The Influence of Surface on Scattering of Carriers and Kinetic Effects in n-PBTE Films

The influence of mechanisms of surface reflection of electrons on the ex-perimental electrical transport and thermoelectric properties of n-PbTe films on various substrates are considered based on the Fuchs–Sondheimer and Mayer models. The thickness dependence of conductivity, Hall coeffi-cient, and...

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Дата:	2017
Автори:	Ruvinskii, M.A., Kostyuk, O.B., Dzundza, B.S., Makovyshyn, V.I.
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Мова:	English
Опубліковано:	Інститут металофізики ім. Г.В. Курдюмова НАН України 2017
Назва видання:	Наносистеми, наноматеріали, нанотехнології
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/133186
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Цитувати:	The Influence of Surface on Scattering of Carriers and Kinetic Effects in n-PBTE Films / M.A. Ruvinskii, O.B. Kostyuk, B.S. Dzundza, V.I. Makovyshyn // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2017. — Т. 15, № 2. — С. 277-288. — Бібліогр.: 16 назв. — англ.

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spelling	irk-123456789-1331862018-05-22T03:03:11Z The Influence of Surface on Scattering of Carriers and Kinetic Effects in n-PBTE Films Ruvinskii, M.A. Kostyuk, O.B. Dzundza, B.S. Makovyshyn, V.I. The influence of mechanisms of surface reflection of electrons on the ex-perimental electrical transport and thermoelectric properties of n-PbTe films on various substrates are considered based on the Fuchs–Sondheimer and Mayer models. The thickness dependence of conductivity, Hall coeffi-cient, and Seebeck coefficient of films based on PbTe are investigated. As shown, for the films on glassceramic substrates, mechanism of completely diffuse scattering of carriers (p ≈ 0) are implemented, and for the films obtained on fresh mica chips, mixed mechanism of specular–diffuse scat-tering of carriers is realized (scattering coefficient p ≈ 0.4). Вивчено вплив механізмів поверхневого відбивання електронів на експериментальне електроперенесення та термоелектричні властивості плівок n-PbTe на різних підкладинках на основі моделів Фукса–Сондхаймера та Маєра. Досліджено залежність від товщини провідности, Голлового коефіцієнта і Зеєбекового коефіцієнта плівок на основі PbTe. Показано, що для плівок на ситалових підкладинках реалізується механізм повністю дифузного розсіяння носіїв заряду (p ≈ 0), а для плівок, одержаних на свіжоприготовлених лоснякових кристаликах, — мішаний дзеркально-дифузний механізм розсіяння носіїв (коефіцієнт розсіяння p ≈ 0,4). Изучено влияние механизмов поверхностного отражения электронов на экспериментальный электроперенос и термоэлектрические свойства плёнок n-PbTe на различных подложках на основе моделей Фукса–Сондхаймера и Майера. Исследована зависимость от толщины прово-димости, коэффициента Холла и коэффициента Зеебека плёнок на ос-нове PbTe. Показано, что для плёнок на ситалловых подложках реали-зуется механизм полностью диффузного рассеяния носителей заряда (p ≈ 0), а для плёнок, полученных на свежеприготовленных слюдяных кристалликах, — смешанный зеркально-диффузный механизм рассея-ния носителей (коэффициент рассеяния p ≈ 0,4). 2017 Article The Influence of Surface on Scattering of Carriers and Kinetic Effects in n-PBTE Films / M.A. Ruvinskii, O.B. Kostyuk, B.S. Dzundza, V.I. Makovyshyn // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2017. — Т. 15, № 2. — С. 277-288. — Бібліогр.: 16 назв. — англ. 1816-5230 PACS: 68.35.Ct, 68.37.Ps, 73.50.Bk, 73.50.Lw, 81.07.Bc, 84.60.Rb, 85.80.Fi http://dspace.nbuv.gov.ua/handle/123456789/133186 en Наносистеми, наноматеріали, нанотехнології Інститут металофізики ім. Г.В. Курдюмова НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	The influence of mechanisms of surface reflection of electrons on the ex-perimental electrical transport and thermoelectric properties of n-PbTe films on various substrates are considered based on the Fuchs–Sondheimer and Mayer models. The thickness dependence of conductivity, Hall coeffi-cient, and Seebeck coefficient of films based on PbTe are investigated. As shown, for the films on glassceramic substrates, mechanism of completely diffuse scattering of carriers (p ≈ 0) are implemented, and for the films obtained on fresh mica chips, mixed mechanism of specular–diffuse scat-tering of carriers is realized (scattering coefficient p ≈ 0.4).
