Thermo opto mechanical properties of AlN (1)

IOP PUBLISHING JOURNAL OFPHYSICSD: APPLIEDPHYSICS J. Phys. D: Appl. Phys.41(2008) 172001 (4pp) doi:10.1088/0022-3727/41/17/172001

FAST TRACK COMMUNICATION

Thermo-opto-mechanical properties of

AlN nanostructures: a promising material

for NEMS applications

G Guisbiers and L Buchaillot

IEMN, UMR8520, Scientific City, Avenue Henri Poincar´e, BP 60069, 59652 Villeneuve d’Ascq, France

E-mail:gregory.guisbiers@isen.iemn.univ-lille1.fr

Received 11 July 2008, in final form 14 July 2008 Published 8 August 2008

Online atstacks.iop.org/JPhysD/41/172001

Abstract

The properties of aluminium nitride (AlN) are investigated at the nanoscale for different shapes of nanostructures. Spherical nanoparticles, cylindrical nanowires and nanofilms are the considered shapes. The size and shape effects on the creep temperature, melting temperature, residual stress and energy bandgap are discussed. The creep behaviour of AlN is analysed and compared with aluminium (Al) pure metal. The higher creep resistance of AlN is demonstrated. The transition from inverse Hall–Petch to the Hall–Petch relation is found to be around∼_{15–18 nm in agreement with other authors. The energy}

bandgap of AlN nanostructures is blue-shifted with the size reduction and the shape of the nanostructure, according to the following relation:Eg(nanoparticle) > Eg(nanowire) > Eg(nanofilm).

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Aluminium nitride (AlN) is a III–V semiconductor material and has many attractive properties [1] (table1) such as high melting temperature, high thermal stability, high thermal conductivity, low thermal expansion coefficient and a wide energy bandgap which make it a promising material for nano/micro applications [2,3] and bulk acoustic wave (BAW) devices [4,5] as resonators and filters. A wide energy bandgap as AlN is often desired for optical applications in deep ultra-violet (UV) spectra such as light emitting diodes (LEDs) and laser diodes [6]. Indeed, to improve the resolution in photolithography, sources with shorter emission wavelength are required in nano/microelectronics. Moreover, creep is an important issue for metallic parts in nano/micro-electro-mechanical systems (N/MEMS) [7]. Aluminium (Al) is a material extensively used in N/MEMS, for example, as bridge material in radio frequency MEMS (MEMS-RF). Nevertheless, this material flows essentially by creep due to its low melting point (a high melting point material has low creep). Therefore, to replace Al and to stay compatible with Al-etch processing which is in use and well characterized, AlN

Table 1.Materials parameters for aluminium and aluminium nitride [33].

Material parameters AlN Al

Tm,∞(K) 3273 933

Hm,∞(J m −3

) 8.75×109 1_.08×109

γs(J m−2) 0.66 1.15

γl(J m−2) 0.04 0.86

E(GPa) 308 70

ν 0.287 0.340

α(K−1_{) 4.84×10}−6 _23.03×10−6

η(Pa s) >1.73×₁₀−3 _1.73×10−3

Eg,∞(eV) 6.2 0

seems to be an interesting alternative. Therefore, we propose in this communication to investigate the thermo-opto-mechanical properties of AlN at the nanoscale.

2. Melting temperature of AlN and

Al nanostructures

Using a thermodynamical model, fully described in [8–11], we can calculate the size and shape effect on the melting

J. Phys. D: Appl. Phys.41(2008) 172001 Fast Track Communication Table 2.Shape parameters for aluminium and aluminium nitride.

Shape parameters AlN Al

αsphere(nm) 0.43 1.56

αcylinder(nm)a 0.29 1.10

αfilm(nm) 0.14 0.52

a_{Calculated for a cylindrical nanowire with a length}

equal to 100 nm.

