Thin Solid Films 365 (2000) 231±241
www.elsevier.com/locate/tsf
A chemical mechanism for in situ boron doping during silicon
chemical vapor deposition
Istvan Lengyel 1, Klavs F. Jensen*
Chemical Engineering Department, Room 66-566, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA
Abstract
We present a systematic approach to formulating chemical mechanisms to chemical vapor deposition processes with the unusually large
growth rate enhancement observed for in situ B doping of Si as a case study. The basic computational tools needed for mechanism
development; quantum chemistry calculations, sensitivity analysis, and ®nite element simulations are combined to develop a mechanism
for the process and to provide quantitative predictions of observed growth and dopant incorporation rates. Ab initio quantum chemistry
computations of small molecules and clusters relevant to the H±B±Cl±Si system are used to determine thermodynamic and kinetics
parameters. Particular emphasis is given to Cl±H exchange reactions between borane and chlorosilanes, which are shown to proceed
with low reaction barriers. The reaction mechanism is incorporated into ®nite element simulation of reported deposition data. The developed
mechanism is capable of representing quantitatively: (a) the silicon deposition from dichlorosilane; (b) etching of silicon by HCl; and (c) Bdoped Si deposition in the SiC12H2/B2H6/H2 deposition system. The most important deposition processes are identi®ed by sensitivity
analysis, and gas-phase decomposition reactions of dichlorosilane are shown to be insigni®cant in the deposition process. q 2000 Elsevier
Science S.A. All rights reserved.
Keywords: Dichlorosilane; Borane; Mechanism; Chemical vapor deposition simulation; Sensitivity analysis; Quantum chemistry predictions
1. Introduction
Quantitative understanding of reaction mechanisms
underlying chemical vapor deposition (CVD) processes is
critical for the semiconductor industry in designing deposition systems and selecting process conditions leading to
uniform growth rates and composition. Models of ¯uid
¯ow and heat and mass transfer capable of simulating ®lm
thickness and composition variations in CVD systems have
been developed over the last decade [1,2]. These models
have provided increased understanding of the in¯uence of
¯uid phenomena on ®lm uniformity and composition, but
they are often limited by the knowledge of reaction pathways and kinetics. Chemical kinetic data and understanding
of reaction mechanisms become particularly important
when predicting doping concentrations where even minor
changes in gas-phase species or surface interactions can lead
to signi®cant effects in dopant concentration levels. For
example, the addition of small amounts of diborane to silicon CVD with dichlorosilane (10 ppm B2H6 with 0.1% of
* Corresponding author. Tel.: 1 1-617-253-4589; fax: 1 1-617-2588224.
E-mail address: [email protected] (K.F. Jensen)
1
Present address. The Dow Chemical Company, 2301 N. Brazosport
Blvd., B-1226, Freeport, TX 77541-3257, USA.
dichlorosilane) increases the silicon growth rate by two
orders of magnitude [3]. In such cases, experimentally
determined rate coef®cients for simpli®ed, overall deposition reactions representing the conversion of gas-phase
species to ®lm constituents are of limited value for predicting growth rate and dopant incorporation. Detailed chemical
mechanisms must be included to provide predictive models
of the process. In addition to simulating the CVD process,
such models provide understanding of important reaction
pathways that may be used to develop alternative deposition
strategies with improved control of uniformity and composition.
The unusually large growth rate enhancement observed
for in situ boron doping of silicon makes it an excellent
vehicle for illustrating issues in the development of chemical mechanisms for CVD systems. The system has the
further advantage of extensive experimental and computational chemistry studies of the underlying dichlorosilane
chemistry [4±6]. Mechanism development for CVD systems
has been limited by the expense and time involved in determining kinetic parameters for the underlying chemical reactions. Macroscopic growth rate data, when decoupled from
diffusion effects, can be used to ®t lumped reaction parameters, but they cannot be used to infer details of reaction
mechanisms. Mechanistic insights must be derived from
0040-6090/00/$ - see front matter q 2000 Elsevier Science S.A. All rights reserved.
PII: S 0040-609 0(00)00758-6
232
I. Lengyel, K.F. Jensen / Thin Solid Films 365 (2000) 231±241
gas-phase or surface experiments aimed at revealing the
underlying elementary reactions. Such experiments are
generally dif®cult and CVD cases are further complicated
by reaction intermediates having short life times and low
concentrations. The extrapolation of reaction data from
ideal conditions, such as ultra high vacuum (UHV) surface
science experiments, to actual deposition conditions, raises
further complications. The lack of experimental data makes
it desirable to predict reactions from ®rst principles quantum
chemistry computations.
Quantum chemistry techniques have been shown to be
effective in studying chemical reactivity and molecular
properties of compounds containing ®rst and second row
elements. Ab initio molecular orbital computations and
density functional theory (DEF) have also provided thermochemical and kinetic insight for development of reaction
mechanisms for CVD of Si and related compounds [4,7±
12]. The accuracy of quantum chemistry predictions is a
critical issue in CVD applications since small variations
(2±5 kcal/mol) in activation energies translate into order
of magnitude changes in rate constants. The accuracy is
usually a function of the level of method used, the highest
accuracy achieved at increased computational expense.
