Magnetic Imaging on the Nanometer Scale
Figure 2: Working principles: (a) The attoMFM uses an optical fiber in close vicinity (distance ~30 µm) to the magnetic cantilever to detect its deflection caused by the magnetic stray field of the specimen. (b) The attoSHPM tip features an STM tip for tip-sample distance control and a small Hall cross (400 nm or 250 nm in size). When experiencing the local magnetic field at each point during the scan, the conventional Hall effect causes a voltage drop across the sensor, which is directly proportional to the magnetic field value.
and superconductors, and it is typically considered preferential because of its ease and speed. In contrast, constant distance mode follows quite exactly the surface topography at a certain separation and is sometimes the only possible way to measure magnetic information of very rough samples. Te drawback of constant distance mode is the image acquisition time, which is considerably longer compared to constant height mode.
Scanning Hall Probe Microscopy In scanning Hall probe microscopy, a small, typically
micron-sized, Hall sensor is scanned in close proximity to the sample surface (see Figure 2b). Mapping the Hall voltage VH as a function of location directly yields the spatial distribution of the local magnetic field. Similar to MFM, SHPM is most frequently conducted in constant height mode, where the sample plane is typically detected by tunneling current measurements (referred to as STM-tracking SHPM) [4,13]. Today’s state-of-the-art Hall sensors are fabricated from
silicon or modulation-doped heterostructures using standard CMOS techniques, molecular beam epitaxy, or e-beam lithography. For ultra-high spatial resolution applications, the Hall bar is typically refined by focused-ion beam milling, yielding areal dimensions well below 500 × 500 nm². Te figures of merit of Hall sensors are sensitivity and
noise. Te sensitivity SHall of a Hall sensor biased with a current I is given by [14]:
SHall = IB
VH en2D 1
, (1)
experienced by the sensor, e = 1.6*1019 [As], and n2D is the carrier density in the case of a modulation-doped Hall sensor with a two-dimensional electron gas layer, referred to as 2DEG. Typical values for the sensitivity are 1000–2000 V/AT in a large temperature range [15]. Together with the noise of the sensor, the sensitivity determines the minimal detectable field or field detection limit (DL) of the sensor. Tere are three sources of noise present in a Hall bar, which are Johnson, 1/f, and generation- recombination noise yielding a magnetic DL of the form
where VH is the measured Hall voltage, B is the magnetic field DL = 36
4kBTR∆f ISHall
+
Rα∆f NSHall
+
β( f )∆f NSHall
(2)
where α and β are (frequency-dependent) proportionality factors, ∆f is the measurement bandwidth, I the Hall current, R the output resistance, kB the Boltzmann constant, T the sensor temperature, and N the number of charge carriers in the active area of the Hall sensor. From equation (2) it is immediately apparent that larger Hall sensors provide lower 1/f noise because of the larger number of charge carriers present. Tis typically leads to a lower DL for larger sensors, but this trend disappears at temperatures below 100 K where heterostructure sensors are typically operated and are dominated by the thermal noise regime. For this temperature range, the magnetic field detection limit is given by
DL =
4kBTR∆f ISHall
∝
n2D µ
. (3) Modern 2DEG Hall sensors such as provided for attocube
systems’ attoSHPM typically provide carrier mobilities larger than 160,000 cm²/Vs at densities of 4 × 1011 cm-2, yielding detection limits of 15 nT/Hz1/2 at 4 K and 40 µA excitation current. In real life, however, the practical attainable field detection limit has so far been limited to the µT range in the few Hertz bandwidth for most experiments [16]. Tis is due to current fluctuations in the current source, which are directly translated into voltage fluctuations because of the intrinsic voltage offsets in the Hall bar.
Examples and Applications Vortices in superconductors. An example of the quantum
objects that are intensely studied with these methods are vortices in superconductors, motivated in large part by the desire to pin down the nature of high-Tc superconductivity, which was discovered in 1986 [17]. Te superconducting state forms below limiting values of temperature (Tc), magnetic field (Hc), and electrical current (jc). Superconducting materials possess two distinct outstanding properties: electrical currents (up to jc) are carried with virtually no electrical resistance, and external magnetic fields are completely expelled from the material’s interior (ideal diamagnetism). Most superconduc- tors show an intermediate state above the lower critical magnetic field Hc1, at which magnetic flux is allowed to enter the specimen in the form of circular supercurrents, each contain- ing exactly one magnetic flux quantum (Φ0 = 2.07*10-15 Tm2).
www.microscopy-today.com • 2011 November
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74 |
Page 75 |
Page 76