THE OCCURRENCE OF THE CLASSIC SIZE EFFECT IN SINGLE CRYSTAL BISMUTH FILMS. V. M. Grabov, V. A. Komarov, E. V. Demidov, and E. E.

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1 THE OCCURRENCE OF THE CLASSIC SIZE EFFECT IN SINGLE CRYSTAL BISMUTH FILMS Herzen State Pedagogical University of Rssia (Received 6 October 00) Abstract The reslts of the research on the galvanomagmetic and thermoelectric properties of monocrystalline bismth films are pblished. The reslts were obtained by means of zone recrystallization nder covering on mica sbstrates. The laws of the classical size effect in monocrystalline films were revealed. The contribtion of the srface to the limitation of mobilities of electrons and holes was determined in examined bismth films. This stdy was spported by the Ministry of Edcation and Science of the Rssian Federation within the framework of the Analytical Departmental Target Program Development of the Scientific Potential of the Higher School (009-00) (project../3847). Introdction Among different methods for prodcing films of metals, semimetals, and semicondctors, the most widely sed method is thermal evaporation in vacm onto a sbstrate with temperatre lower than the melting point of the evaporating material [0]. As a rle, the films prodced by this method have a textred strctre in the form of small crystalline grains (with the size ranging from 0. to 0 m depending on prodction conditions and film thickness [0, 0]) with some order of their crystallographic orientations. Bismth films prodced by the method of thermal evaporation onto mica sbstrates are composed of crystalline grains with axis C 3 orientated mainly perpendiclar to the sbstrate bt with varios orientation of axes parallel to the sbstrate [0, 0]. Films can be prodced on different sbstrates (KBr, KCl) with axis C 3 oriented mainly parallel to the sbstrate [0]. Monograph [] contains the reslts of different researches on the electric properties of bismth films in a wide range of temperatres. Typical temperatre relationships of specific resistance, thermal electromotive force, and galvanomagnetic coefficients in a temperatre range of 80 to 300 K for bismth films with a thickness of 0. to 5 m are obtained in [4, 5]. According to reslts in [4, 5], with decreasing thickness of bismth films with the described textre, the specific resistance increases and its temperatre dependence trns to that typical for semicondctors, and magnetoresistance decreases simltaneosly. Similar definite thickness dependence of thermal electromotive force and Hall coefficient is not observed. The vale of thermal electromotive force at room temperatre remains close to the vale of α component of single crystals regardless of film thicknesses. For the films with eqal thicknesses, the vale of thermal electromotive force at temperatre 77 K can be both higher and lower than α of single crystals. Analysis of transport phenomena research data showed that the concentration of charge carriers in bismth films with thicknesses 0.-5 μm in a temperatre range of 80 to 300 K does not depend mch on thickness, bt mobilities lower with decreasing thickness [4, 5]. Meanwhile,

2 Moldavian Jornal of the Physical Sciences, Vol. 0, N, 0 the mobility ratios remain the same that provides coincidence of thermal electromotive force vales with the data for bismth single crystals. The conclsion made in [4] indicates that the case of the extra scattering of charge carriers that leads to the restriction of mobilities is crystal covering bismth film sbstrate Fig.. The workpiece for bismth film zone recrystallization strctre defects (point defects, dislocations, and pecliarities of crystalline grain borders) rather than the srface of the film itself. The concentration of point defects and dislocation density weakly depend on the thickness, the sizes of crystalline grain decrease with decreasing thickness. This impedes researches of size effect in bismth films. To stdy classical size effect in bismth films cased by interaction between charge carriers and the film srface, it is necessary to significantly redce the concentration of volme defects and their contribtion to the scattering of charge carriers. So, the prodcing was monocrystalline bismth film was reqired.. Method of prodcing monocrystalline bismth films To prodce monocrystalline bismth films, the method of zone recrystallization nder covering was worked ot. The essence of the method is as follows: a bismth film of reqired textre is evaporated onto a sbstrate and then covered with a protecting layer of a dissolble material by means of thermal evaporation. Ths, the bismth film trns ot to be in some sort of a container. The obtained workpiece (Fig. ) is set into the plant for zone recrystallization where monocrystalline film is grown. The protecting covering prevents the melted film from gathering into drops. It is its main aim. Dring the recrystallization process, the protecting covering mst remain intact and not to crack. In addition, the covering mst have the strctre that prevents the srface from contribting to the origination of crystallization centers. NaCl, BaCl, KCl, KBr were sed as sbstrate materials. The best reslts were obtained for KBr. Zone recrystallization of bismth films was performed in argon. Strctres of the films prodced by means of the zone recrystallization method were analyzed by means of metallographic and x-rays methods. The research confirms that prodced bismth films on mica sbstrates have monocrystalline strctre with axis C 3 perpendiclar to the sbstrate. (The pattern of the film after etching is shown in Fig. a). Figre b shows an AFM scan of the textred polygrain film. 88

