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Energetic band structure of Zn3P2 crystals
Physica B 408 (2013) 29–33
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Energetic band structure of Zn3P2 crystals I.G. Stamov a, N.N. Syrbu b,n, A.V. Dorogan b a b
Tiraspol State Corporative University, Lablocicin Street 5, 2069 Tiraspol, Republic of Moldova Technical University of Moldova, 168 Stefan cel Mare Avenue, 2004 Chisinau, Republic of Moldova
a r t i c l e i n f o
abstract
Article history: Received 16 August 2012 Received in revised form 14 September 2012 Accepted 15 September 2012 Available online 23 September 2012
Optical functions n, k, e1, e2 and d2e2/dE2 have been determined from experimental reflection spectra in the region of 1–10 eV. The revealed electronic transitions are localized in the Brillouin zone. The magnitude of valence band splitting caused by the spin–orbital interaction DSO is lower than the splitting caused by the crystal field DCR in the center of Brillouin zone and L and X points. The switching effects are investigated in Zn3P2 crystals. The characteristics of experimental samples with electric switching, adjustable resistors, and time relays based on Zn3P2 are presented. & 2012 Elsevier B.V. All rights reserved.
Keywords: Semiconductor compound Optical reflection spectra Kramers–Kronig relations Optical constants Band structure Switching effects Adjustable resistors
1. Introduction
2. Experimental method
The Zn3P2 compound that belongs to the AII-BV 2 group is crystallizing into a chalcopyrite structure with I42d–D15 4h spatial group. Information about material properties and crystal structure are presented in papers [1–4]. A lot of research data on elaborating solar energy converters using zinc phosphide have been reported [5–9]. Thin film device structures have been obtained on the basis of this compound [6,8]. Photoelectrical properties of surface barrier layered structures Me–Zn3P2 have been investigated [4,5] and practical recommendations for using these structures as a photorreceiver in near IR range have been given [6,9]. Optical properties of these structures have been studied in the papers [10–13]. Experimental optoelectronic device samples, such as ‘‘time relay’’, adjustable resistors, and memory elements, have been created on the basis of these crystals [14–17]. Results of investigation of switching effects in Zn3P2 crystals and optical spectra in the region of fundamental absorption as well as in the depth of the absorption band are presented in this paper. The contours of reflection spectra have been calculated using Kramers– Kronig relations and the optical functions n, k, e1, e2 and d2e2/dE2 in the region 1–10 eV have been determined. The revealed particularities are ascribed to electronic transitions in the frame of theoretical calculations of the energy band structure of these crystals.
Zn3P2 crystals grown in ampoules using the gas transportation method represent bulk pyramids with mirror surfaces of 8 mm 8 mm. If needed, the samples could be polished using mechanical and chemical methods. Reflection spectra in the region of fundamental absorption have been measured using a MDR-2 spectrometer and the optical spectra in the depth of absorption band were investigated using a SPECORD-M40. For low-temperature measurements the samples were mounted on the cold station of a LTS-22 C 330 optical cryogenic system.
