calculation of growth per cycle (gpc) of atomic layer deposited aluminium oxide nanolayers and...

PRAMANA c© Indian Academy of Sciences Vol. 82, No. 3— journal of March 2014

physics pp. 563–569

Calculation of growth per cycle (GPC) of atomic layerdeposited aluminium oxide nanolayers and dependenceof GPC on surface OH concentration

ANU PHILIP, SUBIN THOMAS and K RAJEEV KUMAR*Department of Instrumentation, Cochin University of Science and Technology,Cochin 682 022, IndiaE-mail: [email protected]

MS received 23 May 2013; revised 29 October 2013; accepted 25 November 2013DOI: 10.1007/s12043-014-0715-8; ePublication: 6 March 2014

Abstract. In this paper a theoretical calculation is presented for the growth per cycle (GPC) of thefilm and the variation of GPC with OH concentration on the substrate surface. The calculated GPCrange (0.179 nm–0.075 nm) agrees well with reported experimental values. The present approachyielded a density of 2.95 g/cc for the deposited films. The number of monolayers (ML) as a functionof the OH concentration on the substrate surface is calculated and is found to be in the range of 58.4–24.2% of the total number of cycles of deposition. Effective monolayer thickness is calculated as0.31 nm.

Keywords. Atomic layer deposition; high-k; aluminium oxide.

PACS Nos 81.15.Gh; 77.55.D–

1. Introduction

Large leakage current across the silicon dioxide films of thickness less than 3 nm hasforced 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 atomiclayer deposition (ALD) has been considered as a promising material because of its sev-eral desirable properties like high dielectric constant, small leakage current, large bandgap, 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 gateoxide for MOSFET and dielectrics for trench capacitors. It is a unique thin film deposi-tion method where atomic layer level precision in thickness is possible. ALD is a variantof chemical vapour deposition (CVD). It was invented by Suntola in late 1970s and was

Pramana – J. Phys., Vol. 82, No. 3, March 2014 563

Anu Philip, Subin Thomas and K Rajeev Kumar

initially used as a precision deposition method for electroluminescent display applica-tions. Later, the method was found extremely useful for the deposition of very thin andwell-controlled nanolayers of high-k materials for gate oxide applications. The techniqueis 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) ofAl2O3 (alumina) prepared by ALD using trimethyl aluminum (TMA) and water, fromgeometric considerations and the dependence of GPC on surface OH concentration.The density of the deposited film, number of monolayers as a function of OH con-centration on the substrate surface and the effective monolayer thickness are alsocalculated.

2. Calculation of GPC

ALD technique relies on saturating gas–solid reactions. Two gaseous precursors areusually used in ALD. They are allowed into the chamber as pulses, one after theother, with high-purity argon/nitrogen pulses in between. Precursors are chemicallyadsorbed on to the substrate/previous layer in a saturating fashion. Argon/nitrogenis pulsed into the chamber to purge out any unreacted gases and by-products. Thesefour pulses constitute one cycle of deposition which is expected to form one mono-layer of the product molecules on the substrate surface. This reaction cycle is repeatedtill the required film thickness is obtained. Growth per cycle (GPC) is defined as theincremental increase in the thickness of the film per cycle of deposition. GPC is animportant parameter of ALD technique. In comparison with the similar term ‘rate ofdeposition’ for other thin film deposition methods, GPC of ALD yields generally a lowvalue.

Considering the molar mass and density of α-Al2O3 as 101.96 g and 3.99 g/cc [8] weget the volume of one molecule of Al2O3 as 0.042 nm3 and radius (r) of one molecule as0.216 nm. Assume that the ALD-deposited Al2O3 has a face-centred cubic close packingas shown in figure 1 which is the densest packing.

Volume of the unit cell shown in figure 1 is 0.229 nm3 with radius of a sphere as0.216 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 0.0573 nm3. With maximum OHspecies on the surface of the substrate taken as approximately 12 per nm2, 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

Calculation of growth per cycle

Table 1. Number of OH sites on the surface of 1 nm2 area of sub-strate vs. no. of Al atoms adsorbed/nm2 area [9].

Number of OH/nm2 Number of Al atom adsorbed/nm2

12 6.2510 5.5958 4.856 4.084 3.322 2.57

of 6.25 Al atoms can be chemisorbed per nm2 area [9]. As two Al atoms are requiredfor the formation of one Al2O3 molecule, 3.125 Al2O3 molecules per nm2 area can formunder this condition. Assume that 100 cycles of deposition are done. Then 312.5 Al2O3

molecules are formed on 1 nm2 area of the substrate. Total effective volume occupied by312.5 Al2O3 molecules is 17.92 nm3. Hence total thickness developed above 1 nm2 areais 17.92 nm and this yields a GPC of 0.1792 nm.

Table 1 shows the number of Al atoms adsorbed on the substrate surface (per nm2

area) for different values of OH species on the substrate surface. The surface chemistrywhich yields these values is complete ligand exchange (CLE) together with completedissociation (CD) as proposed in our previous paper [9]. This surface chemistry generatesthe experimentally observed curve of Al atoms per nm2 area vs. OH concentration [1,9].Repeating the above calculation of GPC for different OH concentrations on the substratesurface, we get the values given in table 2.

