Data storage materials suffer from limited lifetime. Thus, there is a necessity for new data storage systems for archiving purposes. Systems based on chemical reactions such as the oxidation of corrosion-resistant metals are attractive candidates because they offer in principle very long-term stability. We have therefore investigated oxidation kinetics of Cr, Al, Ti, V, Zn, Ni, and Co. Here we present the results and discuss in detail fundamental issues of thin film oxidation, the limits of diffusion controlled oxidation, and possible ways to increase the oxidation rate constants. Co showed the highest oxidation rate constant (kp = 2.5 × 10−9 cm2/s at 540 °C) and is therefore considered as a promising candidate for data archiving.
Current data storage technology is tuned for maximal storage capacity, fast writing, fast reading, and cost. Data durability, however, faces severe limitations. Possible data loss is particularly alarming, as the amount of data stored exclusively on digital media is diverging. For many purposes, data storage over many years is mandatory. Indeed, a guaranteed data lifetime of 1000 yr would be a game-changer to provide “digital libraries” to future generations. Such long storage times are not achieved by conventional “non-volatile” storage media but were obviously realized by engraving information in stone and writing on papyrus: clay tablets and papyrus sheets reveal information about ancient times as long as 4000 years ago. The question of long-time data storage unavoidably leads to considering “nominally irreversible structures” characterized by extreme diffusion coefficients of the atomic structure elements involved (low concentration and/or low mobility of defects such as vacancies, interstitials). Such long-term data storage and retrieval raise software issues concerning data formatting, and, of course, the hardware problem of possible storage media and writing processes. Here we address the availability of storage media for the irreversible writing of data for long-term data archiving. We analyze possible data storage based on bits represented by stable compounds produced using chemical reactions of corrosion-resistant metals. The chemical reactions involved in writing the data have to be fast to be attractive for application purposes.
Several basic technologies are commonly used for storing digital data, such as magnetic tapes and disks, solid-state devices (e.g., flash memories based on floating gate transistors, DRAMs), and optical data storage materials. Common failures of these materials arise from chemical reactions such as corrosion, oxidation, and breaking of chemical bonds, from loss or reorientations of magnetic domains, and from the delamination of the recording layers.1–3 The failures are accelerated by elevated temperatures, humidity, and UV light. Optical discs are sensitive to light because the data recording “dye” is photosensitive.1 For all these widespread technologies, the maximal life expectancy of the written data equals in general less than 50 yr (see Fig. 1). Magnetization decreases easily due to environmental conditions such as elevated temperatures and humidity. Therefore, high-quality paper, plastic (but only absence of plasticizers), and ceramic sheets are appealing carriers for data storage, with a life expectancy of several centuries at least.
A number of inventions have been made concerning long-term data storage. For these, data lifetimes of 100-300 yr,4 1000 yr,5 and even several hundred million years are claimed.6 However, these techniques tend to be associated with slower writing speeds (Fig. 1). “Archival Gold Discs” offer life expectancies of 100-300 yr by using protective coatings on the disc surfaces. Here, sputtered gold layers are used to prevent oxidation and data degradation; hard polymer coatings are applied to avoid scratches and stains.4 Milleniata has developed a commercially available disc (M-DISCTM) which is claimed to endure for 1000 yr even under extreme environmental conditions.5 Milleniata uses an inorganic-composite data-recording layer rather than an organic dye. Although the data are readable with standard DVD-readers, an external system is required, for writing, to burn the inorganic-composite layer with a high-power laser. The data recording layer undergoes a permanent physical change; the generated heat of the focused laser causes the innermost layers to melt, thereby creating a hole in the data layer.7 Hitachi has developed a long-term data storage material using fused silica as a storage medium.6 The data are recorded in the silica glass by creating regions (dots) of changed refractive index. Although the data in fused silica can last for millions of years under harsh environmental conditions, data recording requires an ultrahigh laser light intensity of, e.g., 6 × 1014 W/cm2 in Ref.8 that does not seem practical for the end user.
