24November2017

Materials and Electronics Engineering

The relationship between hardness and grain-size in electron-beam evaporated Pb1-xGexTe thin films

Ping Xie, Bin Li1, Suying Zhang, Dingquan Liu

Abstract
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Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, P. R.China

Materials and Electronics Engineering 2014,1:5

Publication Date (Web): December 16, 2014 (Article)

DOI:10.11605/mee-1-5

*Corresponding author. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

 

Abstract

 


Figure 4 A comparison of the hardness of thin films evaporated from ingots with three Ge concentrations x, 0.10, 0.17, and 0.22, to those of PbTe.

      Pb1-xGe­xTe thin films were evaporated on silicon substrates from the ingots of single crystals using electron beam heating. The hardness of thin films was identified by means of nanoindentation measurements. Moreover, the surface topographies and compositions of thin-films were characterized by using scanning electron microscopy (SEM) and energy dispersive X-ray analysis (EDX), respectively. It can be found that Hall–Petch equation can be established to describe the relationship between the hardness and the grain size in Pb1-xGe­xTe thin films. It can be found that Hall–Petch equation can be established to describe the relationship between the hardness and the grain-size in Pb1-xGexTe thin films. Therefore, it can be explained for the relationship between stoichiometry and mechanical properties in thin films, that stoichiometry determines the grain-size and grain-size determines the hardness in thin films according to the Hall–Petch equation.


 

Keywords

Hall-petch equation, Pb1-xGexTe, electron-beam evaporation

 

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Introduction

      The mechanical properties of thin films are of extraordinary importance in the practical applications, which can be characterized by its hardness and stress, as well as adhesion onto substrates. The hardness of thin films is the measurement of its deformation resistance, wear and fracture, which is mainly related to the type of chemical bond and the crystal structure of the thin film materials.

    The relation between yield stress and grain size is described mathematically by the Hall–Petch equation [1]:

          (1)

where  is the yield stress, is a materials constant for the starting stress for dislocation movement (or the resistance of the lattice to dislocation motion), is the strengthening coefficient (a constant unique to each material), and d is the average grain diameter.

      Since, in the absence of appreciable work hardening, the hardness of a material,  , as measured using a pyramidal indenter is proportional to the yield stress through the expression  [2], it follows that equation (1) may be replaced by 

          (3)

where  and  are appropriate constants associated with the hardness measurements.

         Lead germanium telluride (Pb1-xGexTe) is a pseudobinary alloy of IV-VI narrow gap semiconductor compounds of PbTe and GeTe, which shows a ferroelectric phase transition from a cubic, rocksalt (Oh) paraelectric phase to a rhombohedral, arsenic-like (C3v) ferroelectric phase [3,4]. In the past decade, optical constants of thin films of Pb1-xGexTe as a function of wavelength and temperature were studied in more details, both theoretical and experimental [5]. Furthermore, a low-temperature stable infrared narrow-band filter was made using layers of Pb1-xGexTe [6,7]. However, the investigation into the mechanical properties of layers of Pb1-xGexTe remains to be done, with the exception of the composition dependence of microhardness for both molten and heat-pressed Pb1-xGexTe ingots [8].

      In our research, it can be demonstrated that Hall-Petch equation is established in the Pb1-xGexTe thin-films evaporated using electron beam heating, after the investigation into the relationship between hardness and grain-size was carried out. 

Experimental details

      The bulk ingots of Pb1-xGexTe with three Ge concentration x, 0.10, 0.17, and 0.22, together with PbTe, were synthesized at 1100 °C. The inside surfaces of ampoules were pyrolized with carbon to avoid reaction of lead with silica. Subsequently, the resulting ingots were held at 700 °C for 24 hours, then cooled down to room temperature with a rate of 10 °C/h. Finally, the ingots were crushed into small pieces with an approximate size of 5 mm and used as resources for evaporation.

      Deposition of thin films of Pb1-xGexTe was carried out in a KD500 box coater using a type C6 four-pocket electron beam evaporator in a background vacuum 2.0×10-3 Pa. A beam current of around 20 mA at a voltage of 6 kV was reached and a graphite line was used. The silicon wafers polished on both sides, with a diameter of 10 mm and a thickness of 0.8 mm, were used as substrates. A flat calotte carrying samples rotated at a rate of 30 rpm to provide good uniformity of thin films. The substrates were heated below by radiation heaters, and temperature was sensed by a platinum resistance temperature transducer pressed against the upper surface of a substrate. The signals from the transducer were transferred out through a set of electric-brush and slip-ring to operate a temperature controller and thus maintained a constant temperature of 150 °C, which is thought as an optimum temperature. Thickness of all layers was monitored by optical reflection and kept in an approximate value of 2 μm. Five samples in each batch were deposited to prove the repeatability.