Figure 1.Melting temperature versus the dimension of the nanostructure for aluminium (Al) and aluminium nitride (AlN) materials. The thick solid lines represent the bulk behaviour of these materials. The thin solid, dashed and dotted lines represent the nanofilms, cylindrical nanowires and spherical nanoparticles respectively.

temperature of free-standing materials for sizes higher than

L∼4 nm to keep the thermodynamics arguments valid. The

melting temperature of a nanostructure can be calculated by

Tm/Tm,∞ = 1 + [(γl −γs)/Hm,∞][A/V], where Tm,∞ is

the bulk melting temperature,γlandγsare, respectively, the surface energy in the liquid and solid phases, Hm,∞ is the

bulk melting enthalpy andA/V is the area over volume ratio. To quantify the size effect on the melting temperature, for a specific shape, with only one parameter, a shape parameter calledαshapeis defined asαshape=[_(γs−_γl)/Hm,∞](AL/V ).

Therefore, the melting temperature of a nanostructure can be rewritten as

Tm/Tm,∞=1−αshape/L, (1)

where L is the diameter or thickness of the nanostructure. For free-standing nanostructures, the ratiosαfilm/αsphere and

αcylinder/αsphereare, respectively, equal to 1/3 and 2/3 (table2) as already discussed by Wautelet [12]. In figure 1, the nanoscale melting temperature of Al and AlN is plotted versus the size. As already noted for transition metals, the size effect is lower on high melting point materials compared with low melting point materials [11]. For any shape considered here, the nanoscale melting temperature of AlN is always higher than the corresponding one of Al.

3. Higher creep resistance of AlN towards Al

Creep of materials is a time and temperature dependent inelastic deformation process at constant stress [13–15]. The evolution of creep with time can be separated into three different stages: primary creep, secondary creep and ternary creep. Each stage corresponds to a specific creep rate: ˙

εprimary ∝ L−3, ˙εsecondary ∝ L0, ˙εternary ∝ L−2, where Lis the dimension of the material. The primary, secondary and ternary creep are, respectively, due to grain boundary diffusion (Coble creep), dislocation movements (steady-state creep) and bulk diffusion (Nabarro-Herring creep). At low sizes, the creep is dominated by the diffusion process. The creep temperature where creep becomes non-negligible is a function of the melting temperature of the material as formulated here:

Tc=kT_m, (2)

where k depends on the nature of the material, metal or semiconductor (k ∼ 0.3 for metals and ∼0.4 for

semiconductors) [16]. At the macroscale, creep can be neglected when the following condition is satisfied, T < kTm,∞. At the nanoscale, this condition becomesT < kTm [17]. Here we haveTm(AlN) > Tm(Al), which means that the creep temperature of AlN is higher than the corresponding one of Al for any considered shape of nanostructures. Therefore, AlN is more creep resistant than Al whatever the size and shape of the material.

4. Residual stress and hardness of AlN and Al

nanostructures

Size is known to have a significant effect on the mechanical behaviour of materials, in particular, on the residual stress, yield stress and hardness [14,18,19]. Residual stresses appear during the fabrication of nanostructures even without applying any external stress [2,19–26]. The yield stress corresponds to the stress where the material quits the elastic deformation regime. And the yield stress is approximately one-third of the Vickers hardness [27].

Residual stresses have two origins: intrinsic and thermal. Intrinsic stress, also called growth stress, depends on the deposition process. Yacaman [28] showed that the intrinsic stress increases with the size until a given size where a stress release mechanism should dominate. Thermal stress appears during the cooling phase of the fabrication process due to the difference between the thermal expansion coefficients of the deposited material and the substrate. Considering free-standing nanostructures (no substrate), we have only to take into account the intrinsic stress origin. For metals deposited by the evaporation process, we can calculate the intrinsic stress with the following equation [19]:

σ =_(E/1−_ν)α(Tm−_Troom)e−Eh/ηkTm_{, (3)}

whereh and k have the usual meaning. Troom is the room temperature considered to be around∼300 K._E,_ν,_αand_η

are, respectively, Young’s modulus, the Poisson ratio, the

J. Phys. D: Appl. Phys.41(2008) 172001 Fast Track Communication thermal expansion coefficient and the dynamic viscosity of

the material.

