Parameters of the energy spectrum for holes in CuInSe₂

Parameters of the energy spectrum for holes in CuInSe₂

This paper reports the coefficients Ca,b for the k-linear term in dispersion relation E(k) for holes of the upper valence bands Г⁻₆ and Г⁺₇ in p-CuInSe₂ crystals. We also obtained the tensor components for the carrier effective masses, in all three valence sub-bands of the model semiconductor. I...

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Дата:2009
Автори: Gorley, P.М., Prokopenko, I.V., Galochkinа, О.О., Horley, P.P., Vorobiev, Yu.V., González-Hernández, J.
Формат: Стаття
Мова:English
Опубліковано: Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 2009
Назва видання:Semiconductor Physics Quantum Electronics & Optoelectronics
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/118881
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Parameters of the energy spectrum for holes in CuInSe₂ / P.М. Gorley, I.V. Prokopenko, О.О. Galochkinа, P.P. Horley, Yu.V. Vorobiev, J. Gonzalez-Hernandez // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 3. — С. 302-308. — Бібліогр.: 30 назв. — англ.

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spelling irk-123456789-1188812017-06-01T03:06:14Z Parameters of the energy spectrum for holes in CuInSe₂ Gorley, P.М. Prokopenko, I.V. Galochkinа, О.О. Horley, P.P. Vorobiev, Yu.V. González-Hernández, J. This paper reports the coefficients Ca,b for the k-linear term in dispersion relation E(k) for holes of the upper valence bands Г⁻₆ and Г⁺₇ in p-CuInSe₂ crystals. We also obtained the tensor components for the carrier effective masses, in all three valence sub-bands of the model semiconductor. It was shown that the energy spectrum parameters for holes in CuInSe₂ allow successful explanation for the anisotropy of tensor components describing the interband light absorption coefficient and the published data for the temperature variation of the Hall coefficient, total Hall mobility and thermal voltage within the temperature range 100 K ≤ T ≤ 350 K. 2009 Article Parameters of the energy spectrum for holes in CuInSe₂ / P.М. Gorley, I.V. Prokopenko, О.О. Galochkinа, P.P. Horley, Yu.V. Vorobiev, J. Gonzalez-Hernandez // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 3. — С. 302-308. — Бібліогр.: 30 назв. — англ. 1560-8034 PACS 61.50.Ah 71.20.-b, 73.50.Lw http://dspace.nbuv.gov.ua/handle/123456789/118881 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description This paper reports the coefficients Ca,b for the k-linear term in dispersion relation E(k) for holes of the upper valence bands Г⁻₆ and Г⁺₇ in p-CuInSe₂ crystals. We also obtained the tensor components for the carrier effective masses, in all three valence sub-bands of the model semiconductor. It was shown that the energy spectrum parameters for holes in CuInSe₂ allow successful explanation for the anisotropy of tensor components describing the interband light absorption coefficient and the published data for the temperature variation of the Hall coefficient, total Hall mobility and thermal voltage within the temperature range 100 K ≤ T ≤ 350 K.
format Article
author Gorley, P.М.
Prokopenko, I.V.
Galochkinа, О.О.
Horley, P.P.
Vorobiev, Yu.V.
González-Hernández, J.
spellingShingle Gorley, P.М.
Prokopenko, I.V.
Galochkinа, О.О.
Horley, P.P.
Vorobiev, Yu.V.
González-Hernández, J.
Parameters of the energy spectrum for holes in CuInSe₂
Semiconductor Physics Quantum Electronics & Optoelectronics
author_facet Gorley, P.М.
Prokopenko, I.V.
Galochkinа, О.О.
Horley, P.P.
Vorobiev, Yu.V.