n
Corresponding author. Tel.: þ373 222 37508. E-mail address: [email protected] (N.N. Syrbu).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.09.029
3. Experimental data and discussions 3.1. Optical properties of Zn3P2 crystals and Me–Zn3P2–Me structures Fundamental absorption of Zn3P2 single crystals in the region of 1.3–1.6 eV is changing in the range of absorption coefficients K¼ 103–105 cm 1. The measurements, carried out in the region of weak absorption have not revealed a sloping step region caused by direct transitions. Therefore, it was suggested [4,10–13] that the minimum of interband interval is caused by direct transitions. The energy value of the beginning of fundamental absorption is 1.30 eV at 296 K temperature and 1.32 eV at 77 K. The temperature coefficient of the absorption edge shifting equals 10 4 eV/K [1,4]. The change of absorption coefficient of Zn3P2 single crystals
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I.G. Stamov et al. / Physica B 408 (2013) 29–33
with different thicknesses measured at room temperature is shown in Fig. 1. The absorption of Zn3P2 polycrystalline thin films has been measured in the high energy region of K (103–105 cm 1) (Fig. 1, curve a). A pronounced interference pattern is revealed in films with thicknesses of 0.1–3 mm, which does not allow obtaining a thin absorption structure in this region. The interference pattern is not present in films with thicknesses thicker than 4 mm. This allows to measure the absorption coefficient up to 3 105 cm 1 (curve a). The fundamental absorption of single crystal samples and thin films are satisfactory correlating. Temperature decrease leads to the shift of fundamental absorption towards high energy regions (Fig. 1, curve c). The E1 (1.510 eV) line is evident at 80 K (curve b), which is better resolved near 1.550 eV at 10 K. An absorption line at 1.45 eV is revealed in the long wavelength part of the E1 maximum, which is resolved as a doublet (1.45 eV, 1.47 eV) in wavelength modulated spectra (DT/Dl). The line is likely caused by the phosphor vacancy in Zn3P2 crystals. It was observed that the line’s intensity weakly increased with annealing of Zn3P2 crystals in vacuum. The investigations of fundamental absorption of crystals with different thicknesses, beginning with d ¼1 mm up to 2 mm at 10 K and even at T¼2 K temperatures, have not reveal characteristic absorption lines due to indirect transitions. The analysis of results shows that indirect transitions are not present in Zn3P2 crystals. The absorption edge is formed by direct transitions. The results of investigations of the interband absorption edge in this paper are correlating in those previously published [4,10–13]. The dependence K(:o) is strictly exponential and is described by the Urbach relations in the interval of K ¼1 104 cm 1. The temperature coefficient of the absorption edge shifting equals 10 4 eV/K. E2 (1.710 eV) and E3 (1.753 eV) maxima have been revealed in the high energy region of the wavelength modulated spectra DT/Dl at 80 K, which are caused by direct transitions in the G point from valence bands V2 and V3 to the C1 band (Table 1). E1 and E2 maxima are also evident in spectral dependencies of photoconduction Jf at 80 K, practically for the same energies as for DT/Dl spectra (Fig. 1). The switching effect has been revealed while studying spectral and electrical characteristics of Me–Zn3P2–Me structures, i.e. the transition of the crystal state from high-ohmic into a stable low-ohmic state [14,15]. This is observed when a voltage equal to Up is applied to crystal contacts. The switching effect was observed for a large number of materials into a wide range of specific resistance values [16,17]. When a voltage higher than Up is applied to the sample a transition into a low-ohmic state occurs, in which the delay time tz and the switching time tp (the duration of the sharp current increase) can be distinguished. The inverse transition into highohmic state is occurring during recovery. Fig. 2 shows the S-type
Fig. 1. Fundamental absorption of Zn3P2 thin films measured at 80 K (a) and of Zn3P2 single crystals measured at 80 K (b) and 10 K (c) as well as the spectral distribution of DT/Dl and the photoconduction Jf measured at 80 K.
Table 1 The energy of electronic transitions revealed from calculations of reflection spectra by means of Kramers–Kronig relations for Zn3P2 crystals. Indication
R (eV)
e2 (eV)
d2e2/dE2 (eV)
Transitions
e1, E1 E2 e2, E3 e3 e4 e5 e6 e6* e7 e8 e9 e10 e11 e12 e13 e14
1.462, 1.510 1.710 1.753 2.088 2.531 2.743 3.354
1.469 1.746
1.482 1.780
2.099 2.569
2.146 2.579 2.833 3.378 3.535 4.039 4.379 5.118 5.462 6.97 7.59 8.74 9.20
!15(V1)–!1(C1) !15(V2)–!1(C1) !15(V3)–!1(C1) L3(V1)–L1(C1) L3(V2)–L1(C1) L3(V3)–L1(C1)
4.079 4.336 5.089 5.460 6.86 7.54 8.67 9.14
3.345 3.486 4.027 4.265 5.010 5.465 6.86 7.54 8.69 9.14
X5(V1)–X1(C1) X5(V2)–X1(C1) X5(V1)–X3(C2) X5(V2)–X3(C2) !15(V1)–!25(C1) !15(V2)–!25(C1) !15(V3)–!25(C1) !15(V2)–!25(C2), !15(V1)–!25(C2)
Fig. 2. I–V characteristic of a Me–Zn3P2–Me structure with a sharp region of negative differential resistance (NDR) (A), and smooth differential resistance (SDR) (B). Numbers show the temperature at the surface of the sample.
