Bias-voltage-dependent measurement of apparent barrier height on low-work-function thin film

Scanning tunneling microscopy (STM) is a tool for imaging surfaces at the atomic level. One of the reasons for its ability to perform surface observation with atomic resolution is that the tunneling current (I) varies exponentially with the gap distance between the sample and the tip (z).¹ Thus, the tunneling current is governed by the potential barrier, which is defined by the potential height at each point in the tunneling gap. However, the spatial distribution of the potential height cannot actually be acquired. Instead, assuming a uniform potential, the effective barrier height affecting tunneling electrons can be calculated through I–z characteristics. This is called the apparent barrier height.² In other words, what is measured by STM is not the work function itself but the apparent barrier height.³ The apparent barrier height depends not only on the work functions of the tip and sample but also on the bias voltage applied between them. However, there have been few experimental studies directly treating the effect of the bias voltage on the apparent barrier height,^4,5 and the bias voltage dependence of the apparent barrier height is not yet well understood.

Here, we show experimental evidence that a linear relationship exists between the apparent barrier height and the bias voltage. We measured apparent barrier heights of a nitrogen-doped lanthanum hexaboride (N-doped LaB₆) film at different sample bias voltages by STM. As a result, we experimentally proved the existence of a linear relationship between the apparent barrier height and the bias voltage, whose slope was in good agreement with the theoretical prediction of 0.5 eV/V.⁶ Furthermore, we calculated the work function of the film to be 2.35 eV by fitting. This value is consistent with a previously reported value obtained by photoemission spectroscopy.⁷ Our results demonstrate that the work function obtained through apparent barrier height measurements is guaranteed to be highly reliable in spite of the simple one-dimensional model. We anticipate that the sensitivity of the barrier height to the sample work function can be utilized for elemental identification on surfaces with characteristic work functions.

The sample used in this paper was a N-doped LaB₆ film formed on 0.7-nm-thick oxidized Si. LaB₆ (Refs. 8–11) is an excellent material with a low work function of 2.4 eV (Ref. 12) and a high melting point of 2530 °C [Fig. 1(a)] but until recently there have been no reports of a LaB₆ thin film with a work function as low as that of the bulk single crystal. However, a LaB₆ thin film exhibiting a low work function has recently been developed by nitrogen doping.⁷ The work function of the N-doped LaB₆ film was measured to be 2.3 eV by photoemission spectroscopy, and this value is equivalent to that of a pristine LaB₆ (100) surface.¹² By taking advantage of the low work function, this film has already been utilized as an intermediate layer of organic field-effect transistors (OFETs) to improve their device performance.^13–16 

The N-doped LaB₆ film was fabricated by radio frequency (RF) sputtering deposition using a LaB₆ target with a nitrogen concentration of approximately 0.4 wt. %,⁷ and the film thickness was 20 nm. The deposition process was identical to the initial process used to fabricate top-contact/back-gate OFETs in previous studies.^13–16 In order to perform STM measurements, the fabricated sample was mounted on a back plate and clamped from above and below by electrodes to form an ohmic contact [Fig. 1(b)]. Prior to the STM measurements, the sample was cleaned by resistive heating at 500 °C under ultrahigh vacuum conditions. We have already confirmed that the annealing conditions were appropriate for reviving a local electronic structure consistent with that of pristine LaB₆.¹⁷ 

The STM measurements were performed at 77 K using a PtIr tip with an Omicron LT-STM system operated by RHK electronics. The STM topography was obtained in the constant-current mode. The apparent barrier height was derived by analyzing the I–z characteristics, which were acquired under a constant sample bias voltage by ramping the z-piezo voltage.

The apparent barrier height (Φ_A) is defined in terms of the logarithmic change rate of tunneling current: I, with respect to the tip–sample separation z at a certain bias voltage,² 

Figure 2 shows a schematic potential diagram for a tunnel barrier consisting of a PtIr tip. In this model, the apparent barrier for the tunneling electrons is a rectangular barrier above the Fermi level, and the height of the rectangular barrier is specified to be the average height of the trapezoidal barrier. Although the trapezoidal barrier seems more realistic than the rectangular barrier, the tunneling probabilities through them are almost identical within the WKB (Wentzel-Kramers-Brillouin) approximation. Thus, the apparent barrier height can be written in terms of the sample work function (Φ_sample) as

where V_s is the sample bias voltage (<0 V) and Φ_tip is the work function of PtIr tip, which is assumed to be 5.2 eV.^18–20 It should be noted that the apparent barrier height is governed by not only the sample work function but also the tip work function. Consequently, the sample work function is extracted. It should be noted that Eq. (2) clearly figures the linear relationship between the apparent barrier height and the sample bias voltage and the change rate should be 0.5 eV/V.⁵ 

In this model, however, we did not take into account the influence of the image potential. The reason is that previous studies suggested that the image potential does not contribute to the obtained work function in this procedure.^4,5,21–24

Figures 3(a) and 3(b) show typical STM images of the N-doped LaB₆ thin film at different scales, and Figs. 3(c) and 3(d) show the height profiles along the blue lines drawn in Figs. 3(a) and 3(b), respectively. The surface roughness was estimated to be ∼0.5 nm over the entire area, and the average grain size was approximately 3 nm.

