Materials Science-Poland, 33(2), 2015, pp. 340-347 http://www.materialsscience.pwr.wroc.pl/ DOI: 10.1515/msp-2015-0053 Young’s modulus and creep compliance of GaAs and Ga1−xMnxAs ferromagnetic thin films under thermal stress at varied manganese doping levels S.K. KEMEI1∗, M.S.K. KIRUI1 , F.G. NDIRITU1 , R.G. NGUMBU1 , P.M. ODHIAMBO1 , D.M.G. LEITE2 , A.L.J. PEREIRA3 , J.H. DIAS DA SILVA4 1Egerton University, Department of Physics, P.O. Box 536-20115, Egerton, Kenya 2Universidade Federal de Itajuba, Av. BPS, 1303, 37500-903 Itajuba, MG, Brazil 3Universitat Politecnica de Valencia, 46022, Valencia, Spain 4Sao Paulo State University, Advanced Materials Group, Bauru Campus, Av. Luiz Edmundo Carrijo Coube N°14-01, Vargem Limpa Bauru-SP CEP: 17033-360, Brazil Dynamical mechanical analysis yields information about the mechanical properties of a material as a function of deforming factors, such as temperature, oscillating stress and strain amplitudes. GaAs and Mn-doped GaAs at varied levels, used in making electronic devices, suffer from damage due to changes in environmental temperatures. This is a defective factor experienced during winter and summer seasons. Hence, there was a need to establish the best amount of manganese to be doped in GaAs so as to obtain a mechanically stable spin injector material to make electronic devices. Mechanical properties of Ga1−xMnxAs spin injector were studied in relation to temperatures above room temperature (25 °C). Here, creep compliance, Young’s moduli and creep recovery for all studied samples with different manganese doping levels (MDLs) were determined using DMA 2980 Instrument from TA instruments Inc. The study was conducted using displace-recover programme on DMA creep mode with a single cantilever clamp. The samples were prepared using RF sputtering techniques. From the creep compliance study it was found that MDL of 10 % was appropriate at 30 °C and 40 °C. The data obtained can be useful to the spintronic and electronic device engineers in designing the appropriate devices to use at 30 °C and above or equal to 40 °C. Keywords: creep compliance; Young’s modulus; percentage creep recovery; strain jumps; manganese doping levels © Wroclaw University of Technology. 1. Introduction 1.1. GaAs and Ga1−xMnxAs thin films GaAs films are prepared by direct reactions of the elements of gallium and arsenic in three similar industrial processes, namely: 1. vapour phase epitaxy (VPE) reaction of gaseous gallium metal and arsenic trichlo- ride as shown in the chemical equation: 2Ga+2AsCl3 −→ 2GaAs+3Cl2 (1) 2. metal organic chemical vapour deposition (MOCVD) reaction of trimethylgallium and ∗E-mail: solsteshkemei@gmail.com arsine as shown in the chemical equation: Ga(CH3)3 +AsH3 −→ GaAs+3CH4 (2) 3. molecular beam epitaxy (MBE) of gallium and arsenic as represented by chemical equation: 4Ga+As4 −→ 4GaAs or 2Ga+As2 −→ 2GaAs (3) GaAs has a direct band gap and can be used to manufacture devices such as microwave fre- quency integrated circuits, monolithic microwave integrated circuits, infrared light emitting diodes, laser diodes and solar cells. The band gap, elec- tron mobility and electronic conductivity of GaAs can be modified by addition of impurity atoms of http://www.materialsscience.pwr.wroc.pl/ Young’s modulus and creep compliance of GaAs and Ga1−xMnxAs ferromagnetic thin films. . . 341 manganese to form Ga1−xMnxAs for nanoelectron- ics or nanotechnology. The increase in manganese doping level monotonically increases the electron mobility and electron conductivity, hence, the data computing speed [1]. The Ga1−xMnxAs is an anisotropic material consisting of three elements, combined chemically by molecular beam epitaxy (MBE) or magnetron sputtering technique. Manganese atoms are added to the GaAs host substrate as impurities that cre- ate conduction charge carriers with magnetic spin moment. The doped manganese substitutes for Ga site in the host semiconductor, GaAs, to produce Ga1−xMnxAs. 1.2. Creep recovery testing Deformation of a material occurs when a load (force) is applied to it and it deforms plastically under an applied stress depending on the strength of intermolecular forces [2, 3]. After an initial de- formation, the deformation of the material later reaches its maximum. The deformation can then be plotted against time and temperature [4, 5]. More precisely, representative samples of materials can be tested for creep. The sample is loaded with a very low stress level just enough to hold it in place and allow it to stabilize. The testing stress is then applied very quickly, with instantaneous ap- plication, and changes in the material response are recorded as percent strain [6, 7]. The material is then held at this stress for a period of time until it reaches equilibrium. Creep tests can be used in two ways: to obtain fundamental information about a material or to investigate the material response un- der the real use conditions [8, 9]. 