Although these inventions offer relatively long times for reliable data storage, the microscopic mechanisms underlying their working principles are complex. In the present work, the approach for data-archiving materials is very simple: storing a bit in a spot by laser-induced chemical reactions, such as oxidation, sulphuration, or halogenation of a corrosion-resistant metal film. It is required that the metal can be triggered fast to react with its partner such as atmospheric oxygen. The implementation of such processes demands an understanding and control of the reaction kinetics of thin metal films. Whereas the same principles apply for sulphuration, halogenation, and related processes, the focus of the present study is centered on the oxidation of thin metal films, as oxidation seems advantageous due to the availability of atmospheric oxygen. The stored data are to be read optically, by using, for example, the locally modified reflectivity or by measuring the electrical conductivity locally.
The envisaged solution for a long-term data storage material is the fast and local oxidation of corrosion-resistant metallic films by laser-induced, localized heating to temperatures up to 600 °C. Such temperatures appear demanding but achievable in storage units integrated into standard personal computers. After writing of the data, the corrosion-resistant metal, as well as its oxide, is required to be stable at 25 °C for at least 1000 yr. The writing speed and the storage lifetime provide constraints on the oxidation rate constant (kp), as calculated from the parabolic rate law (Eq. (1), see below for its range of validity). While short writing times of the order of nanoseconds (corresponding to a recording speed of 125 MB/s) are desirable, it seems unrealistic to achieve nanosecond oxidation times owing to fundamental limits of diffusion processes (as discussed in more detail in the supplementary material). We therefore differentiate between oxidation times of, for instance, microseconds, and much faster heating times by the laser pulse of nanoseconds. To achieve data stability for more than 1000 yr (∼3 × 1010 s) in 10 nm thick films, kp at room temperature needs to be below 3 × 10−23 cm2/s. To gain a writing speed (oxidation time) of the order of microseconds, kp has to be ≥1 × 10−7 cm2/s at 600 °C as displayed in Fig. 2. The average activation energy of the oxidation, therefore, has to exceed 1.4 eV. While there is no strict upper bound on this activation energy, typical activation energies of such oxidation processes do not exceed 4-5 eV. The term “average activation energy” takes account of the fact that the mechanism of oxidation may change with temperature. With this activation energy, the lifetime of the pristine metal film, held at a persistent elevated temperature of 60 °C, decreases from 1000 yr to 3.4 yr. We assume that films with stored data will be exposed to temperatures of 60 °C or higher for few days only at most.
According to the literature, oxidation kinetics of thin metallic films have not been investigated in much detail. We therefore analyze in the following the microscopic oxidation processes by experimental studies and some model calculations that may match the needs of data archiving. For simplicity, the oxidation of entire metal films rather than that of locally heated spots is considered.
For the growth of an adhering and crack-free oxide layer on a metal film, the metal has to diffuse outward towards the atmosphere, and/or the oxygen must diffuse inward towards the substrate, comprising the transport of ionic and electronic species. Depending on the microscopic processes involved, different models to describe the oxidation kinetics (see, e.g., Atkinson’s review)9 apply: (i) The Cabrera-Mott theory10 describes the formation of very thin films at relatively low temperatures (e.g., the native oxide layer). In this case, the electric field generated by tunneling of electrons from the metal to chemisorbed oxygen species at the oxide surface accelerates ionic transport across the film. The decrease of the electric field with increasing film thickness leads to a negligible growth rate once a “limiting oxide thickness” of a few nanometers is reached. (ii) For the oxidation of thicker films, at high temperatures, for which the electric fields are negligible, the reaction kinetics is controlled either by chemical diffusion (Wagner theory) or by surface reactions. The initial oxidation layer is compact if the molar volumes of the growing oxide layer and the metal do not differ much.11,12 First, observations of the parabolic rate law,
were reported by Tammann,13 and Pilling and Bedworth11 for the formation of dense oxide, sulfide, fluoride layers, and related compounds. Here, kp is the parabolic rate constant (referred in the text as oxidation rate constant), X the oxide film thickness, and t denotes the time. As one can recognize from the units (cm2/s), the rate constant kp actually represents a diffusion coefficient not the surface rate constant.
