2-3-1 The growth mechanism and the surface morphology of the post- deposited Al2O3 films.
Figure 2-7 illustrates the growth rate of the ALD system at 200 °C which is the temperature associated with the thickest Al2O3 film in Fig. 2-8 − the growth mechanism of an ALD system. In literature [4], it had pointed out that an ALD system shows almost complete reactions of the two self-cease sequential cycles and more than 80 % (~ 100 % at temperature− 300 K) of coverage of the reactants on alumina membranes during deposition process (explained below) at the temperature of highest growth rate. We also labeled the calculated growth rate (~ 1.2 angstrom/cycle) in Fig.
2-7. The growth rate is similar to that reported somewhere and implies that it is unnecessary to consider the transient region during an initial stage of atomic layer deposition [19] and precursor concentration effect [20] duriing the deposition process. This means that the ALD system has been fine tuned so that we could avoid mentioning the problems might be considered in application of an ALD system.
Referring to some publications [19, 21] and combining our hypothesis inspired from Statistical Mechanics, we did further simulation of the growth mechanism of the ALD system for constant deposition cycles in Fig 2-8 by the following equation;
θ e
film O Al ALD an of
Thickness 2 3 ∝ −ΔUS(internalenergy)kT ⋅ (2.1)
k is the Boltzmann constant and T is temperature in Kevin. Besides, θ and ( ), respectively, stand for the surface coverage of reactants and the difference of internal energy of the reactants before and after transforming into a surface complex while adsorbing on the surface. As soon as a surface complex (explained later) formed, it transforms into the surface species such as Al(CH
energy) (internal
ΔUs ≥0
3)2- or Al(OH)2- adsorbance [4, 22] on alumina membranes. In Fig. 2-8, the thicknesses of the films deposited at 60 cycles were estimated from the results of the measurements by High Resolution Transmission Electron Microscopy (HRTEM), arranged in Fig.
2-9; and, in addition, we employed Electron-Dispersive-Spectra (EDS) technique to check the composition of the dielectric films roughly in Fig. 2-10. In eq. 2.1, we assumed approximately that, in a reaction cycle, the distribution of the binding and nonbinding reactants, as the TMA- and H2O-surface complexes, of a precursor followed the classical Boltzmann distribution despite an open system arising during the deposition process. Based on this ideal, we presumed that the probability, P (binding), of the reactants bind while adsorbing on the surface in a reaction cycle could be represented by this equation;
e
(binding)
P ∝ −ΔUS(internalenergy)kT (2.2) Besides, moreover, it is well known that the adsorption rate can generally be expressed in the following equation [19, 21] without taking account of dissociation of
the precursors;
In many cases, the adsorption rate is much higher than the desorption rate, so that desorption rate can be ignored in deriving eq. 2.3 [19]. Supposing that ideal 2-dimention (2-D) growth occurred (set n=1) during the reactions and solving eq. 2.3, we obtained the solution;
t} A(T)is an arbitrary function of temperature that can be determined by a proper boundary condition (B.C). Since the ALD system has been fine adjusted, we can always obtained saturated coverage of the absorbances in per pulse of precursor injection. Then, we further considered the probability of dissociation of the precursor− TMA, which had been pointed out that it dissociated appreciably and deposited aluminum on the surface [23] at temperature above 650 K [4]. We replaced the ideal coverage, 1 (for 300K), by a function of pressure and temperature −
( , for 2-D growth). Furthermore, from the researches of A.W. Ott’s et al. [4] and by P) B(T,
≤1
intuition of mathematics somewhat, it was conjecturable that this function was almost linearly proportional to temperature, and eq. 2.4 could be rewritten as eq. 2.5 at saturation mode; It has the relationship to effective adsorption constant ( ) and complete-dissociated temperature ( ). Both are related to the partial pressure of a precursor in reactor.