1.3. Creep - recovery analysis Creep-recovery data results can be interpreted in three ways: a plot of strain versus stress can be done and data fitted to the model (four ele- ment model) or a plot of strain versus stress and quantitative analysis done in terms of irrecoverable creep, viscosity, modulus and relaxation time [10]. Lastly, a plot of creep compliance versus time (tem- perature) can be drawn. The creep compliance is a mechanical property that measures the tendency of a material to respond to deformation and con- firms material softness above glass transition tem- perature (Tg) [9]. As stated earlier, there is an im- midiate response of a material to an applied stress (load) and the point at which the stress is applied is assumed to be the starting point (time zero) for the creep experiment. For the recovery portion, the time zero point is when the stress is removed. The initial jump is equivalent to the applied stress di- vided by a spring constant ( σ E1 ) which is envisioned as an immediate stretching and locking into its ex- tended condition. Practically, this region is very small and could be difficult to be seen and the strain time derivative may be used to locate it. After the spring is extended, the independent dashpot and the Voigt element can respond. When the load is removed there is an immediate recovery of this spring, equivalent to σ E1 [11, 12]. This can be observed as an elastic deformation of material chains. The slope of the straight equilib- rium region of the creep curve gives the strain rate. Initial and recoverable strains can be determined, and in the region of a constant strain rate, equil- librium viscosity (ηC) can be obtained [4, 13, 14]. Percent recovery can also be calculated to pro- vide information on how much of a material re- gains its original properties (resilience) after the stress (load) is released. Recovery time provides the amount of time required for strain to recover to 36.79 % of its original value [16]. A plot of creep compliance versus temperature can be analysed to observe, where the properties degrade as tempera- ture increases. Temperature can be raised and low- ered so as to simulate the effect of an environmental thermal cycle [17]. When the stress on a sample is increased, the material may creep under the applied load and when the load is removed the sample may attempt to recover its original dimensions (property of stress relaxation) [11, 12]. GaAs and manganese doped GaAs used in mak- ing electronic devices endure damage caused by adverse environmental temperatures. This causes mechanical instability of the associated devices which is a major problem to spintronic device engi- neers. Hence, there was a need to determine the ap- propriate amount of manganese that can be doped 342 S.K. KEMEI et al. in GaAs to achieve a mechanically stable spin in- jector material that can withstand harsh environ- mental temperature conditions. 2. GaAs and Ga1−xMnxAs ferro- magnetic sample preparation The Ga1−xMnxAs films were deposited by radio frequency (RF) magnetron sputtering technique in the Laboratory of Semiconductor Films, São Paulo State University (Bauru/Brazil), courtesy of Ad- vanced Materials Group. The films were grown in an Ar atmosphere (99.9999 % purity). A 100 mm diameter, 6 mm thick, electronic grade undoped GaAs wafer (Ramet Technology) was used as a tar- get in a planar diode configuration. The amorphous silica (a-SiO2) substrate was fixed directly opposite to the target at a distance of 50 mm. Manganese was added to the films by a co-sputtering process; that is, pure Mn slabs (99.99 %) were placed onto the GaAs target which was also subjected to the sputtering process, resulting in incorporation of Mn into the films. The concentration of Mn incorpo- rated into the films was controlled by covering dif- ferent fractions of the target area with Mn slabs. The thin films of a thickness of 500 to 1000 nm were then removed from the chamber and cut into rectangular samples of the length of 12.96 mm and width of 0.99 mm. 2.1. Experimental The prepared samples, due to their short lengths, were designed to fit the