Wafer Curvature Measurements Research Articles

Extra half-plane shortening of dislocations as an origin of tensile strain in Si-doped (Al)GaN

Si doping of (Al,Ga)N layers grown by metalorganic chemical vapor deposition induces an inclination of threading dislocations (TDs). This inclination leads to a change of the extra half-plane size of edge and mixed type dislocations. Depending on the dislocation density and the doping concentration, these effects are accompanied by the generation of tensile strain, which can also lead to crack formation. Several models have been published in the past in order to explain this process. Different models result in opposite TD inclination directions with respect to the extra half-plane position. Therefore, this work examines the correlation between the extra half-plane position and the inclination direction to clarify the origin of the tensile strain increase using scanning transmission electron microscopy. With this approach, it can be unambiguously experimentally verified that Si doping leads to a shortening of the dislocations half-plane. An analysis of in situ wafer curvature measurement proves that the increase of tensile strain in GaN caused by Si doping can be explained by this process. Aside from the inclination caused by Si doping, a TD inclination in undoped GaN layers has been analyzed. Possible explanations for the inclination process are discussed.

Correlation between the wafer curvature and fluorescence of pulsed laser deposited ruby thin films stressed to ∼2 GPa

Here, the room temperature piezospectroscopic response of highly-fluorescent, ∼330 nm-thick pulsed laser deposited crystalline ruby (0.05 wt. % Cr3+ doped α-Al2O3) thin films on either (001)-oriented sapphire or (001)-oriented yttria-stabilized zirconia wafers was investigated and calibrated against biaxial film stress measurements obtained from a multibeam optical stress sensor or profilometry-determined wafer curvature measurements. The piezospectroscopic frequency shift from 0 to 1.9 GPa of compressive biaxial stress for the phase-pure (001)-oriented ruby films produced here had the same piezospectroscopic Π11 and Π22 tensor coefficient values as bulk ruby over its previously calibrated 0–0.9 GPa range. This extended calibration may be useful when using ruby to measure the amount of biaxial stress in a variety of multilayer devices and coatings.

Atomic-scale diffusion rates during growth of thin metal films on weakly-interacting substrates

We use a combined experimental and theoretical approach to study the rates of surface diffusion processes that govern early stages of thin Ag and Cu film morphological evolution on weakly-interacting amorphous carbon substrates. Films are deposited by magnetron sputtering, at temperatures TS between 298 and 413 K, and vapor arrival rates F in the range 0.08 to 5.38 monolayers/s. By employing in situ and real-time sheet-resistance and wafer-curvature measurements, we determine the nominal film thickness Θ at percolation (Θperc) and continuous film formation (Θcont) transition. Subsequently, we use the scaling behavior of Θperc and Θcont as a function of F and Ts, to estimate, experimentally, the temperature-dependent diffusivity on the substrate surface, from which we calculate Ag and Cu surface migration energy barriers {{boldsymbol{E}}}_{{boldsymbol{D}}}^{{bf{exp }}} and attempt frequencies {{boldsymbol{nu }}}_{{bf{0}}}^{{bf{exp }}}. By critically comparing {{boldsymbol{E}}}_{{boldsymbol{D}}}^{{bf{exp }}} and {{boldsymbol{nu }}}_{{bf{0}}}^{{bf{exp }}} with literature data, as well as with results from our ab initio molecular dynamics simulations for single Ag and Cu adatom diffusion on graphite surfaces, we suggest that: (i) {{boldsymbol{E}}}_{{boldsymbol{D}}}^{{bf{exp }}} and {{boldsymbol{nu }}}_{{bf{0}}}^{{bf{exp }}} correspond to diffusion of multiatomic clusters, rather than to diffusion of monomers; and (ii) the mean size of mobile clusters during Ag growth is larger compared to that of Cu. The overall results of this work pave the way for studying growth dynamics in a wide range of technologically-relevant weakly-interacting film/substrate systems—including metals on 2D materials and oxides—which are building blocks in next-generation nanoelectronic, optoelectronic, and catalytic devices.