format	Article
author	Ruvinskii, M.A. Kostyuk, O.B. Dzundza, B.S. Makovyshyn, V.I.
spellingShingle	Ruvinskii, M.A. Kostyuk, O.B. Dzundza, B.S. Makovyshyn, V.I. The Influence of Surface on Scattering of Carriers and Kinetic Effects in n-PBTE Films Наносистеми, наноматеріали, нанотехнології
author_facet	Ruvinskii, M.A. Kostyuk, O.B. Dzundza, B.S. Makovyshyn, V.I.
author_sort	Ruvinskii, M.A.
title	The Influence of Surface on Scattering of Carriers and Kinetic Effects in n-PBTE Films
title_short	The Influence of Surface on Scattering of Carriers and Kinetic Effects in n-PBTE Films
title_full	The Influence of Surface on Scattering of Carriers and Kinetic Effects in n-PBTE Films
title_fullStr	The Influence of Surface on Scattering of Carriers and Kinetic Effects in n-PBTE Films
title_full_unstemmed	The Influence of Surface on Scattering of Carriers and Kinetic Effects in n-PBTE Films
title_sort	influence of surface on scattering of carriers and kinetic effects in n-pbte films
publisher	Інститут металофізики ім. Г.В. Курдюмова НАН України
publishDate	2017
url	http://dspace.nbuv.gov.ua/handle/123456789/133186
citation_txt	The Influence of Surface on Scattering of Carriers and Kinetic Effects in n-PBTE Films / M.A. Ruvinskii, O.B. Kostyuk, B.S. Dzundza, V.I. Makovyshyn // Наносистеми, наноматеріали, нанотехнології: Зб. наук. пр. — К.: РВВ ІМФ, 2017. — Т. 15, № 2. — С. 277-288. — Бібліогр.: 16 назв. — англ.
series	Наносистеми, наноматеріали, нанотехнології
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fulltext	277 PACS numbers: 68.35.Ct, 68.37.Ps, 73.50.Bk, 73.50.Lw, 81.07.Bc, 84.60.Rb, 85.80.Fi The Influence of Surface on Scattering of Carriers and Kinetic Effects in n-PBTE Films M. A. Ruvinskii, O. B. Kostyuk, B. S. Dzundza, and V. I. Makovyshyn Vasyl Stefanyk Precarpathian University, Shevchenko Str., 57, 76018 Ivano-Frankivsk, Ukraine The influence of mechanisms of surface reflection of electrons on the ex- perimental electrical transport and thermoelectric properties of n-PbTe films on various substrates are considered based on the Fuchs–Sondheimer and Mayer models. The thickness dependence of conductivity, Hall coeffi- cient, and Seebeck coefficient of films based on PbTe are investigated. As shown, for the films on glassceramic substrates, mechanism of completely diffuse scattering of carriers (p0) are implemented, and for the films obtained on fresh mica chips, mixed mechanism of specular–diffuse scat- tering of carriers is realized (scattering coefficient p0.4). Вивчено вплив механізмів поверхневого відбивання електронів на екс- периментальне електроперенесення та термоелектричні властивості плівок n-PbTe на різних підкладинках на основі моделів Фукса– Сондхаймера та Маєра. Досліджено залежність від товщини провіднос- ти, Голлового коефіцієнта і Зеєбекового коефіцієнта плівок на основі PbTe. Показано, що для плівок на ситалових підкладинках реалізуєть- ся механізм повністю дифузного розсіяння носіїв заряду (p0), а для плівок, одержаних на свіжоприготовлених лоснякових кристаликах, — мішаний дзеркально-дифузний механізм розсіяння носіїв (коефіцієнт розсіяння p0,4). Изучено влияние механизмов поверхностного отражения электронов на экспериментальный электроперенос и термоэлектрические свойства плёнок n-PbTe на различных подложках на основе моделей Фукса– Сондхаймера и Майера. Исследована зависимость от толщины прово- димости, коэффициента Холла и коэффициента Зеебека плёнок на ос- нове PbTe. Показано, что для плёнок на ситалловых подложках реали- зуется механизм полностью диффузного рассеяния носителей заряда (p0), а для плёнок, полученных на свежеприготовленных