10. ANEXOS
10.2. MEDICIONES DE RUIDO DE SALA LECHE
Crashed Tip
may have an oxide layer covering it or it may have multiple protrusions.
Hockett and Creager [98] report current spikes due to untreated oxide layers.
When etching tungsten electrochemically the build-up of an oxide layer (W03 ) during the etching process cannot be avoided. The oxide layer has a thickness of about 5 to 10 nm, which is thicker than the native oxide layer on tungsten. The layer can be removed by high vacuum annealing at high temperatures [51] or by chemical dissolution with hydrofiuoric acid (HF) [98]. Since vacuum equipment was not available and HF is a very hazardous substance, the oxide layer was not removed. Before tunneling with atomic resolution is possible, the tip still has to be treated, which can be done in situ by gentle collision with the sample or by high-field treatment. Both techniques will not completely remove the oxide layer and as a consequence tungsten tips formed in this way should not be used for the recording of characteristic I-V curves, since the oxide layer will make the curve look like that of a semiconductor.
Tips that are too blunt or which have been crashed, such as the one shown in figure 3.12, are likely to have more than one minitip close to the sample surface. When the tip moves horizontally, during a scan or after an induced vibration, tunneling can shift from one minitip to another, depending on the sample roughness. The speed of current change will often lie outside of the con troller bandwidth. In the best case the observed tunneling current will appear noisy, in the worst case highly erratic. A crashed tip has to be replaced. Review of Other Etching Techniques
The etching technique used in this project evolved from the immersion method. Here the bottom part of the wire is completely immersed in the electrolyte. This immersion technique is still frequently used [1 1 , 67, 98, 146] .
Fotino [70] has reviewed all common tip-sharpening techniques extensively.
He dismisses mechanical tip preparation as being poorly reproducible and pro ducing asymmetric, broad tips with possibly more than one protrusion at the apex. Fotino considers electrochemical etching to be a superior technique and discusses the immersion method at great length. Due to bubble dynamics the tips produced by the standard immersion technique all have sharp cones on the /.Lm scale but are relatively blunt at higher resolutions with a typical radius of curvature of 100 nm. To produce sharper tips, Fotino suggests that the wire be etched upside down so that instead of blunting the tip, the bubble dynamics help in sharpening the tip.
3.2. STM TIP
53 Apart from upside-down etching the standard immersion technique can be improved in two other ways. The etching region can be limited and the etching process can be rapidly terminated. Several methods to limit the etching region have been described in the review article of Melmed [132] . More recently, Hackeret al. [82] protected the immersed part of the wire from etching with wax, while
Bourque and Leblanc [33] used shrink-tube for the same purpose. The loop technique used here naturally limits the region over which etching occurs and is convenient and reasonably reliable. A sophisticated set-up using the loop technique has recently been described by K lein and Schwitzgebel [1 16] .
If the etching region is limited, the bottom part of the wire drops off. The etching of this part tops naturally. The top part i still part of the etching circuit and is etched further until the etching current is shut off. This can be done rapidly by means of an electronic circuit. Electronic etching-current shut-off has been mentioned by agahara [140] , Anwei et al. [1 1] , Fainchtein and Zarriello [67] , Oliva et al. [146] , Dickmann et al. [56] and Ibe et al. [105] . Just before rupture of the thread of etched wire, the etching current starts to decrease rapidly. This sudden decline is used to trigger an electronic circuit to shut off the etching current. This prevents further etching of the wire and a sharp tip remains.
The loop technique with an electronic shut-off circuit combines the advantage of short shanks production for the top part of the wire and rapid interruption of the etching current just after the bottom part drops off. An automated shut off circuit similar to the one reported by Anwei et al. [1 1] has recently been devised and built by an MSc student in this laboratory, Mark Hunter. The tips he has produced are indeed superior in shank length, symmetry and radius of curvature. Detailed results will be reported elsewhere [104] . A combination of loop technique and electronic shut-off has not been published previously.
3 . 3 Vibration Isolation
3 . 3 . 1 Necessity of Vibration Isolation
Unwanted tip-sample displacement can occur when the probe head is mechani cally excited by external sources of vibration, such as building movements and acoustical noise. Normal floor movements in buildings can be up to several mi crometers in size. While scanning, the microscope cannot distinguish between the movements of the floor and a change in the sample topography. Despite the ground movement the tip-sample distance should ideally not change by more than about 1 pm [156] . The influence of such external movement can be mini mized through the use of vibrational damping.