I–V characteristics of Me–Zn3P2–Me structures with a sharp region of negative differential resistance (NDR) and a smooth one for SDR (B). Numbers show the temperature on the surface of the sample. The I–V parameters can be varied by selecting the outer circuit parameters (bias voltage, serial resistance). The S-type I–V characteristic is reversible in the region of negative differential resistance in each point. It is possible to pass multiple times all the I–V regions in any direction by changing the bias voltage and serial resistance. The hysteresis phenomenon was not observed. The temperature was increasing on the surface of the sample for Me–Zn3P2–Me structures with a smooth change of SDR (Fig. 2B). A thermocouple cooper–constantan was installed on the surface directly under the spring contact and an automatic recording of surface temperature was made. At the same time, the change of current value as a function of applied voltage J¼f(U) was recorded in a continuous regime. Fig. 2B shows the I–V characteristic for Me–Zn3P2–Me structure with indication of the surface temperature under the contact in various points of the curve. The increase of surface temperature was starting at the same time as the current increased in the NDR region. The temperature increased, practically, up to 150 K in short time.
I.G. Stamov et al. / Physica B 408 (2013) 29–33
Fig. 2A shows the I–V characteristics that do not possess a stable region of negative resistance. A voltage breakdown occurred at a value of Up ¼7 V and the sample abruptly switched into a low-ohmic state. The transfer into low-ohmic state can also occur in a smooth regime (Fig. 2B). The S-type I–V characteristic with a smooth change of NDR can be transferred into a characteristic with a sharp voltage breakdown and a current increase through the structure. This was done by connecting to the Me–Zn3P2–Me structure a lower-ohmic serial resistance. A low load resistance Rtherm (RB 4Rtherm 4R) was connected to the sample when the transfer into low-ohmic state was investigated in order to prevent an irreversible thermal breakdown (RB, RH are the resistances of low- and high-ohmic states, respectively). The I–V characteristics of Me–Zn3P2–Me structures were symmetric relatively to the polarity of the applied voltage and were not dependent on the type of the contact material [15]. The electrode geometry does not influence the I–V characteristics. The replacement of fused contacts by spring contacts does not change the I–V characteristics [14,15]. These observations indicate on a bulk nature of the switching effect in Zn3P2 crystals. The sample resistance in the low-ohmic state was by 3–5 orders of magnitude lower as compared to the high-ohmic state. A linear increase of current with voltage was observed after the sample switching into a low-ohmic state. The sample was in a low-ohmic state if the value of the current through the sample was higher than 10 2 A. The high-ohmic state was restored at a current lower than this value. The conductivity in low-ohmic state was not dependent on the contact surface, which was an evidence of current pinching in a switched on state. Fig. 3A shows the switch resistance dependence on the dissipated power (a) and on the crystal temperature (b). Curve B in Fig. 3 shows the dependence of the switch resistance on the current through the sample. The switching character of zinc phosphide is essentially determined by the value of applied voltage. The delay time and the rate of the current increase were changing in dependence on the value of the applied voltage. Fig. 3 shows the change of the current that flows through Me–Zn3P2–Me structure in time for a crystal with d ¼640 mm thickness at various bias voltages. The delay time decreases with the voltage increase, while the rate of the current change increases. The delay time was changing inverse proportionally to the bias voltage. The delay time tends to zero and the dependence tz ¼f(U) undergoes almost an abrupt change in the region of high voltages (Fig. 3, curve 12, U¼105 V). Such structure is functioning as time relay [16–18]. An evident current increase and switching delay time decrease is observed as the voltage increases. At the same time, the current increase front is sharply changing and the rate of increasing is exponentially depending on the bias voltage. The switching voltage of zinc
Fig. 3. (A) Switch resistance dependence on the dissipated power (a) and temperature (b). (B) Switch resistance dependence on the current.