clamp by mount- ing them on long microscope slides of the same dimensions as the standard steel sample at their centres, as shown in Fig. 1. A control sample was also prepared to correct the error caused by micro- scope slides by mounting SiO2 microscope slides of the same thickness and lengths as the GaAs and Ga1−xMnxAs as shown in Fig. 2. DMA 2980 instrument from TA instruments was used to carry out the tensile tests. The sin- gle cantilever clamp was used because of rect- angular shape of the samples of dimensions 39.81 mm × 12.7 mm × 0.99 mm. The DMA creep mode was also used on a displace-recover Fig. 1. Study sample mounted on a microscope slide. Fig. 2. SiO2 mounted on a microscope slide at the cen- ter. programme of 10 minutes: 10 minutes, respec- tively, at 30 °C and 40 °C. The same procedure was used for all studied samples and the actual ten- sile parameter values were obtained by calculating the deviations (shifts) from the values of undoped GaAs, recorded in Tables 1 and 2. The samples were clamped as shown in Fig. 3. Fig. 3. Modified study sample clamped with a single cantilever. 2.1.1. Computational theory The creep compliance and Young’s moduli are crucial parameters in this study as they rep- resent the stiffness of the material and further- more explain how a material response to all sorts of deformation due to changes in stress ampli- tude, strain amplitude and temperature. The ther- mal stress-thermal strain relationships for GaAs and Ga1−xMnxAs were plotted by simulation of the data obtained with the DMA 2980 using the TA Young’s modulus and creep compliance of GaAs and Ga1−xMnxAs ferromagnetic thin films. . . 343 universal analysis software. Similar process was followed for the case of creep compliance. The Young’s moduli were calculated from the slopes of the linear regions of thermal stress-thermal strain graphs at 30 °C and 40 °C and tabulated as func- tions of MDLs. 30 °C was used as a working tem- perature during the study to represent the average room temperature. It was also necessary to study the mechanical stability situation of the thin films at an elevated temperature. Therefore, 40 °C was also used because it was assumed that the mechani- cal properties of the thin films under study between 30 °C and 40 °C will provide useful information. 3. Results and discussion 3.1. Creep compliance at 30 °C Fig. 4 shows creep compliance: MDLs relation- ships at 30 °C and 40 °C plotted from the data in Table 1. From the two data sets, it is apparent that creep compliance is in an increasing trend with the MDLs. Pure GaAs has the smallest creep com- pliance value of 0.0604 µm2/N and GaAs doped with 50 % manganese atoms shows the highest value of 0.7864 µm2/N. The creep compliance for MDLs of 1 %, 10 % and 20 % are 0.0996 µm2/N, 0.4704 µm2/N and 0.5614 µm2/N, respectively. In- ferring from the gradients of the graphs plotted for MDLs of 0 % to 10 %, the creep compliance increases monotonically. However, beyond 10 %, the creep compliance increases gently. This means that the manganese impurity atoms have a signifi- cant influence on the creep compliance of the dilute magnetic semiconductor. It is believed to cause a profound alteration of the GaAs crystal structure that makes it porous and softer. This is because the atoms have enough space to accommodate the changes resulting from deformation [9]. The im- perfections beyond MDL of 10 % are minimal. So, generally, at 30 °C, the Ga1−xMnxAs with MDLs of 20 % to 50 % provides the best results because of their respective high creep compliance compared to the other samples. Intrinsically, the mechanical behaviour of a material is closely related to its structure, in- cluding bond strength. However, the mechanical behaviour of a crystalline material is also con- trolled by imperfections, such as vacancies and in- terstitials [18, 19]. Therefore, here, the higher creep compliance implies that the material is not on the verge of breaking as it responds well to the im- perfections and deformations. At elevated temper- ature of 40 °C, the responses of creep compliances to the variations in MDLs are significantly similar to those at 30 °C. This can be observed in Fig. 4 plotted from the data in Table 1. Fig. 4. Creep compliance versus MDL at 30 ◦C and 40 ◦C. Table 1. Creep compliance at different MDLs. MDLs Creep compliance (µm2/N) 30 °C 40 °C 0 % 0.0604 4.0394 1 % 0.0996 4.3750 10 % 0.4704 5.2501 20 % 0.5614 5.2530 50 % 0.7864 5.8512 3.2. Creep compliance at 40 °C From Fig. 4 and Table 1, it can be seen that MDL