An external mechanical perturbation can be temporary in form of a shock, or continuous as an ongoing vibration. The damping system has to minimize both types of influence. Generally speaking, vibration and shock can be pre vented from reaching the probe head and the sample by shielding the source of the perturbation, isolating the probe head or desensitizing the probe head to vibrations [91].
Containing external sources of vibration is not always practical12 , especially since many vibrations are caused by wind-induced swaying of the building, peo ple walking or using elevators in the building or the operation of rotating ma chines, such as drills and centrifuges. Operating the microscope after hours will help to reduce the amplitude of unwanted vibrations, but cannot be the only means of vibrational damping.
The usual way to protect the probe head from vibrations is to isolate it, by impeding the transmission of vibrations to it, as well as minimizing the sensitivity of the probe head to vibrations. Both measures combine to form the vibrational damping system, which can be modeled as a mechanical system resonating at high frequencies isolated by a mechanical low-pass filter.
In contrast to the simple low-pass filter, commonly used in electronics, nei ther compliance of materials nor mass can be avoided with a mechanical low-pass filter. This means that the vibrational damping will always be a second-order system, which may resonate, if it is underdamped. A certain amount of damping in the system ensures that large resonance amplitudes are avoided. To maximize isolation more than one stage of vibration isolation is usually used.
3 .3 . 2 Simple Spring-Mass System
A simple spring-mass system can be used as a model when designing a vi brational damping system. For the time being a spring-mass system without damping is considered. The natural frequency (wo) of this system is
Wo =
If,
(3.10)where k is the spring constant and m the suspended mass. Physically small and rigid construction elements will have a high spring constant k and when paired with low mass, give rise to a high natural frequency. Choosing large masses and soft springs on the other hand will give a rather low natural frequency.
1 2 An extraordinary elaborate vibration isolation system involving an especially built acous
3.3. VIBRATION ISOLATION
55The probe head and the sample holder are designed to be small and rigid so as to give a high mechanical resonance frequency. If this approach is taken probe head resonance frequencies of several kilohertz can be achieved. In our apparatus the probe head and sample holder are isolated by two stages of vibrational damping; a pneumatically damped table and a stack of metal plates damped with rubber o-rings (viton) . The resonance frequency of the isolator has to be set to a low value in comparison to the eigen-frequencies of the probe head and sample holder. Since most external vibrations are in the 1 to 100 Hz frequency band, the resonance of the vibrational damping should be at the lower end of this range [156] .
The vibration isolation used in this system is primarily designed to isolate the probe head from vertical movements. A vertically mounted spring-mass system can be viewed in force balance as mg = kuo, where Uo is the static spring extension. In equation (3. 10) the ratio k/m can now be replaced to yield
Wo =
(3. 1 1 )which gives the natural frequency in terms of the static spring extension. As a consequence of equation (3. 1 1 ) , a spring with a static extension of 25 cm is needed to achieve a low natural frequency of 1 Hz [168] . It is not uncommon to place the probe head of an SPM on a heavy plate suspended from bungi ropes of one or more meters lengths [145J . The bungi ropes provide a very low eigenfrequency but are not well damped.
To describe the vibrational damping system more accurately the damping force must be taken into consideration. Often a damping force can be assumed that is proportional to the velocity of the oscillation. The damping force is then expressed as
F = -(3u (3. 12)
with a damping constant (3.
The ground movement is driving the damped spring-mass system. The move ment (ug) is assumed to be cyclic in the following derivations with
In this equation, ug is the amplitude of the ground movement, j is the imaginary unit, w is the assumed frequency of ground movement and t is time. Accounting for the relative movement between the ground (ug) and the moving mass (um ) , the force on the mass is
where kgm and (3gm describe the ground-mass system. This results in the equa tion of motion given by [31, 88, 143J
(3. 13) If a damped spring-mass system is excited into vibration then it will oscillate at its damped natural frequency Wd , which is lower than the natural frequency of the undamped system [31 , 120] . The sinusoidal motion decays exponentially
with a decay constant
£5,
which is related to the mass m and the damping constant (3 by£5 = � .
2
m(3.14)
Oscillatory motion only occurs if the damping is less than a critical damping1 3 ,
i.e.
(3 < 2&.
This can also be expressed as