Effect of Ge doping on growth stress and conductivity in AlxGa1-xN

Silicon (Si) is a common n-type donor in AlxGa1-xN; however, it induces bending of edge-type threading dislocations which can generate tensile stress in the film leading to the formation of channeling cracks in thick layers. Germanium (Ge) has previously been investigated as an alternative to Si for n-type doping of GaN, but its impact on film stress in AlxGa1-xN has not been investigated in detail. In this study, we employ in situ wafer curvature measurements combined with postgrowth characterization to investigate Ge doping of AlxGa1-xN (x = 0–0.62) layers grown on 6H-SiC by metalorganic chemical vapor deposition. It was found that Ge doping (n ∼ 1.6 × 1019 cm−3) of Al0.30Ga0.70N does not induce tensile stress during growth in contrast to that observed with a similar level of Si doping. In addition, the average inclination angle of edge dislocations was similar for undoped and Ge doped films indicating that Ge does not promote surface-mediated dislocation climb. High n-type doping was achieved in Ge doped AlxGa1-xN for lower Al fraction range (x < 0.5), but resistivity increased and carrier density decreased significantly for higher Al fractions. The results demonstrate Ge doping as a viable alternative to Si doping of AlxGa1-xN (x < 0.5) for achieving thick, crack-free layers.

Ion-induced nanopatterning of silicon: Toward a predictive model

We review recent progress toward the development of predictive models of ion-induced pattern formation on room-temperature silicon, with a particular emphasis on efforts to eliminate fit parameters in the linear regime by means of experimental measurements or atomistic simulations. Analytical approaches considered include “mechanistic” models of the impact-induced collision cascade, the Crater Function Framework, and continuum treatments of ion-induced stress and viscous flow. Parameter evaluation methods include molecular dynamics and binary collision approximation simulations, as well as wafer curvature measurements and grazing incidence small-angle x-ray scattering. Mathematical detail is provided in the context of key results from pattern formation theory, which are also briefly summarized.

The influence of alloying interactions on thin film growth stresses

A series of W-Fe and W-Cr thin films were sputter deposited and the intrinsic growth stresses determined by in situ wafer curvature measurements. Under the growth conditions studied, the elemental W film grew in a compressive stress state whereas the elemental Fe and Cr films grew in a tensile stress condition. By mixing Fe or Cr with W, the alloy stress state was bounded between the two elemental stresses which included a zero stress condition. The specific stress response is reported as a function of alloy type that is affected by grain size, grain boundary composition, localized phase separation, and energetic peening effects. Using the ambient temperature deposited zero stress composition, these films were re-deposited at 673K to drive the microstructure towards equilibrium. Under these conditions, both alloys exhibited similar compressive stress states during post-coalescence growth, with the post-deposition stress recovery being greater in the W-Fe film than that of the W-Cr film. This difference was contributed to the dissimilarity in grain sizes between the two films as well as how the solute partitioned in the matrix, i.e. at the grain boundary or as phase separated laths within the grains.

Stress evolution in elastic-plastic electrodes during electrochemical processes: A numerical method and its applications

Monitoring in real time the stress state in high capacity electrodes during charge-discharge processes is pivotal to the performance assessment and structural optimization of advanced batteries. The wafer curvature measurement technique broadly employed in thin-film industry, together with stress analysis using the Stoney equation, has been successfully adopted to measure in situ the stress in thin film electrodes. How large plastic deformation or interfacial delamination during electrochemical cycles in such electrodes affects the applicability of Stoney equation remains unclear. Here we develop a robust electrochemical-mechanical coupled numerical procedure to investigate the influence of large plastic deformation and interfacial failure on the measured stress in thin film electrodes. We identify how the constitutive behavior of electrode materials and film-substrate interfacial properties affect the measured stress-capacity curves of electrodes, and hence establish the relationship of electrode material parameters with the characteristics of stress-capacity curves. Using Li-ions batteries as examples, we show that plastic deformation and interfacial delamination account for the asymmetric stress-capacity loops seen in in situ stress measurements. The methods used here, along with the finite-element code in the supplementary material, may be used to model the electrode behavior as a function of the state of charge.

Coefficient of thermal expansion and biaxial Young's modulus in Si-rich silicon nitride thin films

The coefficient of thermal expansion (α) and biaxial Young's modulus is determined by comparing the differential thermal stress induced in Si-rich silicon nitride thin films deposited on single-crystal Si and sapphire substrates. The amorphous films are deposited in mixtures of dichlorosilane and ammonia, by low pressure chemical vapor deposition, in a temperature range of 1050–1115 K. Temperature-dependent wafer curvature measurements are performed to determine the differential thermal stress, across a temperature range spanning 300–800 K. Observations indicate that both α and the biaxial modulus decrease as the silicon content in the films increases. The trend of reduction in α is consistent with the relative α values for the limiting-case compositions of cubic-Si3N4 and amorphous Si. The decrease in α is attributed to a reduction in anharmonicity associated with Si–Si bonds relative to Si–N bonds. The biaxial modulus is observed to be proportional to the inverse cube root of the amorphous Si volume fraction. This observation is shown to be consistent with volumetric dilation of basal Si-SiyN4-y tetrahedra (y = 0–4), when substoichiometric films are formed through the substitution of Si for N. Additionally, the intrinsic film stress is observed to vary in proportion to the square of the inverse cube root of the amorphous Si volume fraction, which is shown to be consistent with compositionally induced intrinsic strain variation in Si-rich silicon nitride thin films.