Therefore, sensitivity analysis needs to be included in the
mechanism development process to identify which reaction
pathways will require particular attention. Additionally,
correction schemes based on experimental data for selected
compounds have been developed to provide thermochemical estimates with improved accuracy using fewer computations than would be needed for high-order methods. The
bond additivity correction (BAC) method pioneered by
Melius and Binkley [13] has been used extensively in
studies of Si and related compounds relevant to CVD
[4,8,10,13±15]. The systematic ab initio quantum chemistry
BAC computations of SiBxHyClz compounds performed by
Ho et al. [4] are particularly relevant to the present mechanism development effort.
In this contribution we investigate additional reactions of
the Si-B±H±Cl system that contribute to the growth rate
enhancement observed when diborane is added to silicon
growth from chlorosilane. The work also incorporates recent
results of surface chemistry calculations in which desorption
barriers of hydrogen and HCl from silicon±boron dimers
were estimated using small clusters as a representation of
the boron-doped silicon surface [16]. The basic computational tools needed for CVD mechanism development; speci®cally, quantum chemistry calculations, sensitivity analysis,
and ®nite element simulations are combined to gain new
insight into the mechanism underlying boron doping during
silicon CVD, and to provide quantitative predictions of
observed growth and dopant incorporation rates.
the boron-doping mechanism. The process starts with a
proposed chemical mechanism based on current understanding of the chemistry, and with a selection of perceived reaction pathways. Literature and experimental data are the ®rst
sources of thermodynamic and kinetic data for the proposed
mechanism, but they rarely have suf®cient information for a
complete CVD simulation. Consequently, quantum chemistry calculations of molecular structure and energies have to
be combined with transition state theory estimates of reaction rates to develop a complete database of thermochemical
properties and reaction rates. The mechanisms can then be
included in reactor simulations and the predictions
compared with experimental data. The mechanism generation process is iterative. A ®rst proposed mechanism might
not be consistent with experimental observations and an
alternative reaction pathway must then be considered and
tested against data. Sensitivity analysis is useful in the
process to determine important reaction pathways and to
reduce the number of reaction steps in the mechanism.
Here, the ®nite element method was used to solve the
heat, mass, and momentum transfer equations coupled
with chemical kinetics for realistic reactor con®gurations.
as in previous CVD simulations [1,17]. In the sensitivity
analysis, the normalized sensitivity of the growth rate
(GR) to the rate constant of each individual reaction
(2lnGR/2lnki, i ˆ 1¼number of reactions) was computed
2. Methodology
Fig. 1 shows schematically the approach used to develop
Fig. 1. Schematic of the CVD reaction mechanism development process.
I. Lengyel, K.F. Jensen / Thin Solid Films 365 (2000) 231±241
by ®nite difference approximation. The use of normalized
sensitivities allowed comparisons of reaction rates and
species concentrations differing by orders of magnitude.
Each ®nite element node on the growth surface had its
own sensitivity vector. The average values over these
vectors were used to determine the importance of different
reactions in the mechanism, and to simplify the mechanism.
The average deviation of normalized sensitivities was less
than 0.1% because of the relatively uniform growth rate in
most cases.
Rate constants of individual reactions were estimated by
transition-state theory (TST) [18,19]. Geometry optimizations of transition-state structures were performed by the
TS, QST2 or QST3 Gaussian94 procedures [20]. In order
to verify that the transition state corresponds to the reaction
of interest, an intrinsic reaction coordinate (IRC) calculation
was performed [21]. The normal modes of vibrations of
each reactant, product and transition state were computed
and used, along with molecular properties, to calculate
partition functions and reaction rates.
3. Results
3.1. Overview of the proposed mechanism
The proposed mechanism is shown schematically in Fig.
2. The main part of the mechanism is depicted on the left
side (species A±G), which is comprised of Si deposition
reactions from dichlorosilane in the absence of borane.
Additional reactions on the right side are related to the
presence of boron (species H±J). The Si growth mechanism
can be described by the following reaction sequence: (a)
adsorption of Si-containing gas-phase species on free
adsorption dimer sites (A) to form Si adatoms (B) and Cl
on the surface; (b) Si adatoms pair up to form new dimers
and the lattice (C); (c) equilibration of H and Cl on the
dimers to form doubly hydrogenated, double chlorinated
Fig. 2. Overview of the proposed mechanism for B doping during Si CVD
from dichlorosilane.
233
and mixed dimers (2D ˆ E 1 F); (d) desorption of H2
(E ! A 1 H2) and HCl (D $ A 1 HCl) from the surface;
and (e) double chlorinated dimers lead to break-up of dimers
(G) and desorption of SiCl2 from the surface.
The boron-doping part encompasses the following reaction sequence: (a) BH3 adsorbs on the surface to form
adducts (H) with surface-bound chlorine, and participate
in Cl±H exchange reactions (BH2Cl leaves the surface) or
form direct bonds with Si surface atoms (I); (b) boron on the
surface may form Si±B dimers (J) with Si adatoms; (c) H
and Cl on the surface diffuses onto Si±B dimers from which
H2 and HCl can desorb with lower than the normal barrier ±
this may be considered as B-catalyzed desorption of H2 and
HCl; and (d) Si±B dimers are trapped by the growing Si and
B becomes part of the lattice.