González-Hernández, J.
author_sort Gorley, P.М.
title Parameters of the energy spectrum for holes in CuInSe₂
title_short Parameters of the energy spectrum for holes in CuInSe₂
title_full Parameters of the energy spectrum for holes in CuInSe₂
title_fullStr Parameters of the energy spectrum for holes in CuInSe₂
title_full_unstemmed Parameters of the energy spectrum for holes in CuInSe₂
title_sort parameters of the energy spectrum for holes in cuinse₂
publisher Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
publishDate 2009
url http://dspace.nbuv.gov.ua/handle/123456789/118881
citation_txt Parameters of the energy spectrum for holes in CuInSe₂ / P.М. Gorley, I.V. Prokopenko, О.О. Galochkinа, P.P. Horley, Yu.V. Vorobiev, J. Gonzalez-Hernandez // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 3. — С. 302-308. — Бібліогр.: 30 назв. — англ.
series Semiconductor Physics Quantum Electronics & Optoelectronics
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AT horleypp parametersoftheenergyspectrumforholesincuinse2
AT vorobievyuv parametersoftheenergyspectrumforholesincuinse2
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fulltext Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 302-308. © 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 302 PACS 61.50.Ah 71.20.-b, 73.50.Lw Parameters of the energy spectrum for holes in CuInSe2 P.М. Gorley1, I.V. Prokopenko2, О.О. Galochkinа1, P.P. Horley1,3, Yu.V. Vorobiev4, J. González-Hernández5 1Yu. Fedkovych Chernivtsi National University, 2, Kotsyubynsky str., 58012 Chernivtsi, Ukraine, phone: +38 (03722) 46-877, e-mail: semicon-dpt@chnu.edu.ua 2V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, 41, prospect Nauky, 03028 Kyiv, Ukraine 3Centro de Física das Interacções Fundamentais (CFIF), Instituto Superior Técnico, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal 4CINVESTAV-IPN Unidad Querétaro, Libramiento Norponiente 2000, Fracc. Real Juriquilla, 76230 Querétaro, México 5CIMAV, Miguel de Cervantes 120, Complejo Industrial Chihuahua, 31109 Chihuahua, México Abstract. This paper reports the coefficients BAC , for the k-linear term in dispersion relation E(k) for holes of the upper valence bands 6 and 7 in p-CuInSe2 crystals. We also obtained the tensor components for the carrier effective masses CBAm ,, ||, in all three valence sub-bands of the model semiconductor. It was shown that the energy spectrum parameters for holes in CuInSe2 allow successful explanation for the anisotropy of tensor components describing the interband light absorption coefficient and the published data for the temperature variation of the Hall coefficient, total Hall mobility and thermal voltage within the temperature range 100 K ≤ T ≤ 350 K. Keywords: chalcopyrite structure, СuInSe2, non-parabolic dispersion relation, components of the effective mass tensor, kinetic coefficient, light absorption coefficient. Manuscript received 28.04.09; accepted for publication 00.00.09; published online 00.00.09. 1. Introduction Direct-band chalcopyrite compound СuInSe2 belongs to AIBIICVI 2 semiconductors that are considered as analogs to AIIBVI binary systems. Due to their high absorption coefficient [1] (about (3…6)∙107m–1) these materials are very promising for the efficient photovoltaic device applications [2]. In general, СuInSe2 crystals are studied in deeper detail comparing with the other AIBIICVI 2 compounds (e.g., [3-5]). However, the exact nature of some of their properties is not clearly revealed yet. In particular, it concerns the fundamental parameters characterizing the valence band structure. According to the results of the theoretical calculations [6, 7], the band structure of the bulk AIBIICVI 2 semiconductors in the center of the Brillouin zone obeys anisotropic non- parabolic dispersion relation E(k) including a k-linear term. To the best of the authors’ knowledge, the numerical values of the coefficients С describing the aforementioned term are not determined yet for p- CuInSe2 crystals, while they are known for the AIIBVI materials p-CdS, p-CdSe and p-ZnO. Moreover, only three out of six components of the hole effective masses for p-CuInSe2 were determined so far from the optical studies [8]: those for spin-split band holes (msh /m0 ≈ 0.085), heavy (mhh /m0 ≈ 0.71) and light holes (mhl /m0 ≈ 0.092). Our previous research [9] considered non- parabolicity of the dispersion relation E(k) for the holes in chalcopyrite-structure crystals under non-degenerate statistics of the electron gas, deriving the analytical expressions allowing to calculate the