Calculation of growth per cycle (GPC) of atomic layer deposited aluminium oxide nanolayers and dependence of GPC on surface OH concentration

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1 PRAMANA c Indian Academy of Sciences Vol. 82, No. 3 journal of March 2014 physics pp Calculation of growth per cycle (GPC) of atomic layer deposited aluminium oxide nanolayers and dependence of GPC on surface OH concentration ANU PHILIP, SUBIN THOMAS and K RAJEEV KUMAR* Department of Instrumentation, Cochin University of Science and Technology, Cochin , India rajeev@cusat.ac.in MS received 23 May 2013; revised 29 October 2013; accepted 25 November 2013 DOI: /s ; epublication: 6 March 2014 Abstract. In this paper a theoretical calculation is presented for the growth per cycle (GPC) of the film and the variation of GPC with OH concentration on the substrate surface. The calculated GPC range (0.179 nm nm) agrees well with reported experimental values. The present approach yielded a density of 2.95 g/cc for the deposited films. The number of monolayers (ML) as a function of the OH concentration on the substrate surface is calculated and is found to be in the range of % of the total number of cycles of deposition. Effective monolayer thickness is calculated as 0.31 nm. Keywords. Atomic layer deposition; high-k; aluminium oxide. PACS Nos Gh; D 1. Introduction Large leakage current across the silicon dioxide films of thickness less than 3 nm has forced the processor industry to search for alternate high dielectric constant (high-k) materials as the gate oxide of MOSFET [1 3]. Aluminium oxide prepared by atomic layer deposition (ALD) has been considered as a promising material because of its several desirable properties like high dielectric constant, small leakage current, large band gap, large band offset with silicon, thermal stability on silicon, amorphous nature, etc. [1, 4 6]. ALD has become the technique of choice for the deposition of extremely thin gate oxide for MOSFET and dielectrics for trench capacitors. It is a unique thin film deposition method where atomic layer level precision in thickness is possible. ALD is a variant of chemical vapour deposition (CVD). It was invented by Suntola in late 1970s and was Pramana J. Phys., Vol. 82, No. 3, March

2 Anu Philip, Subin Thomas and K Rajeev Kumar initially used as a precision deposition method for electroluminescent display applications. Later, the method was found extremely useful for the deposition of very thin and well-controlled nanolayers of high-k materials for gate oxide applications. The technique is based on surface area controlled self-limiting reactions and the coating is highly dense, conformal and pinhole free [1,6,7]. In this communication we report the calculation of growth per cycle (GPC) of Al 2 O 3 (alumina) prepared by ALD using trimethyl aluminum (TMA) and water, from geometric considerations and the dependence of GPC on surface OH concentration. The density of the deposited film, number of monolayers as a function of OH concentration on the substrate surface and the effective monolayer thickness are also calculated. 2. Calculation of GPC ALD technique relies on saturating gas solid reactions. Two gaseous precursors are usually used in ALD. They are allowed into the chamber as pulses, one after the other, with high-purity argon/nitrogen pulses in between. Precursors are chemically adsorbed on to the substrate/previous layer in a saturating fashion. Argon/nitrogen is pulsed into the chamber to purge out any unreacted gases and by-products. These four pulses constitute one cycle of deposition which is expected to form one monolayer of the product molecules on the substrate surface. This reaction cycle is repeated till the required film thickness is obtained. Growth per cycle (GPC) is defined as the incremental increase in the thickness of the film per cycle of deposition. GPC is an important parameter of ALD technique. In comparison with the similar term rate of deposition for other thin film deposition methods, GPC of ALD yields generally a low value. Considering the molar mass and density of α-al 2 O 3 as g and 3.99 g/cc [8] we get the volume of one molecule of Al 2 O 3 as nm 3 and radius (r) of one molecule as nm. Assume that the ALD-deposited Al 2 O 3 has a face-centred cubic close packing as shown in figure 1 which is the densest packing. Volume of the unit cell shown in figure 1 is nm 3 with radius of a sphere as nm. As the total number of spheres in a face centred cubic (fcc) unit cell is 4, the effective volume occupied by a single sphere is nm 3. With maximum OH species on the surface of the substrate taken as approximately 12 per nm 2, a maximum Figure 1. A unit cell of face-centred cubic close packing. r is the radius of a sphere. 564 Pramana J. Phys., Vol. 82, No. 3, March 2014