The Wagner theory describes the thickness increase of a compact oxide layer, with the assumption of a diffusion-controlled oxidation.14 After the formation of a gas-tight initial oxide layer, the metal diffuses outward towards the atmosphere by ambipolar (chemical) diffusion of metal ions and electronic carriers, and/or oxygen diffuses inward towards the substrate. This oxidation process is therefore determined by the ambipolar conductivities ( or ) and by the chemical potential gradient (Fig. 3(b)). As a result, the flux of the metal ions decreases with increasing oxide film thickness (Eq. (2)). The atom flux is given by
where is the ambipolar conductivity, which approximately equals the ionic conductivity for , where is the transference number of ions and the transference number of electrons). Further, is the Faraday constant and the chemical potential difference for the metal and gas phases. The bar indicates averaging across the oxide film. The rate constant kp is related to the tracer diffusion coefficient D* by
where is the diffusivity of metal ions, the diffusivity of oxygen ions in an oxide, kB the Boltzmann constant, and the Avogadro number.
For first row transition-metal oxides such as CoO, NiO, and FeO, the typical parameters and result in
The parameter varies among the different stable binary oxides at most by a factor of 2–3. Therefore kp mainly depends on which is a function of the defect concentration in the growing oxide film, e.g., for Ni diffusion in NiO,
where is the concentration of doubly ionized Ni vacancies and the defect diffusion coefficient. Therefore can be altered by doping over several orders of magnitudes. Since is only weakly pO2 dependent (due to the feeble pO2-dependence of ; depending on the defect chemical model, similar power laws resulting in a weak pO2 dependence may appear also for the other binary oxides discussed in the present study), kp also depends only weakly on pO2. Resulting is calculated from measured kp using chemical potential difference for the oxidation with the standard molar Gibbs energy from the literature.15 While is 1 bar, pO2 is the actual oxygen partial pressure.
If the reaction is surface-controlled, the chemical potential is homogeneous within the growing oxide film, and the chemical potential step at the surface acts as a driving force for the insertion of oxygen ions (Fig. 3(a)). The flux of oxygen ions is given by
where is the effective surface rate constant and presents the variation of the ion concentration across the oxide film-gas surface. Since remains constant as long as some metal remains beneath the growing film, Eq. (6) gives a constant and therefore a constant growth rate for the oxide layer thickness.
For the experimental investigations, Cr, Al, Ti, V, Zn, Ni, and Co polycrystalline metal films were grown with a thickness of 10-150 nm on polycrystalline (KERAFOL, 0.25 mm thick) and single crystalline Al2O3 (CrysTec, 0.25 mm thick) substrates of 8 × 8 mm2 size. The films were deposited at room temperature by electron-beam evaporation at ∼10−6 Torr. The metal film thicknesses were measured with a surface profilometer (, Dektak XT, Bruker). Using a shadow mask, ∼400 nm thick platinum electrodes were sputter-deposited (Edwards Auto 306 at 5 × 10−2 mbar, Ar, 60 W) close to the edges of the sample. Oxidation measurements were performed in air.
The resistances of the metal films were measured during their oxidation in a tube furnace. These measurements were done by performing two-point electrical impedance spectroscopy laterally across the sample using a Newton PSM1700 Phase Sensitive Multimeter. In these measurements, AC-signals of 100 mV amplitude were applied in the frequency range of 100 Hz–1 MHz. The resulting impedance spectra were fitted using the ZView software (Scribner Associates, Inc.). The conductance measured during the oxidation is that of the remaining metallic film because the conductivity of the metals well exceeds the ones of the oxides. Thus, the oxide thickness was derived from the resistance values (R = ρl/A) of the remaining metallic part of the film.
The metals studied in this work were chosen according to the requirements given by the application, such as high corrosion resistance provided by a well-adhering oxide film. The latter requires that the difference between the molar volumes of the metal and the oxide is insignificant, as described by the Pilling–Bedworth ratio. The native oxide layer on such metals has a typical thickness of 1-2 nm. Also, the metals investigated are characterized by an oxidation activation energy >1.4 eV, as required for a long lifetime of the data storage material (see Figs. 2 and 4). Therefore Cr, Al, Ti, V, Zn, Ni, and Co were selected. Films with thicknesses of 50 nm were grown on polycrystalline Al2O3 substrates, and their oxidation kinetics was measured (the resulting oxides were polycrystalline, as found by scanning and transmission electron microscopy studies16,17). The results of these measurements are presented in Fig. 4. We find the oxidation of the films to be diffusion-controlled because (i) their oxidation kinetics follows the parabolic rate law, (ii) kp as well as its activation energy is independent of growing oxide film thickness, and (iii) the oxidation rate depends only weakly on the oxygen partial pressure pO2. Details can be found in a further study.16 Note that for surface-reaction-controlled oxidation, a strong change with pO2 was expected. Furthermore, a thickness of 50 nm exceeds the validity range of the Cabrera-Mott model because electron tunneling is only up to a few nm relevant (cf. discussion in Atkinson’s review9). From the absence of any significant changes in absolute kp values and the respective activation energy for Ni films thinner than 50 nm, we conclude that also these films follow the parabolic rate law. For Al2O3 formation, a Cabrera-Mott logarithmic rate law had been found at 650 °C up to ∼20 nm.18 Because the diffusivity in alumina and correspondingly the oxidation rate is much lower than in NiO, it is not surprising that for Al2O3 the electric field effects of the Cabrera-Mott model have a more pronounced influence.