Mechanical, thermal, and electrochemical properties of Pr doped ceria from wafer curvature measurements.

This work demonstrates, for the first time, that a variety of disparate and technologically-relevent thermal, mechanical, and electrochemical oxygen-exchange material properties can all be obtained from in situ, current-collector-free wafer curvature measurements. Specifically, temperature or oxygen partial pressure induced changes in the curvature of 230 nm thick (100)-oriented Pr0.1Ce0.9O1.95-x (10PCO) films atop 200 μm thick single crystal yttria stabilized zirconia or magnesium oxide substrates were used to measure the biaxial modulus, Young's modulus, thermal expansion coefficient, thermo-chemical expansion coefficient, oxygen nonstoichiometry, chemical oxygen surface exchange coefficient, oxygen surface exchange resistance, thermal stress, chemical stress, thermal strain, and chemical strain of the model mixed ionic electronic conducting material 10PCO. The (100)-oriented thin film 10PCO thermal expansion coefficient, thermo-chemical expansion coefficient, oxygen nonstoichiometry, and Young's modulus (which is essentially constant, at ∼200 MPa, over the entire 280-700 °C temperature range in air) measured here were similar to those from other bulk and thin film 10PCO studies. In addition, the measured PCO10 oxygen surface coefficients were in agreement with those reported by other in situ, current-collector-free techniques. Taken together, this work highlights the advantages of using a sample's mechanical response, instead of the more traditional electrical response, to probe the electrochemical properties of the ion-exchange materials used in solid oxide fuel cell, solid oxide electrolysis cell, gas-sensing, battery, emission control, water splitting, water purification, and other electrochemically-active devices.

In Situ Stress, Elastic Constant, Oxygen Surface Exchange Coefficient, and Thermo-Chemical Expansion Coefficient Measurements on Praseodymium Doped Ceria Thin Films

A Multi-beam Optical Stress Sensor provides a noncontact, in situ method for measuring thin film stress based on the curvature of a multilayer sample. Originally, this technique was used to measure film stresses during thin film deposition. However, as demonstrated here using praseodymium doped ceria, when combined with an optically accessible tube furnace, wafer curvature measurements can be used as an in situ, electrode-free platform for measuring film stress, biaxial modulus, thermal expansion coefficient, chemical expansion coefficient, and oxygen surface exchange coefficient.

Improved luminescence from InGaN/GaN MQWs by reducing initial nucleation density using sputtered AlN on sapphire substrate

The edge dislocations in GaN film were reduced by lowering initial islands density and extending islands coalescence time in MOVPE, which were achieved more effectively on an ex situ sputtered AlN seed layer than on an in situ LT-GaN seed layer. GaN film with low dislocation density was achieved on an ex situ sputtered AlN seed layer by initial growth optimization as indicated by the dark spots density of 1.5×108cm−2 of cathode-luminescence mapping measurement. Stress relaxation was observed for the GaN film grown from sparse initial islands on an ex situ sputtered AlN seed layer as indicated by in situ wafer curvature measurement. Temperature quenching of photoluminescence from InGaN/GaN multiple quantum wells grown on a GaN template was mitigated when an ex situ sputtered AlN seed layer was employed compared with the case with an in situ LT-GaN seed layer, confirming that the reduced nucleation density by both the use of a sputtered AlN seed and the optimization of GaN growth condition is effective for suppressing non-radiative recombination in InGaN by the reduction in edge dislocation density.

A novel setup for wafer curvature measurement at very high heating rates.

The curvature evolution of a thin film layer stack containing a top Al layer is measured during temperature cycles with very high heating rates. The temperature cycles are generated by means of programmable electrical power pulses applied to miniaturized polysilicon heater systems embedded inside a semiconductor chip and the curvature is measured by a fast wafer curvature measurement setup. Fast temperature cycles with heating duration of 100 ms are created to heat the specimen up to 270 °C providing an average heating rate of 2500 K/s. As a second approach, curvature measurement utilizing laser scanning Doppler vibrometry is also demonstrated which verifies the results obtained from the fast wafer curvature measurement setup. Film stresses calculated from the measured curvature values compare well to literature results, indicating that the new method can be used to measure curvature during fast temperature cycling.

