Journal of Materials Science: Materials in Electronics

, Volume 21, Issue 11, pp 1202–1206

Interdiffusion studies in bulk Au–Ti system


  • A. K. Kumar
    • Department of Materials Engineering and Centre for Electronics Design and TechnologyIndian Institute of Science
    • Department of Materials Engineering and Centre for Electronics Design and TechnologyIndian Institute of Science

DOI: 10.1007/s10854-009-0047-5

Cite this article as:
Kumar, A.K. & Paul, A. J Mater Sci: Mater Electron (2010) 21: 1202. doi:10.1007/s10854-009-0047-5


The performance of the contacts, where Au/Ti layers are used in the metallization scheme, largely depends on the product phases grown by interdiffusion at the interface. It is found that four intermetallic compounds grow with narrow homogeneity range and wavy interfaces in the interdiffusion zone. The presence of wavy interfaces is the indication of high anisotropy in diffusion of the product phases. This also reflects in the deviation of parabolic growth from the average. Further, we have determined the relevant diffusion parameters, such as interdiffusion coefficient in the penetrated region of the end members and integrated diffusion coefficients of the intermetallic compounds.

1 Introduction

Ti/Au layers are the part of the metallization schemes to produce a good contact in high power GaAs or n type GaN devices [16]. The primary prerequisite to achieve improved performance is reasonable adhesion with excellent thermal stability. Further, the electrical performance (or the specific contact resistance) largely depends on the evolution, growth, and the morphological features of the product phases developed because of interdiffusion between Au and Ti. There are several studies available on the change in electrical performance with the increase in annealing time at elevated temperatures [26]. However, the reason for the change in electrical performance that is the formation and growth of the intermetallic compounds at the interface is not much studied yet. To date, very few interdiffusion studies were conducted on thin films in this system [7, 8]. However, although, the study in thin film condition is justified from the application point of view, it should be pointed out that as a first step, the study on interdiffusion in this condition is not ideal. Sometimes unexpected phenomenon might be found, such as, the development of amorphous phases [9]. Further, sequential growth of the phases is often found in many studies [10] and stress also plays an influential role on the interdiffusional fluxes [11]. Moreover, the early stage of the process might be controlled by the grain boundary diffusion. On the other hand, interdiffusion studies with bulk specimens help to understand the interdiffusion process, where the stress effect can be avoided. Further, since the annealing time with the bulk specimen can be relatively high, we can exclude the early stage of the process controlled mainly by the grain boundary diffusion to study the growth of the phase layers following lattice diffusion. Very few interdiffusion studies are available, where bulk diffusion couples were considered to study the diffusion process in this system. In one case just the parabolic growth constant was determined [12]. However, since the parabolic growth constant is dependent on the end member compositions, the diffusion parameters, such as, interdiffusion coefficient or integrated diffusion coefficient, which are materials constant and independent of the end member compositions should be determined. In another case, the diffusion parameters were determined [13] but the outcome is rather questionable. There was problem in the alloy used as end member to produce diffusion couples. They reported that the AuTi phase was prepared with stoichiometric composition; however, it had mixture of phases. It is well possible that some amount Ti was lost during melting, which is very often seen during the preparation of Ti-based alloys. For their calculations they considered the stoichiometric composition only and also proper calculation methodology was not followed to determine the diffusion parameters. In multiphase growth one needs to consider the concept of integrated or interdiffusion coefficient and the calculation of average diffusion coefficient following 2D ≈ kp (where D is the average diffusion coefficient and kp is the parabolic growth constant) could lead to significant error.

The main aim of this article is to determine the diffusion parameters (interdiffusion or integrated diffusion coefficient as applicable) of different product phases in bulk diffusion couples. The growth kinetics and diffusion parameters should not be calculated only from one annealing time, since, phases with different crystal structures grow at the same time. Anisotropy of diffusion with respect to the crystal orientation might play significant role to develop phase layers with wavy interfaces. To decrease the error in calculation, the average parabolic growth rate of the phase layers is calculated from the thickness developed at different annealing times. Then the diffusion parameters are calculated from the composition profile considering the average thickness of the phase layers.