The Arrhenius plot for the oxidation of 50 nm thick Cr, Al, Ti, V, Zn, Ni, and Co samples is displayed in Fig. 4. The activation energies are in the same range as found for corresponding polycrystalline materials in the literature, for which accelerated diffusion along grain boundaries has been invoked,15,19,20 cf. Fig. 5. While Cr is characterized by the smallest oxidation rate constant, Co, followed by Ni, has the highest.17 Indeed, Fig. 4 shows that the oxidation rate of Co exceeds the one of Ni by two orders of magnitude. The crystal structures of NiO and CoO are the same (rocksalt), i.e., the difference of the oxidation rates is not caused by the crystal structure. Also, the defect chemistry of the two oxides is similar.9 The main difference between both systems is the typically much higher defect concentration in CoO, which exceeds the one of NiO by up to two orders of magnitude. As a result, the cation diffusivity in CoO is larger than in NiO (Eq. (5)). Regarding Co oxidation, one specific point has to be mentioned: Under the conditions of the present study (T ≤ 500 °C, high pO2), the thermodynamically stable phase is Co3O4. In situ X-ray absorption spectroscopy and X-ray diffraction measurements performed during the oxidation of thin Co metal foils indicate that as long as some metal is still present, however, CoO is predominantly formed.21 Only after the complete consumption of the metal, CoO transforms into Co3O4 in a slower process. In the present investigation, in which the oxidation kinetics is followed by measuring the conductivity of the remaining metal, only the first process is captured, i.e., the kp found corresponds to the outward diffusion of Co through the CoO. According to the literature, Al is oxidized to in the temperature range explored.22,23 It is only at higher temperatures that transforms into the thermodynamically stable polymorph. Because is kinetically very stable, this does not, however, impair potential data storage applications.
The analysis of the oxidation rate constant measurements reveals Co and Ni to be candidate materials for data archiving. For these metals, the required oxidation rates are possibly within reach. For Co thin films, for example, millisecond oxidation times (kp = 2.5 × 10−9 cm2/s) are expected for heating to 540 °C.
For the metals investigated in this work (10-50 nm thick films, oxidized at 250-500 °C), approaches to speed up the surface reaction (UV illumination, exposure to ozone, high pO2) will not accelerate the overall process because the oxidation is diffusion controlled, i.e., the surface reaction is faster than the bulk diffusion. On the other hand, doping can increase the defect concentration of the oxide film and therefore the oxidation rate constant, as will be investigated in a forthcoming study.16 Furthermore, below 1000 °C, Ni oxidation is determined by the fast grain boundary diffusion of Ni in NiO.24,25 We therefore expect that the optimization of the film microstructure by decreasing the oxide grain size will enhance the relevant diffusivity.
The effective tracer-diffusion coefficient of 10−13 cm2/s at ∼500 °C calculated from measured kp values for grain sizes of 10-30 nm in the growing NiO film is five orders of magnitude larger than those of single crystals reported in the literature (Fig. 5).26,27 The oxidation-rate constant for Ni reported here is in fact the highest measured so far. Fast grain boundary diffusion in growing oxide films was also found for other binary oxides, such as CoO, ZnO, Al2O3, and TiO2.17 Controlling the grain size in a growing oxide is not an easy task, however. For the films studied here, this is particularly difficult because of the already very small grain sizes (10-30 nm) in the NiO films.
