The mechanical stress is a force in the plane of film acting per unit aria of the film cross section. The mechanical stress may be compressive or tensile in character. The total mechanical stress s of a film consists of two terms

where s_i is so-called intrinsic stress, which is apparently a fundamental result of the conditions and method of film growth and is to a large degree a reflection of the film structure and the presence of impurities, and s_T is the thermal stress in the film, given by the expression

where E_f and n_f are respectively the Young modulus and Poisson ratio for the film, a_f and a_s are average thermal coefficients of the film and the substrate and T_d and T_M are the film deposition temperature and the temperature during the stress measurements, respectively. Therefore, the thermal stress of the film is a result of the difference in the temperatures of the film during deposition and measurement.

The thin DLC films were deposited in an ion plating system described in detail in our previous study [5]. A cylindrical electron reflector, an anode grid, a hot cathode and a disc electron deflector formed an electrostatic ion gun for a preliminary argon ion cleaning of the substrates of polished (100) silicon mounted on an electrically-isolated water-cooled metal substrate holder, and for a subsequent deposition of thin films from ionised products. The technique for deposition is based on decomposition and ionisation of hydrocarbon working gas. We used benzene (C₆H₆) vapours at working pressure p = 2 ё 5.5 x 10^-4 Torr to initiate a glow discharge in the electrostatic ion gun. High negative biases U_b from 0.5 kV up to 3 kV were applied to the substrate. At p = 4 x 10^-4 Torr and U_b = 2 kV the ion current density measured at the substrate surface was 0.15 mA/cm² and the growth rate was approximately 22 nm/min. Substrate temperature was maintained below 20⁰C by the effective water cooling.

The determination of the mechanical stresses was performed by measuring the radius of wafer curvature using the Newton rings method [14,15]. Assuming that the temperature of the film during the process of deposition is approximately equal to the room temperature due to water-cooling of the substrate holder, only the intrinsic portion of the stress (Eq.1) was used for calculating of the mechanical stresses. The intrinsic stress s_i was calculated by the expression

The experimental dependence of the intrinsic stress s_i on the working gas pressure p is shown in Fig.1. All measured stresses are compressive (negative one) and approximately constant to pressures up to 4.1 x 10^-4 Torr, which can be explain as follow. Due to the specific construction of our deposition system (electrostatic ion gun with hot filament), there is a direct connection between the mechanical dimensions of the system and the physical parameters of the discharge. Generally, at pressures lower than 4.1 x 10^-4 Torr there are smaller number of electron impacts on ionized hydrocarbon particles, the latter have a higher kinetic energy and arrive on the surface with elevated impact energies. As a result the deposited neutralized hydrocarbon particles migrate easier and create more organised layers with minimum number of imperfections, which means that the intrinsic stress is not so high and is approximately constant. At some critical pressure, which in our case seems to be about 4.1 x 10^-4 Torr, hydrocarbon ionized particles free path length gets equalized to the distance between the electrodes. There is a well-pronounced minimum in the values of s_i, which corresponds to the transition from diamond-like to graphite-like thin carbon films. At pressure higher than 4.1 x 10^-4 Torr the ions are more thermalized, the layers become graphitized and as a result s_i decreases.

The same mechanism can be revealed to the dependence of s_i on the negative bias voltage to the substrate, shown in Fig.2. Increasing U_b, we increase the kinetic energy of the ions, and finally we have a lower amount of disorder in the film. This effect is combined with the process of graphitization at high U_b. As a result we obtained a strong decrease of s_i at higher bias voltages and a very good agreement with the same dependence obtained from Nakaue et al. [16].

Figure 3 gives the experimental dependence of the intrinsic stress s_i on the film thickness d_f after 3 steps of postdeposition ion etching. As the stress s_i is the average stress along the total thickness of the film, it is seen from Fig.3 that the highest values of stress are in the interface film/substrate due to the contact between two different structures. When we take away layers, we increase the total sum of the stress per unit film thickness, which leads to the higher values of the compressive stress.

Figure 4 and Figure 5 present the dependence of the stress on the film thickness at two different negative substrate biases U_b of 2 and 1.5 kV, respectively. In the case of U_b = 2 kV the samples with thickness d_f < 2 ё 2.5 mm possess high compressive stresses (from -1.5 to -6 GPa). Those with d_f > 2 ё 2.5 mm have a moderate tensile stress (approximately 2 GPa). The values of the intrinsic compressive (positive one) stress obtained in our investigations are comparable to the highest intrinsic stresses observed only for the case of titanium nitride (TiN) thin films deposited at higher negative substrate bias (> 100 V) [17]. The observed course of the dependence of stresses s_i vs. film thickness d_f passing through zero value of the stress can be explained in the following way. As s_i is the average stress value along the thickness of the film, it follows from the figure that the majority of the stresses are concentrated near the interface film/substrate, at which the greatest number of imperfections are to be expected in the growing of the film structure, owing to the difference between the two structures. Due to the long time of deposition, the process of cooling is not so effective and the temperature on the surface of the outer layer of the deposited film is increasing; as a result the thermal stress start influencing and can’t be neglected.

The same results of the passing of s_i from tensile stress through zero values with the increasing of the film thickness during the deposition were obtained at another lower bias voltage U_b = 1.5 kV too. This confirms the proposed explanation of the dependence. But the major conclusion from this dependency is the possibility to deposit such films with low, even zero values of the intrinsic stress, which is very important from a technological point of view.

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