3 Calculation of growth per cycle Table 1. Number of OH sites on the surface of 1 nm 2 area of substrate vs. no. of Al atoms adsorbed/nm 2 area [9]. Number of OH/nm 2 Number of Al atom adsorbed/nm of 6.25 Al atoms can be chemisorbed per nm 2 area [9]. As two Al atoms are required for the formation of one Al 2 O 3 molecule, Al 2 O 3 molecules per nm 2 area can form under this condition. Assume that 100 cycles of deposition are done. Then Al 2 O 3 molecules are formed on 1 nm 2 area of the substrate. Total effective volume occupied by Al 2 O 3 molecules is nm 3. Hence total thickness developed above 1 nm 2 area is nm and this yields a GPC of nm. Table 1 shows the number of Al atoms adsorbed on the substrate surface (per nm 2 area) for different values of OH species on the substrate surface. The surface chemistry which yields these values is complete ligand exchange (CLE) together with complete dissociation (CD) as proposed in our previous paper [9]. This surface chemistry generates the experimentally observed curve of Al atoms per nm 2 area vs. OH concentration [1,9]. Repeating the above calculation of GPC for different OH concentrations on the substrate surface, we get the values given in table 2. Therangeof GPCgivenintable2 agreeswellwith variousreportedvalues [5,6,10 17]. It is important to note here that for any particular deposition process, the number of surface species depends on the type of substrate and the substrate temperature [1]. Hence, the deposition may start with a GPC appropriate for that substrate at that temperature. Later, after a few cycles of deposition, the substrate will be covered with layers of alumina Table 2. OH concentration on the substrate surface vs. calculated GPC. No. of OH/nm 2 Calculated GPC (nm) Pramana J. Phys., Vol. 82, No. 3, March

4 Anu Philip, Subin Thomas and K Rajeev Kumar and the number of the substrate species will change to the characteristic value for alumina. Hence the GPC may change to a new value and continue at that value throughout the rest of the coating [1,18]. 3. Density of Al 2 O 3 deposited by ALD The density of as-deposited thin films in general is less than that of the bulk value. This is mainly due to the low energy of the evaporants or reactants in various physical and chemical deposition methods. Usually this is compensated by supplying additional energy in the form of substrate heating, plasma enhancement or ion assistance. In atomic layer deposition, substrate heating and plasma assistance are regularly employed to improve the film quality. However, a high substrate temperature during deposition can also cause re-evaporation of the adsorbed atoms from the substrate surface. Moreover, the fact that TMA decomposes approximately at 300 C[1,17,19] imposes an upper limit to the substrate temperature. From figure 1, we get the volume of a unit cell as 0.23 nm 3 and this volume contains four molecules. Hence the number of molecules per nm 3 is and the corresponding mass of molecules is g. This yields density of ALD-deposited Al 2 O 3 as g/nm 3 or 2.95 g/cc. The value of density obtained here is less than the bulk value of alumina [8]. However, this is in agreement with the experimentally reported values for ALD alumina [20 22]. The density of alumina deposited by ALD may also depend on the type of growth mode like two-dimensional/island/or random growth modes [1,17]. Figure 2. Five monolayers, stacked one above the other are shown. The total thickness of the film is the sum of the thicknesses of the two unit cells and the two radii one at the top and the other at the bottom of the layers. 566 Pramana J. Phys., Vol. 82, No. 3, March 2014