2 Experimental procedure

Titanium (99.98 wt%) with a thickness of 1 mm and gold (99.99 wt%) with a thickness of 0.5 mm are used in this study. Slices with dimensions of 5 × 5 mm2 were cut by slow speed diamond saw and the bonding faces were ground and polished following standard metallographic preparation down to 1 µm finish. Polished specimens were then clamped together and annealed at 900 °C for 24–120 h in vacuum (~10−6 mbar). After the experiment, bonded specimens were cross-sectioned by slow speed diamond saw and the interdiffusion zone was examined in a scanning electron microscope (SEM) and the composition profile was measured using energy dispersive X-ray spectrometer (EDX).

3 Results and discussion

Figure 1 shows the interdiffusion zone that is developed at 900 °C and annealed for 120 h. All the four intermetallic phases, following the phase diagram [14] are found in the interdiffusion zone. Since the crystal structures of all the phases are not cubic, wavy interfaces in the interdiffusion zone are expected as found in the present case. The composition profile measured in the interdiffusion zone is shown in Fig. 2. It is evident that there is a reasonable penetration of elements in the Au and Ti end members. Further, all the phase layers, Ti3Au, TiAu, TiAu2, and TiAu4 grow with very narrow homogeneity range. Even the AuTi phase, which has considerable homogeneity range at the annealing temperature of 900 °C, grows with small homogeneity range in the interdiffusion zone. This can be visualized from the composition profile shown in the inset of Fig. 2. This kind of behavior is very common, especially, if the phase grows mainly from one interface because of relatively high diffusion rate of one species compared to the other. The presence of a line of cracks in Fig. 1 might be the indication of the presence of the Kirkendall marker plane. To check the parabolic nature of the growth and to confirm the diffusion controlled process, the layer thickness of the phases are plotted following
$$ \Updelta x^{2} = 2k_{\text{p}} \left( {t - t_{0} } \right) $$
where Δx is the thickness of a phase layer, kp is the parabolic growth constant, t is the annealing time, and t0 is the incubation period. Figure 3 shows the plots of growth of different phases following Eq. 1. It can be seen that three phase layers TiAu4, TiAu, and Ti3Au grow following more or less parabolic law. On the other hand, TiAu2 phase layer grows with high scatter in the experimental data with respect to the parabolic growth. However, considering the tetragonal crystal structure of two phases (TiAu4 and TiAu2), which are anisotropic in terms of diffusion, this is not a surprising result. It is the fact that layers grow following very complicated process, where, at one side of the interface one particular phase layer grows by consuming the next neighbouring phase and on the other hand, at the same time, the phase layer gets consumed because of the growth of the same neighbouring phase [15, 16]. The ultimate layer thickness of a phase depends not only on the average interdiffusion coefficient or the integrated diffusion coefficient of that particular phase, but also depends on the diffusion parameters of the other phases and composition of the end members. The anisotropy in diffusion with respect to the crystal orientations is added to the complication [17]. Even if the growth of one phase is also anisotropic, it will affect the growth of other phases. This might be the reason that we see wavy interfaces in the interdiffusion zone. Similarly, it is also expected to find reasonable deviation from the ideal parabolic growth of the phase layers. However, since we have calculated the average parabolic growth of the phase layers from a reasonable range of annealing time, the error in the calculation is minimized. To calculate the diffusion parameters, we have opted the diffusion couple annealed for 120 h. The composition profile in the penetrated region in the Au and Ti end members (mentioned as gold solid solution, Au(ss) and titanium solid solution, Ti(ss) in Fig. 1) is considered as measured following EDX analysis. However, the average thickness of the phase layers are calculated from the average parabolic growth constants as determined in Fig. 3. Since the change in molar volume of the phases in this system does not follow the ideality, the interdiffusion coefficient, \( \tilde{D} \) in the penetrated part of end member was calculated following the Wagner’s equation as expressed by [18]
$$ \tilde{D}\left( {Y^{*} } \right) = {\frac{{V_{\text{m}}^{*} }}{2t}}\left( {{\frac{dx}{dY}}} \right)^{*} \left[ {\left( {1 - Y^{*} } \right)\int\limits_{ - \infty }^{{x^{*} }} {{\frac{Y}{{V_{\text{m}} }}}\,dx + Y^{*} \int\limits_{{x^{*} }}^{\infty } {{\frac{{\left( {1 - Y} \right)}}{{V_{\text{m}} }}}\,dx} } } \right] $$
where Y is the normalized composition and can be expressed by Y = (Ni − Ni+)/(Ni+ − Ni). Here Ni, Ni, and Ni+ are the composition of species, i, composition of the left hand side of the end member and composition of the right hand side of the end member, respectively. Vm is the molar volume and x is the position parameter. “*” represents the point of interest. “−∞” and “+∞” represents the unaffected left and right hand part of the end members, respectively. However, note that we cannot calculate the interdiffusion coefficient in the phase layers grown with reasonably narrow homogeneity range, simply because, we can not determine the slope in the interdiffusion zone. To circumvent this problem, Wagner [18] introduced the concept of integrated diffusion coefficient, which is basically the interdiffusion coefficient integrated over the composition range and can be expressed as
$$ \begin{aligned} \tilde{D}_{\text{int}}^{\beta } = & \int\limits_{{N_{B}^{{\beta_{1} }} }}^{{N_{B}^{{\beta_{2} }} }} {\tilde{D}dN_{i} } = {\frac{{\left( {N_{i}^{\beta } - N_{i}^{ - } } \right)\left( {N_{i}^{ + } - N_{i}^{\beta } } \right)}}{{N_{B}^{ + } - N_{B}^{ - } }}}{\frac{{\Updelta x_{\beta }^{2} }}{2t}} \\ + & {\frac{{\Updelta x_{\beta } }}{2t}}\left[ {{\frac{{N_{i}^{ + } - N_{i}^{\beta } }}{{N_{i}^{ + } - N_{i}^{ - } }}} \times \int\limits_{ - \infty }^{{x^{{\beta_{1} }} }} {{\frac{{V_{\text{m}}^{\beta } }}{{V_{\text{m}} }}}\left( {N_{i} - N_{i}^{ - } } \right)\,dx + {\frac{{N_{i}^{\beta } - N_{i}^{ - } }}{{N_{i}^{ + } - N_{i}^{ - } }}} \times \int\limits_{{x^{{\beta_{2} }} }}^{\infty } {{\frac{{V_{\text{m}}^{\beta } }}{{V_{\text{m}} }}}\left( {N_{i}^{ + } - N_{i} } \right)\,dx} } } \right] \\ \end{aligned} $$
here β phase is the phase of interest for which, we want to calculate the integrated diffusion coefficient. \( N_{B}^{{\beta_{1} }} \) and \( N_{B}^{{\beta_{2} }} \) measures the unknown homogeneity range and NBβ is the average composition of the β phase.
Fig. 1