слюдяных кристалликах, — смешанный зеркально-диффузный механизм рассея- ния носителей (коэффициент рассеяния p0,4). Наносистеми, наноматеріали, нанотехнології Nanosistemi, Nanomateriali, Nanotehnologii 2017, т. 15, № 2, сс. 277–288  2017 ІÌÔ (Іíñòèòóò ìåòàëîôіçèêè іì. Ã. Â. Êóðäþìîâà ÍÀÍ Óêðàїíи) Надруковано в Óкраїні. Фотокопіювання дозволено тільки відповідно до ліцензії 278 M. A. RUVINSKII, O. B. KOSTYUK, B. S. DZUNDZA, and V. I. MAKOVYSHYN Key words: size effect, thin film, lead telluride, thermoelectric properties. Ключові слова: розмірний ефект, тонка плівка, телурид свинцю, тер- моелектричні властивості. Ключевые слова: размерный эффект, тонкая плёнка, теллурид свинца, термоэлектрические свойства. (Received 27 December, 2016) 1. INTRODUCTION Lead telluride is well-known thermoelectric material for semicon- ductor technology. Interest in research of it is not reduced over the years due to the unique physical and chemical properties. As it is a narrow semiconductor A4B6, so it is suitable for use in infrared la- sers, optical detectors, and a thermoelectric material in average temperatures (500–750 K) [1–3]. In thin films, due to the transi- tion from 2D to 3D material, new dimensional effects occur in pro- files of thermoelectric parameters. Today the problem of calculation of the conductivity of thin films is particularly relevant due to the rapid development of micro- and nanoelectronics. Necessity of modern society in new energy sources is accompanied by the rapid development of thermoelectric material. Many studies considered that the scattering coefficient p for sem- iconductor films is zero. However, this is not always true [4]. In this paper, the influence of mechanism of surface reflection of elec- trons on the thermoelectric properties of n-PbTe films on various substrates is considered, and the thickness dependence of the See- beck coefficient of films based on PbTe is investigated. 2. EXPERIMENTAL DETAILS Films for research are obtained by vapour deposition of synthesized material n-PbTe in a vacuum on the substrate of fresh chips (1000) of mica-muscovite and sitall. The temperature of the evaporator was Te870 K, and the temperature substrates Ts470 K. The thick- nesses of films are set by the deposition time of 0.5–13 min and are measured by microinterferometer MII-4. Measurement of electrical parameters of films was carried out on air at room temperature and at constant magnetic field on the au- tomated device. It provides a process for measuring electrical pa- rameters and initial registration and processing of data. Measured sample had four Hall contacts and two current contacts. As the ohmic contacts, a silver film was used. The current through the THE INFLUENCE OF SURFACE ON SCATTERING OF CARRIERS IN n-PBTE 279 sample was  1 mA. The magnetic field was directed perpendicular- ly to film surface. The induction of magnetic field was 1.2 Tesla. For measurements of the Seebeck coefficient S, an integral meth- od was used. One end of film had a constant temperature, and the temperature of other end was changed. The ends of film were at- tached to the massive copper plates to provide a constant tempera- ture. For the measurement of temperature, platinum thermoresis- tors were used. The sign of RH and S define type of carriers. Dependences of conductivity , Hall coefficient RH, mobility , Seebeck coefficient S on the thickness of n-PbTe films is shown in Figs. 1–8. Calculations of the (d), RH(d), (d), and S(d) dependenc- es were performed with the use of mathematical package Maple 18. 