Electric field effects in scanning tunneling microscope imaging

Abstract

We present a high-voltage extension of the Tersoff– Hamann theory of scanning tunneling microscope (STM) images, which includes the effect of the electric field between the tip and the sample. The theoretical model is based on first-principles electronic structure calculations and has no adjustable parameters. We use the method to calculate theoretical STM images of the monohydrate Si(100)−H(2×1) surface with missing hydrogen defects at −2 V and find an enhanced corrugation due to the electric field, in good agreement with experimental images. First-principles electronic structure calculations have become an important tool in interpreting scanning tunneling microscope (STM) experiments. Calculations of theoretical STM images are often based on the theory by Tersoff and Hamann [1], which states that the the STM current is proportional to the local density of states (LDOS) of the sample. In this theory it is assumed that the potential is flat between the tip and the sample and the vacuum level given by the sample workfunction. However, for relatively high biases (> 2 V), which are often used in STM experiments on semiconductor surfaces, the electric field strength in the tunnel region can be relatively high and must be included in the theoretical model [2]. In this paper we extend the Tersoff–Hamann formalism to include the electric field in the tunnel region, and apply the theory to calculate the corrugation of a single missing hydrogen defect on the monohydride Si(100)−H(2×1) surface. We find that the corrugation is strongly increased by the electric field, mainly due to polarization effects and partly due to changes in the tunnel barrier. The organization of the paper as follows. In Sect. 1 we present the basic theory for calculating field-dependent STM images, and in Sect. 2 we show how the electric field effect can be included in the first-principles calculation. In Sect. 3 we apply the formalism to calculate the corrugation of a missing hydrogen defect on the monohydrate Si(100)−H(2×1) surface and in Sect. 4 we conclude. 1 Theory In this section we present the basic theory for calculating field-dependent STM images. The derivation will follow Chen’s [3] closely. Figure 1 shows the tunnel junction between the tip and sample. Using the modified Bardeen approach [3], the tunnel current is given by