In order to derive the apparent barrier heights, the I–z characteristics were measured. In order to avoid the artifact caused by the geometry effect,²⁵ the I–z spectroscopy was performed on a flat area around the center of grains. The reproducibility of the I–z characteristics was confirmed by repeated measurements within the imaged area. Figures 4(a) and 4(b) show typical I–z characteristics in linear and logarithmic scales, respectively. The blue dots indicates the experimental data, where the set point current was 0.5 nA at Vs = −3.5 V. From the fit with Eq. (1), the apparent barrier height at Vs = −3.5 V was obtained to be 1.92 eV.

Similarly, the I–z measurements were sequentially performed at different sample bias voltages, and the corresponding apparent barrier height was evaluated at each sample bias voltage.

Figure 4(c) displays the apparent barrier height plotted against the sample bias voltage. The apparent barrier height increases linearly with the sample bias voltage. The dashed line corresponds to a fit of Eq. (2) to our measurements. Consequently, the work function of the film can be determined to be Φsample = 2.35 eV by the fit.

This value is comparable to the work function of the film measured by photoemission spectroscopy.⁷ This suggests that the use of the bias dependence of the apparent barrier height is highly reliable for determining the work function.

Here, we discuss the validity of our model. We found that a linear relationship exists between the bias voltage and the apparent barrier height. In particular, the change rate is 0.5 eV/V as can be seen from Eq. (2). This value is introduced using the simple model shown in Fig. 2. We supposed that the Schottky effect would cause, i.e., the barrier height would be lowered by the image potential of the tip and sample. However, in reality, the Schottky effect was negligible or canceled by other factors. Consequently, Eq. (2) holds as a good approximation for our series of measurements. The validity of the approximation has already been evaluated by Olesen et al.²¹ They investigated the gap distance dependence of the apparent barrier height and showed that the apparent barrier height is constant rather than decreasing until the point contact is reached at a small tunneling gap distance. Moreover, since a low-work-function material such as LaB₆ allows a large tunneling gap, the influence of the Schottky effect should be rather small in our system. Therefore, our experimental results can be considered to remain within the validity range of the approximation, indicating that Eq. (2) phenomenologically reproduces the experimental results reasonably well.

Also, the derived work function was almost equal to that of the clean LaB₆ (100) surface of 2.3 eV.¹² This is reasonable for the following two reasons. First, the local density of states (LDOS) of an identical film has already been measured with the scanning tunneling spectroscopy, and the obtained LDOS had good agreement with that of the pristine LaB₆ (Ref. 17). Second, the crystallinity of the film has also been analyzed by x-ray diffraction measurements, and the data suggested that the dominant surface orientation was the (100) surface.⁷ Therefore, the fact that the derived work function was almost equal to that of the clean LaB₆ (100) surface is reasonable.

STM measurements were performed on a 20-nm-thick N-doped LaB₆ thin film. Although the sample was prepared by RF sputtering deposition, the grain size of the thin film was 3–5 nm with a surface roughness of less than 0.5 nm. In order to evaluate the apparent barrier height, I–z characteristics were measured at different bias voltages, and the bias voltage dependence of the apparent barrier height was examined. As a result, the linear relationship between the apparent barrier height and the sample bias voltage was experimentally proved, in which the slope was in good agreement with the theoretical prediction of 0.5 eV/V. Furthermore, the work function of the film was derived to be 2.35 eV by theoretical fitting. This value is consistent with that obtained by photoemission spectroscopy. Our results demonstrate that the work function obtained through apparent barrier height measurements is guaranteed to be highly reliable in spite of the simple one-dimensional model. We anticipate that the sensitivity of the barrier height to the sample work function can be utilized for elemental identification on surfaces with characteristic work functions.

The authors would like to thank the late Professor Emeritus T. Ohmi and Professor T. Goto of Tohoku University, Mr. K. Takahashi of Sumitomo Osaka Cement, Dr. W. Hayami and Dr. S. Otani of the National Institute for Materials Science, and Mr. K. Park, Ms. M. Hiroki, and Mr. Y. Komatsu for their useful discussion and support in this research. This work was partly supported by JSPS KAKENHI (Grant Nos. 17K05066, 19H00758, and 15K13969).