Diffusion of Paired Hydrogen on Si(001)

J.H.G.Owen, D.R.Bowler, K.Miki and G.A.D.Briggs

Abstract

An understanding diffusion of hydrogen is important in the gas-source growth of silicon and silicon-germanium alloys, because the surface hydrogen blocks diffusion and prevents germanium segregation. In this regime, the hydrogen is paired up on the surface dimers, and so must move in a concerted fashion. To study this, the monohydride (2x1) surface has been investigated at temperatures between 600-700 K using an elevated-temperature STM, and the diffusion of pairs of hydrogen atoms along and across the dimer rows has been observed.

Introduction

During low-temperature gas-source growth of silicon using disilane, the morphology is controlled by the surface hydrogen coverage, which blocks diffusion of the silicon (1), increasing the apparent diffusion barrier from 0.67 eV to 1.35 eV. The silicon islands that form during gas-source growth are much shorter than those grown by MBE(2). In previous work (3), we have measured the diffusion barrier for the motion of single hydrogen atoms. However, the population of single hydrogen atoms is very small at coverages above 0.1 ML (4).
Under growth conditions, the surface hydrogen coverage is mostly made up of the monohydride phase (5), in which a pair of hydrogen atoms saturates the dangling bonds of a single substrate. This configuration is energetically favourable because it maximises the number of silicon pi-orbitals, worth about 0.2 eV (6). In order to maintain this configuration, the two hydrogen atoms must diffuse in a concerted fashion.
In this work, the Si(001) surface at coverages near one monolayer (ML) have been investigated over the temperature range of 6-700 K, using an elevated-temperature STM. By taking sequential images of the same area, we have been able to track the motion of the hydrogen atoms directly, and measure the speed of their motion.

Experimental Methods

Our experiments were performed in a JEOL JSTM-4500XT variable temperature STM, with a sample stage specified for STM imaging up to 1400 K. Tips were prepared by electrochemical etching in 2M KOH. Silicon samples 1.5 mm wide were cleaved from an n-doped Si(001) wafer. They were prepared with an peroxide/sulphuric acid etch before being introduced into UHV and degassed at 7-800 K for several hours. They were then cleaned by repeated flashing to 1400 K for half a minute until the pressure stayed below 10-7 Pa during the flash. It was then cooled as fast as possible to 900 K to minimise surface reactions, and then very slowly to 600 K, below which essentially no further changes occur. Atomic hydrogen was generated by the thermal cracking of molecular hydrogen on a tungsten filament sited about 3 cm away from the sample. The amount of hydrogen required to saturate the surface was found empirically by gradually increasing the exposure until a suitable surface was obtained. The main contaminant in the hydrogen was water. Due to the problems of maintaining stable conditions at elevated temperatures, the samples were cleaned by flashing in-situin the STM stage. Silicon from the flashing process adhered to the tungsten filament, and some was re-emitted during the hydrogen exposure. Our surfaces were therefore contaminated with a small amount of silicon.

The measurement of temperature over the ranges of interest presents considerable challenges. A thermocouple gives an accurate measure of the point to which it is attached, but this is not necessarily representative of the surface in the region of interest. Infrared pyrometers operating at wavelengths at which silicon is not transparent are limited in the bottom of their temperature range, and they generally require larger sample area than we have available. The most accurate method is to use a disappearing filament pyrometer, which can work with very narrow samples. However this is limited by the temperature range at which visible light is given off to above 1000 K. We therefore developed a calibration curve based on a combination of these techniques and assuming a combination of conduction and radiation losses. This gave an estimated accuracy of ±30 K, which was undoubtedly the greatest source of uncertainty in our experiments.

Theoretical Methods

The modelling for this work has been done using a semi-empirical method known as tight-binding. This method is much faster than ab initio methods, but has significant systematic errors. For a calculation of the barrier for single-atom diffusion, the result was 1.96 eV, considerably higher than the experimental result (1.68 eV (3)). Thus while the absolute values for the barriers are too high, the differences between the barriers calculated for different mechanisms may be trusted, within an error of 0.1-0.2 eV. For further information about the modelling, please contact David Bowler.

Results and Discussion

The voltage contrast of clean vs. monohydride dimers has been discussed elsewhere (2) (5). The adsorbed hydrogen removes the pi-bond, and so the energy of the highest filled orbital shifts from 0.7 eV to about 2.5 eV below the Fermi level. This energy change corresponds to a contrast change of about 1 Angstrom, and so the monohydride dimers appear dark. A large scale picture of the hydrogen-covered surface, 40 nm square, is shown in Figure 1. In pictures where the surface is nearly covered, the background features are the dark, monohydride, dimers and the foreground features are the few, bright, clean dimers. In empty states, it is the pi*-antibonding orbital which is imaged, and this appears as a double-lobed blob. An example of a clean dimer is circled (A). Another feature of these pictures is the small white dot circled (B). We believe that these are SiH2 groups sitting on top of the dimer row. These are formed from silicon which has been deposited on the hydrogen filament during sample flashing, and re-evaporated during the hydrogen dose, as described above. The identity of a third, large feature, circled C, is unknown.