of 10 % reveals the highest creep compliance of 5.2501 µm2/N which is of 29.9723 % higher in comparison to pure GaAs with creep compliance of 4.0394 µm2/N. MDLs of 0 % and 1 % show the least creep compliance of 4.0394 µm2/N and 4.3750 µm2/N at 40 °C. At these MDLs, the Ga1−xMnxAs samples are on the verge of breaking as they do not re- spond easily to the temperature deformation. This is attributed to the perceived reduced interatomic 344 S.K. KEMEI et al. spacing (free volume) that reduces allowance for expansion or molecular movements upon defor- mation [12, 20]. At MDL of 50 %, the man- ganese underfill becomes saturated as it is per- ceived to create excess atoms with more space for interatomic movements. Hence, the creep compli- ance increases to 5.8512 µm2/N. Beyond MDL of 20 % manganese atoms create extra internal move- ments as a result of enough interatomic space that is in increasing trend. Therefore, MDL of 50 % has more molecular motions than other MDLs, which is expressed by the high creep compliance of 5.8512 µm2/N. This implies that at 40 °C, the in- creasing levels of MDLs gradually soften the GaAs crystal lattice by creating more interatomic spacing that allows the material to respond well to the de- formation and avoid sudden breakages. Generally, the noticeable effect of temperature on the creep compliance was observed. By consid- ering Fig. 4, it can be seen that at MDL of 0 %, the creep compliance is 0.0604 µm2/N at 30 °C and 4.0394 µm2/N at 40 °C. This shows that the crys- talline structure of GaAs becomes more disordered at temperature of 40 °C compared to the structure at lower temperature of 30 °C. This implies that more free volumes are created so that any aspect of de- formation causes excessive molecular motion. This is consistent with a sharp increase in creep compli- ance to 4.0394 µm2/N. 3.3. Young’s modulus for MDLs samples at 30 °C Young’s modulus is a measure of mechanical strength of a material, given as a ratio of stress to strain. This mechanical parameter gives infor- mation about the tendency of a material to re- sist deformative forces. In Fig. 5, Young’s mod- ulus vs. MDL has been drawn using the data from Table 2 at 30 °C. The Young’s modulus drops to 3.2870 × 107 Pa for MDL of 1 % from 4.1873 × 107 Pa for MDL of 0 %, then it further decreases to 3.1375 × 107 Pa for MDL of 10 %. Be- tween 10 % and 50 % MDLs, the Young’s modulus increases gently up to 3.2470 × 107 Pa for MDL of 50 %. The addition of manganese impurity into the pure GaAs up to 1 % causes an irregular increase in thermal strain and a reduction in thermal stress. The reduction in thermal stress implies that the cross sectional area increases, while the thermal force is relatively constant. Temperature of 30 °C is suffi- cient to generate an increased mechanical strength up to 3.2430 × 107 Pa for MDL of 50 %. Table 2. Young’s moduli at different MDLs. MDLs Young’s modulus (×107 Pa) 30 °C 40 °C 0 % 4.1875 3.5331 1 % 3.2870 2.7970 10 % 3.1375 2.9196 20 % 3.1745 3.0062 50 % 3.2430 3.0106 Fig. 5. Young’s modulus versus MDL at 30 ◦C and 40 ◦C. 3.4. Young’s modulus for MDLs samples at 40 °C In Fig. 5, Young’s modulus vs. MDL has been plotted using the data from Table 2 at 40 °C. It can be observed that the change in mechanical strength with MDLs takes a similar pattern as in 30 °C. Pure GaAs seems to be the strongest, with Young’s modulus of 3.5331 × 107 Pa which then drops drastically upon addition of 1 % MDLs to 2.797 × 107 Pa. For MDLs between 10 % and 50 %, Young’s modulus increases monotonically up to 3.0106 × 107 Pa. This shows that the Mn- doped GaAs at MDL of 1 % and 10 % are not strong enough to resist the breakage due to thermal strain forces at 40 °C. Young’s modulus and creep compliance of GaAs and Ga1−xMnxAs ferromagnetic thin films. . . 345 3.5. Creep recovery and initial deforma- tion analysis at 30 °C According to Fig. 6 and Table 3, the initial strain jump at 30 °C generally decreases with an increase in MDL. At MDL of 1 %, there is an in- crease in strain jump from 1.6578 × 10−4 % for pure GaAs to 1.7368 × 10−4 %. This implies that the applied stress, in case of manganese dopant of 1 %, creates more space (free volume) for internal molecular motions (chain slippage) and the mate- rial becomes softer. For the range of MDL from 1 to 10 %, the manganese atoms occupy intermolecular spaces and reduce the space that would have been available for internal movements [20, 24–26]. This makes the material rigid. With further increase in MDL, the strain decreases