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phosphide single crystals increases proportionally to the sample thickness, while the current through the crystal during switching is practically unchanged and equal to 10 4 A at 300 K. The switching effect was observed both in case of continuous current and of alternative sinusoidal voltage of a 50 Hz frequency. The sample switching voltage was decreasing when a sinusoidal voltage was applied to the sample. This fact is in accordance with the final recovery time of high-ohmic state. The all other switching peculiarities were maintained. The current does not change in time at low shifting voltage, i.e. UoUp. The switching parameters can be controlled in a wide time interval by changing the resistance value, serially connected with the sample in a circuit, by changing the crystal thickness or the voltage value. The delay time and the current increasing time are decreased if the current is limited, although the switching time is decreasing. The Me–Zn3P2–Me structure is in a low-ohmic state if a current of about 10 5 10 4 A is flowing through the sample. The crystal turns back into a high-ohmic state after the voltage is switched off. As it was mentioned above, temperature influences the S-type I–V characteristics of Zn3P2 single crystals. As the temperature increases the switching occurs at lower voltages. The S-shape of L–V characteristics disappears at high temperatures and the samples possess a positive differential resistance in all the investigated voltage range. The dependence of the switching voltage on the inversed temperature in a half logarithmic scale represents a straight line. After switching, the I–V characteristic possesses a linear character and the sample resistance does not depend on temperature and light irradiation in a low-ohmic state. At the same time, crystals with electrical memory properties were revealed [18–20]. The sample can remain in low-ohmic switched state (memory state) for a long period of time without an applied bias voltage. The transfer into high-ohmic state for these samples is done by heating at the temperature 400 K. The influence of integral light irradiation on switching is similar to the change of sample temperature. The I–V characteristic was shifting towards low voltages part and the threshold voltage was decreasing as the light intensity increased, and the S-shape of the I–V characteristic disappeared at high intensities ( 10 lx). Two processes can be revealed in the case of high-state recovery: recovery of high resistance and recovery of the threshold voltage. The recovery of high resistance occurs practically instantly after the bias voltage is switched off for samples without electrical memory. However, if the bias voltage Up is switched on again after a short period of time 1 s, then the sample immediately occurs in a low-ohmic state without switching, i.e. switching occurs at lower threshold voltages Up0 . The recovery time of threshold voltage increases if the sample is maintained in the low-ohmic state for a longer period of time Fig. 4.
Fig. 4. Switching time into low-ohmic state dependence on bias voltage U¼ 50 V(1), 55 V(2), 60 V(3), 65 V(4), 70 V(5), 75 V(6), 80 V(7), 85 V(8), 90 V(9), 95 V(10), 100 V(11), 105 V(12).