3 Fig. a. An etched srface of a melted bismth film with a thickness of.9 μm on mica (X 500). Fig. -b. AFM scan of an etched-srface poly-grain bismth film with a thickness of 0.3 μm on mica. Monocrystalline films with thicknesses of 0. to 5 μm were prodced by the techniqe described above. The film thicknesses were determined by interference method sing a Linnik interferometer. 3. Electric properties of bismth films The following properties of monocrystalline bismth films were examined: specific resistance (ρ), thermal electromotive force (α), magnetoresistance (Δρ/ρ), and Hall coefficient (R) in a magnetic field p to 0.6 T. The reslts are shown n Figs It is evident from the figres that the temperatre dependence of specific resistance for monocrystalline films is qalitatively the same as for textred films that did not ndergo the process of zone recrystallization. However, we shold note that the specific resistance of monocrystalline films with a particlar thickness is lower than that of textred films with the same thickness. The transition to the dependence ρ(t) typical for semicondctor takes place in monocrystalline films with lower thicknesses. The most remarkable difference is the behavior of thermal electromotive force. Vales of thermal electromotive force of thermally evaporated films are close to the vales α of single crystals in the entire temperatre range K, bt they can be higher or lower depending on the ratio of grain sizes and film thicknesses. Temperatre falls in a range of K, the absolte vales of thermal electromotive force of monocrystalline films decrease compared to vales α of single crystals starting from some temperatre. Meanwhile, the point of the beginning of decrease moves to the region of higher temperatre with decreasing film thicknesses. At temperatres close to 00 K, the vale of thermal electromotive force in films with thicknesses d < 0.3 μm increases p to positive vales. The Hall coefficient of monocrystalline films is positive and increases with decreasing film thicknesses. 89

4 Moldavian Jornal of the Physical Sciences, Vol. 0, N, 0 Fig. 3. Temperatre dependence of specific resistance for monocrystalline and polycrystalline bismth films on mica. Fig. 4. Temperatre dependence of magnetoresistance for monocrystalline and polycrystalline bismth films on mica. Fig. 5. Temperatre dependence of thermal electromotive force for monocrystalline and polycrystalline bismth films with different thicknesses on mica. Fig. 6. Temperatre dependence of Hall coefficient for monocrystalline and polycrystalline bismth films with different thicknesses on mica. 90

5 4. Changes of electron and hole mobilities depending on temperatre and thickness of monocrystalline film It was shown in [5] that at temperatres close to room temperatre the concentration of charge carriers in bismth films on mica hardly depends on thickness in a range of 0.-5 μm and is nearly similar to vales in bismth single crystals. When temperatre lowers, compared to single crystals, the concentration of charge carriers in films falls de to deformation cased by the difference of thermal expansion coefficients of the film and its sbstrate. At 00 K, the noticed difference between vales of concentration of charge carriers did not exceed 5% [5], and it was not considered while analyzing the experimental reslts in this research. To analyze experimental data, the approach worked ot by G. A. Ivanov for bismth monocrystallines [5, 6] is sed. The following eqations can be written for electrocondctivity and thermal electromotive force coefficients and Hall coefficient in a weak magnetic field for bismth zone strctre neglecting the inclination angle of electron srfaces of eqal energies: en[ ( ) ] R R 3,,3 en( en [ en [ ) ( ( Eqation () can be simplified taking into accont the crystallographic strctre of the films and the fact that for electrons. As a reslt, the following eqations can be obtained for transport coefficients measred in the films: en( ) R,3 en [ ) ( ) ) ] ] Considering the approximations mentioned above, vales of concentration of charge carriers, partial thermal electromotive force of electrons and holes obtained for a blk bismth single crystal [0] can be sed to determine mobilities of electrons and holes in films ot of experimental data. With n,, given, two eqations can be derived to determine and holes respectively: en( ) ] and () () of electrons. (3) 9

6 Moldavian Jornal of the Physical Sciences, Vol. 0, N, 0 Figres 7 and 8 show the compting reslts for mobilities of electrons and holes and according to eqations (3) obtained with se of experimental reslts for electrocondctivity and thermal electromotive force in monocrystalline films with different thicknesses in a temperatre range of K. We shold note that the following marks are settled to: and. To check the accracy of the reslts, Hall coefficient vales in weak magnetic field were compted. The compted vales agree with experimental data. Fig. 7. Temperatre dependence of electron mobility in films of different thicknesses. Fig. 8. Temperatre dependence of hole mobility in films of different thicknesses. 5. Analysis of behavior of charge carriers in monocrystalline bismth films Mobilities of electrons and holes in monocrystalline bismth films depend on film thicknesses, being lower than in volme single crystals in the entire temperatre range. Meanwhile, mobility of electrons is limited more severely than that of holes. To reveal the correlation between mobilities of charge carriers and thicknesses of the films, the graphs of f were plotted for different temperatres. The graphs are presented in Figs. d 9 and 0. 9