In all these pictures, the feature which can be traced from picture to picture is the clean dimer; however, the silicon is immobile; it is the hydrogen atoms on top of the dimers which are diffusing. The clean dimers may be thought of as vacancies in the hydrogen layer, and so the motion of the pairs of hydrogen atoms may be described by the diffusion of these vacancies, in the same way that bulk diffusion is described as the diffusion of vacancies. We must, however, remain cognizant of the fact that the speed of motion of a vacancy is not the same as the speed of the atoms around it.
An example of a moving hydrogen vacancy is seen in Figure 2, taken at 700 K. The time interval between these images is 10 seconds. During this time, two vacancies have moved closer together, which implies that two pairs of hydrogen atoms have moved apart.


A larger area image is shown in Figure 3, taken at 650 K. In many cases, the hydrogen is stationary when imaged, but has moved between pictures (A,B). In other instances, long streaky features, several dimers long, are seen (C). These streaks are similar to the smudges seen on the clean surface during silicon dimer diffusion (7) and atomic hydrogen diffusion (3), and so it is reasonable to assume that they are atoms moving around as the tip scans them. Over the course of a few frames, a clean dimer may become a streak, and then go back to being a clean dimer again, so we may be sure that these are the hydrogen atoms imaged while moving. In order for the two hydrogens to diffuse, they must move concertedly. The two hydrogen atoms are not bonded to each other, but they are connected via the silicon dimer they sit on, because two dimers each with one hydrogen is a higher-energy situation than one clean dimer and one monohydride dimer. The streaks that we see may be an indication of how this is happening.


A animated version of these images reveals the highly mobile nature of this surface.


The full movie is too large to fit in this page; it may be found here, but be warned, the file is 3.2 Mb!

These events are happening quite slowly; the hopping probability at 650 K is about 10-2 hops s-1 parallel to the dimer rows and 10-4 hops s-1 perpendicular to them. By comparison, at low coverages, single hydrogen atoms are moving at about 20 hops s -1 along the dimer rows.
To obtain an accurate activation barrier would require a much wider temperature range; in this case, the minimum temperature range at which motion of paired hydrogens is observed is 600 K, and above 700 K, the hydrogen begins to desorb, so this is not possible with our temperature errors. Also this is the rate of vacancy diffusion, not atom diffusion.

Two different mechanisms for this process have been modelled. The simultaneous motion of the hydrogen atoms has a barrier of 3.2 eV, much too high to be operating at this temperature (Fig. 4a). The far more likely mechanism for this motion is that first one of the two atoms hops onto the clean dimer (Fig. 4b).
By assuming that the rate-limiting step is the motion of the first hydrogen atom, which breaks the pi-bond, followed quickly by the second atom pairing up again, we can estimate an activation barrier from our experiments by using a prefactor of 1013 s-1, which we found was appropriate for single-atom diffusion (3). For the above hopping probabilities, estimated activation barriers (parallel and perpendicular to the dimer rows) are 1.95 eV and 2.3 eV respectively. The barrier for the motion of the first atom has been modelled and has been found to be 2.2 eV. This is an unstable state, and the next move is for the two to hop back together again. The vacancy will then have moved either zero or one dimer (Fig.4c). The motion of this second atom is much easier, the modelled barrier for this process is only 1.9 eV. Thus once one atom has moved, the other atom will follow very quickly, and it will appear that the two atoms have moved simultaneously, preserving the pairing. The values for the barriers found from the STM data, and from modelling agree with each other within experimental error, and the error of the calculation method, and are about 0.2 eV higher than the activation barrier for single-atom diffusion (1.68 eV) (3).

An alternative possibility, however, is for an atom to hop from a third dimer onto one of the unpaired dimers, which would leave two unpaired dimers separated by a paired dimer. Although this is a high-energy state, the two unpaired hydrogens are unable to pair up. In this situation, they are likely to oscillate back and forth until the right combinations of motions allows the two hydrogen atoms to pair up again. This oscillation will be seen as a streak. A streak resolving into a clean dimer is seen in Figure 3(C).

Conclusions

We have been able to image the motion of hydrogen on the saturated Si(001) surface at temperatures between 600 and 700 K. This motion is observed as the 'vacancy diffusion' of the few clean dimers that are present, and the rate of hopping along the dimer row is about four orders of magnitude slower than the motion of single hydrogen atoms at this temperature. The barrier for this process has been estimated at 1.9 eV from our STM data, and has been modelled as 2.2eV using DFT calculations. Motion across the dimer rows has occasionally been observed, and the barrier for this process has been estimated to be at least 2.3 eV. There seems to be no preference for the dimers to move together; the motion appears to be random.

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