temperature and concentration dependences of tensor components for the thermal voltage, Hall coefficient and carrier mobility. Carrier scattering by crystalline lattice defects was considered in the approximation of time relaxation. For the upper valence sub-bands 6 and 7 of p-CuInSe2, we estimated the coefficients   76 , С characterizing the contribution of k-linear term into E(k). The results of further calculations agreed well with the experimental temperature dependences of the Hall coefficient and total Hall carrier mobility. To improve the approach used in [9], we suggest also to account for the symmetry relations binding the tensor components of the inverse effective masses for Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 302-308. © 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 303 the holes 1 ,, )( 776   m in chalcopyrite (wurtzite) crystals [10-12]. This methodological improvement would change the values of   76 , С obtained in [9], leading to more exact results concerning the influence of k-linear term of E(k) on the values and temperature behavior of the kinetic coefficients in p-CuInSe2. Moreover, proper accounting of the symmetry for the components 1 ,, )( 776   m allows to get an accurate magnitude estimation for all the inverse effective mass components describing the holes in three valence sub- bands of the material studied. Fitting the theoretical calculations to the experimental data on temperature dependences for the Hall coefficient, Hall mobility and thermal voltage in p-CuInSe2 crystals allowed to improve precision in determining   76 , С coefficients. We have also shown that non-parabolicity contribution to E(k) in the total Hall mobility decreased from about 50 % (T = 100 K) to 17 % (T = 300 K), enhancing the previously reported data of ≈20 % and ≈10 %, respectively [9]. 2. Theory Schematic depiction of the valence band diagram [4, 13] for p-CuInSe2 around the center of the Brillouin zone is shown in Fig. 1. The dispersion relation for the carriers populating the valence bands 6 , 7 and 7 (taking into account spin-orbital interaction) can be written in the following form [7]: , 2 )/( 2 )( , || 2 || 2 22 , , , 2 , 0, 76 BABA BA BA BA m k Cmk m EkE          (1) Fig. 1. Band diagram for р-CuInSe2; the designations are explained in the text. )( 2 )( || 2 || 22 07 СС С m k m k EkE      , (2) with transversal k = (kx 2+ky 2)1/2 and longitudinal k|| = kz components of the wave vector k for CBAm ,,  and CBAm ,, || effective mass tensors describing the holes in the sub- bands 6 (index А), 7 (index В) and 7 (index С) regarding the high-symmetry axis of the crystal. The coefficients BAC , characterize the deviation from parabolicity in the dispersion relation E(k) for the corresponding valence sub-bands. CBAE ,, 0 in (1) and (2) describe the position of their extrema. As the dispersion relation (1) is characteristic for the semiconductors with chalcopyrite or wurtzite structure of [14-17], it is natural to assume that the components of the effective mass tensors for p-CuInSe2 would also satisfy the relations obtained for wurtzite crystals [11, 12]:           ACBACB m m m m m m m m , || , || , 32 1 || 1 )2)(( CC rg m m m m AA     ,           ACAB m m m m C m m m m ||,||, 1 ||,||, ,           AACC m m m m C m m m m || 2 || ,           AABB m m m m C m m m m || 3 || . (3) Here g, r, s, t denote m2/2 -normalized (ħ is Planck’s constant and m is the free electron mass) matrix elements for the interband interaction operators [12], with adjustment parameters gs rt    , rg ts   1 ,    11 2 2 1  CqС , )1()1( 11 2 3 CqC  . (4) The coefficient )1/( 22 1 qqС  (5) with           9/8 1 2 1 2 2 x x q (6) depends on the energy split 3/1/  socrx caused by the crystalline field cr and spin-orbital interaction so [10]. It is important that the mc-normalized (m is the electron mass and c is the speed of light) matrix elements for the optical transitions from В/С valence Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 302-308. © 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 304 sub-bands to the conduction band [10] also depends on q2 2 || 2 qMM CB   , 2 || 12 qMM BC   , (7) while for the A-band 0|| AM , 5.0 AM . The experimental values eV006.0cr and eV233.0 so [18] lead to C1 ≈ 1.9 > 1, proving that for p-CuInSe2 (and also CdSe, ZnSe) the components of the effective mass tensor for holes in the valence sub- bands would satisfy the condition [12]: Bm|| < Сm|| < Am|| , Am < Сm < Bm . (8) It is important that for С1 < 1 (which is valid for CdS, ZnS, ZnO and GaN), the components of symmetry for the effective mass tensor are [10-12] Сm|| < Bm|| < Am|| , Am < Bm < Сm . (9) Comparison of (8) and (9) shows that changing C1 > 1 for С1 < 1 will result in swapping of the valence sub-bands В and С. Formulas (5) and (7) yield a proportion CB MMC ||||1 / BC MM  / saying that the coefficient C1 depends on the ratio of matrix elements for the optical transitions (with the same polarization) from the bands В/С into conduction band. Therefore, one can assume that C1 should contribute somehow to the anisotropy of the light absorption coefficient  /|| (with parallel and perpendicular subscripts denoting light polarization regarding the main optical axis of the crystal). 