7 Fig. 9. Dependence of electron mobility on thicknesses of bismth films. Fig. 0. Dependence of hole mobility on thicknesses of bismth films. It is evident from the figres that the dependence f is close to linear both for d electrons and holes. Extrapolation to d, 0 corresponds to mobilities of charge d carriers in blk single crystals at a given temperatre. 5 The graphs f T presented in Figs. and are almost linear at a wide 5 temperatre range, which indicates a linear dependence f T typical for blk single crystals de to the scattering of charge carriers by phonons [6]. These reslts jstify the fact that there is an additional scattering mechanism that contribtes to the limitation of mobilities of charge carriers. This mechanism weakly depends on temperatre, bt it essentially depends on film thicknesses. Figres 9- show that the mobilities of electrons and holes are described properly by the Matthiessen's rle:. (4) ( T) ( d) We shold note that ( d) for electrons has a greater vale than for holes, and so ratio of mobilities changes significantly with film thicknesses. At the same time, the dependence of this ratio on film thicknesses for the films prodced by thermal evaporation bt withot recrystallization is considerably weaker. Therefore, an additional scattering of charge carriers in monocrystalline bismth films is cased by the film srface rather than by crystal strctre defects. 93

8 Moldavian Jornal of the Physical Sciences, Vol. 0, N, 0 Fig.. Dependence of electrons on T for monocrystalline films. 5 Fig.. Dependence of holes on T for monocrystalline films. 5 A difference in the scattering of electrons and holes on the srface in bismth films can be cased by different conditions of reflection of charge carriers by the srface de to the srface crvatre of zones [0]. At low temperatres T 4. K, this crvatre of zones leads to significant 0 growth of electrocondctivity with decreasing thickness d 000 A [9]. The data obtained for for electrons and holes by means of the Fermi Sondheimer ( d) theory [0] allow s to determine the reflectivity parameter p when electrons and holes interact with the srface: d 3 ( p). (5) 0 8 d In eqation (5), (d) stands for the mobility of charge carriers in a film with thickness d, 0 stands for the mobility of charge carriers in a volme single crystal, d stands for the hickness of a monocrystalline film, and p stands for the reglar reflectance of charge carriers by the film srface. According to reslts pelectrons pholes we can conclde that the srface bending of zones in films prodced by the described method on mica is similar to that shown in Fig. 3. The srface bending of zones leads to a higher diffseness of scattering of electrons than of holes at the srface layer. 94

9 Fig. 3. Srface bending of zones in bismth films. 6. Conclsions In monocrystalline bismth films, the amont of volme defects redces significantly compared to non-recrystallizated textred films. Therefore, limitation of mobilities de to the scattering on the srface is an additional mechanism to phonon scattering of charge carriers. The Matthiessen's rle holds for contribtions of the mentioned scattering mechanisms to limitation mobilities of charge carriers in monocrystalline bismth films. Becase of scattering on the film srface, the electron mobility is mch more limited than the mobility of holes. This fact is related with the srface bending of zones, which, in trn, provides a higher reglar reflectance of holes than of electrons when they interact with the film srface. The reslts for mobilities of charge carriers in monocrystalline films provide an opportnity to divide the contribtions of the srface and strctre imperfections to limitation of mobilities of charge carriers in textred polycrystalline films which were not recrystallized. De to more perfect strctre and higher vales of mobilities of charge carriers, monocrystalline films possess a nmber of advantages in practical se. The developed method of transport phenomena research in monocrystalline and textred bismth films can be sed for films based on other metals and semicondctors. References [] Komnik,Y.F., Physics of Metal Films. Dimensional and Strctral Effects. Moscow: Atomizdat [] Grabov V.M., Demidov E.V., and Komarov V.A. Fiz. Tverd. Tela (St. Petersbrg) 008, 50 (7), p. 3. [Phys. Solid State 50 (7), 365 (008)]. [3] Grabov V.M., Demidov E.V., Komarov V.A., and Klimantov, M.M. Fiz. Tverd. Tela (St. Petersbrg) (4). p [Phys. Solid State 5 (4), 846 (009)]. [4] G. A. Ivanov, V. M. Grabov, and T. V. Mikhaoelichenko, Fiz. Tverd. Tela (Leningrad) 5 (), 573 (973) [Sov. Phys. Solid State 5 (), 397 (973)]. [5] Komarov, V.A., Klimantov, M.M., Logntsova М.М., Pylina S. N., and Demidov E.V. Kinetic Phenomena and bismth film strctre // Izvestia: Herzen University Jornal of Hmanities & Sciences (5) P [6] Ivanov, G.A. and Grabov, V.M. Fiz. Tekh. Polprovodn. (St. Petersbrg) (6). p [Semicondctors 9 (6), 538 (995)]. 95