STM operation

Chapter 2: Instrumentation and Methodology

2.1 Scanning tunneling microscopy (STM) system

2.1.2 STM operation

materials, we can control their deformation and, therefore, the tip that is connected to these materials. Through the bias applied to the piezoelectric material, we can also obtain information about the location of the tip and control the tip to scan over areas of the sample surface on demand. With the introduction of the feedback loop, we can even maintain the distance between the tip and the sample during the scan. Combining the information acquired from the tip-sample distance as a function of the tip location in the XY-plane, we can obtain a topologic image of the sample surface, as illustrated in Figure 2.4 (b).

Figure 2.4: (a) Different distortion modes of piezoelectric materials. When a voltage is applied to both sides of the piezoelectric, it could deform into shear motion, contraction/expansion, and bend. We can use different types of deformations to design the proper piezo drive for the STM tube scanner and the sample stage. (b) Illustration of a realistic STM configuration. Here a piezo drive is used to move the tip in x, y, z directions. When a bias voltage is applied across the tip and sample, a tunneling current is induced. The controller provides the feedback and selects the desirable STM operational mode for measurements.

Topography scan

For a quick topography scan, the bias voltage between the tip and sample is fixed. The tip is moved along the surface of the sample to obtain tunneling current or height information.

Since the data is continuously taken, we can get a high-resolution image within a short time.

We can also let tip stop by at each pixel to take spectroscopy and get the density of the states to form the topography map later. Depending on the mode we use, we can derive different information. (Figure 2.5)

Figure 2.5: Topology scan and its different modes of operation. (a) For the topography scan, we use a piezoelectric drive to move the tip and scan the sample surface line by line. (b) left and middle: Different modes for topology scan. Constant height mode turns off the feedback for z position and keeps the bias voltage constant; the resulting tunneling current, therefore, correlates with the surface topology of the sample. Constant current mode uses a feedback loop to adjust the z position and to keep the current constant. The topography profile can be recorded during the scan, and thus we obtain the topographic images directly. (b) right: If we add a small AC bias and use lock-in techniques to extract the AC response, we can measure the DOS at the same time with a topology scan.

Constant height mode: In this case, as shown in figure 2.5 (b) left, the feedback for the z- direction is turned off, and the STM tip scans the surface of the sample at a constant tip height and a constant bias voltage and then measures the current. If the surface is relatively flat, the current would be positively correlated to the sample topography. Nevertheless, the topography can only be determined qualitatively not quantitatively, because when the

sample-tip distance changes, the transmission coefficient |𝑀𝑀|² changes too. Also, this is a very dangerous mode because it is impossible to ensure atomic flatness over the scan areas of the sample, and so the fast constant-height scan could risk crashing the tip onto possible protrusion from the sample surface. A more practical way is to reduce the speed of feedback so that the tip only responds to large scale features. Then the large scale features can be seen on the topography map while small scale features can be seen on the current map.

Constant current mode: In this case, as shown in figure 2.5 (b) middle, the feedback of the z-direction is used to maintain the current constant during the scan on the surface of the sample. Since we know the z height along with the scan, the z height is usually proportional to the topography (strictly speaking DOS). For this mode, the feedback needs to be fast enough to maintain the constant current. However, it should not be too fast; otherwise, it could falsely respond to the noise in the current. In the spectroscopy scan, the tip would stop at each pixel and hold onto the same tunneling junction resistance as initialization. This setup is virtually a constant current mode at a much slower pace, and therefore, we can also obtain topographic images while doing spectroscopy scan. The image we derive from this constant current mode is not a simple topography of the surface. Rather, it is a topography of constant DOS. Therefore, by applying different biases, we can explore the DOS map at different energy of the band. Since different orbitals or spin states have different energy levels, we may even explore the DOS map for different bonding or spin states of the sample.

Spectroscopy scan (Scanning Tunneling Spectroscopy or STS)

In this mode, we want to acquire the current-voltage characteristics (I-vs.-V curve) for each point so that we can calculate the tunneling conductance (dI/dV) to obtain the tunneling conductance map (and thus the DOS map) for different bias voltages. For the spectroscopy scan, the tip stops at each pixel (Figure 2.6), where the tip holds its height with a set R_junction. Then the bias voltage is swept through a range we set, and the tunneling current is measured and recorded. In this way, we can obtain the I-vs.-V curve at each pixel. Since we hold the same R_junction value at each point as an initial condition, we can also derive height information and thus the topography from the spectroscopy scan. With an I-vs.-V plot for

each point, we can calculate the corresponding (dI/dV)-vs.-V for each pixel and obtain the conductance map at different bias voltages. To reduce the noise and errors, a typical approach is to measure a backward sweep and then average it with the forward sweep to remove systematic errors. The sweeps are taken several times at the same pixel point to remove random noises.

Spectroscopy scan with a lock-in amplifier

The calculation of dI/dV from I-vs.-V involves differentiation, which could introduce lots of noise for the raw data. Therefore, measuring dI/dV directly would be a better approach.

To measure dI/dV directly, we add a small sinusoidal bias voltage ∆V cos (ωt) onto the DC bias voltage and measure the response sinusoidal current ∆I cos (ωt) through a lock-in amplifier. We know that

∆I(V_DC = V_bias, I = I_set) = ∆I

∆V∆𝑒𝑒(V_DC = V_bias, I = I_set). (2.7)

Because ∆I≪Iset and ∆V = constant≪Vbias, ^∆I

∆V≈ _{𝑑𝑑𝑒𝑒}^{𝑑𝑑𝑑𝑑} (VDC = Vbias, I = Iset). We get

∆I∝ 𝑑𝑑𝑑𝑑

𝑑𝑑𝑒𝑒(VDC = V_bias, I = I_set). (2.8)

Thus, through a lock-in amplifier, we can get ∆I (V) which is proportional to ^{𝑑𝑑𝑑𝑑}

𝑑𝑑𝑒𝑒(𝑒𝑒). To make the lock-in method work, ω⁻¹ needs to be much less than the feedback response time, so that the tunneling junction resistance is maintained based on the DC bias and current. The lock-in takes time to recognize a sinusoidal output. When the controller sweeps through the range of bias, it needs to wait at each value of bias for a much longer time. (figure 2.6 (b) right)

Figure 2.6: Schematic illustration of the spectroscopy scan. (a) Measurement is taken on each pixel point of the grid over the area we would like to scan. Whenever the tip moves to the new pixel point, the tip height is initialized to the set tunneling junction resistance and hold its position before sweeping the voltage. (b) Two modes that we can use to obtain DOS-vs.-V spectrum. One is to measure I-vs.-V and then calculate dI/dV-vs.-V from it. The other is to use the lock-in technique to derive signal LIX, which is proportional to (dI/dV) so that dI/dV-vs.-V can be measured directly.

Although, in theory, the lock-in technique is a better way to obtain the conductance map data, this method could take up to several days to complete a scan so that the average location of the tip relative to the sample may have drifted significantly. Additionally, for low- temperature measurements, time is more limited because of a finite evaporation rate of liquid helium. The presence of AC noises from electrical cables could also introduce excess noises to the lock-in response and make the measured response unstable. Therefore, for most experiments, we only measured I-vs.-V for STS. On the other hand, our controller provides a built-in lock-in function module that can be used for direct (dI/dV)-vs.-V measurements so that we can choose the lock-in option when needed.