Journal of Crystal Growth 401 (2014) 511–513
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Journal of Crystal Growth
journal homepage: www.elsevier.com/locate/jcrysgro
4H-SiC surface structure transitions during crystal growth following
bunching in a fast sublimation process
Filip Krzyżewski n
Institute of Physics Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
art ic l e i nf o
a b s t r a c t
Available online 16 November 2013
Kinetic Monte Carlo wurtzite structure crystals of 4H-SiC simulations were performed. The first stage of
system evolution was the sublimation process which ended when bunched structure appeared. Then the
crystal growth started. Vanishing of bunched structure and its transition to the double stepped one was
observed on setting the proper parameters during growth up. For high incoming fluxes during growth 2D
nucleation happened at wide terraces and surface debunching was blocked. Application of low resulting
flux of incoming and out-coming particles have also blocked the surface smoothing process.
& 2013 Elsevier B.V. All rights reserved.
Keywords:
A1. Crystal growth
A1. Kinetic Monte Carlo
A1. Sublimation
A1. Surface structure
Experimental processes of crystal growth are always preceded
by etching or chemical polishing procedures [1–6]. Such a surface
preparation is carried out due to the removal of impurities and
cleaning the surface in order to obtain the highest possible
substrate quality. After such a process experimental parameters
change and crystal growth starts. Here the results of kinetic Monte
Carlo simulations reproducing two successive processes of etching
followed by crystal growth are presented.
Previous simulations performed for wurtzite structure crystals
[7–10] contained modeling of growth or sublimation processes
only. It was shown that step doubling or step meandering occurs
during growth [7,8], however during crystal etching step bunching
was observed [9,10]. It is also known [8,11,12] that during crystal
growth step bunching occurs when electromigration, Ehrlich–
Schwoebel effect [13] or defects are present in the system.
Otherwise step movement equalizes step widths and smoothing
of bunched surface phenomenon occurs. On the other hand,
during annealing of crystal surface step velocity has opposite sign
hence step movement which leads to the bunching process. It is
interesting how vicinal crystal surface evolves when growth
process takes place after sublimation. Especially worth investigation is the case when after desorption stage bunched structure is
present at the surface and then the growth starts.
During simulations kinetic Monte Carlo (kMC) lattice model of
hexagonal crystal structure is used. Two species of atoms are taken
into account in order to reproduce 4H politype of silicon carbide
(SiC). 4H-SiC elementary cell consists of four diatomic layers which
contain single Si and single C atom. Layers are shifted towards
each other and form ABAC stack [14]. The paper concerns Si face of
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silicon carbide hence on the top of every double layer Si atoms are
situated. Nearest (NN) and next nearest neighbours (NNN) attractive interactions are present in the model. All the particle neighbours are chosen in such a way to reproduce geometry of bonds which
characterizes 4H-SiC crystals. Hence direction of inter-atomic bonds
varies for consecutive atomic layers. NN forces are present between
atoms of different types (silicon and carbon) however NNN attraction
occurs between atoms of the same type, two Si or C particles.
Following interaction values are used F SiC ¼ 0:75 eV for nearest
neighbours and F SiSi ¼ 0:35 eV or F CC ¼ 0:65 eV for silicon–silicon or
carbon–carbon bonds respectively [15]. Every lattice site of the system
is equivalent to the simulated crystal elementary cell. Transition rates
for particle jumps from one site to the neighbouring one are given by a
common Boltzmann factor:
P D ¼ ν expð BD =kB TÞ;
ð1Þ
where BD is a jump barrier dependent on initial and final configurations of jumping atoms NN and NNN [7–10], kB is the Boltzmann constant and T is the system temperature. Prefactor ν ¼ 1
sets the system time scale up. Sublimation process occurs with
probability
P sub ¼ ν expð ðEi þ Bsub Þ=kB TÞ;
ð2Þ
where Ei is the energy of bonds with all NN and NNN of
sublimating particle which corresponds to the depth of potential
well where particle resides. Bsub is the additional parameter which
is added to the particle energy in order to control speed of
sublimation process. It can be negative or positive as well.
