Interview with Ken Jordan
Yet despite its ubiquity, certain aspects of the surface chemistry of silicon (Si) crystals remain a mystery. A particularly hot area of research is the mechanism of desorption (removal) of hydrogen from the surface of Si(100), a critical step in semicon- ductor manufacture. The measured kinetics of hydrogen desorption are not as expected, which sends many theorists back to the drawing board -- or the computer.
One of those theorists is Ken Jordan, professor of chemistry at the University of Pittsburgh. Jordan and his collaborators are using NCSA's SGI POWER CHALLENGEarray system, along with the Pittsburgh Supercomputing Center's (PSC's) CRAY C90 computer, to construct Si(100) surface chemistry models that may resolve the problem.
Model used by Ken Jordan and colleagues to study desorption, or removal,
of hydrogen from the surface of Si(100).
On again, off again
Si(100) is the most important surface in the semiconductor industry. The
numbers 1, 0, and 0 refer to the crystallographic orientation of the silicon
atoms with respect to the surface. In the most stable arrangement, the surface
atoms are arranged in pairs, or dimers, with each atom of each dimer pair also
bonded to two silicon atoms in the second layer. The process of slicing the
silicon crystal into thin, round wafers leaves unpaired electrons, resulting in
a chemically reactive surface. "You couldn't have such a reactive surface being
used in devices," said Jordan, "because oxygen and water vapor in the
atmosphere would react with the surface and change its properties in an
unpredictable manner."
Scientists usually deal with this problem by flooding the newly cut silicon surface with hydrogen gas to tie up the unpaired electrons. This gives rise to a stable surface. In order to make useful semiconductor devices, one must first etch the surface or deposit more silicon atoms. In either case it is necessary to displace those hydrogen atoms, usually by heating the surface. The displacement of hydrogen from the surface sounds fairly straightforward, but the mechanism for this process has turned out to be surprisingly controversial. One might think that each hydrogen-silicon bond would be broken directly, leaving hydrogen atoms free to form H2 (hydrogen gas). But that requires a lot more energy than is actually used; it is clearly not the correct mechanism. A more likely process involves an intermediate species with two adjacent hydrogen atoms partially bonded to each other and to one silicon atom. To test this theory, Jordan created a computer cluster model -- a minisilicon surface consisting of nine silicon atoms, the two surface hydrogen atoms, and 12 additional hydrogen atoms to properly terminate the subsurface silicon atoms.
Jordan used a variant of the widely used density functional theory, or DFT, to describe the silicon-hydrogen interactions. (DFT calculates the total energy of the system from the electron density and is less computationally demanding than methods that are based on wavefunctions.) While density functional methods are not in general known for their accuracy in describing hydrogen bonding, Jordan used PSC's CRAY C90 system to compare a variety of density functional methods to a highly accurate many-body method. He found one method, or functional as they are called, to be particularly well suited to describing the interactions between the silicon surface and hydrogen bonds: Becke3-LYP.
Applying the Becke3-LYP functional to the Si9H14 clusters, Jordan "found that the activation energy for going through the intermediate is appreciably higher than experiment, although other researchers using other models and theoretical methods get a lower energy for this process."
To counter criticism that the Si9H14 clusters were too small to reflect the behavior of a silicon surface, Jordan and coworkers have recently adopted more realistic models containing up to 21 silicon atoms. "So far," Jordan said, "the energy barrier for H2 desorption does decrease with adoption of larger cluster models, but not by enough to be consistent with experiment."
Not surprisingly the 21-atom model necessitated an increase in computing power. "We had really gone about as far as we could on the small clusters on our workstations," said Jordan. "Having access to the POWER CHALLENGE systems at NCSA has made feasible extending the calculations to these larger clusters." Jordan estimates that he has used 2,000 service units on NCSA's POWER CHALLENGE over the past year. Most of the cluster model calculations were carried out using the Gaussian 94 program. "The Gaussian 94 DFT code is well suited for the POWER CHALLENGE," said Jordan. "We get good speedup on up to six processors."
Recently Jordan's group and two others have proposed that the mechanism for hydrogen removal from the surface may involve defects. Surface defects come in a variety of types. Jordan and coworkers have focused their attention on defects involving unpaired surface silicon atoms. "One might expect the hydrogen atoms to move around the surface until 'captured' by the defects," said Jordan. "We have established the existence of a lower energy path that works through a bond-shifting mechanism; the net result is that it looks like the defect has moved."
Models for two states of desorption (reading from left to right):
Final transition state from H2 desorption from a defect site;
dihydride intermediate along the defect mechanism reactyion path.
Other approaches
Jordan is not alone in his search for better methods to uncover the mechanism
for hydrogen removal. Two other research groups, using NCSA's resources, are
searching for the elusive mechanism.
Richard Martin, UIUC physics professor and coworkers, have recently used NCSA's POWER CHALLENGE and TMC's CM-5 systems to model giant fullerenes containing as many as 3,000 carbon atoms and a DNA molecule segment, using density functional methods. Martin is also developing "Order N" or linear scaling methods in which the computational time increases linearly with the size of the system. Martin notes that present methods scale as a power, usually a cube, of the size of the system. He is also evaluating a number of density functional methods for their efficacy in modeling silicon surface defects and the interactions between hydrogen and silicon surfaces. The latter project, Martin stressed, is still in the development stage. Workstations were used to study small cluster models before scaling up to NCSA's POWER CHALLENGE, which is Martin's machine of choice.
Jeffrey Grossman, UIUC graduate research assistant at NCSA, and Lubos Mitas, UIUC postdoctoral research associate at NCSA, while not studying the interaction between hydrogen and silicon clusters per se, are using a Quantum Monte Carlo (QMC) method to study large silicon and carbon structures. QMC methods, initiated by (among others) David Ceperley, UIUC physics professor and NCSA research scientist/leader of the Quantum Physics Group, employ a stochastic approach to solve the many-body Schrodinger equation with a high degree of accuracy. It is a more general approach that, while computationally expensive, can be applied to a wide range of systems. Grossman and Mitas have shown that a QMC method can be applied equally well to systems ranging from one atom to clusters of 20 atoms, even to solids -- essentially an infinite system. "Usually," Mitas said, "very different methods are required to study such a range of systems." Grossman and Mitas used PSC's CRAY C90 system and NCSA's SGI POWER CHALLENGE and HP/CONVEX Exemplar systems. Martin notes that QMC methods might be useful to calibrate the accuracy of less computationally demanding but more specialized density functional approaches.
Matters of practicality
Studying the removal of hydrogen from silicon surfaces has great practical
importance. "Suppose that H2 desorption really proceeds through defects as we
proposed," said Jordan. "Then if one could remove or 'block' those defects, H2
removal would have to go through a higher energy process, and the surface would
be more stable at elevated temperatures. This could be important in some
applications."
There is another, more fundamental reason for pursuing the elusive H2 desorption mechanism. "It serves as a testing ground for various theoretical methods," said Jordan. "Before extending our studies to more complicated surface processes, we want to be sure that the methods we are using are 'up to the task'."
Jordan's collaborators on silicon surfaces are Petr Nachtigall, Czech Academy of Sciences in Prague, Czech Republic; Carlos Sosa, Cray Research Inc.; and Hannes Jonsson and Arthur Smith, University of Washington. Martin's colleagues on developing DFT methods are Pablo Ordejon, former postdoctoral research associate now at University of Orviedo, Spain, and Satoshi Itoh, former UIUC visitor now at Hitachi Central Research Lab, Tokyo.
Return to the Table of Contents.