       The crystallographic structures of thin films were studied by X-ray diffraction using Cu  radiation on a D/max 2550V diffractometer from 10° to 68° with an accuracy of 0.02°. The energy-dispersive X-ray analysis (EDX) was done to decide the compositions of thin films from a Horiba EX-220 energy-dispersive X-ray microanalyzer (model 6853-H) attached to the FE-SEM without coating the surfaces of thin films. The surface characteristics were observed using a Hitachi S-4300 cold field emission scanning electron microscope (FE-SEM). Nanoindentation measurements were performed using a Nano Indenter G200 (MTS Cooperation, Nano Instruments, Oak Ridge, TN, USA) with a three-side pyramidal Berkovich diamond indenter of 50 nm radius (faces 65.3° from vertical axis), under the continuous stiffness measurement (CSM) option. In all cases the loading rate was 1 mN S-1. At least ten indents were performed on each layer with a maximum load of 13 mN, accompanied with a corresponding indentation depths no more than 500 nm. Following the analytic method proposed by Oliver and Pharr [9], the average values and standard deviations of the hardness and Young’s modulus of thin films can be extracted from the load–displacement results. A typical load–displacement curve is presented in Fig. 1 for thin films of Pb1-xGexTe deposited from a resource material with a Ge concentration of 0.17.

Figure 1 A typical load–displacement curve for thin films of Pb1-xGexTe deposited from an ingot with a Ge concentration of 0.17, the average values and standard deviations are also shown.

Figure 1 A typical load–displacement curve for thin films of Pb1-xGexTe deposited from an ingot with a Ge concentration of 0.17, the average values and standard deviations are also shown.

Results and discussions

          It has been commonly accepted that, in practice, a strictly congruent melt composition will typically not be established due to preferential evaporation losses of one component originated from a large difference between vapor pressures of PbTe and GeTe [10]. However, it can be surprisingly observed Ge concentration in thin films which is deposited by electron beam heating is in a very good consistence with Ge concentration x in ingot resources [11]. Therefore, in our investigation the Pb1-xGexTe thin-films were evaporated using electron beam heating.

      EDX analysis indicates that element of oxygen cannot be found on the surfaces; therefore, the possibility of formation of lead oxide on the surface can be excluded. In addition, other elements related to contaminations are undetectable, either.

Figure 2 The XRD results of thin films of Pb1-xGexTe deposited from a resource material with a Ge concentration of 0.17.

Figure 2 The XRD results of thin films of Pb1-xGexTe deposited from a resource material with a Ge concentration of 0.17.

     XRD analysis performed on thin films of Pb1-xGexTe reveals all of them are single-phase with polycrystalline characteristics, which suggests the formation of a completed solid solution of PbTe and GeTe. The XRD results of thin films of Pb1-xGexTe deposited from a resource material with a Ge concentration of 0.17 are illustrated in Fig 2. 

      The investigation using scanning electron microscope into the surface topographies of electron beam evaporated Pb1-xGexTe thin films with Ge concentration x = 0.10, 0.17, 0.22 and PbTe thin films are shown in Fig. 3 (a)–(d). The more pronounced contrast, which indicates the higher surface roughness, was observed in all of thin films. The topography of thin films reflects clearly a surface characteristic of homogeneously and compactly arranged grains. Because substrate temperature in the course of evaporating Pb1-xGexTe thin films using electron beam heating is lower than the one-third of evaporant melting temperature, the structure of thin films is almost invariably a columnar one, with the columns running along the direction of growth, normal to the film interfaces [12]. Therefore, the granular structure of the surface topography can be interpreted as end domes of the columns, which have grown starting on the surface of silicon substrate to the surface of the layer. The columns are roughly cylindrical in shape. An interesting feature for the microstructures of Pb1-xGexTe films evaporated using electron beam heating is their grains with a shape in plates of rectangle, which is typical for ingots of single-crystal of PbTe-based semiconductors.

Figure 3 The surface morphologies examined using SEM for Pb1-xGexTe films with different concentration x, (a) 0.10, (b) 0.17, (c) 0.22 and PbTe thin films (d).

Figure 3 The surface morphologies examined using SEM for Pb1-xGexTe films with different concentration x, (a) 0.10, (b) 0.17, (c) 0.22 and PbTe thin films (d).