Combing eq. 2.2 with eq. 2.4, we arrived at the eq. 2.1. For associating eq. 2.1 with temperature and pressure only, we made the use of eq. 2.5 to modify the equation in a more acceptable form below;
αO Then, by multiplying an independent constant C, the growth rate equation could be rewritten as; Constant C could be determined approximately by simulating the outcome of an experiment with the value of the complete-dissociated temperature ( , the result of A.W. Ott et al.), the temperature of highest growth rate ( defined below, at which it has the almost 80 % coverage and calculated
K 800 TO=
THGR
αO~ 0.0023 1/K for ), and the solution of eq. 2.12 (explained later). Additionally, the temperature corresponding to highest growth rate in our study (see Fig. 2-8) is higher
K 800 TO =
than that reported somewhere [3, 4]. In A. W. Ott′s article, it showed the outcome on cleaned Si wafers followed by H20 plasma treatment that oxidized the Si (100) sample and left the SiO2 surface completely hydroxyllated.
To further discuss the shift in the temperature of highest growth rate (HGR) (abbreviated as THGR below), we did the simulations involving modulating the four parameters (C , αO, , and ) encountered in eq. 2.7 individually and investigated the effects of the modulations on the curves of growth rate in Figs.
2-12~15. Before discussing in depth, we must have a sketch of the range of values and the characteristics of those parameters and their relationship. Equation 2.8 shows the first differentiation of eq. 2.7 for calculating T
TO ΔUS
For getting this temperature, it is necessary that eq. 2.8 be equal to zero;
0
By solving the quadratic equations with Quadratic Formula and extracting directly, we have all the possible solutions;
(K)
And above all, the solution makes sense is;
(K)
We could, next, further rewire eq. 2.11 and associate with in a more
After substituting the parameters with the available values ( and ) in A.W. Ott’s article and regarding the reasonable range of (~ 600 – 800, 900 K) [24, 25], we got the computation that (~ 600 − 1200 k Joule) has order of value about 10
K
-1 ~ 5x10-2 eV consistent with that calculated by First Principle in Mathew D. Halls’s research [26], in which it describes that the reactant complex between TMA and the surface is more weakly bound than the H2O-surface complex with a calculated binding energy of only 0.03 and 0.04 eV. We had summarized the calculation results in Fig. 2-11 and Table 2-1. Besides, we could estimate the value of
the independent constant, C (~ 5.2 ), and the effective adsorption constant, (~ 0.0023 1/K ). Since the value of is close to the energy to break a (weak) chemical bond involving electromagnetic force, we do really have a self-consistent derivation of the ALD mechanism and reasonable estimation of the values of the parameters. Taking a look at eq. 2.12, moreover, we could suggest that being almost independent of the parameter−
/cycle
shift of THGR would be related to different partial pressures of the precursors, surface
It is ready now to discuss the results of the simulation in Figs. 2-12~15. Figs.
2-12 and 2-13 show the curves corresponding to the modulation of the two parameters− CandαO. The range of values of αO (corresponding to 5 % ~ 95%
coverage of the reactants on the surface) in the simulation was the possible coverage level at the temperature, , about 450 K. For parameter− , it was just chosen around the value estimated through the simulation of the growth rate of A.W. Ott’s results to observe the variation related to it. We found that the growth rate is up with increase of the values of and
THGR C
C αO (a function of partial pressure of the precursors), but the temperature, , is almost independent of what referred above (in Fig. 2-12 (d) and 2-13 (d)). This observation is consistent with what concluded from eq. 2.1. And, moreover, the pressure during deposition processes and the growth rate calculated in our studies were higher than that recorded in A.W. Ott’s article. By intuition, higher deposition pressure might lead to higher partial pressure and surface coverage of the precursors; and, then, resulted in higher growth rate calculated in our research. Then, let’s go on to Figs. 2-14 and 2-15 which explain the shift of T
THGR
HGR
intimately. In Fig. 2-14, the range of the value of was about 600 to 800-900 K,
which were close to the values ever emerged in references. It shows that the growth rate of an ALD system and the temperature of a HGR point, , would go up with the increase of complete-dissociated temperature, , related to the partial pressure
TO
THGR
TO
of the precursors in reactor to a certain extent. But, something different for the simulation of the modulation of , we could find that in contrast with , the growth rate decreases with the increase of . In our study compared with that of A.W. Ott et al., in which the data we exploited most, we carried out the deposition process at a higher pressure and on a substrate with different clean technique involving a last-HF dip to make the surface H-terminated that would show higher barrier for reactants adsorbing on to the surface. Then, based on the results of the simulation and by intuition somewhat, we came to the conclusion that higher growth rate and observed in our research were resulted from higher
ΔUS THGR
ΔUS
THGR αO, , and
occurred during the processes.