gradually and tends to the value of 1.1569 × 10−4 % at MDL of 50 %. In Fig. 7 and Table 4 at 30 °C, it can be seen that the material recovers upon withdrawal of stress at MDL of 1 % with 100.00 % creep recovery. This shows that at 30 °C, the GaAs doped with 1 % man- ganese becomes disordered but upon withdrawal of stress it recovers fully to its original dimension. This implies that the material becomes softer (more compliant) and plastic. Table 3. Initial strain jump at different MDLs. MDLs Initial strain jump (× 10−4%) 30 °C 40 °C 0 % 1.6578 3.9737 1 % 1.7368 3.375 10 % 1.3026 3.5625 20 % 1.2763 3.3125 50 % 1.1569 3.1875 The trend persists (at 100 %) up to MDL of 50 %. This shows that at MDL beyond 1 % there is no loss of stored energy through thermodegrada- tion at 30 °C. 3.6. Creep recovery and initial deforma- tion analysis at 40 °C At 40 °C, according to Fig. 6 and Table 3, MDL of 1 % causes a reduction in the initial strain Fig. 6. Initial strain jump versus MDL at 30 ◦C and 40 ◦C. Fig. 7. Creep recovery versus MDL at 30 ◦C and 40 ◦C. jump which is contrary to the situation at 30 °C. This suggests a reduced free volume for chain slip- page [14]. So, a 10 °C temperature increase sup- presses the manganese of 1 % and causes a de- crease of creep percentage recovery to 97.42 % as shown in Table 4 and Fig. 7. Beyond MDL of 1 %, the creep recovery almost plateaus up to 97.43 % at MDL of 50 %. The general reduction in creep percentage recovery at 40 °C implies that a lot of stored energy is being dissipated by in- ternal friction as a result of chain slippage which has been restricted by a reduced free volume [20– 23]. This makes the Mn-doped GaAs more rigid. The initial reduction in the initial deformation to 3.375 × 10−4 % at MDL of 1 % is followed by a drastic increase up to 3.5625 × 10−4 % at MDL of 10 %. Beyond MDL of 10 %, initial strain jump generally drops to 3.1875 × 10−4 % at MDL of 50 %. This can be observed in Fig. 6 and Table 3 which provide a similar pattern as the observations made at 30 °C. 346 S.K. KEMEI et al. Generally, the two different observations at 30 °C and 40 °C show that temperature variation has an impact on the deformation stress compli- ance of Mn-doped GaAs. Temperature variation does not have a significant effect on the creep per- centage recovery as shown in Fig. 7. In Fig. 7 the trend of the variation of creep percentage recovery with MDLs at 30 °C and 40 °C is similar. The effect of deformation stress that causes varying initial de- formation is purely a function of temperature and it is responsible for increasing and reducing free vol- umes at different MDLs. Table 4. Creep recovery at different MDL. MDLs Creep recovery 30 °C 40 °C 0 % 97.98 % 95.33 % 1 % 100.00 % 97.42 % 10 % 100.00 % 97.33 % 20 % 99.82 % 97.40 % 50 % 100.00 % 97.43 % It is also apparent that MDLs have an effect on deformation stress at a given temperature. The presence of lattice defects also influences the me- chanical strength. A qualitative explanation for the composition dependence of hardness can be given in terms of two contributions. One is the lattice con- tribution and another one is the presence of defects, such as vacancies, impurity-vacancy pairs and dis- locations [27, 28]. In spintronic device designing the material to use ought to recover fully from deformation stresses and increase in free volume (softening) at relatively high temperature. This is to appropriately operate in hotter regions of the world and increase the mechanical stability of such de- vices. The increased mechanical stability has sig- nificant influence on the fabrication and processing of spintronic devices. It makes the devices easy to polish with less cracking [29]. 4. Conclusions Electronic devices, such as transistors made from GaAs and Ga1−xMnxAs, should be used at en- vironmental temperatures of approximately 30 °C and with MDLs of between 10 % and 50 %. This is because the Ga1−xMnxAs spin injector is not in any danger of breakage due to its high creep compli- ance of 0.4704 µm2/N at 30 °C and 5.2501 µm2/N at 40 °C and high creep percentage recovery of 100 % at 30 °C and 97.33 % at 40 °C. Thus, it can stretch and recover without breaking and without creating an obstruction to the flow of spin charge carriers responsible for the conduction of the spin current. The electronic devices made of Ga1−xMnxAs are not suitable for the use at en- vironmental temperatures of approximately 40 °C and above as they have shown to be defective. 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