       
It can be demonstrated clearly that the mean grain size d increased with increasing Ge concentration. In particular, the crystallite in thin films with a Ge concentration x= 0.22 is much larger, with a size about 150 nm, than others, about 45~55 nm. Therefore, it is deduced that grain size d in Pb1-xGexTe thin films can be also linked to the ferroelectric phase transformation at room temperature.

    In Fig. 4, in order to make a comparison, the hardness of thin films with three Ge concentrations x, 0.10, 0.17, and 0.22, together with PbTe, as a function of the displacement of diamond dips which are pressed into the surfaces of thin films, are demonstrated. It is obviously shown that thin films of Pb1-xGexTe have a higher value of hardness than that of PbTe. The hardness for sample with x = 0.22, is not high as same as those for other samples with x = 0.10 and 0.17, respectively.

Figure 4 A comparison of the hardness of thin films evaporated from ingots with three Ge concentrations x, 0.10, 0.17, and 0.22, to those of PbTe.

Figure 4 A comparison of the hardness of thin films evaporated from ingots with three Ge concentrations x, 0.10, 0.17, and 0.22, to those of PbTe.

Table 1 Hardness Hv in Pb1-xGexTe thin films obtained at the maximum penetration

      As a rule of thumb, to avoid the affect from substrates, a maximum penetration depth (10% of thickness of thin films) is defined as the displacement at which hardness and elastic modulus values are obtained. Therefore, the values of hardness obtained are listed in Table 1.

      It is shown in Fig. 5 the plot of hardness Hv against the reciprocal of square root of grain size d in Pb1-xGexTe thin films evaporated using electron beam heating. A linear fitting also presented for the eye-guidance. It is apparent that Hall–Petch equation can be established to describe the relationship between the hardness and the grain size in Pb1-xGexTe thin films with a formula:

          (4)

Figure 5 The plot of hardness Hv against the reciprocal of square root of grain size d in Pb1-xGexTe thin films evaporated using electron beam heating

Figure 5 The plot of hardness Hv against the reciprocal of square root of grain size d in Pb1-xGexTe thin films evaporated using electron beam heating

Conclusion

        Although it has been well recognized that, for some alloys and compounds, the relation between hardness and grain size can be described mathematically by the Hall–Petch equation, the investigation into the relationship between hardness and grain size in Pb1-xGexTe thin films has not been carried out. Here, an experimental result confirms that Hall–Petch equation can be established to describe the relationship between the hardness and the grain size in Pb1-xGexTe thin films.

References

1. W.F. Smith, J. Hashemi, Foundations of Materials Science and Engineering 2006.
2. M.F. Ashby, D.R.H. Jones, Eng. Mater. 1980.
3. D.K. Hohnke, H. Holloway, S. Kaiser, Phase relations and transformations in the system PbTe-GeTe. J. Phys. Chem. Solids 33, 2053 (1972). doi:10.1016/S0022-3697(72)80235-X
4. J. Sariel, I. Dahan, Y. Gelbstein, Rhombohedral-cubic phase transition characterization of (Pb, Ge) Te using high-temperature XRD. Powder Diffr. 23, 137 (2008). doi:10.1154/1.2912439
5. B. Li, J.C. Jiang, S.Y. Zhang, F.S. Zhang, Low-temperature dependence of midinfrared optical constants of lead–germanium–telluride thin film. J. Appl. Phys. 91, 3556 (2002). doi:10.1063/1.1448866
6. B. Li, S.Y. Zhang, J.C. Jiang, B. Fan, F.S. Zhang, Improving low-temperature performance of infrared thin-film interference filters utilizing the intrinsic properties of IV–VI narrow-gap semiconductors. Opt. Express 12, 401 (2004). doi:10.1364/OPEX.12.000401
7. B. Li, S.Y. Zhang, J.C. Jiang, D.Q. Liu, F.S. Zhang, Recent progress in improving low-temperature stability of infrared thin-film interference filters. Opt. Express 13, 6376 (2005). doi:10.1364/OPEX.13.006376
8. E.I. Rogacheva, T.V. Tavrina, I.M. Krivul’kin, Inorg. Mater. 35, 236 (1999).
9. W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992). doi:10.1557/JMR.1992.1564
10. D.L. Partin, Growth of lead‐germanium‐telluride thin film structures by molecular beam epitaxy. J. Vac. Sci. Technol. 21, 1 (1982). doi:10.1116/1.571714
11. B. Li, P. Xie, S.Y. Zhang, D.Q. Liu, Compositional congruency, correlation and high pressure polymorphism in electron-beam evaporated Pb1−xGexTe thin films. J. Alloy. Compd. 589, 109 (2014). doi:10.1016/j.jallcom.2013.11.179
12. H.A. Macleod, Thin-Film Optical Filters. (4th Ed.) CRC/Taylor & Francis, Boca Raton (2010).