Aluminum oxide/titanium dioxide nanolaminates grown by atomic layer deposition: Growth and mechanical properties

Atomic layer deposition (ALD) is based on self-limiting surface reactions. This and cyclic process enable the growth of conformal thin films with precise thickness control and sharp interfaces. A multilayered thin film, which is nanolaminate, can be grown using ALD with tuneable electrical and optical properties to be exploited, for example, in the microelectromechanical systems. In this work, the tunability of the residual stress, adhesion, and mechanical properties of the ALD nanolaminates composed of aluminum oxide (Al2O3) and titanium dioxide (TiO2) films on silicon were explored as a function of growth temperature (110–300 °C), film thickness (20–300 nm), bilayer thickness (0.1–100 nm), and TiO2 content (0%–100%). Al2O3 was grown from Me3Al and H2O, and TiO2 from TiCl4 and H2O. According to wafer curvature measurements, Al2O3/TiO2 nanolaminates were under tensile stress; bilayer thickness and growth temperature were the major parameters affecting the stress; the residual stress decreased with increasing bilayer thickness and ALD temperature. Hardness increased with increasing ALD temperature and decreased with increasing TiO2 fraction. Contact modulus remained approximately stable. The adhesion of the nanolaminate film was good on silicon.

Measuring stiffness and residual stress of thin films by contact resonance atomic force microscopy

A method based on contact resonance atomic force microscopy (AFM) was proposed to determine the mechanical properties of thin films. By analyzing the contact resonance frequencies of an AFM probe while the tip was in contact with the sample, the stiffness and residual stress of a freestanding circular SiNx membrane were evaluated quantitatively. The obtained magnitude of residual stress was in reasonable agreement with that determined by wafer curvature measurement. The method was verified to have much better mechanical sensitivity than the popular AFM bending test method. Its promising application to fast, nondestructive mechanical mapping of thin-film-type structures at the nanoscale was also demonstrated.

Practical Considerations for Determining Thin Film Oxygen Surface Exchange Coefficients, Elastic Constants, Thermal Expansion Coefficients, Thermo-Chemically Induced Stresses, and Thermo-Chemically Induced Strains from Wafer Curvature Measurements

Wafer curvature measurements have recently been developed as a new, electrode-free method for simultaneously measuring dense or porous thin film chemical oxygen surface exchange coefficients and stress states.1, 2 In addition to being one of today’s cheapest electrode-free oxygen surface exchange coefficient measurement techniques (and the only one presently yielding simultaneous surface exchange coefficient and stress data) these measurements allow for the in situ/in operando determination of thin film elastic constants, thermal expansion coefficients, and chemical expansion coefficients.3 Hence, wafer curvature measurements promise to be an important tool in establishing the links between the mechanical state and electrochemical performance of the materials used in solid state battery, fuel cell, memristor, catalytic reactor, and other solid state ionic devices. This presentation will review the recent progress made in applying wafer curvature measurements to the study of oxygen ion conducting materials. Specifically, the presentation will provide 1) an overview of the fitting equations used to extract the aforementioned thin film materials properties from wafer curvature relaxation experiments, 2) materials case studies highlighting use of the technique, 3) a comparison of the technique’s benefits and limitations compared to alternative approaches, 4) a review of the sample geometric considerations and substrate material properties necessary to obtain reliable data, 5) a detailed description of the experimental setup used at Michigan State to conduct these experiments, 6) a breakdown of the system costs, and 7) a series of practical tips for successful implementation of the technique. Acknowledgements This work was supported by National Science Foundation Award Number CBET-1254453.

Growth, structural and mechanical properties of magnetron-sputtered ZrN/SiNx nanolaminated coatings

