The result is
r = 3.52 × 1022 P (torr)
pm(a.m.u)T (K)/cm2s
Using nitrogen of mass 28, room temperature is 300K and the nitrogen pressure is 1 × 10−6torr to demonstrate the frequency of gas collide on the sample surface, we obtain r = 3.84 × 1014 bombardments /cm2s. Assume that 100% nitrogen molecules will stick on the sample surface, after 0.1 seconds, well have about 2 ML1 nitrogen atoms on or sample surface of 0.5 cm2.
To reach UHV condition, the pumping system and process play important roles.
Usually we use a mechanical pump to fore-pumping down to the pressure about 10−2 to 10−3 torr, then a turbo pump is capably on to help further pumping to 10−7 torr while the main chamber is also baked by about 120 oC for 24 hours and reach about 10−8 to 10−10 torr after baking stopped and cool down to room temperature.
3.1. Multi-functional UHV systems 19 When the base pressure is near 10−7 torr, we on and off the ion pump to out gas, the ion pump will continuously on until it is clean enough. During the process with the base pressure is under 10−6 torr, TSP (titanium sublimation pump) is applied to help pumping and keep UHV getting better.
Figure 3.1: Illustation of the UHV system in lab. C207 in NTNU.
Figure 3.2: The translation of sample in the UHV system in C207 in NTNU.
August 14, 2009
3.2. Home-made Evaporation Gun 20
Figure 3.3: The real set up of the UHV system in lab. C207 in NTNU.
3.2 Home-made Evaporation Gun
With the same concept of EFM, a tungsten filament is heated by DC current about 1.5-2 A, an additional high voltage(1 KV) difference between filament and source is also applied, therefore hot electrons escape from tungsten filament to the source in center, the hot electron current can be read from the current meter con-nected to the source, with the quantity is about 10 mA when the source evaporates in our expeiriment. Since all the parameters are kept fixed, the source evaporant is stable. The working power is usually about 10 W (10 mA × 1000 V).
Figure 3.5 shows the structure of our gun, the gun body is made of thin Ta plate.
A shutter is additionaly applied close to e-gun to ”stop” the evaporance while we wanting to. Thus the hole deposition system takes two ports on our chamber.
3.3. LEED and I/V-LEED 21
Figure 3.4: Another view of the multi-functional UHV system
Figure 3.5: a)Home made e-gun with Ta shell, and b) a view without shell
3.3 LEED and I/V-LEED
Low Energy Electron Diffraction (LEED) is a technique to determine the surface structure of crystalline materials, which applied two fundamental physics, the de August 14, 2009
3.3. LEED and I/V-LEED 22 Broglie matter-wave and Bragg diffraction. For the development of LEED, Louis de Broglie introduced matter-wave in 1924, Clinton Davis and Lester Germer discover the electron in 1927, but LEED was popular used until the improvement of ultra high vacuum technique and detect method in the late 1960s.
There are two applications for a LEED system, to determine surface crystalline structure and to accurate the atomic position.
Figure 3.6: Schematic display of a LEED structure
The apparatus is also the same as LEED with the only difference that the sample is rotated by θ = 5o, thus the LEED (00) beams can be observed clearly. The I/V-LEED curve, can be obtained by continuously changing the incident electron beam energy and by recording the ensuing change of the (00) beam intensity. From theBragg condition and the de Brogile relation, we have
2dcosθ = nλ = nh
p = n h
p2m(Ek− V ) (3.1)
with d the vertical interlayer distance, Ek the kinetic energy of the incident electron beam, and V the potential cost for electrons to escape from the atoms.
Therefore Eq. 3.2 is got as
3.3. LEED and I/V-LEED 23
Ek = n2· h2
8m·d2cos2θ + V (3.2)
August 14, 2009
3.4. Scanning Tunneling Microscopy (STM) 24
3.4 Scanning Tunneling Microscopy (STM)
Scanning tunneling microscope (STM) is a helpful instument to view surface of conductors in atomic level, the idea to build STM is based on the concept of quantum tunneling. in 1981,Gerd Binning and Heinrich Hohrer developed STM then they earned the Nobel Prize in Physics in 1986.
It is very flexible to use STM, not only in ultra high vacuum, but also in air and in liquid or gas enviroments, and at temperatures ranging from near zero kelvin to about few hundred kelvin. In the real operation, STM probes the density of states with lateral resolution of 0.1nm (1˚A) and depth resolution of 0.01 nm (0.1˚A). For the sample is applied low voltages, the tunneling current will be the function of the local density of states (LDOS) at the Fermi level that we also interest in. Since STM is such a micro-probing machine, a clean surface,a sharp tip and a stable ambient are highly required.
The basic working theory of STM is as fallow: We start form the Schr¨odinger equation, the fundamental equation in quantum physics.