Acknowledgements

      This study is supported by the National Science Foundation of China (NSFC) under grant No. 61178039 and Excellence Award from President of Chinese Academy of Sciences. Authors would like to thank Prof. X. M. Meng in Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, for his helps in performing the SEM and EDX analyzes. Also thank Dr. J. L. Li in Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, for his helps in the nanoindentation measurements.

References

1. W.F. Smith, J. Hashemi, Foundations of Materials Science and Engineering 2006.
2. M.F. Ashby, D.R.H. Jones, Eng. Mater. 1980. 
3. D.K. Hohnke, H. Holloway, S. Kaiser, Phase relations and transformations in the system PbTe-GeTe. J. Phys. Chem. Solids 33, 2053 (1972). doi:10.1016/S0022-3697(72)80235-X 
4. J. Sariel, I. Dahan, Y. Gelbstein, Rhombohedral-cubic phase transition characterization of (Pb, Ge) Te using high-temperature XRD. Powder Diffr. 23, 137 (2008). doi:10.1154/1.2912439 
5. B. Li, J.C. Jiang, S.Y. Zhang, F.S. Zhang, Low-temperature dependence of midinfrared optical constants of lead–germanium–telluride thin film. J. Appl. Phys. 91, 3556 (2002). doi:10.1063/1.1448866 
6. B. Li, S.Y. Zhang, J.C. Jiang, B. Fan, F.S. Zhang, Improving low-temperature performance of infrared thin-film interference filters utilizing the intrinsic properties of IV–VI narrow-gap semiconductors. Opt. Express 12, 401 (2004). doi:10.1364/OPEX.12.000401 
7. B. Li, S.Y. Zhang, J.C. Jiang, D.Q. Liu, F.S. Zhang, Recent progress in improving low-temperature stability of infrared thin-film interference filters. Opt. Express 13, 6376 (2005). doi:10.1364/OPEX.13.006376 
8. E.I. Rogacheva, T.V. Tavrina, I.M. Krivul’kin, Inorg. Mater. 35, 236 (1999).
9. W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992). doi:10.1557/JMR.1992.1564 
10. D.L. Partin, Growth of lead‐germanium‐telluride thin film structures by molecular beam epitaxy. J. Vac. Sci. Technol. 21, 1 (1982). doi:10.1116/1.571714 
11. B. Li, P. Xie, S.Y. Zhang, D.Q. Liu, Compositional congruency, correlation and high pressure polymorphism in electron-beam evaporated Pb1−xGexTe thin films. J. Alloy. Compd. 589, 109 (2014). doi:10.1016/j.jallcom.2013.11.179 
12. H.A. Macleod, Thin-Film Optical Filters. (4th Ed.) CRC/Taylor & Francis, Boca Raton (2010).

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Additional Info

  • Type of Publishing: JOUR - Journal
  • Title:

    The relationship between hardness and grain-size in electron-beam evaporated Pb1-xGexTe thin films

  • Author: Ping Xie, Bin Li, Suying Zhang, Dingquan Liu
  • Year: 2014
  • Volume: 1
  • Issue: 1
  • Journal Name: Materials and Electronics Engineering
  • Publisher: Nicety Press Company Limited
  • ISSN: 2410-1648
  • URL: http://www.meej.org/volume-1/december-2014/item/365-the-relationship-between-hardness-and-grain-size-in-electron-beam-evaporated-pb1-xgexte-thin-films
  • Abstract:

    Pb1-xGe­xTe thin films were evaporated on silicon substrates from the ingots of single crystals using electron beam heating. The hardness of thin films was identified by means of nanoindentation measurements. Moreover, the surface topographies and compositions of thin-films were characterized by using scanning electron microscopy (SEM) and energy dispersive X-ray analysis (EDX), respectively. It can be found that Hall–Petch equation can be established to describe the relationship between the hardness and the grain size in Pb1-xGe­xTe thin films. It can be found that Hall–Petch equation can be established to describe the relationship between the hardness and the grain-size in Pb1-xGexTe thin films. Therefore, it can be explained for the relationship between stoichiometry and mechanical properties in thin films, that stoichiometry determines the grain-size and grain-size determines the hardness in thin films according to the Hall–Petch equation.

  • Publish Date: Tuesday, 16 December 2014
  • Start Page: 5
  • DOI: 10.11605/mee-1-5