TO
ΔUS
Now, we must show consideration for the surface morphology, measured by Atomic Force Microscopy (AFM) in Fig. 2-16. It might be related strongly to uniformity of the film, Chemical Vapor Deposition (CVD) behavior for an ALD system designed imperfectly, crystal phase of the film, and crystallization of a dielectric film during processes, etc. In this figure, it shows an acute issue involving CVD reaction while depositing a film at a lower temperature and this symptom alleviated at deposition temperature above 200 °C. We speculated that the CVD phenomenon should be due to an imperfect designed ALD chamber and higher viscosity of TMA at lower deposition temperature. Although less CVD reaction occurred at higher
deposition temperatures, it would result in severe formation of pinhole related to Ge out-diffusion through the formation of vapor-like GeO from the substrate surface at deposition temperature higher than 200°C. So it is better to deposit an ALD film at temperature around 200 °C for a more sound surface and less CVD reaction.
2-3-2 Analyses of Angle-Resolved X-ray Photoelectron Spectroscopy (AR-XPS) and Secondary Ion Mass Spectroscopy (SIMS).
Figure 2-17 illustrates the setup for AR-XPS measurement and the definition of take-off angle. Fig. 2-18 shows the inelastic mean free path (IMFP) versus (photo-) electron kinetic energy and the universal curve calculated by M. P. Seah and W. A.
Dench [27, 28, 29]. Before discussing the results of AR-XPS measurements of the samples deposited at 60 cycles, we should estimate the range of detectable depth (DD) of the elements monitored by combining the outcome of the measurement and the information in Fig. 2-18. We could trace back where the photoelectron (PE) came from and conjecture what happened within this distance from sample surface through the estimation of IMFP alone with the measurement results. But, our case is incompatible with the calculation of IMFP in M. P. Seah′s research. However, around the mid-1980s, it was suggested that the appropriate length scale to substitute into the quantification equation was not the IMFP but the “attenuation length (AL)”. Powell [30, 31] defined the AL as “a value resulting from overlayer-film experiments on the
basis of a model in which elastic electron scattering is assumed to be insignificant. So, we applied the C. J. Powell′s formula, eq. 2.13 for calculating AL, to estimate the length so called, “IMFP,” in the past and summarized the calculation in Table 2-2.
(nm)
Additionally, in Table 2-2, effective detectable depth (EDD) represents a DD that we had token the take-off angle into account. We could find that it is well to deposit the ALD films with ~ 60 cycles for investigating the MOS gate stack characteristics. From the calculation of EDD and the thicknesses estimated in Fig. 2-9, it is conjecturable that all the Ge 2p3 XPS core-level signals should almost come from the bulk of the Al2O3 films. So, we could monitor if the Ge incorporates into and diffuses away from the dielectric films. Furthermore, by monitoring the signal of Ge 3d compared with that of Ge 2p3, we could also sure if the near interface consists of a few layers containing Ge atoms in intermediate oxidation states i.e., GeOx, etc. during
deposition processes.