Several possible reaction pathways were investigated to
gain insight into likely primary causes of the observed silicon growth rate enhancement upon diborane addition. The
®rst explanation is that the increased deposition rate originates from gas-phase reactions leading to reactive intermediates. This explanation, however, is not likely, since
the largest effect of diborane occurs at lower deposition
temperatures (~6008C). Low-temperature deposition
processes are generally controlled by surface reactions,
speci®cally desorption of reaction products from the
surface. In the present case, these are H2 and HCl. In
order for diborane or related boron compounds to compete
effectively with dichlorosilane for free adsorption sites, the
boron-containing compounds should have about three
orders of magnitude higher sticking probability than that
of dichlorosilane. Since the latter is larger than 0.001, it is
not physically realistic for any boron compounds formed in
the gas phase to effectively compete with dichlorosilane and
be responsible for a two to three orders of magnitude growth
rate enhancement.
A second, and more plausible explanation for the
increased growth rate is that the presence of boron on the
silicon surface enhances the desorption rates of H2 and/or
HCl thereby providing more free adsorption sites. This
process has been investigated by Hay et al. [16] using
DFT calculations of silicon clusters with and without
boron substitution. They ®nd that both desorption of H2
and HCl have lower barriers from Si±B dimers than from
Si±Si dimers. However, for the changed desorption characteristics to be responsible for growth rate enhancement, it is
necessary to rationalize how borane from the gas phase can
bind to a highly covered silicon surface, especially when the
diborane concentration in the gas phase is only 0.01% of the
dichlorosilane concentration.
Considering that the surface is covered with chlorine or
chlorinated surface species at lower temperatures when the
effect of borane is highest, reactions between adsorbed
surface and gas-phase species need to be considered.
Although only a few unambiguous examples of surface
processes [22] with Eley±Rideal kinetics are known, several
experimental observations indicate that an Eley±Rideal type
234
I. Lengyel, K.F. Jensen / Thin Solid Films 365 (2000) 231±241
of process could occur. First, the apparent activation barrier
of the overall deposition process (the slope of ln[growth
rate] vs. 1/T curve) is signi®cantly lower below 7008C,
than above [3]. Furthermore, this apparent barrier is lower
than that of the desorption of H2 or HCl (~48±58 and 62
kcal/mol, respectively) [23,24], and even lower than the
barrier of surface diffusion processes involving hydrogen
or chlorine (above 30 kcal/mol) or Si adatoms.
In the Eley±Rideal reaction mechanism, boron does not
need to bind directly to silicon atoms on the surface to
generate its effect on the growth rate. Since borane is an
electron de®cient compound (Lewis acid) and chlorine
bound to silicon has non-bonding free electron pairs
(Lewis base), donor±acceptor type complexes would be
expected to form from borane and chlorinated silanes.
Such adduct formations could also explain the strong binding of dichlorosilane on boron-covered silicon surfaces at
low temperatures [25]. Subsequent Cl±H exchange reactions between Si and B bridges of the adducts could play
an important role in removal of Cl from the surface as illustrated schematically in Fig. 2. The removal of strongly
bound Cl for weaker H not only decreases the rate of Cl
etching reactions, but also opens lower barrier desorption
pathways for generating more free adsorption sites, since H2
molecules desorb much easier from the silicon surface than
HCl or SiCl2. In order to gain insight into the possible behavior of a chlorine-covered silicon surface, we have studied
structure±activity relationships of Si and B compounds of
different chlorination levels and molecular sizes. These
studies have included quantum chemistry computations of
small silicon clusters as an approximate model of the silicon
surface.
At low temperatures and less than monolayer coverage of
H or Cl, the dominant adsorption sites are silicon dimers. H2
and HCl desorption takes place from these dimers and the
dimer structure is not broken by the adsorption of many
chemical species, including H [26], SiH2, SiH4, SiCl2H2,
HCl [27], and C12 [28]. Also, adsorbents on the surface
tend to occupy both Si atoms on the same dimer because
of the favorable energetics of weak p-bond formation
between the unpaired p-electrons of the two Si atoms of
an unoccupied dimer. The kinetic difference between
assuming dimers or atoms as adsorption/desorption sites
appear mainly at lower temperatures, when the surface is
highly covered and the deposition is controlled by the desorption processes. With the assumption of dimers as adsorption/desorption sites on the silicon surface, it is easy to
implement reactions with the experimentally observed
kinetics, e.g. H2 desorption, into a proposed mechanism.
However, additional `bookkeeping' becomes necessary to
carefully account for diffusion and reaction of individual
adsorbed species and dimers on the surface.
Computational results in support of the above deposition
and doping mechanism are described in the following
sections starting with adduct formation between chlorinated
silanes and borane and related Cl±H exchange reactions
between Si and B bridge atoms. Surface reactions, equilibration and the role of diffusion will be discussed in view of
the Si dimer representation of the surface.
3.2. Accuracy of quantum chemistry estimates
The geometry of all compounds, with the exception of
adducts, was estimated accurately for all of the quantum
chemistry methods used, including Hartree±Fock (HF),
density functional theory (DFT) with the BLYP exchange
correlation functional, DFT with the hybrid functional
B3LYP, and Mùller±Plesset perturbation theory on
Hartree±Fock to second order (MP2) ± all methods as
implemented in the suite of Gaussian94 programs [20].