3. ELEMENTS OF THEORY The thin film has many sources of scattering of electrons. In our paper, the size effects associated with scattering on the outer sur- faces of film are considered. Fuchs and Sondheimer examined the dependence of the current density j(z) on the film thickness d in de- tail in works [5, 6]. Conductivity of film  is determined from the kinetic Boltzmann equation, taking into account boundary condi- tions according to [5]:  3 5 1 3 3 1 1 1 exp 8 2 b kt dt k k t t               , (1) where b—electrical conductivity of bulk samples, dimensionless thickness equals to the film thickness divided to the length of the average free path of electrons l: k d l . (2) For the limiting case of k1 (thick film), we obtain [6]:   1 3 1 1 8 b p k            ( 1k  ). (3) For quite thin films (k1), 3 1 1 ln 4 1 b p k p k      (k1). (4) Here, p—the scattering coefficient (i.e., probability of specular re- flection); 0 1p  . When p0, it is a diffuse reflectance; p1 corresponds to a pure specular reflection; and if 0 1p  , there is a mixed specular–diffuse reflection. The case of a massive film is 280 M. A. RUVINSKII, O. B. KOSTYUK, B. S. DZUNDZA, and V. I. MAKOVYSHYN realized with d  . The Fuchs–Sondheimer model is based on the assumption that the statistical properties of the upper and lower surfaces of film can be described by the same parameter p. However, by the example of gold films, Lucas [7] experimentally showed that the scattering pro- cesses on surfaces vary independently. In work [8], it was suggested that the conductivity of film is characterized by two parameters: scattering at the interface of film and free surface, p, and scatter- ing at the interface of film and substrate, q. For the thick films, equation for  has the form: 1 3 1 1 8 2 b p q k               (k1). (5) Let us consider the manifestation of size effect in dependence of Hall coefficient RH on thickness in case of directional magnetic field perpendicular to the surface of film and the current direction. Within the Sondheimer model, Hall coefficient can be determined from the following equation [6]:   2 14 1 1 ln 3 1 H Hb p R R k p k     (k1). (6) It should be mentioned that Sondheimer considered only the re- gion of small k, because the Hall coefficient is mainly affected by the external surface of scattering at low thicknesses. In Ref. [9], the analytical expression for the Hall coefficient is given and relatively easy leads to numerical evaluation of RН:   1 2 2 2 H Hb R R B A B     , (7) where l D  —reduced mean free path (D—Larmor radius),     2 2 2 2 1 2 2 3 1 2 2 1 3 2 1 11 1 ln 2 tan , 2 2 1 1 A                                    (8)     2 1 2 2 2 2 2 3 1 2 2 1 1 13 1 ln tan , 2 1 1 B                                    1 1 lnk p       . THE INFLUENCE OF SURFACE ON SCATTERING OF CARRIERS IN n-PBTE 281 Experimentally obtained the thickness-dependent mobility () can be explained by the mechanisms of carrier scattering on the surface of the condensate. The mobility of carriers in case of diffuse scat- tering on the surface is defined as follows [9]: 1 (1 ) b k     ; (8) here, b—the mobility of carriers in the bulk material. According to works of E. Justi [10] and H. Mayer [11], thermos- e.m.f. S of films with a thickness dl is given as follows: 3 1 (1 ) 8 1 b l U S S p d U        . (9) For thin films with a thickness dl, ln 1.42 1 1 ln 0.42 b l U d S S lU d                     , p 0, (10) where Sb—Seebeck coefficient for bulk samples, and parameter ( ln ( ) / ln ) E U l E E      characterizes the energy-dependent l, E— energy of electron, —Fermi energy. In the quadratic dispersion law, U2 is predicted by the Bloch’s free-electron hypothesis. 