Now, let′s discuss the Ge 3d spectra with peak fitting by the commercial XPSPEAK software package (the XPS peak fitting parameters had been summarized in Table 2-3) in Figs. 19, 21, 23, and 25 that are corresponding to the ALD films deposited at R.T. (~ 50 °C), 100 °C, 200 °C, and 300 °C, respectively. Although the Gibbs free energy of GeO2 is larger in magnitude than that of Ge native oxide [32], we found that the formation of Ge native oxide (GeOx, x ~ 1) was easier than that of Ge dioxide for the as-deposited ALD films. We considered it is because that higher concentration (conc.) of Ge(s) and GeO2 (s) occurred initially promoted GeOx to form through the reaction mechanism − eqs. 2.15 and 2-16 [33] − at initial stage; but, the onset of disproportionation through eq. 2.17 was observed at temperature about 245±25 °C [34, 35], so that we obtained a GeOx-rich film rather than a GeO2-rich one for the rudeness ALD films.
GeO GeO
Ge(s) + 2(s)→ (g) (2.15) GeO
GeO(g) → (s) (2.16)
(s) 2 (s)
(s) Ge GeO
GeO → + (2.17)
After PMA 400 °C, we can see that the amount of GeO2 increases but decreases for that of GeOx since the annealing temperature had triggered off disproportionation to produce Ge and GeO2. Further increasing the annealing temperature to 600 °C, we
had almost lost track of the Ge oxide signal of the film deposited at R.T. (~ 50 °C), 100 °C, and 300 °C due to the Ge out-diffusion and full disproportionation (at temperature about 525±50 °C) [34, 35] happened during the thermal process. Ge out-diffusion was confirmed by monitoring the Ge 2ps XPS spectra in Figs. 20 (a), 22 (a), 24 (a), and 26 (a); and, it also shows that the Ge 2p3 peak position gets close to original position gradually. But something different for the 200 °C ALD film in Fig.
2-23, the oxide signal enhanced while suffering to such a high annealing temperature.
Through inspecting the oxygen (O) SIMS spectra of the as-deposited film in Fig 2-34 (a), we supposed that because of higher O conc. permeated into the substrate during film deposition and thicker film showed in Fig. 2-9 or 2-33 leaded to such dense GeO2
residue in the 200 °C ALD Al2O3 film. By the way, let′s take a look at the carbon (C) SIMS spectra of the as-deposited film in Fig 2-34 (b). In this figure, it reveals severe C incorporation into the dielectrics for a lower deposition temperature since incomplete ALD reaction could lead to non-reacted CH3− bond remained. The variation of Ge oxide in the film subjected to various thermal processes had been summarized in Fig.
2-29 through the XPS PE intensity ratio of Ge oxide to Ge as eq. 2-18;
% I 100
I ratio I
Intensity
Ge GeO
GeO + 2 ×
= (2.18)
After studying the Ge 3d and Ge 2p3 XPS spectra, we surveyed the Al 2p and O
1s XPS core-level spectra related to how stoichiometric the film is in Figs 20 (b) (c), 22 (b) (c), 24 (b) (c), and 26 (b) (c). In those figures, the peak position of the Aluminum-hydrogen-carbonate (AHC), gamma (γ), and alpha (α) aluminum oxide had been labeled as guide for eyes. Those spectra imply that we would get a more and more destroyed film when increase the annealing temperature but a less destroyed film when deposited it at temperature about 200 °C due to a more complete ALD reaction. The extent of destruction can be represented somewhat by the extent of shift of the Al 2p and O 1s XPS peak position in Fig. 2-30. All the films show an energy rising-up phenomenon which were conjectured due to C and H residues in the film or near the surface (see Fig. 2-34 (b)). Furthermore, by extracting the XPS spectra areas, we can calculate the elementary ratio between the detected elements through eq. 2.19 [36, 37, 38] with some error due to using this equation on an improper case.