3. Results and discussion Using the symmetry relations (3) one can show that for the present experimental effective mass values describing the holes of p-CuInSe2 [8] the inequalities (8) would be valid for these two particular cases (within parameters with the precision of experimental measurements): Case D1: ,091.0 ||  m mA ,074.0 ||  m mB ,081.0||  m mС ,087.0 m mA ,73.0 m mB ;162.0 m mС (10) Case D2: ,71.0||  m m A ,165.0||  m mB ,260.0||  m mС ,078.0 m mA ,092.0 m mB .085.0 m mС (11) Table 1 presents the anisotropy coefficients for effective masses of holes CBA CBA CBA m m m K ,, ,, ||,, ||,    . We calculated the data both for p-CuInSe2 crystals and their AIIBVI analogs using the experimental mass values for CdSe, CdS [10] and ZnO [14]. Table 1. Anisotropy coefficients for hole effective masses in p-СuInSe2 and AIIBVI analogs. Material A mK B mK C mK Eg, eV С1 Case C1 1.05 0.10 0.50 p-CIS Case C2 9.10 1.79 3.06 1.010[22] 1.90 p-CdSe 2.66 0.53 0.91 1.756[23] 1.65 p-CdS 4.70 0.76 0.48 2.485[23] 0.73 p-ZnO 5.07 3.76 0.24 3.370[23] 0.035 As one can see, for the case C1 (10) with increasing band gap Eg (parameter С1 decreases) the anisotropy coefficient for effective masses of the holes populating А and В valence bands also increases. At the same time, the coefficient for the С-band decreases for all the studied materials except for CdSe. Effective mass components calculated for the case D2 (11) for CuInSe2 violate this regularity for А and В-bands, to the contrary restoring it for the С-band. To define which of the cases D1 or D2 is correct for р-CuInSe2, we used analytical expressions from [9] to calculate temperature behavior of the tensors describing the specific conductivity, Hall mobility and thermal voltage. To define the fixed CBAm ,, ||, , the coefficients BAC , in the dispersion relation (1) were considered as parameters and adjusted to achieve the best fitting of the calculated data to the experimental temperature curves for the kinetic coefficients. The numerical values of BAC , for р-CuInSe2 and AIIBVI are given in Table 2. It is noteworthy that for all the studied compounds we achieved an essentially linear dependence )15.4(1065.4 2 gB EC   eV·Å (Fig. 2, line 2), allowing to assume the linearity of )( gA EC  as well. To obtain the latter (Fig. 2, line 1) the values of AC for CdSe and CdS should be used in the place of those from [15], which will allow to get the refined coefficients (Table 2). Validity of )( 0,, gBABA EEkC  dependence for various wurtzite and chalcopyrite crystals makes it possible to estimate the limit values of BAC , coefficients for the case 0gE , yielding 263.0max AC eV·Å and 193.0max BC eV·Å, respectively. On the other hand, for semiconductor with the considered crystalline structure and a bandgap of eV15.4gE , the contribution of k-linear term into E(k) should be negligibly small. Due to this fact, for example, the bandgap of BeO is not determined yet exactly, so that the publication [19] usually mentions the data in a wide range of 7.8-10.6 eV. The fact that the linear dependence )( 0,, gBABA EEkC  holds for p- СuInSe2 crystals and their AIIBVI analogs suggests that the obtained BAC , coefficients are determined correctly and reliably. Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 302-308. © 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 305 Fig. 3. Temperature dependence of the total Hall mobility for holes in р-CuInSe2. The curve numbering is discussed in the text. Error bars illustrate precision of the experiment. Fig. 2. Dependence of CA (line 1) and CB (line 2) coefficients from (1) on the bandgap of p-СuInSe2 crystals and their AIIBVI analogs. The arrows mark the refined CA for CdSe and CdS, which fits the linear dependence CA = 6.3410-2(4.15 – Eg) eV∙Å. Table 2. Coefficients CA,B for p-СuInSe2 and their AIIBVI analogs (eV∙Å units). M at er ia l p- C uI nS e 2 ou r da ta p- C dS e da ta [1 5] / re fi ne d p- C dS da ta [1 5] / re fi ne d p- Z nO da ta f ro m [1 5] CA 0.200 0.230/0.150 0.082/0.105 0.051 CB 0.144 0.114 0.070 0.035 Concerning the temperature behavior of kinetic coefficients in р-CuInSe2, our calculations show that the carrier contribution to the valence band 7 is negligibly small in comparison with that of the holes populating 6 and 7 bands. Let us consider the system with a single acceptor level formed by interstitial selenium atoms [20] with the concentration Na ≈ 4.0×1018 cm-3 and depth EV + 0.019±0.002 eV correlating with the data from [21]. We performed calculations for this system by using carrier effective masses calculated for either of C1 and C2 cases (10), (11). The results revealed good agreement between theoretical and experimental [9] results concerning the temperature dependence of the Hall coefficient R = f(1/T). The calculated thermal voltage degenerates into a scalar value, fitting the experimental data [9] within the precision limits of the experimental measurements. Solid and dashed curves in Figure 3 present calculation results for the cases D1 and D2, respectively. The curves designated numbers with primes 1', 2' were obtained for 0, BAC . The temperature dependence of the total Hall mobility for holes uH(T) in р-CuInSe2 crystals for the different experimental results are shown with circles (data [24]) and triangles (data [25]). Comparing the results presented by curves 1 and 1' with 2 and 2', one can see that for the case when non- parabolicity of E(k) is neglected, one obtains the excess mobility and markedly different shape of the curve uH(T). For 0, BAC , the calculated and experimental curves for uH(T) fit each other well for the temperatures 170 K ≤ T ≤ 350 K. The existing mismatch between theory and experiment for uH(T) in р-CuInSe2 crystals under Т < 150 K may stem from neglecting the hopping scattering, which becomes quite significant at these temperatures [20]. Under the temperature increase from 100 to 300 K the contribution of non-parabolicity into the hole mobility was calculated using the masses (10), (11) and the experimental data [24, 25]. We observed a decrease of aforementioned contribution for approximately 33 percents (from ≈50 % at 100 K to ≈ 17 % at 300 K), which is illustrated at the inset to Fig. 2 for the parameter /)0((/ ,H  BACuuu %100)1)0( ,H BACu . The resulting difference between the values of the total mobility calculated using D1 and D2 effective hole masses for р-CuInSe2 (the corresponding solid and dashed curves in Fig. 2) are within the experimental precision. Due to this, it is hard to say which set of CBAm ,, ||, (D1 or D2) is preferable for the description of temperature variation of the kinetic coefficients in р-CuInSe2. To solve this problem, we used the experimental spectrum [26] for imaginary part ki of the refraction coefficient n of CuInSe2, measured for different polarizations ||,i regarding the main crystalline axis and the incident light wave with a wavelength . The knowledge of the latter allowed us to apply the formula [26]  /4 ii k (12) to determine the components of absorption coefficient i. On the other hand [20], the expression for i at the fundamental absorption edge in semiconductor material can be written as: gii EAn   , (13) Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 302-308. © 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 306 where 2 ,, 2/3 2 2 0 2/3 )()/2( 6 n i CBAn n iri Mmm e V mc A        . (14) Here n is the carrier concentration,  is the photon energy, n i e i n ir mmm 111  describes the і-th component of the reduced mass of electron-hole pair ( e im is the і-th component of effective mass tensor for conduction band electrons), n iM are matrix elements for optical transitions (6), V is the volume of the crystal, е is the elementary charge, and 0 is the absolute dielectric permittivity. Calculating D1 and D2 effective masses for the holes (Table 1) and using electron effective masses (for CuInSe2 – ,10.0/  mm 11.0/|| mm [24], for CdSe – ,13.0/  mm 14.0/|| mm [15], for CdS – ,21.0/  mm 22.0/|| mm [15] and for ZnO – ,30.0/  mm 31.0/|| mm [27]), we calculated dimensionless variable ||, 2 2/3 0* 6 ||,           A e mc V A  as a function of semiconductor bandgap Eg (Fig. 4). As it can be seen from the figure, the dependence )(* ||, gEfA  can be quite well described within experimental precision for CBAm ,, ||, , cr and so as )/( ||, 2 ||, * ||,   gg EEA . (15) Fig. 4. * ||A (1) and * A (2) coefficients as the function of Eg for р-CuInSe2 and its AIIBVI analogs (solid and