Probability of adsorption depends on chemical potentials μSi and
μC for silicon and carbon respectively,
P ax ¼ ν expð μx =kB TÞ;
where subscript x ¼Si for silicon and C or carbon atoms.
ð3Þ
512
F. Krzyżewski / Journal of Crystal Growth 401 (2014) 511–513
Every simulation starts with N straight, parallel steps. Steps
with silicon on the topmost layer alternate with the ones with
carbon on the top. N is the number divisible by eight. It is due to
the fact that model reproduces 4H-SiC crystal with elementary cell
containing eight layers, and helical [7–10] boundary conditions,
applied to the system. First stage of every simulation is the
annealing process. Beginning of the system evolution is presented
in Fig. 1. It shows the system state after first Monte Carlo step so
steps are already rough according to the studied temperature, but
they did not change their relative position yet. All simulations
presented below were done for N ¼48, which is the number that
corresponds to the height of six silicon carbide elementary cells.
During annealing stage system temperature is T ¼1600 1C
which is used during similar experimental processes [16]. Silicon
and carbon chemical potentials are μSi ¼ μC ¼ 1 which in fact
means no adsorption at the surface. Desorption parameters for
silicon and carbon from Eq. (2) are equal and Bsub ¼ 4 eV.
It means that desorption is the dominating process in the system.
However the model used allows for particle diffusion it is
particularly absent due to the fact that every single surface particle
desorbs immediately. Moreover, desorption from the step edges is
faster then the diffusion of particle which detaches from the step
edge. Such sublimation conditions were chosen due to the fact
that this is the simplest and the fastest way to obtain explicit step
bunches in the described system. Bunch structure obtained after
annealing process is shown in Fig. 2. Colours in the picture
represent height i.e. the number of layers in every site. Brighter
areas are higher than the darker ones. Sharp change of the colour
from bright one to the dark indicates position of the bunch. In this
case bunch consists of 42 steps.
When bunched surface structure is present growth process
starts. Temperature rises to T ¼2300 1C which is the value used
during SiC growth [2]. Desorption barriers also change and
Bsub ¼ 1 eV for silicon and carbon, hence sublimation process is
slow. In the first case chemical potentials for silicon and carbon
were μSi ¼ μC ¼ 3:3 eV and bunch obtained during annealing
changed into even double steps, hence the surface smoothing
was observed. Step doubling is the result of different strength of
inter-atomic bonds for two species of atoms forming SiC crystals.
Carbon is binded more strongly than silicon, and in conditions
where adsorption and desorption barriers are equal for C and Si,
the first one covers whole crystal surface. Such a double stepped,
smooth structure is shown in Fig. 3. Evolution of the surface is
presented in Fig. 4 where time dependent root mean square (RMS)
roughness parameter is plotted, red solid line corresponds to the
smoothed system.
Three stages of the system evolution can be found there. First,
when sublimation process takes place and RMS parameter grows
slowly. The first stage finishes, when sudden jump of the RMS
occurs. This is the moment when bunch appears at the crystal
surface. One can notice that creation of a bunch is very sudden. If
only, as a result of a fluctuation, one of the terraces becomes
significantly wider then the others it expands further very fast and
squeezes the rest. Such a sudden bunching is the result of very fast
sublimation process. In such conditions very fast step movement
causes rapid bunching.
When bunch is already present growth stage takes place. One
can see, the slow decrease of RMS parameter which corresponds
to the surface smoothing process. During the last stage RMS
parameter is constant exact to the system fluctuations. It means
that debunching process came to the end, and further significant
changes of the crystal surface are finished.