Interdiffusion zone developed in the Au/Ti diffusion couple annealed at 900 °C for 120 h is shown. The unaffected parts of Au and Ti end member are beyond the limit of the image as indicated by the arrows. Cracks might be the indication of the position of the Kirkendall marker plane
Fig. 2

Composition profile of the interdiffusion zone measured by EDX is shown. The composition profile of the line compounds is shown in the inset
Fig. 3

The parabolic growth of the phases a Ti3Au, b TiAu, c TiAu2, and d TiAu4 are shown calculated at 900 °C is shown

The interdiffusion coefficient because of penetration in the end members is shown in Fig. 4 and the integrated diffusion coefficient of different phases calculated at the stoichiometric composition are listed in Table 1, along with the information on crystal structure, molar volume and parabolic growth constant of the phases. We further targeted to calculate the activation energy following Arrhenius equation and by conducting experiments at different temperatures. However, because of waviness of the growth of the phase layer and anisotropy in diffusion, it was found to be difficult to formulate the growth of the product phases following the Arrhenius equation.
Fig. 4

The change in interdiffusion coefficient in the penetrated region of Au that is Au(ss) and Ti that is Ti(ss) is shown

Table 1

The details on crystal structure, molar volume (Vm), parabolic growth constant (kp) and integrated diffusion coefficients (\( \tilde{D}_{\text{int}} \)) are listed


Crystal structure

Vm × 10−6 (m3/mol)

kp × 10−17 (m2/s)

\( \tilde{D}_{\text{int}} \times 10^{ - 16} \,({\text{m}}^{2} /{\text{s}}) \)





















4 Conclusion

It is the known fact that the functional properties of the contact depends on the growth of the product phases at the interface. The interfacial product layers grow by interdiffusion and it is important to understand the interdiffusion process. We found that the layers grow with wavy interfaces because of anisotropy in the diffusion process. So we have studied the growth of the product phases for different annealing times to calculate the diffusion parameters from the average parabolic growth constant to minimize the error in the calculations. This study will help to understand the performance of the Au/Ti layer as contact.


A. Paul would like to acknowledge the financial support received from Department of Science and Technology, Govt. of India (SR/FTP/ETA-18/2006) for this research work.

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© Springer Science+Business Media, LLC 2009