The largest deviation between the computations and experiÊ , implying that low-level
mental values was less than 0.1 A
geometry optimizations is suf®cient for all the stable
compounds involved. For transition states, the difference
between geometries computed with different quantum
chemistry methods reached as much as 20%. Since the
formation of Lewis acid±base type of compounds between
chlorosilanes and borane has not been investigated
previously, the geometry of the simplest adduct,
SiH3Cl:BH3, was explored at different levels of theory and
Ê
basis sets. HF geometry optimizations gave about 1 A
longer Cl±B distance than any other higher order methods,
including MP2, MP4, BLYP, B3LYP, that takes electron
correlation into account. The geometry optimized by
B3LYP was not sensitive to the size of the basis function
set larger than 6±31G(2d,p), and this basis set was used in
the mechanism development.
Heats of formation of several compounds were computed
and compared with available literature data. These are listed
in Table 1. For molecules that contain only B, H and Cl
atoms, B3LYP/6±31G(2d,p)//B3LYP/6±31G(2d,p) computed heats of formation are within experimental uncertainties. However, heats of formation for Si±Cl compounds are
Table 1
Comparison of computed and experimental heats of formation of B±H±Cl
and Si±H±Cl compounds at B3LYP/6±31G(2d,p)//IB3LYP/6±31G(2d,p)
level of theory with no correction (a) and with 24.62 kcal/mol correction
(b) for each Si±Cl bond; atomization enthalpies of B and Si atoms were
135.0 and 107.6 kcal/mol, respectively
Compound
HCl
BH3
BH2Cl
BHCl2
BCl3
SiH4
SiClH3
SiCl2H2
SiCl3H
SiCl4
DH 298K (kcal/mol)
(a)
(b)
Experiment
222.3
20.4
221.9
261.4
296.5
8.8
228.7
267.4
2105.5
2141.1
222.3
20.4
221.9
261.4
296.5
8.8
233.4
276.6
2119.4
2159.6
222.1
21.0 ^ 2.4
219.3 ^ 4.8
260.2 ^ 1.0
296.7 ^ 0.3
8.2
233.9
276.6
2118.6
2158.4
I. Lengyel, K.F. Jensen / Thin Solid Films 365 (2000) 231±241
underestimated by an average of 4±5 kcal/mol for each Si±
Cl bond. This error is high compared to the performance of
MP2 or MP4 methods [5,29], but it can be adjusted empirically by a simple bond additivity correction. An adjustment
of 24.62 kcal/mol/Si±Cl (based on known thermodynamic
data) yields heats of formation within ^1.0 kcal/mol of
experimental values.
The lack of experimental data, to our knowledge, for the
kinetics of Cl±H exchange reactions between Si and B
bridge atoms makes it dif®cult to correct the systematic
error in the Si±Cl bond energetics. The following heuristic
was used to re¯ect that Si±Cl bonding in the transition states
is partial. As a ®rst approximation, the bond order of the Si±
Cl bond in the transition states was assumed to be 0.5, and
the correction factor was correspondingly half of the 24.62
kcal/mol/Si±Cl bond correction.
3.3. Adduct formation and Cl±H exchange reactions
We focused on chemical interactions between chlorinated
silanes and borane since Lewis acid±base interactions could
potentially explain the speci®c binding of borane to chlorine-covered silicon surfaces [25]. Chlorosilanes, including
mono-, disilanes, and clusters form similar adducts with
borane. The free energy of adduct formation is positive
because of the large entropy decrease. Consequently, the
equilibrium of adduct formation is shifted to the side of
separated molecules. The role of adduct formations may
be more important on surfaces, however, since the surface
concentration of chlorine atoms is much higher. The release
of borane from chlorine on the surface does not necessarily
imply its release to the gas phase, since borane could readsorb in neighboring chlorine atoms. This process is energe-
235
Fig. 3. Reaction path from reactants to products in the MCl 1 BH3 Y
MH 1 BH2Cl reaction.
tically favored, and unlike gas-phase reactions, no entropy
decrease is involved. One could therefore envision that a
chlorine-terminated silicon surface could capture borane
molecules and keep them coordinated for a suf®ciently
long enough time to have an increased probability for the
occurence of chemical reactions; speci®cally, Cl±H
exchange reactions.
Cl±H exchange reactions could be important both in the
gas phase and on the surface. Additionally, HCl, which is a
desorption product from the surface, could readsorb and
compete with dichlorosilane for free adsorption sites. Its
reaction with borane in the gas phase would decrease HCl
concentration close to the surface to increase the chance for
other species to adsorb on free surface sites. The exchange
reactions can be written in the following general form:
MCl 1 BHx Cl32x Y MH 1 BHx21 Cl42x …x : 1¼3†
…1†
where M represents the surface or a cluster in the gas phase.
The potential energy curve along the reaction coordinate,
Fig. 4. Transition state structures for the reactions: (a) BH3 1 HCl Y BH2Cl 1 H2; (b) SiCl2H2 1 BH3 Y SiClH3 1 BH2Cl; and (c) Si9H13Cl 1 BH3 Y
Si9H14 1 BH2Cl.
236
I. Lengyel, K.F. Jensen / Thin Solid Films 365 (2000) 231±241
Table 2
List of Cl±H exchange reactions, their reaction enthalpies and rate parameters in Arrhenius form studied at the B3LYP/6±31G(2d,p)//B3LYP/6±31G(2d,p)
level of theory corrected with 24.62 kcal/Si±Cl bond correction factor; enthalpies and energies are in kcal/mol, pre-exponentials are in cm 3/mol/s
No.