Inderivation, E > V is true for wave function inside the tip or inside the sample.
k = p2m(E − V )
~
(3.1) E<V is for inside a barrier as between tip and sample, the wave function is decaying.
k = p2m(V − E)
~ (3.2)
In scanning tunneling microscopy, a small bias voltage V is applied so that due to the electric field the tunneling of electrons results in a tunneling current I. The height of the barrier can roughly be approximated by the average work function of sample and
Φ = 1
2(sample+tip) (3.3)
tip. If the voltage (eV) is much smaller than the work function (), Eq. 00 can be simplified to
k '
√2m
(3.4)
3.4. Scanning Tunneling Microscopy (STM) 25 The tunneling current is from the electrons near the Fermi level, and is propor-tional to the probability of the decaying wave function.
I ∝
EF
X
En=EF−eV
| Ψn(0)2|e−2kd (3.5)
Ψ(d) = Ψ(0)e−k·d (3.6)
The probability of finding an electron behind the barrier of the width d is W (d) =| Ψ(d)2 |=| Ψ(0)2|e−2kd (3.7)
Figure 3.7: Schematic diagram of electron tunneling
It should be also mentioned that the number of empty states will affect the magnitude of tunneling current. See figure 3.8.
Figure 3.8: The number of empty states effests the tunneling current.
There are three ways that STM images:
August 14, 2009
3.4. Scanning Tunneling Microscopy (STM) 26
Figure 3.9: The loop of a working STM Constant current mode:
By using a feedback loop, the tip is vertically adjusted in such a way that the current always stays constant. As the current isproportional to the local density of states, the tip follows acontour of a constant density of states during scanning.
Recording the vertical position of the tip generates a kind of a topographicimage of the surface.
Figure 3.10: STM constant current mode.
Constant height mode:
3.4. Scanning Tunneling Microscopy (STM) 27 In this mode the vertical position of the tip is not changed, equivalent to a slow or disabled feedback. The current as a function of lateral position represents the surface image. This mode is only appropriate for atomically flat surfaces as otherwise a tip crash would be inevitable. One of its advantages is that it can be used at high scanning frequencies (up to 10 KHz). In comparison, the scanning frequency in the constant current mode is about 1 image per second or even per several minutes.
Figure 3.11: STM constant height mode.
Current imaging tunneling spectroscopy, CITS
Equipment structure in NTNU The tip is made from Pt and the shock proof is consists of two level of springs.
Figure 3.12: Schematic display of STM stage in NTNU
August 14, 2009
3.5. Magneto-Optical Kerr Effect (MOKE) 28
3.5 Magneto-Optical Kerr Effect (MOKE)
Magneto-optics effect is a phenomenon similar to optic activity. When a linear polarized electro-magnetic wave (EM wave, light) pass through a material which is with self-magnetism of induced magnetism, The propagation speed of right and left circular palorized light will be different, that a linear polarized EM wave which consists of right and left circular palorized EM wave will change its polarization angle, this is called Faraday effect, discovered by Faraday in 1845.
In 1877, Kerr found a result similar to Faraday’s. If a linear polarized light is incident into a ferromagnetic sample, since of the different reflection coefficients of right and left circular polarization components, the reflection beam will become el-liptical polarized. This phenomenon is called magneto-optical Kerr effect. The angle between the primary axis of the elliptical polarization and the linear polarization is called Kerr rotation, and the ellipticity of the elliptical polarization is called Kerr elliptical.
Let r+eiθ+ and r−eiθ− stand for the reflection coefficients of right and left circular polarization, respectively. The Kerr rotation and Kerr ellipticity can be illustrated as ϕk = −θ+−θ2 + and εk = ba = rr+−r−
++r− , respectively. Both of them are proven to be proportional to the magnetization of sample. Thus by measuring ϕk and εk with cyclic applied magnetic field, we can get thehysteresis loop. In general, there are three types of MOKEmeasurement. Each of them has different geometry of the magnetization and the light path, In the polar Kerr effect, the magnetization lies in the plane of incidenceand is perpendicular to the surface. In the longitudinal Kerr effect, the magnetization lies in the plane of incidence and is parallel to the surface. In the transverse geometry, the magnetization is perpendicular to the plane of incidence and on the surface.
The angle between the primary axis of the elliptical polarization and the linear polarization is called Kerr rotation, and the ellipticity of the elliptical polarization is called Kerr elliptical, as shown in Fig. 3.13.
In magnetic ultrathin films, the Kerr signal is so small that the noise may result
3.5. Magneto-Optical Kerr Effect (MOKE) 29
Figure 3.13: Schematic illustration of magneto optical Kerr effect. After reflected from the ferromagnetic sample, the linear polarized laser beam becomes elliptical polarized.
Figure 3.14: Different geometry for MOKE measurement.
August 14, 2009
3.5. Magneto-Optical Kerr Effect (MOKE) 30
Figure 3.15: Schematic illustration of AC MOKE.
in significant effect. Therefore, Practically in experiment here, a modulator is added on the laser sourcer and modulated signal can be taken by lock-in technique with a larger ratio of signal to noise. The schematic illustration is shown in Fig. 3.16.