For ceramics, as the relaxation process is different from metals, we cannot use equation (4) to calculate the intrinsic stress due to the exponential factor which corresponds to a creep-yielding relaxation process. Indeed ceramics do not have a yielding part in the stress–strain curve and they relax directly by cracks [27]. Therefore, we propose equation (4) to calculate the intrinsic stress in ceramics before cracking:

σ =_(E/1−_ν)α(Tm−_Troom). (4)

To be in the condition to use equation (4), we consider AlN nanostructures built from evaporated Al material under nitrogen atmosphere.

For a spherical nanoparticle with a size equal to 10 nm, we get an internal stress around∼100 MPa for Al and∼6 GPa

for AlN. In a previous paper [11], we have indicated, for sizes below ∼15 nm, the link between the yield stress (hardness)

of material and the intrinsic residual stress. As also noted by Meyers [14], the stress first increases before decreasing as the grain size increases. The grain size corresponding to the maximum stress value depends on the strain rate.

Furthermore, Lucaset al [29] have studied the nitrogen diffusion effect on the hardness of aluminium coating. Their results are interesting; they noted an increase in hardness with nitrogen incorporation into aluminium coating. Nitrogen forms with aluminium precipitates of aluminium nitride into the coating. These AlN precipitates act like a barrier to dislocation motions: cutting or bowing mechanisms. In the aluminium coating, the stress required to bend dislocations around an AlN precipitate of diameter 2 nm, called the bowing stress, is around 7.8 GPa [29]. This value can be compared with the internal stress value (∼6 GPa) which is quite similar.

The transition between the two dislocations motions occurs when the shear stress equals the bowing stress. This transition occurs atL≈18 nm [29]. The maximal strength is obtained

when the shear stress is equal to the bowing stress. This transition can explain the inverse Hall–Petch behaviour where dislocation motion seems to play a very important role. Below ∼15–18 nm, there is no relaxation process, and the

stress/hardness increases with the size. Above∼15–18 nm,

the dislocations decrease the hardness of the material. For

Zhaoet al[30], the transition between the inverse Hall–Petch

relation and the Hall–Petch relation occurs between 15 and 30 nm, which is quite the same as ours.

As a harder material is more creep resistant, this calculation confirms the superior creep resistance behaviour of AlN towards Al. Furthermore, a harder material exhibits a higher fatigue endurance limit [31]; therefore, AlN is particularly suitable as bridge material in MEMS-RF.

5. Energy bandgap of AlN nanostructures

It has been detailed in [32] that with the sameαshapeparameter (defined in section1), we can describe the size effect on the energy bandgap of semiconductors, Eg, with the following equation:

Eg/Eg,∞=1 +αshape/L, (5)

Figure 2.Energy bandgap versus the diameter of the aluminium nitride (AlN) nanoparticle, nanocylinder (h=_{100 nm) and versus} the thickness of the nanofilm. The bulk energy bandgap is indicated at 6.2 eV. This figure highlights the blue shift with size reduction.

whereEg,∞is the energy bandgap of the bulk semiconductor.

It can be easily understood by writing the energy bandgap as a function of the enthalpy and entropy between the conduction and valence electronic bands:Eg=_Hcv−_{T Scv}.

In figure2, the energy bandgap of AlN has been plotted versus the size of free-standing nanostructures. A blue shift appears with size reduction for all considered nanostructures. For a given size, the blue shift magnitude varies with the shape of the nanostructure, according to the following relation:

Eg(nanoparticle) > Eg(nanowire) > Eg(nanofilm).