4. THE RESULTS AND DISCUSSION Theoretical dependence and experimental data for conductivity , Hall coefficient RH, mobility , Seebeck coefficient Sx on the thick- ness of films based on n-PbTe are shown in Figs. 1–8. For the mas- sive-sample parameters, experimental data for sufficiently thick films, which are well consistent with data for bulk samples [12], were used: for the film on mica substrates: b150 Ohm 1cm 1, RHb–0.75 cm3/C, b158 cm2/Vs, Sb120 V/K; for the film on sitall substrates: b9 Ohm 1cm 1, RHb–3.5 cm3/C, b27 cm2/Vs, Sb93 V/K. Figures 1 and 2 show the dependence of conductivity  on the film thickness of n-PbTe on mica substrates and experimental data. As seen, with increasing film thickness d, conductivity increases greatly with reached saturation at d300 nm for samples on mica substrates and at d600 nm for samples on sitall ones. In this case, dimensional effects have a significant impact, which is vanishing with increasing thickness. The theoretical curve was calculated us- 282 M. A. RUVINSKII, O. B. KOSTYUK, B. S. DZUNDZA, and V. I. MAKOVYSHYN ing the formula (3), and parameter p, and l was found. Best matches of theoretical curve and experimental data were obtained by the least squares method with special features in the Maple 18. The cal- culated values for the reflectivity coefficient were as follow: p0.4, q0.37 for the films on mica, and p0.08, q0.03 for the films on sitall. Note that the values of coefficients of specular scattering are comparable for both surfaces of film (Table 1). Regarding the impact of the type of substrate, for the films ob- tained on fresh chips of mica, specular–diffuse scattering mecha- nism of carriers is realized, and for the films on sitall, scattering mechanism of carriers closes to diffuse one completely (p0). This is due to higher structural perfection of films on mica unlike films on sitall. Fig. 1. Thickness dependence of conductivity  of the n-PbTe films on fresh chips of (1000) mica-muscovite. Points—experiment, solid line— calculation models according to Fuchs–Sondheimer theory. Fig. 2. Thickness dependence of conductivity  of the n-PbTe films on sitall. Points—experiment, solid line—calculation models according to Fuchs–Sondheimer theory. THE INFLUENCE OF SURFACE ON SCATTERING OF CARRIERS IN n-PBTE 283 The dependence of Hall coefficient on the thickness was calculat- ed according to Eq. (6) (Fig. 3; Fig. 4, curve 1). For films on mica (Fig. 3), calculation for Eq. (6) satisfactorily describe experimental data, and for the films on sitall, Eq. (6) only describes the range of thin films, as noted by Sondheimer in Ref. [5]. Therefore, to de- scribe the dependence of the Hall coefficient on the thickness, nu- merical score with (7) proposed by Tellier et al. [9] was applied (Fig. TABLE 1. The calculated values of parameter for the specular scattering of carriers. Type of substrate l, nm p q U mica 265 0.4 0.37 0.60 sitall 548 0.08 0.03 0.62 Fig. 3. Thickness dependence of Hall coefficient RH of the n-PbTe films on fresh chips of (1000) mica. Points—experiment, solid line—calculation models according to Fuchs–Sondheimer theory. Fig. 4. Thickness dependence of Hall coefficient RH of the n-PbTe films on sitall. Points—experiment, solid lines—calculation models according to Fuchs–Sondheimer theory. 