5 Calculation of growth per cycle 4. Calculation of the number of monolayers (ML) Consider figure 2, where five monolayers of Al 2 O 3 are shown. The total thickness (t) means total thickness of two unit cells plus one radius (r) at the top side and one radius at the bottom side of the film. Total thickness t = (C 2 2r) + 2r, (1) where C is the number of unit cells. Therefore, C = (t 2r)/2 2r. (2) Each unit cell contains effectively two monolayers. One radius at the bottom of the film and one radius at the top effectively add one ML to this. Hence the number of ML (n) can be written as n = (2C + 1) i.e., n ={[(t 2r)/ 2r]+1}. (3) Using figure 2, the total thickness of the film is calculated as t = 1.65 nm. Substituting this value of t in eq. (3), we get the number of ML as n = 5. In 2 of this paper, we found that the total thickness t developedafter 100 cyclesof ALD operationfor a GPC of is17.9 nm. For this thickness, the number of MLs obtained using eq. (3) is In an ideal ALD, one expects one ML per cycle. However, this is never observed in practice [1,9,17,19]. This calculation shows that a maximum of 58% of the ideal number of ML value which one expects from the number of cycles only, will be formed during ALD. From table 2 in 3 it can be observed that as GPC decreases from to (which again corresponds to a decrease in OH concentration from 12 to 2 on the substrate surface) number of ML decreases from 58.4 to Most of the reported values [17,19] support this observation. This reduction in the number of MLs can be due to the steric hindrance caused by ligand molecules of trimethyl aluminum during its chemisorption [20]. 5. Monolayer thickness The monolayer thickness (h) predicted by the equation h = (M/ρN A ) 1/3 where M and ρ are the molar mass and density of Al 2 O 3 [20] yields a value of 0.39 nm (for a density of 2.95 g/cc calculated in 2). But Puurunen has considered monolayer thickness as Table 3. Variation of percentage of monolayer with OH concentration for a single cycle of deposition. Number of OH/nm 2 % of ML for single cycle of deposition Pramana J. Phys., Vol. 82, No. 3, March

6 Anu Philip, Subin Thomas and K Rajeev Kumar the height of a cube containing one product molecule MZ x which in the present case is Al 2 O 3. This gives absolute value of a monolayer thickness and is of interest only when one monolayer is deposited. In practical applications, the film will be composed of several monolayers and the effective thickness of a monolayer is more important. Effective monolayer thickness will be less than the above value due to the face-centred cubic close packing of the deposited film (figures 1 and 2). From figure 1 it is evident that a unit cell contains two monolayers and hence the effective thickness of a monolayer is 2r or 0.31 nm. In 4 it was found that 58.4 MLs are formed for 100 cycles of deposition with nm GPC. This yields an effective ML thickness of 0.31 nm. (This can be naturally expected as the GPC and number of ML calculations use the dimensions of the unit cell). It is evident that as the OH concentration on the surface of the substrate decreases from 12 to 2 the number of monolayers decreases from 58.4 to 24.2 for 100 cycles of deposition. It can be interpreted in another way as, effectively 58.4% to 24.2% of a monolayer only is formed during one cycle of deposition corresponding to the maximum and minimum number of surface sites. These data are given in table 3. The monolayer thickness remains the same in all cases and can be approximated to 0.31 nm. 6. Conclusion Atomic layer deposition is a technique which is ideally suited for the deposition of nanolayers of high-k oxide dielectrics especially alumina. Even though many reports have been published on various aspects of atomic layer deposition of alumina, still there are various gray areas like dependence of GPC on substrate type, surface species, deposition temperature, growth mode, etc. which are not conclusively settled. In this article we have tried to calculate GPC as a function of surface OH concentration. For this we have assumed the surface chemistry proposed in one of our earlier papers which agrees well with the reported experimental observations [9]. The range of GPC values so obtained matches very well with various reported values. The density of atomic layer deposition of alumina film was calculated to be 2.95 g/cc. This value is lower than the density of bulk alumina, but agrees very well with various reported experimental values for amorphous alumina films. The number of monolayers (ML) as a function of the total film thickness was calculated and was found to be in the range of % of the total number of cycles of deposition. This also means that during one cycle of deposition % of a monolayer is formed which is an experimentally observed fact in atomic layer deposition of alumina. By using the unit cell dimensions of a cubic close packed system, the effective monolayer thicknesses was calculated to be 0.31 nm. Acknowledgement One of the authors (AP) acknowledges the research fellowship by Department of Science and Technology. The work was carried out with the financial assistance of Kerala State Council for Science, Technology and Environment (KSCSTE). 568 Pramana J. Phys., Vol. 82, No. 3, March 2014

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