Reaction
DH 298K
Af
Ea,f
Ar
1
2
3
4
5
6
7
8
9
10
11
12
13
BH3 1 HCl ˆ BH2Cl 1 H2
BH2Cl 1 HCl ˆ BHCl2 1 H2
BHCl2 1 HCl ˆ BCl3 1 H2
SiClH3 1 BH3 ˆ SiH4 1 BH2Cl
SiCl2H2 1 BH3 ˆ SiClH3 1 BH2Cl
SiCl3H 1 BH3 ˆ SiCl2H2 1 BH2Cl
SiCl4 1 BH3 ˆ SiCl3H 1 BH2Cl
SiClH3 1 BH2Cl ˆ SiH4 1 BHCl2
SiClH3 1 BHCl2 ˆ SiH4 1 BCl3
SiCl2H2 1 BH2Cl ˆ SiClH3 1 BHCl2
SiCl2H2 1 BHCl2 ˆ SiClH3 1 BCl3
Si2H5Cl 1 BH3 ˆ Si2H6 1 BH2Cl
Si9H13C1 1 BH3 ˆ Si9H14 1 BH2Cl
221.4
218.2
213.7
20.4
1.0
0.4
21.9
2.9
7.4
4.2
8.7
20.6
22.7
9.93 £ 10 12
2.99 £ 10 12
1.42 £ 10 12
4.59 £ 10 12
4.71 £ 10 11
1.34 £ 10 12
1.97 £ 10 12
3.96 £ 10 12
1.17 £ 10 12
2.24 £ 10 11
1.39 £ 10 11
1.39 £ 10 12
3.02 £ 10 12
10.4
21.0
30.3
21.2
21.6
22.8
25.1
30.5
38.0
28.9
37.2
21.6
21.0
1.74 £
8.86 £
9.81 £
1.43 £
4.11 £
3.41 £
1.44 £
2.10 £
1.44 £
3.33 £
4.82 £
4.34 £
9.77 £
starting from MCl 1 BH3 reactants to products MH 1
BH2Cl, is shown in Fig. 3. As BH3 approaches Cl bound
to Si, the potential energy minimum corresponds to the
formation of an adduct. The exchange reaction has a fourcentered transition state - some representative examples of
which are shown in Fig. 4. At high temperatures in the gas
phase, which is relevant to reactor operating conditions,
adduct formation is not favored because of the entropy
change. However, the kinetic energy of the molecules is
suf®cient to carry the reactants through the relatively low
energy barrier to exchange the Cl on Si for H from B.
Reaction enthalpies at standard conditions, and kinetics
parameters of several exchange reactions, are listed in
Table 2. Standard Arrhenius parameters are used for
compactness and ease of comparison, but the Arrhenius
form is not a completely accurate representation of the
temperature-dependent rate constants computed from transition state theory. Parameters listed in Table 2 represent the
rate constants between 300 and 1500 K with less than 20%
deviations from the transition state theory results
Ea,r
10 13
10 12
10 12
10 12
10 11
10 11
10 11
10 12
10 12
10 11
10 11
10 11
10 11
31.3
38.4
43.2
21.8
20.8
22.8
27.3
27.5
30.5
24.8
28.5
22.4
24.0
For the transition state of the Si9 silicon cluster, there are
two, nonequivalent pathways for the exchange reaction: (1)
BH3 approaches from the direction of the ®ve-membered
ring (Fig. 4c), and (2) BH3 approaches from the direction
of six-membered ring on the right side of the cluster. Steric
hindrance in a real Si surface could favor the transition state
shown in Fig. 4c even though this has a 0.3 kcal/mol higher
activation barrier than the second pathway.
3.4. Surface processes
The silicon surface is modeled as a collection of dimers
rather than the typical approach of individual Si atoms
serving as reactive surface sites. At low surface coverage
and high temperatures, it makes no difference which
approach is used since the deposition is controlled by gasphase transport processes to the surface. However, for lowtemperature deposition a dimer-based kinetic formulation
will have advantages in describing desorption processes.
For example, with dimers as reactive sites, H2 desorption
Fig. 5. Possible distribution of Cl and H atoms on silicon dimers after HCl adsorption.
I. Lengyel, K.F. Jensen / Thin Solid Films 365 (2000) 231±241
will follow the experimentally determined kinetics both in
reaction order and parameters [23]. The desorption of HCl
from Si(100) competes with the lower temperature process
of H2 desorption in addition to the higher temperature
process of SiCl2 desorption. If silicon atoms were used as
reactive sites, then it would not be possible to differentiate
between H atoms originating from HCl or other H-atom
sources. H2 should desorb easily at low temperatures from
an HCl-dosed silicon surface because of the lower activation
barrier. Consequently, no HCl desorption should be
observed, but the remaining Cl would result in SiCl2 desorption at higher temperatures. However, experimentally HCl
desorption can easily be detected in parallel with higher
temperature H2 desorption. With the dimer formulation of
the surface, H2 can desorb from doubly hydrogenated
dimers and HCl can desorb from HCl-capped dimers.
The distribution of dimer species is important for determining the relative rate of desorption and etching processes.