Figure 3.16: Schematic display of a DC-MOKE loop in C207, NTNU
3.5. Magneto-Optical Kerr Effect (MOKE) 31
Figure 3.17: The switch of controlling the monopolar DC-power supply for inverse current
Figure 3.18: Schematic display of various magnetic field direction switch.
The production of magnetic field are consist of four eletrical magnets, with the max field of 1500 Oe each and 4300 Oe combinatively.
August 14, 2009
3.5. Magneto-Optical Kerr Effect (MOKE) 32
Figure 3.19: In-plane measurement with associated perpendicular field by the MOKE in C207, Department of physics, NTNU. The magnetic field intensity of in-plane file is stable; but due to the sample or the light spotposition, the inten-sity of perpendicular field in in-plane measurement has a range of±70%. The max perpendicular field in in-plane peasurement is about10%.
Chapter 4
Experiment and results
All the experiments are under UHV environment, usually less than 8.0 × 10−10torr.
Before preparing sample, we fill the cold trap with liquid nitrogen, that would help TSP working better. Sometimes, we isolate main chamber to get the base pressure reach 3.0 × 10−10 torr to preserve sample from pollution in a time.
4.1 Si (111)7 × 7 obseavation
The silicon(111) slab as a substrate we used is n-type high doped, which can easily be heated by low voltage due to its small resistance about 4 Ω. When the silicon substrate was sent into the UHV chamber, it must be heated at 600 oC for more than 6 hours to completely get rid of the oxidation.
In the earlier time, our silicon slab were from Unisoku company, with it’s size of 2×12 × 0.5mm3 and resistance about4.6 Ω at room temperature. Later, we use the silicon slab from prof. Kuo Chien-Cheng’s laboratory in National Sun Yat-Sen university, with its size of 2×9 × 0.5mm3 and resistance about12 Ω at room tem-perature. Although both these silicon slab are all high doped, but we cannot apply the same current to degas or flash, since the resistance is different, after overheating and breaking few silicon slabs, we can catch the temperature by observing the color.
33
4.1. Si (111)7 × 7 obseavation 34
Figure 4.1: The process of preparation Si(111)7 × 7 of (a)Si(111)from Unisoku com-pany and (b)from prof. Kuo Chien-Cheng’s laboratory in National Sun Yat-Sen university.
The last flash process is the very key to obtain large Si(111)7 × 7 terrace or narrow terrace. If the current finally reduced rapidly from 1000 oC, or said, fast cooling down, there will be narrow terrace on the Silicon surface; on the contrary, a larger terraces is possibly available as the current is reduced very slowly. The pressure is higher than 1.0 × 10−8 torr only during the early degassing process, the maximum pressure of other flash process is under 2.0 ×10−9 torr. No matter which process we choosed, there is always 7 × 7 structure on silicon(111) surface. The morphology analysis in main chamber is equipped with a STM(RT-STM, Unisoku).
4.1. Si (111)7 × 7 obseavation 35
Figure 4.2: The STM image first obtained in our laboratory.
Figure 4.3: A comparison with reference to calibrate [59]
In figure 4.2, we can see a terrace with the width about 30nm and its recon-struction of Si (111)7 × 7. There are few defects, this is becuase the cooling process August 14, 2009
4.1. Si (111)7 × 7 obseavation 36 is still not slow enough. In figure 4.3, we drag a line and have a lineprofile to see the high between two terraces, and compare with a reference, the high defference in these two detail illustraton is about 5 %. Then in figure 4.4 we can calibrate the size of our STM image with a theoretical model of Si (111)7 × 7.
Figure 4.4: A scale comparison for calibration. (a) Our STM image, (b) a Si (111)7×
7 model.
And we can see the faulted half and un-faulted half unit cell of Si (111)7 × 7 in larger scale. Another special structure of Si (111)7 × 7, the fualted and unfualted half unit cell can also be distinguished in our STM image showed in figure 4.5. Usu-ally, to see the ualted and unfualted half unit cell image by STM, a 100nm × 100nm scale (or larger, 200nm × 200nm) is better for us in our system.
Figure 4.5: (a)The triangles indicate the fualted half and un-faulted half unit cell and (b)the shcemic picture from Omicro company.
4.2. Highly ordered pyrolytic graphite (HOPG) 37
4.2 Highly ordered pyrolytic graphite (HOPG)
We use a commercial graphite to calibrate our STM image. Figure 4.6 shows two STM HOPG images we took with the model comparision at the right side, the discussion of varios STM images of HOPG was mentioned in the previous section in chapter 1. Figure 4.7 is the geometrical, or the long-width scale, comparison
We use a commercial graphite to calibrate our STM image. Figure 4.6 shows two STM HOPG images we took with the model comparision at the right side, the discussion of varios STM images of HOPG was mentioned in the previous section in chapter 1. Figure 4.7 is the geometrical, or the long-width scale, comparison