Coatings with nanoscale architectures, such as nanocomposites or nanolaminates, offer improved mechanical properties and resistance to radiation environments due to their increased interface area per unit volume. Here, we present a systematic study of the evolution of structure, stress state and mechanical properties of nanoscale ZrN/SiNx multilayers with different thickness of elementary layers, grown at Ts=300°C by reactive magnetron sputter-deposition from Zr and Si3N4 targets. Both the multilayer period Λ (7–41nm range) and ZrN thickness ratio, fMe, (0.24–0.95 range) were varied. X-ray reflectivity and transmission electron microscopy revealed the presence of planar interfaces, with roughness lower than 1nm, yielding to the formation of a highly periodic layer stacking throughout the entire film thickness. X-ray diffraction (XRD) show that the presence of amorphous SiNx layer (for elementary thickness ha≥1nm) induces a change in the preferred orientation of the cubic (B1-type) ZrN layers from (111) to (002), while the ZrN layer becomes X-ray amorphous at thickness hMe lower than 2nm. Using in situ wafer curvature measurements we show that both SiNx and ZrN layers are growing under an intrinsic compressive stress state, of a constant value of −1GPa for SiNx and varying from −5.7 to −4GPa with increasing ZrN layer thickness. Nanoindentation tests revealed a gradual increase of the elastic modulus from 200 to 265GPa with fMe, while the hardness showed a maximum (H=24.1GPa) for the ZrN(8nm)/SiNx(0.4nm) multilayer, corresponding to an 3–4GPa increase compared to monolithic ZrN (21.0GPa) and Si3N4 (19.2GPa) films. We ascribe this enhancement of mechanical properties to local epitaxy and stronger bonding at (001) ZrN/SiNx interfaces when the SiNx thickness reduces down to 0.4nm, as confirmed by XRD results obtained from ZrN/SiNx superlattices grown on MgO (001) substrate.

Internal stress due to solvent co-intercalation in graphite electrodes for Li ion batteries

Thin film graphite electrodes were investigated in Li half-cells, to investigate the stresses induced by propylene carbonate (PC) additions to a standard liquid electrolyte. In situ wafer curvature measurements indicate that substantial compressive stress occurs above 0.5 V, before there is significant Li intercalation into the graphite. Transmission electron microscopy shows that this cycling produces voids throughout the film, via delamination between graphene layers. To explain these observations, a model based on interlaminar debonding and the subsequent buckling of graphite layers is proposed. Existing mechanics models of these phenomena are in good agreement with the experimental observations. Based on this analysis, it appears that the PC additions lead to a very low value of the interlaminar fracture resistance.

In-situ control of large area (11–22)-GaN growth on patterned r-plane sapphire

This report describes in-situ measurements of multi-wavelength reflectance, wafer curvature and growth temperature during epitaxy of semi-polar (11–22)-GaN on 100mm diameter r-plane PSS. Reflectance transients at 405nm can be correlated with the development of GaN facets prior to coalescence and with the final layer morphology after coalescence. It is shown that emissivity-corrected near-IR pyrometry may give deficient growth temperature readings on pockets with low reflecting patterned substrates. Near-UV pyrometry has been used to quantify wafer temperature depending on process parameters and wafer bow. In-situ curvature measurements reveal a tensile-strained growth mode for the GaN nucleation applied and additional curvature components due to a higher thermal gradient in growth direction than for planar growth. Room temperature wafer bow of 7µm thick (11–22)-GaN on r-PSS is spherical and comparable to c-oriented layers.

Growth of high quality and uniformity AlGaN/GaN heterostructures on Si substrates using a single AlGaN layer with low Al composition.

By employing a single AlGaN layer with low Al composition, high quality and uniformity AlGaN/GaN heterostructures have been successfully grown on Si substrates by metal-organic chemical vapor deposition (MOCVD). The heterostructures exhibit a high electron mobility of 2150 cm2/Vs with an electron density of 9.3 × 1012 cm−2. The sheet resistance is 313 ± 4 Ω/◻ with ±1.3% variation. The high uniformity is attributed to the reduced wafer bow resulting from the balance of the compressive stress induced and consumed during the growth, and the thermal tensile stress induced during the cooling down process. By a combination of theoretical calculations and in situ wafer curvature measurements, we find that the compressive stress consumed by the dislocation relaxation (~1.2 GPa) is comparable to the value of the thermal tensile stress (~1.4 GPa) and we should pay more attention to it during growth of GaN on Si substrates. Our results demonstrate a promising approach to simplifying the growth processes of GaN-on-Si to reduce the wafer bow and lower the cost while maintaining high material quality.

In situ stress observation in oxide films and how tensile stress influences oxygen ion conduction.

Many properties of materials can be changed by varying the interatomic distances in the crystal lattice by applying stress. Ideal model systems for investigations are heteroepitaxial thin films where lattice distortions can be induced by the crystallographic mismatch with the substrate. Here we describe an in situ simultaneous diagnostic of growth mode and stress during pulsed laser deposition of oxide thin films. The stress state and evolution up to the relaxation onset are monitored during the growth of oxygen ion conducting Ce0.85Sm0.15O2-δ thin films via optical wafer curvature measurements. Increasing tensile stress lowers the activation energy for charge transport and a thorough characterization of stress and morphology allows quantifying this effect using samples with the conductive properties of single crystals. The combined in situ application of optical deflectometry and electron diffraction provides an invaluable tool for strain engineering in Materials Science to fabricate novel devices with intriguing functionalities.