The species shown in Fig. 5 could result from adsorption of
two HCl molecules on two neighboring Si dimers along a
row. Quantum chemistry calculations at the B3LYP/6±
31G(d)//HF/6±31G levels were performed to determine
energies of the structures. The valences of lower layer silicon atoms were saturated with hydrogen atoms. The
distances between the Cl atoms in the three structures are
Ê , respectively. The structure in Fig. 5c is
4.0, 4.2 and 5.7 A
energetically favored by 2 kcal/mol. On an extended
surface, this alternating structure is likely to be even more
favored because of nearest neighbor interactions from the
other side of the dimers. The energy difference between the
reactants and products of this reaction may represent the
difference between the energy barriers of diffusion of a
chlorine atom onto a dimer, which already has a chlorine
atom or a hydrogen atom on it. The higher entropy of the
HCl capped dimers (Fig. 5b,c) also favors the structure. The
free energy change is about 23.0 kcal/mol at 300 K and
decreases to 22.7 kcal/mol at 1300 K.
The presence of a dynamic equilibrium between doubly
chlorinated dimers, doubly hydrogenated dimers, and HCl
capped dimers is consistent with the experimental observation that HCl desorption can compete with H2 desorption, even if the desorption barrier is signi®cantly higher.
From the free energy change of the process, we can
compute an approximate equilibrium constant at different
temperatures. A ®t of the temperature dependent equilibrium constant in the form of Ae 2DG/(RT) describes the equilibrium constant accurately between 300 and 1400 K with
A ˆ 0:092 and DG ˆ 22:6 kcal/mol. Rate constants for the
forward and reverse equilibration processes were chosen
from transition state theory estimates to satisfy this equilibrium condition.
Surface diffusion is not included explicitly in the model
since diffusion processes are not rate limiting. The barriers
for surface diffusion of Si, H, and Cl adatoms are much less
than those associated with surface desorption processes.
This approximation is reasonable when predicting overall
237
Table 3
Proposed mechanism of silicon deposition in the SiCl2H2/B2H6/H2 reaction
system, where `d' represents surface dimers
b
No.
Reaction
A
1
2
3
4
5a
6a
7a
8a
9
10
11
12
13
14
15
16
SiCl2H2 ˆ SiCl2 1 H2
SiCl2 1 H2 ˆ SiCl2H2
SiCl2H2 ˆ HSiCl 1 HCl
HSiCl 1 HCl ˆ SiCl2H2
SiCl2H2 1 d ˆ 11C1 1 CldSiH
HCl 1 d ˆ HdCl
HSiCl 1 d ˆ CldSiH
SiCl2 1 d ˆ CldSiCl
HdH ˆ H2 1 d
2HdH ˆ 2H2 1 2d
HdCl ˆ HC1 1 d
2HdCl ˆ HdH 1 CldCl
HdH 1 CldCl ˆ 2HdCl
CldCl 1 Si ˆ SiCl2 1 d
2CldSiH ˆ 2HdCl 1 2Si
CldSiH 1 CldSiCl ˆ HdCl 1
CldCl 1 2Si
2CldSiCl ˆ 2CldCl 1 2Si
B2H6 ˆ 2BH3
2BH3 ˆ B2H6
BH 1 H2 ˆ BH3
BH3 1 d ˆ H2 1 dBH
BH 1 d ˆ dBH
BH3 1 CldCl ˆ BClH2 1 HdCl
BH3 1 HdCl ˆ BClH2 1 HdH
BH3 1 CldCl ˆ 2HCl 1 dBH
BH3 1 HdCl ˆ HCl 1 H2 1
dBH
dBH 1 CldSiCl ˆ dBSiH 1
CldCl
dBH 1 CldSiH ˆ dBSiH 1
HdCl
HdH ˆ H2 1 d
HdCl ˆ HCl 1 d
dBSiH ˆ d 1 B 1 Si
dBSiH ˆ BH 1 d 1 Si
dBH ˆ BH 1 d
CldCl 1 B 1 Si ˆ SiCl2 1
BH 1 d
dBSiH 1 2C1dSiH ˆ 2HdCl 1
d 1 B 1 3Si
dBSiH 1 CldSiH 1 CldSiCl ˆ
HdCl 1 d 1 C1dC1 1 B 1 3Si
dBSiH 1 2CldSiC1 ˆ d 1
2CldC1 1 B 1 3Si
1.4 £ 10 34
2.0 £ 10 29
8.6 £ 10 33
1.7 £ 10 28
0.008
0.2
0.1
0.1
2.0 £ 10 15
1.0 £ 10 24
2.0 £ 10 15
9.0 £ 10 22
1.0 £ 10 24
1.0 £ 10 15
1.0 £ 10 24
1.0 £ 10 24
26.3
25.3
25.9
24.9
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
85.4
20.6
83.0
14.6
0.0
0.0
0.0
0.0
57.0
48.0
62.0
34.6
32.0
72.0
32.0
34.0
1.0 £ 10 24
5.9 £ 10 49
5.9 £ 10 44
1.0 £ 10 12
0.01
0.1
0.001
0.001
1.0 £ 10 25
1.0 £ 10 25
0.0
210.8
29.8
0.0
0.0
0.0
0.0
0.0
0.0
0.0
36.0
50.9
10.7
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.0 £ 10 24
0.0
32.0
1.0 £ 10 24
0.0
32.0
10 24
10 24
10 8
10 12
10 12
10 15
0.0
0.0
0.0
0.0
0.0
0.0
35.0
45.0
35.0
52.0
45.0
72.0
1.0 £ 10 24
0.0
32.0
1.0 £ 10 24
0.0
34.0
1.0 £ 10 24
0.0
36.0
17
18
19
20
21 a
22 a
23 a
24 a
25 a
26 a
27
28
29
30
31
32
33
34
35 b
36 b
37 b
1.0 £
1.0 £
1.0 £
1.0 £
1.0 £
1.0 £
Ea
p
Pre-exponentials are sticking coef®cient, multiplier to RT= 2pM collision limit expression.