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3.2. Optical properties of Zn3P2 crystals in the depth of absorption line Reflection spectra were measured in the depth of fundamental absorption band in the energy interval of 1–6 eV at 80 K, as well as in the interval of 6–10 eV at 300 K (Fig. 5). The absorption coefficient and optical functions n, k, e1, e2, d2e1/dE2 and d2e2/dE2 were calculated from reflection spectra by means of Kramers– Kronig relations (Figs. 6 and 7). The maximum e1 is observed at 80 K in the fundamental absorption region of reflection spectra, which practically coincides with E1 peak in DT/Dl spectra (Fig. 1). e2–e14 are revealed in the fundamental reflection spectra (E 1.5– 10 eV). These maxima are also evident in optical functions n, k, e1, e2 and d2e2/dE2 (Figs. 5 and 6). The peculiarities in reflection spectra and optical functions are due to direct electronic transitions in special points of the Brillouin zone. The revealed values of electronic transitions in experimental reflection spectra and in calculations of optical functions have been interpreted in the frame of theoretical calculations of Zn3P2 crystals in the points of high symmetry of Brillouin zone [21]. The Brillouin zone represents a rectangular prism with 14 special points [22]. Theoretical calculations of dispersion relations in actual points of the Brillouin zone as well as calculations of the selection rules for Zn3P2 have been previously reported [23]. The actual points of Brillouin zone (points of zero energy slope), the dispersion relations, and the selection rules in these points have been determined. The zero energy slopes in !, Z, M, R, X, A points is realized in two directions from three Kx, Ky, Kz available. The zero slope is realized in all the three directions in the !, M, R points without taking into account the spin–orbital interaction. The zero energy slope is realized in all the directions in the ! point taking into account the spin. The analysis of dispersion relations shows that they have a most common view in G, V, U, S, D points. According to the selection rules, the transitions in R, X, Y, T, S and S points are not polarized. The selection rules in the center of the Brillouin zone prove that the transitions possess different energetic intervals for
Fig. 6. Spectral dependence of optical functions e1, e2 and d2e2/dE2.
Fig. 7. Energy band structure of Zn3P2 crystals [21].
Fig. 5. Spectral dependence of reflection coefficient R, absorption coefficient K, phase of the reflected beam F and optical functions n, k.
each polarization. In the E:c polarization at K ¼0 the transitions between the !1,2,3,4-!4,3,2,1 states are allowed, while transitions between the !1,2,3,4-!10,9,10,9 states are allowed in E?c polarization [1,4,22]. In the R point, the transitions between the R1,2-R1,2 states are allowed by the selection rules in E:c polarization, while transitions between the R1,2-R1 þR2 states are allowed in E?c polarization. In the X(L) point of the Brillouin zone, the transitions between the X(L)1,2-X(L)1,2 states are allowed in E:c polarization, while transitions between the X(L)1,2-X(L)1 þX(L)2 states are allowed in E?c polarization [22]. The theoretical calculations of the energy band structure using the pseudo-potential method for Zn3P2 crystals have been carried out by Lin-Chung in a wide energy range and in different points of the Brillouin zone [21]. The crystal lattice of Zn3P2 and Cd3P2 has been considered in theoretical calculations as an analog of the fluorite lattice. The Zn and Cd atoms are introduced as vacancies periodically arranged in the
I.G. Stamov et al. / Physica B 408 (2013) 29–33
crystal lattice. The Zn3P2 band structure calculated by Lin-Chung along several symmetry directions is presented in Fig. 7. The maximum of the valence band and the minimum of the conduction band are situated in the center of the Brillouin zone, in the ! point. The spin–orbital interaction and other relativistic effects have not been taken into account in calculations. The maximum of the valence band in the ! point is triple degenerated. The calculated value of the bandgap is Eg ¼1.886 eV. Taking into account the potential of the crystal field and the spin–orbital interaction in real crystals will lead to splitting of the valence bands. The maximum of the valence band !15 will split into three bands due to the removal of degeneracy. The maxima E1 at 1.510 eV, E2 at 1.710 eV, and E3 at 1.753 eV have been revealed in the region of the bandgap in DT/Dl spectra (Fig. 1, Table 1). The E1–E2 maxima are separated by each other by an