284 M. A. RUVINSKII, O. B. KOSTYUK, B. S. DZUNDZA, and V. I. MAKOVYSHYN 4, curve 2). The Larmor radius was calculated by the method of the least squares D4.2510 7 m. This result coincides well with the calcula- tion by the first approximation with the formula Dmv/(eB), where m—mass of carrier, e—module of charge, B—magnetic field, v—velocity of carrier. For these films, D4.5910 7 m. Figures 6 and 7 present the dependence of Seebeck coefficient S on the thickness of the n-PbTe film under the proposed model for substrates from mica-muscovite and sitall. For the films on mica, solid curve in Fig. 7 is calculated according to Eq. (9). For these samples, the theory for the thick films well coincides with experi- ment. The value of U0.6 was obtained by the least-squares meth- od. It indicates a deviation from a quadratic dispersion law (U2 for quadratic dispersion law). Various researches give different values of U. Huebner [13] ob- Fig. 5. Thickness dependence of Hall mobility  of the n-PbTe films on fresh chips of (1000) mica. Points—experiment, solid line—calculation models according to Fuchs–Sondheimer theory. Fig. 6. Thickness dependence of Hall mobility  of the n-PbTe films on sitall. Points—experiment, solid line—calculation models according to Fuchs–Sondheimer theory. THE INFLUENCE OF SURFACE ON SCATTERING OF CARRIERS IN n-PBTE 285 tained U0.530.19 for the thin gold film at the temperature between 77 K and 296 K. Chopra et al. [14] obtained U18.7 for the thin copper films at T483 K. Thornburg and Wayman [15] obtained U2.2 for the thin Au–Ni films. For the films on sitall, similar behaviour was observed. The laws for the thick films described the experimental data. The value U0.62 was obtained by the least-squares method for the mica substrates. It is also worth noting that the examined samples have relatively high Seebeck coefficient S200 V/K. However, higher values of conductivity  for the films on mica give greater thermoelectric figure of merit for the films on mica, S24 W/K2cm, compared with films on sitall, S20.4 W/K2cm. An important parameter that affects to the value of the scatter- ing coefficient is surface roughness, z. Ziman [16] proposed a mod- el, in which, by analogy with optics, there is possibility of obtaining mathematically exact expression for the scattering coefficient p. Fig. 7. Thickness dependence of Seebeck coefficient S of the n-PbTe films on fresh chips of (1000) mica. Points—experiment, solid line—calculation models according to Mayer theory. Fig. 8. Thickness dependence of Seebeck coefficient S of the n-PbTe films on sitall. Points—experiment, solid line—calculation models according to Mayer theory. 286 M. A. RUVINSKII, O. B. KOSTYUK, B. S. DZUNDZA, and V. I. MAKOVYSHYN Then, according to [16], p is defined as  3 2 2 exp 16p z l   , (11) where z—standard deviation for the height from the reference plane (surface roughness), l—mean free path. 1a 1b 2a 2b Fig. 9. 3D AFM image of the surface of thin PbTe films deposited on chips (0001) mica-muscovite (1) and ceramics (2) with thickness, d, nm: 270 (1b and 2b), 810 (1a), 1350 (2a). TABLE 2. Dependence of the scattering coefficient on the surface rough- ness. mica sitall N o . o f s a m p le T h ic k n e s s d , n m T h e m e a n s q u a r e r o u g h n e s s z , n m T h e s c a tt e r in g c o e ff ic ie n t, p N o . o f s a m p le T h ic k n e s s d , n m T h e m e a n s q u a r e r o u g h n e s s z , n m T h e s c a tt e r in g c o e ff ic ie n t, p 1a 810 10.62 0.45 2a 1350 35.67 0.12 1a2 540 6.73 0.73 2b 270 6.77 0.93 1b 270 5.02 0.84 THE INFLUENCE OF SURFACE ON SCATTERING OF CARRIERS IN n-PBTE 287 Figure 9 presents AFM images of a surface of studied films based on PbTe. We see that the surface of film consists of nanosize crys- tallites of pyramidal shape. It is established that the average size of the nanocrystals increased with the thickness of condensate and the surface roughness