dashed curves correspond to D1 and D2 hole masses, respectively). The inset shows the ratio  AA /* || with variation of the parameter С1: line 1 – for the masses (11) and line 2 – for the masses (10). The error bars illustrate dispersion of the theoretical values obtained for the different experimental data. The asterisk denotes the experimental result for р-CuInSe2 [22]. For further calculations, one should use the following values for ||, (in eV-1) and ||, (in eV): for the case D1 (10) – ;28.4,83.9,03.8,65.11 ||||   (16) for the case D2 (11) – 32.2,22.7,47.10,20.14 ||||   . (17) As it follows from the latter formulas, the components of absorption coefficient are bounded with the proportion ** |||||| ///   AAkk . According to [26], the experimental ratio kk /|| for the case of the fundamental absorption in CuInSe2 crystals varies within the range 1.05 – 1.10. The same ratio, calculated according from (15) using (16) and (17), would yield the values 1.44 and 1.75 for the cases D1 and D2, respectively. Therefore, the best fit of theoretical curves to the experimental data regarding  /|| ratio can be attained by using the hole effective masses according to the case D1 (formula (10)). It was experimentally proven [28, 29] that in quasi- cubic model approximation for the crystals with chalcopyrite structure [30] illuminated by light wave with the polarization vector perpendicular to the main optical axis of the crystal, the ratio of intensity peak in electro-reflection spectra ( ||I and I ) obeys the following expressions: 2 , |||| )/3/2(9,0 so CBA E I I I I    (18) with          crsocrsocrsoE 3 8 )(5.0 2 . (19) The discussed peaks correspond to electron transitions from the valence to conduction band in the crystals AIIBIVCV 2. It is worth noting that for the limit case 0so the ratio soE  / tends to 2/3. Taking into account (5), (6), one can show that for the crystals with С1 > 1 1 || 1 || /2,2 C I I C I I BC   . (20) For the case С1 < 1, the subscripts “В” and “С” should be swapped in (20). In this way, one can treat the ratio  /|| = AA /|| as a function of the parameter С1 for the crystals with chalcopyrite or wurtzite structure. The inset to Fig. 4 proves that the dependence   %100)0(/)0(/ * || * ||      AAAA is linear and equal to (81)С1 or (212)С1 for the hole masses calculated for the cases D1 and D2. Experimental data on this ratio for р- CuInSe2 (shown as the asterisk in the inset to Fig. 4) fits better to the case when the effective mass estimations are done with the formula (10). The obtained correlations Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 302-308. © 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 307 between ||,A and their ratio for the different wurtzite and chalcopyrite crystals (e.g., CuInSe2, CdSe, CdS and ZnO, see Fig. 4) suggests that the most accurate description of the effective mass tensor for р-CuInSe2 is that provided with the formulas (10). 4. Conclusions We show that p-CuInSe2 crystals with the components of hole effective mass tensor obeying the symmetry relations (3) is characterized with two sets of CBAm ,, ||, , describing temperature dependence of the total conductivity, Hall coefficient and thermal voltage within experimental precision. For the upper valence sub-bands 6 and 7 , we have estimated the coefficients BAC , characterizing deviation of the dispersion relation E(k) from its parabolic form, which yielded an acceptable agreement of the calculated and experimental temperature dependences for the kinetic coefficients in this material. It was found that )( 0,, gBABA EEkC  for p-СuInSe2 and their AIIBVI analogs, allowing to refine the values of AC for CdSe and CdS. We also obtained a phenomenological expression (15) for the coefficients ||,A in formula (13) describing the spectral dependence of light absorption tensor close to the fundamental absorption edge as a function of Eg. Moreover, the dependence   %100)0(/)0(/ * || * ||      AAAA =  1Cf proved to be linear in the first approximation for CdSe, CdS, ZnO and CuInSe2 with wurtzite and chalcopyrite structure; the experimental data known for р-CuInSe2 fits reasonably our theoretical calculations performed for the components of the effective masses given by the formula (10). The obtained effective mass values make it possible to properly explain the component anisotropy for the interband light absorption tensor, as well as the experimental data on temperature dependence of the kinetic coefficients within p-CuInSe2 in the temperature range 100 – 350 K. 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