6. Conclusions

The following properties of aluminium nitride: melting temperature, creep temperature, intrinsic residual stress and energy bandgap, have been investigated at the nanoscale. Not only the size but also the shape of the nanostructure has an influence on the material properties. From a thermodynamical analysis, the higher creep resistance of AlN towards Al has been demonstrated for all sizes and shapes of nanostructures. The free-standing AlN nanostructures, with an energy bandgap of >6.2 eV, are particularly well adapted for deep UV nano/micro-applications. With the same shape parameter,

αshape, it allows one to calculate the melting temperature, creep temperature, intrinsic residual stress and energy bandgap for a given material at the nanoscale. Nevertheless, some other effects such as segregation and composition can slightly modify the surface properties such as surface tension and then the related nano-properties of AlN. These effects will be the subject another work.

Acknowledgment

G Guisbiers thanks the ANR PNANO M&NEMS project for financial support.

J. Phys. D: Appl. Phys.41(2008) 172001 Fast Track Communication

References

[1] Vurgaftman I, Meyer J R and Ram-Mohan L R 2001J. Appl.

Phys.895815

[2] Madou M J 2002Fundamentals of Microfabrication: the

Science of Miniaturization(Boca Raton, FL: CRC Press)

[3] Rao C N R, Deepak F L, Gundiah G and Govindaraj A 2003

Prog. Solid State Chem.315

[4] Loebl H P, Klee M, Metzmacher C, Brand W, Milsom R and Lok P 2003Mater. Chem. Phys.79143

[5] L¨obl H P, Klee M, Milsom R, Dekker R, Metzmacher C, Brand W and Lok P 2001J. Eur. Ceram. Soc.212633

[6] Taniyasu Y, Kasu M and Makimoto T 2006Nature441325

[7] Spengen W M V 2003Microelectron. Reliab.431049

[8] Guisbiers G and Wautelet M 2006Nanotechnology172008

[9] Abudukelimu G, Guisbiers G and Wautelet M 2006J. Mater.

Res.212829

[10] Guisbiers G, Abudukelimu G, Clement F and Wautelet M

2007J. Comput. Theor. Nanosci.4309

[11] Guisbiers G, Kazan M, Van Overschelde O, Wautelet M and Pereira S 2008J. Phys. Chem.C1124097

[12] Wautelet M 1998Phys. Lett.A246341

[13] Tjong S C and Chen H 2004Mater. Sci. Eng.R451

[14] Meyers M A, Mishra A and Benson D J 2006Prog. Mater. Sci. 51427

[15] Bull S J 1998Surf. Coat. Technol.107101

[16] Driver J H 2004Scr. Mater.51819

[17] Guisbiers G and Buchaillot L 2008Nanotechnologysubmitted

[18] Arzt E 1998Acta Mater.465611

[19] Guisbiers G, Van Overschelde O and Wautelet M 2007Acta

Mater.553541

[20] Ohring M 2002Materials Science of Thin Films Deposition

and Structure(New York: Academic)

[21] Thornton J A and Hoffman D W 1989Thin Solid Films1715

[22] Thompson C V and Carel R 1996J. Mech. Phys. Solids 44657

[23] Nix W D and Clemens B M 1999J. Mater. Res.143467

[24] Koch R 1994J. Phys.: Condens. Matter69519

[25] Doerner M F and Nix W D 1988Crc Crit. Rev. Solid State

Mater. Sci.14225

[26] Freund L B and Chason E 2001J. Appl. Phys.94866 [27] Gere J M 2002Mechanics of Materials(Cheltenham, UK:

Nelson Thornes)

[28] Yacaman M J, Ascencio J A, Liu H B and Gardea-Torresdey J

2001J. Vac. Sci. Technol. B— Microelectron. Nanometer

Struct.—Process. Meas. Phenom.191091

[29] Lucas S, Chevallier J and Chechenin N G 1994Surf. Coat.

Technol.66334

[30] Zhao M, Li J C and Jiang Q 2003J. Alloys Compounds 361160

[31] Wei G, Bhushan B and Jacobs SJ 2004J. Vac. Sci. Technol.A

221397

[32] Guisbiers G, Van Overschelde O and Wautelet M 2008Appl.

Phys. Lett.92103121

[33] Martienssen W and Warlimont H 2005Springer Handbook of

Condensed Matter and Materials Data(Berlin: Springer)