b
Trapping reactions. The rates of reactions 35±37 were calculated by
multiplying the rates of reactions 15±17 by the dimensionless surface
coverage of dBSiH.
a
growth rates, but surface diffusion clearly must be included
in simulations of surface morphology evolution.
The mechanism of H2 desorption from a Si(100) surface
is not completely understood [23]. In this contribution, we
use the experimentally measured kinetics, based on dimers
as desorption sites on the surface. Speci®cally, H2 desorption occurs through two separate channels, the lower barrier
238
I. Lengyel, K.F. Jensen / Thin Solid Films 365 (2000) 231±241
Fig. 6. Model (continuous curve) and experiments (dots) for Si deposition from dichlorosilane (a) without HCl, and (b) with HCl. SiCl2H2 concentration is 4%
in H2 carrier gas for both cases, pressure is 2 Torr. T ˆ 1223 K for (b). Experimental data from Regolini et al. [32]. Model chemistry consisting of reactions 1±
17 of Table 3.
(48 kcal/mol) has a second order and the higher barrier (58
kcal/mol) has a ®rst-order dependence on the hydrogen
coverage. HCl and SiCl2 desorb with barriers of 62±65
and 67±72 kcal/mol, respectively [24]. All of these species
desorb more easily from boron-doped silicon surfaces, as
shown experimentally by Koleske et al. [30]. Hay et al. [16]
performed quantum chemistry computations of barriers for
H2 and HCl desorption from Si±B surface dimers and found
lowered barriers relative to the pure Si case, 35 kcal/mol for
H2 and 45 kcal/mol for HCl.
3.5. Proposed mechanism
Fig. 7. Normalized sensitivities of the Si growth rate in the model reactions
1±17 for Si deposition without the addition of B2H6. Conditions are the
same as for Fig. 6a.
The proposed mechanism is summarized in Table 3. The
mechanism is constructed so that in the absence of diborane
it describes the deposition of silicon from dichlorosilane and
the growth/etching process in the presence of HCl. That part
of the mechanism consists of reactions 1±17. Reactions 1±4
are the gas-phase thermal decomposition of dichlorosilane
within parameters from Su and Schlegl's work [5,29]. Reactions leading to disilane formation [6] are neglected because
of the low concentration of intermediates. Sensitivity analysis of the model justi®es this assumption. Reactions 5±8
represent the reactions of gas-phase species with silicon
dimers. The sticking coef®cient of dichlorosilane is adjusted
to describe the experiments of Regolini et al. [31]. This
value also gives good agreement with the observations of
Agnello et al. [3]. Reactions 9 and 10 are the desorption
channels of H2. Reactions 11 and 12 are the equilibration
of surface H and Cl to form dimers shown in Fig. 5. These
I. Lengyel, K.F. Jensen / Thin Solid Films 365 (2000) 231±241
239
Fig. 8. Model (continuous curves) and experiments (dots) of B-doped Si deposition in the SiCl2H2/B2H6/H2 deposition system. Growth rate (a) and boron
incorporation in silicon (b). Pressure is 760 Torr, SiH2Cl2 is 1%, B2H6 is 10 ppm. Dashed line is the simulated deposition rate without B2H6. Experimental data
are from Agnello et al. [3]. All the reactions in Table 3 were used in the chemical mechanism.
two reactions are important in determining the ratios of
double hydrogenated, double chlorinated and mixed dimers
at different temperatures and consequently the relative rate
of desorption and etching processes. Reaction 14 is the etching process in the form of SiCl2. The actual mechanism
leading to SiCl2 is more complex, involving ®rst breakup
of the dimers, then possible migration of dimer vacancies
and, ultimately, desorption [32]. The experimentally determined barrier is used without additional reaction steps since
the actual deposition rate is not sensitive to additional steps
as long as the barrier of the rate-limiting step is ®xed at the
experimental value. Reactions 15±17 are lattice formation
reactions, in which Si adatoms form new dimers. In order to
represent the bond strength between two Si atoms that have
different chemical environments, the barrier for lattice
formation is increased by 2 kcal/mol for Si adatoms with
Cl. The sensitivity analysis (described below) shows that the
deposition rate is not sensitive to the exact values of these
parameters.
Fig. 6 shows the ability of reactions 1±17 to describe the
deposition of silicon with and without HCl present. The
model predictions are consistent with the data, even in the
absence of detailed information about the reactor geometry.
The residence time in the simulated stagnation ¯ow reactor
was adjusted to provide correct transport limited deposition
rates of Fig. 6a. Fig. 7 shows sensitivity analysis results at
two different temperatures. At lower temperature the
deposition is controlled by desorption of HCl from the
surface (reaction 11) and etching (reaction 14). Although
necessary to describe the growth process, reactions 15±17
are not rate-limiting steps. At higher temperature the most
important process is the transport of SiH2Cl2 to the surface.