increased (Fig. 9). The substrate of film does not significantly affect to the form of nanocrystals. However, the size of crystallites for the films on sitall is larger than for the films on mica. Accordingly, the surface roughness for the films on a mica substrate is less than for the films on a sitall substrate (Fig. 9, Ta- ble 2). The calculated values of the scattering coefficient depending on the roughness are shown in Table 2. As seen, for the coefficient p, a clear dependence on the thickness of condensate for studied samples is traced: it increases with the decreasing film thickness. For the thin films, p is close to one that is indicating the mirror mechanism of carrier scattering from the surface of film. In other words, mi- nor irregularities of surface, which are compared to the mean free path l, are not strongly impact on the characteristics of carriers’ flow. It should be noted that the formula (11) is a fairly approxima- tion, and description of the surface with only one parameter z2 is rather simplistic. For the thick films, the scattering coefficient p is smaller and quite close to the values calculated within the Fuchs– Sondheimer model (Tables 1, 2). 5. CONCLUSIONS 1. The analysis on theoretical calculation of electrical parameters of films based on the Fuchs–Sondheimer and Mayer models. 2. The electrical parameters of n-PbTe films on substrates of mica and sitall are experimentally studied. The influence of mechanism of surface reflection of electrons on the thickness dependence of conductivity, Hall coefficient, and thermo-e.m.f. is determined. 3. The probability of specular scattering of charge carriers on both the free surface of film and the film–substrate boundary is deter- mined. As shown, for the films on sitall substrates, completely dif- fuse scattering of carriers (p0) is implemented, and for the films obtained on fresh chips of mica, the scattering coefficient p0.4. REFERENCES 1. D. M. Freik, S. I. Mudryi, I. V. Gorichok, R. O. Dzumedzey, O. S. Krynytskyi, and T. S. Lyuba, Ukr. J. Phys., 59, No. 7: 706 (2014). 2. L. P. Bulat, D. A. Pshenay-Severyn, and V. B. Osvenskyy, Fiz. Tverd. Tela, 58, No. 8: 1483 (2016) (in Russian). 3. U. P. Khairnar, S. S. Behere, and P. H. Pawar, Journal of Chemical, 288 M. A. RUVINSKII, O. B. KOSTYUK, B. S. DZUNDZA, and V. I. MAKOVYSHYN Biological and Physical Sciences, 2, No. 3: 1529 (2012). 4. M. A. Ruvinskii, O. B. Kostyuk, B. S. Dzundza, Journal of Nano- and Electronic Physics, 8, No. 2: 02051-1 (2016). 5. K. Fuchs, Proc. Cambridge Phil. Soc., 34: 100 (1938). 6. E. H. Sondheimer, Phys. Rev., 80: 401 (1950). 7. M. S. P. Lucas, Appl. Phys. Lett., 4: 73 (1964). 8. M. S. P. Lucas, J. Appl. Phys., 36: 1632 (1965). 9. C. R. Tellier, M. Rabel, and A. J. Tosser, J. Phys. F: Metal Phys., 8: 2357 (1978). 10. E. Justi, K. Kohler, and G. Lautz, Z. Naturforsch., 6A: 456 (1951). 11. H. Mayer, Physik dünne Schichten [Physics of Thin Layers] (Stuttgart: Wissenschaftliche-Verlagsgesellschaft MBH: 1955) (in German). 12. Ihor Horichok, Rasit Ahiska, Dmytro Freik, Lyubomyr Nykyruy, Stepan Mudry, Ostap Matkivskiy, and Taras Semko, Journal of Electronic Materials, 2015. (DOI 10.1007/s11664-015-4122-9). 13. R. P. Huebner, Phys. Rev., 136A: 1740 (1964). 14. K. L. Chopra, S. K. Bahl, and M. R. Randlett, J. Appl. Phys., 39: 1525 (1968). 15. D. D. Thornburg and C. M. Wayman, J. Appl. Phys., 40: 3007 (1969). 16. J. M. Ziman, Electrons and Phonons (London: Oxford University Press: 1962).

The Influence of Surface on Scattering of Carriers and Kinetic Effects in n-PBTE Films

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