The kinetics of the oxygen-stoichiometry change (complete oxidation or small modification of oxygen stoichiometry in an oxide) is expected to change at a critical film thickness from being diffusion-controlled to surface-reaction-controlled. This critical thickness is determined by (k: effective surface rate constant, lc: critical sample thickness, : diffusion coefficient). For small stoichiometry changes in mixed conducting perovskites, lc is usually in the range of 1-100 .28 Interestingly, we could not observe a change from the diffusion-controlled to the surface-reaction controlled mechanism, although the films studied were as thin as 10 nm. Fig. 6 illustrates why the formation of binary oxide films remain diffusion controlled down to very low oxide thickness. While in perovskites the relevant diffusivity () is high,29,30 is low in NiO. The surface reaction rate constant is not known for NiO. However, assuming that k of NiO and of the perovskites are comparable, lc of NiO is predicted to be lower than that of perovskites by orders of magnitude. These considerations offer an explanation why at elevated temperatures thin Ni films oxidize according to the parabolic rate law.
In this paragraph, we discuss several options to accelerate the oxidation process: (i) Laser irradiation focused on a small spot may be effective as it is expected to cause helpful nonlinear effects. Detailed experimental investigations of these effects are necessary. (ii) Since the native concentrations of the relevant mobile defects in the studied binary oxides are extremely low, controlling their concentration in the growing oxide layer by doping has the potential for a significant acceleration. Doping experiments for NiO will be discussed in a forthcoming publication.16 (iii) Oxides used as electrolyte materials typically have high D* values (e.g., Y-doped ZrO2 close to the orange line in Fig. 6). Since their electronic conductivity is extremely low, the thermal oxidation of, e.g., a Y–Zr alloy film would be slow (cf. Eq. (3)). However, photogenerated electronic conductivity (UV irradiation) could overcome this bottleneck. (iv) Higher ionic defect mobilities and corresponding tracer diffusivities compared to oxides are known, e.g., for sulfides. While the practical implementation would be more complex than for an oxidation reaction, a sulphuration reaction might lead to larger kp. (v) Instead of completing the whole writing in a single step, one may envision a combination of a very short localized initialization step followed by further propagation of a triggered reaction or by a nonlocal “development treatment” applied on a longer time scale.
While the present study is focussed on the underlying oxidation kinetics rather than actual data writing, we nevertheless want to comment on the physical limits. A calculation based on the thermal properties of the Al2O3 substrate indicates that—given the exponential temperature dependence of kp—the broadening of the irradiated oxidation spot by thermal diffusion is of minor importance. To heat a spot with, e.g., 3 diameter to 600 °C, about 10−8 J are necessary. If this is to be done within 1 , the required laser power is still smaller than 0.1 W, i.e., comparable to the power of laser pointers. Simultaneous writing of bits appears feasible.
We performed first steps to explore the viability of writing oxide structures into metal films by laser heating, and Fig. 7 shows some preliminary results. Here a typical oxidized spot is imaged. The spot size is about 20 due to restrictions by the laser optics. For the local heating, a continuous wave laser with 0.3 W ( nm) and 10 s irradiation time was used. Although these conditions are not optimized, it is possible to locally oxidize the metallic films as shown in Fig. 7. Cross-sectional imaging of the film with focused ion beam-scanning electron microscopy (FIB-SEM) confirmed that the oxidized spots in a 100 nm thick Ni film consist of NiO.
We conclude that long-term data archiving using the oxidation of corrosion-resistant metal films faces challenging boundary conditions of the oxidation kinetics, in particular to achieve the required fast writing speed and long-term stability. We have therefore analyzed the rate-determining process for the oxidation of Cr, Al, Ti, V, Zn, Ni, and Co films at temperatures of 250-500 °C. The oxidation is microscopically given by the chemical diffusion of ionic and electronic species through the oxide layer, as quantitatively described by the Wagner theory of oxidation. Of all metals investigated, Co features the highest oxidation rate constant (kp = 2.5 × 10−9 cm2/s), with a millisecond oxidation time at 540 °C. While it appears unlikely that currently available Co films meet the technological requirements, they are clear candidate materials for data-archiving. Possible ways to enhance the data writing speeds are, for example, the combination of nanosecond laser pulses with microsecond heating times or modifications of the films’ microstructures.
See supplementary material for a detailed discussion of the physical limits of oxidation rate constants.
We gratefully acknowledge Yvonne Stuhlhofer, Bernhard Fenk, Marion Kelsch, Gelon Albrecht, Armin Schulz, Sarah Parks, and Jone Zabaleta for technical support and useful discussions.