In another case, when growth process is faster with μ ¼ μSi ¼
μC ¼ 2:7 eV, 2D nucleation of surface atoms is observed. Islands
are created at the widest terrace, and the process of the surface
Fig. 3. Even double steps after slow growth stage. Crystal growth was carried out
for chemical potentials μ ¼ μC ¼ μSi ¼ 3:3 eV, desorption parameter Bsub ¼ 1 eV and
system temperature T¼ 2300 1C.
Fig. 1. Top view of the simulated surface at the beginning of the system evolution,
step number N ¼ 48.
Fig. 2. Top view of the bunched surface at the end of the sublimation stage and
before the crystal growth process. Sublimation was carried out for desorption
parameters Bsub ¼ 4 eV and temperature T ¼1600 1C. Black oval shows position of
the 42-step bunch. (For interpretation of the references to colour in this figure
caption, the reader is referred to the web version of this article.)
Fig. 4. Time dependent RMS roughness parameter for the slowly (red solid line)
and fast (green dashed line) grown system. Sublimation and growth stages are
clearly visible. (For interpretation of the references to colour in this figure caption,
the reader is referred to the web version of this article.)
F. Krzyżewski / Journal of Crystal Growth 401 (2014) 511–513
Fig. 5. 2D nucleation at the widest terrace observed after growth in high incoming
Si and C fluxes. Crystal growth was carried out for chemical potentials
μC ¼ μSi ¼ 2:7 eV, desorption parameter Bsub ¼ 1 eV and system temperature
T ¼ 2300 1C.
513
one where 2D nucleations occurs at the widest terraces. In such a
case island catch particles diffusing at surfaces and number of
atoms that attach to the steps are very low. Hence the step
movement is very slow and smoothing process is blocked. In the
third schema (blue asterisks in Fig. 6) resultant flux of adsorbing
and desorbing particles is very low. Hence only few particles
attach to the edges, steps move slowly and debunching process
does not occur again.
To conclude, one can state that kMC simulations have shown
how properly tuned condition of 4H-SiC crystals growth can lead
to the smoothing of bunched surface. It was also shown that the
2D nucleation which is present any time when the external fluxes
of incoming atoms are very high blocks the debunching process.
Similar situation occurs when resultant flux of incoming and outcoming particles is very low. In the last two cases step movement
is blocked and surface smoothing cannot take place. Hence, the
results presented in the text confirm that the debunching phenomenon is the effect of step movement which is in agreement
with the previous knowledge [8,11,12]. It was also shown that low
step velocity blocks the surface smoothing process. It is worth
noting that the phenomenon of step debunching during crystal
growth following step sublimation is weakly investigated and
seems to be an interesting topic for further, theoretical and
experimental research.
Acknowledgments
This research was carried out within the SICMAT Project
financed under the European Funds for Regional Development
(Contract no. UDA-POIG.01.03.01-14-155/09).
Fig. 6. Phase diagram representing schemes of system evolution in β μ space. Red
crosses correspond to the debunching, green -s correspond to 2D nucleation
which blocks surface smoothing and blue asterisks represent area where debunching does not occur due to the very low resultant flux of adsorbing and desorbing
particles. (For interpretation of the references to colour in this figure caption, the
reader is referred to the web version of this article.)
smoothing is blocked. Such a state is plotted in Fig. 5. Time
evolution RMS parameter for that process is shown in Fig. 4 in
green dashed line. One can notice that after sublimation stage
which is similar to the one of the previous system, drop of RMS
parameter does not occur. It means that debunching process is
blocked by 2-dimensional structures that evolved during fast
growth.
Above and other results of simulations are gathered into the
phase diagram presented in Fig. 6. In the space of β ¼ 1=kB T and μ
one can observe three different phases which correspond to three
schemas of system evolution during growth stage. Desorption
stage was always carried out in the same conditions. At the first
schema of crystal growth step movement leads to the debunching
process. Results of such simulations are represented by red crosses
in Fig. 6. Second scheme (green -s at the phase diagram) is the
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