%)
XPS sensitivities of Ge 2p3 (=24.15), Al 2p (=0.537), and O 1s (=2.89) core-level against the sensitivity of C 1s (=1.00), respectively. Similarly, we could also calculate the at. % {Ge} and {Al} of the films; and all the results of calculation were summarized in Figs. 2-27, 2-28, and Table. 2-4. However, what should be further mentioned is that this equation is more correct and useful to calculate a uniform and unique composed film for the detected elements. The calculation shows that the ALD films got more stoichiometric when increased the deposition (but not for the 300 °C case) and anneal temperature. But this is inconsistent with the conclusion what followed the discussions on the shift of the Al 2p, O 1s, and Ge 2p3 XPS peak position in Fig. 2-30. In addition, the calculation of the film deposited at 300 °C shows a contradictive behavior due to an improper use of eq. 2-19. All the questions mentioned can be explained as a result of the mixed signals from Ge substrate. But despite this, it is still worthy to see the conc. of O and Ge decreased when increased the deposition and anneal temperature in Fig 2-28. This implies the Ge out-diffusion through the formation of vapor-like GeO. We need a credible method to judge the extent of stoichiometry of those ALD films yet. Energy spacing might be a trusty and convenient definition to show how stoichiometric a film is [12, 39]. It is explained as the inst in Fig 2-32 and eq. 2-20;
This equation describes that energy spacing is the difference between the binding energy of O 1s and Al 2p XPS peak position in magnitude. Fig. 2-32 shows the energy spacings of various phases of aluminum oxide as references for determining what the phase an ALD film has. Fig. 2-31 summarized the energy spacings of those ALD films subjected to different thermal processes and the energy spacing of γ- and α- aluminum oxide also labeled in it. It shows a more consistent result with what mentioned above than that concluded from the calculation of at. % {element}. So far along with Fig.
2-31, we can conclude the results of AR-XPS analysis that;
1- We get a more stoichiometric and Ge incorporated ALD film with increase of deposition temperature.
2- We get a more GeOx and C (might be due to non-reacted CH3− bond remained ) incorporated ALD film with decrease of deposition temperature.
3- The incomplete reacted ALD films get more destroyed with increase of annealing temperature.
4- The almost complete reacted ALD films (deposited at temperature~ 200
°C) get less destroyed with increase of annealing temperature in comparison to that described in point 2 but have more O permeated into
the substrate during film deposition.
5- We have a proper range of temperature about 140 °C ~ 170 °C to deposit a more stoichiometric, complete reacted, and less GeOx and C incorporated ALD Al2O3 film.
In order to get further comprehending more information about the density and interface roughness of the ALD films, we must applied the GI-XRR technique to figure out the possible composite layers through the films; and, then, individual film thicknesses, roughnesses, and densities of a multilayer stack can be extracted.
2-3-3 Analyses of Grazing-Incidence X-ray Reflectivity.
We use a Bede GI-XRR system to measure the as-deposited and semi-manufactured samples (without Pt gate electrodes and Al back-contact) to estimate the thicknesses, densities, roughnesses, and possible distributions of elements of the ALD Al2O3 films deposited at various temperatures. Fig. 2-36 collects all the measured results to show what is different between those as-deposited films. After measurements, data evaluations were carried out with the commercial Bede REFS Mercury software package. For a better consistency of the fitting results and a minimization of the number of fitting parameters, we took the available data from
parameters and kept them fixed during the fitting. Table. 2-5 summarizes the thermal-dynamics related formation energy of the possible formed compounds as reference for helping modeling a multilayer stack to fit the obtained raw data.
Combining with the results of the analysis of AR-XPS and Table 2-5, we model a stack with 5 layers showed in Figs. 2-37, 38, 39, and 40 for figuring out the possible distributions of the elements overall the dielectrics. Figs. 2-35 displaces the fitting outcomes with minimized cost functions, χ2, and gets fitting curves compared with the measured data to show how better the fitting is. From the best fitting with the 5 layer
Combining with the results of the analysis of AR-XPS and Table 2-5, we model a stack with 5 layers showed in Figs. 2-37, 38, 39, and 40 for figuring out the possible distributions of the elements overall the dielectrics. Figs. 2-35 displaces the fitting outcomes with minimized cost functions, χ2, and gets fitting curves compared with the measured data to show how better the fitting is. From the best fitting with the 5 layer