The sensitivity analysis further shows that gas-phase reactions are too slow, even at high temperatures, to make a
signi®cant contribution and they could therefore be
neglected.
The additional reactions (beyond reactions 1±17) in Table
3 are needed to describe B-doped Si deposition when B2H6
is added to the reactant SiH2Cl2. Above 800 K, which is
relevant to process conditions, BH3 is the dominant boron
species in the gas phase. Decomposition of diborane could
lead to boron-cluster formation of different sizes, but clusters are not signi®cant under the conditions of Si growth
(high temperature, low concentration of diborane, high
excess of H2 carrier gas). BH originates from the surface
and recombines with the carrier gas to produce BH3. These
B-species can adsorb on free Si dimers (reactions 21 and
22). In order to simplify the potentially complex mechanism
of reactions between BH3 and the Cl-covered Si surface, the
following approach is adopted.
The formation of adducts occurs with zero barrier independent of the size of the Si cluster, as indicated by the
quantum chemistry calculations. Diffusion of BH3 on a
Cl-covered Si surface can occur through break-up and refor-
240
I. Lengyel, K.F. Jensen / Thin Solid Films 365 (2000) 231±241
mation of adducts, which provides additional opportunities
for Cl±H exchange reactions. In the absence of detailed
kinetic data, the process is described by a single reaction
probability (reactions 23 and 24). In addition to the Cl±H
exchange reaction, BH3 can also react with the surface to
form direct Si±B bonds. Since this reaction has a higher
activation barrier than the exchange reaction, the reaction
probability was set two orders of magnitude lower. The ratio
of reaction probabilities for exchange and Si±B formation
determines the B concentration on the surface and consequently the B concentration in the Si lattice. The 100 times
higher exchange to transfer ratio is consistent with B-incorporation data. BH on the surface may form B±Si dimers
(reactions 27 and 28) which can participate in reactions to
remove H2 and HCl from the surface with lower barriers
(reactions 29 and 30). The energy barriers for these reactions derived from the calculations of Hay et al. [16]. The
Si±B dimers either break up at higher temperatures or
become trapped by the growing silicon. The sharp decrease
of B-content between 600 and 700 K is an indication of a
surface reaction from a precursor. Reaction 32 is chosen to
represent this process. Reaction 34 parallels the silicon etching process (reaction 14) implying that Cl also removes the
incorporated B under Si etching conditions. B out-diffusion
from the Si lattice was not included because of the moderate
growth temperatures. This reaction with the appropriate
barrier (~80 kcal/mol) can be added if one would like to
predict B-autodoping at higher temperatures. The performance of the full model in describing silicon deposition in
the presence of B2H6 is shown in Fig. 8. The model represents the important features of the experiments. The sensitivity analysis (Fig. 9) reveals that the transport of B to and
from the surface critical to determining the B content.
4. Conclusions
In this contribution we have demonstrated a systematic
approach to formulating chemical mechanisms to CVD
processes. Models of ¯uid ¯ow and heat and mass transfer
capable of simulating ®lm thickness and composition variations in CVD systems provide understanding of the in¯uence of ¯uid phenomena on ®lm uniformity and
composition, but they are often limited by the knowledge
of reaction pathways and kinetics. Chemical kinetic data
and understanding of reaction mechanisms become particularly important when predicting doping concentrations
where even minor changes in gas-phase species or surface
interactions can lead to signi®cant effects in dopant concentration levels. The unusually large growth rate enhancement
observed for in situ B-doping of Si was used to exemplify
issues in the development of chemical mechanisms for CVD
systems. The basic computational tools needed for mechanism development; quantum chemistry calculations, sensitivity analysis, and ®nite element simulations were combined
to develop a mechanism for the process and to provide
Fig. 9. Sensitivity analysis results of silicon and boron growth rate for
reactions listed in Table 3. Conditions are the same as those of Fig. 8.
Temperature is 873 K.
quantitative predictions of observed growth and dopant
incorporation rates. Ab initio quantum chemistry computations of small molecules and clusters relevant to the H±B±
Cl±Si system was used to determine thermodynamic and
kinetics parameters. In particular, Cl±H exchange reactions
between borane and chlorosilanes were studied and shown
to proceed with low reaction barriers. The reaction mechanism was incorporated into ®nite element simulation of
reported deposition data. The developed mechanism was
able to describe (a) the silicon deposition from dichlorosilane; (b) etching of silicon by HCl; and (c) B-doped Si
deposition in the SiCl2H2/B2H6/H2 deposition system. The
most important deposition processes were identi®ed by
sensitivity analysis. Gas-phase decomposition reactions of
dichlorosilane did not contribute signi®cantly to the deposition process and could be eliminated to simplify the model.
The study demonstrates the utility of a systematic approach
to chemical mechanism development for CVD processes.
Acknowledgements
The Semiconductor Research Corporation supported this
work. The authors also thank Jeff Hay, Joel Kress, and
I. Lengyel, K.F. Jensen / Thin Solid Films 365 (2000) 231±241
Pauline Ho for discussions of the chemistry of the H±B±Cl±
Si system.
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