The range of GPC given in table 2 agrees well with various reported values [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. calculatedGPC.

No. of OH/nm2 Calculated GPC (nm)

12 0.17910 0.1608 0.1396 0.1174 0.0952 0.075



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 restof the coating [1,18].

3. Density of Al2O3 deposited by ALD

The density of as-deposited thin films in general is less than that of the bulk value. This ismainly due to the low energy of the evaporants or reactants in various physical and chem-ical deposition methods. Usually this is compensated by supplying additional energy inthe form of substrate heating, plasma enhancement or ion assistance. In atomic layerdeposition, substrate heating and plasma assistance are regularly employed to improvethe film quality. However, a high substrate temperature during deposition can also causere-evaporation of the adsorbed atoms from the substrate surface. Moreover, the factthat TMA decomposes approximately at 300◦C [1,17,19] imposes an upper limit to thesubstrate temperature.

From figure 1, we get the volume of a unit cell as 0.23 nm3 and this volume containsfour molecules. Hence the number of molecules per nm3 is 17.44 and the correspondingmass of 17.44 molecules is 2.95 × 10−21 g. This yields density of ALD-deposited Al2O3

as 2.95 × 10 −21 g/nm3 or 2.95 g/cc. The value of density obtained here is less thanthe bulk value of alumina [8]. However, this is in agreement with the experimentallyreported values for ALD alumina [20–22]. The density of alumina deposited by ALDmay also depend on the type of growth mode like two-dimensional/island/or randomgrowth modes [1,17].

Figure 2. Five monolayers, stacked one above the other are shown. The total thick-ness 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.



4. Calculation of the number of monolayers (ML)

Consider figure 2, where five monolayers of Al2O3 are shown. The total thickness (t)means total thickness of two unit cells plus one radius (r) at the top side and one radius atthe 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 filmand one radius at the top effectively add one ML to this. Hence the number of ML (n) canbe 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. Substitutingthis value of t in eq. (3), we get the number of ML as n = 5. In §2 of this paper, we foundthat the total thickness t developed after 100 cycles of ALD operation for a GPC of 0.179is17.9 nm. For this thickness, the number of MLs obtained using eq. (3) is 58.4. In anideal 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 MLvalue 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 0.179 to 0.075 (whichagain corresponds to a decrease in OH concentration from 12 to 2 on the substrate surface)number of ML decreases from 58.4 to 24.2. Most of the reported values [17,19] supportthis observation. This reduction in the number of MLs can be due to the steric hindrancecaused by ligand molecules of trimethyl aluminum during its chemisorption [20].

5. Monolayer thickness

The monolayer thickness (h) predicted by the equation h = (M/ρNA)1/3 where M and

ρ are the molar mass and density of Al2O3 [20] yields a value of 0.39 nm (for a den-sity of 2.95 g/cc calculated in §2). But Puurunen has considered monolayer thickness as

Table 3. Variation of percentage of monolayer with OH concen-tration for a single cycle of deposition.

Number of OH/nm2 % of ML for single cycle of deposition

12 58.410 52.08 45.26 37.94 30.72 24.2



the height of a cube containing one product molecule MZx which in the present case isAl2O3. This gives absolute value of a monolayer thickness and is of interest only whenone monolayer is deposited. In practical applications, the film will be composed of sev-eral monolayers and the effective thickness of a monolayer is more important. Effectivemonolayer thickness will be less than the above value due to the face-centred cubic closepacking of the deposited film (figures 1 and 2). From figure 1 it is evident that a unitcell 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 with0.179 nm GPC. This yields an effective ML thickness of 0.31 nm. (This can be naturallyexpected 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 12to 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 onlyis formed during one cycle of deposition corresponding to the maximum and minimumnumber of surface sites. These data are given in table 3. The monolayer thickness remainsthe 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 ofnanolayers of high-k oxide dielectrics especially alumina. Even though many reportshave been published on various aspects of atomic layer deposition of alumina, still thereare various gray areas like dependence of GPC on substrate type, surface species, deposi-tion temperature, growth mode, etc. which are not conclusively settled. In this article wehave tried to calculate GPC as a function of surface OH concentration. For this we haveassumed the surface chemistry proposed in one of our earlier papers which agrees wellwith the reported experimental observations [9]. The range of GPC values so obtainedmatches very well with various reported values. The density of atomic layer deposition ofalumina film was calculated to be 2.95 g/cc. This value is lower than the density of bulkalumina, but agrees very well with various reported experimental values for amorphousalumina films. The number of monolayers (ML) as a function of the total film thicknesswas calculated and was found to be in the range of 58.4–24.2% of the total number ofcycles of deposition. This also means that during one cycle of deposition 58.4–24.2% ofa monolayer is formed which is an experimentally observed fact in atomic layer deposi-tion of alumina. By using the unit cell dimensions of a cubic close packed system, theeffective monolayer thicknesses was calculated to be 0.31 nm.

Acknowledgement

One of the authors (AP) acknowledges the research fellowship by Department of Scienceand Technology. The work was carried out with the financial assistance of Kerala StateCouncil for Science, Technology and Environment (KSCSTE).



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