energetic interval of 200 meV, while the distance between the E1 – E3 maxima is of 43 meV. The value of spin–orbital slitting of the valence band in Zn3P2 crystals was estimated in the approximation of covalent bonds it being equal to Dso ¼0.06 eV, while estimations in the approximation of singly and doubly ionized Zn ions give the value of Dso ¼0.15 and 0.30 eV, respectively. The splitting due to the crystal field should be of the order of 0.01 eV by analogy with known anisotropic crystals. Taking into account these data, we suppose that E1, E2, and E3 maxima are due to transitions G15(V1)–G1(C1), G15(V2)–G1(C1), and G15(V3)–G1(C1), respectively. Therefore, one can conclude from our experimental data that the valence band splitting caused by the crystal field V1 V2(V3) equals 43 meV, while that caused by the spin–orbital interaction is equal to 200–243 meV. The next energetic intervals are situated in the L point of Brillouin zone as the energy increases. The e3 (2.146 eV), e4 (2.579 eV), and e5 (2.833 eV) maxima determined from experimental data are caused by the electronic transitions L3(V1)–L1(C1), L3(V2)–L1(C1), and L3(V3)–L1(C1), respectively. Consequently, the valence band splitting in the L point of the Brillouin zone caused by the spin–orbital interaction equals DSO ¼0.433 eV, and that caused by the crystal field is equal to DCR ¼0.254 eV. The value of valence band splitting due to spin–orbital interaction DSO is higher as compared to the magnitude of the crystal field splitting DCR in the L point as well as in the G point of the Brillouin zone. The experimentally revealed energetic interval e7 (4039 eV) is caused by the transitions X5(V1)–X1(C1), and the energetic interval e8 (4.379 eV) is due to the transitions X5(V2)–X1(C1). The energetic distance between the bands X5(V1) and X5(V2) equals 0.340 eV. These states are split due to spin–orbital interaction. The energetic intervals e9 (5.118 eV) are caused by the electronic transitions X5(V1)–X3(C2), and e10 (5.460 eV) are due to electronic transitions X5(V2)–X3(C2). In this case, the X5(V1)–X5(V2) splitting equals 0.342 eV. Therefore, this splitting value corresponds to the splitting value of the same bands determined from the difference of transitions e7 e8 (0.340 eV). Consequently, the energetic distance between the bands X1(C1) and X3(C2) equals 1.079 eV. The higher energetic transitions e11, e12, e13 and e14 occur most probably in the center of Brillouin zone and are caused by the transitions G15(V1)–G25(C1), G15(V2)–G25(C1), G15(V3)–G25(C1) and G15(V2)–G25(C2), respectively. The order of these transitions is difficult to be determined because the number of bands and the splitting value of the G25 state were not theoretically estimated.
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4. Conclusions The investigated spectral dependences of the fundamental absorption at 80 K and 10 K show that the minimum of interband intervals is formed by direct transitions in Zn3P2 crystals. The absorption coefficient and the optical functions n, k, e1, e2, d2e1/dE2 and d2e2/dE2 were calculated by means of Kramers–Kronig relations from experimentally measured reflection spectra in the region of 1–10 eV. The energies of direct electronic transitions were determined and their localization in actual points of the Brillouin zone was carried out according to the theoretical calculations of the energy band structure. The splitting value of the valence bands caused by the crystal field DCR in the high symmetry points of the Brillouin zone G, L and X is lower as compared to that caused by the spin–orbital interaction DSO. The switching effect is observed in bulk Zn3P2 single crystals and in thin Zn3P2 films with a multiplicity 106. The switching mechanism is electrometric. The linear current increase is caused by the injection of charge carriers. Electrical switches, adjustable resistances, and time relays have been manufactured on the basis on Zn3P2 crystals. Time relays with active region based on Zn3P2 crystals work both with continuous and sinusoidal or pulsed current. In contrast to the currently existing switches with adjustable delay, the switch investigated in this work does not need application of an inverse bias for returning into the initial state. The returning into the high-ohmic state is performed by disrupting the circuit. The delay time is determined by the amplitude and frequency of the applied sinusoidal or pulsed voltage, and it is linearly decreasing as the amplitude and frequency increase. Recording and optical data storage devices can be manufactured on the basis of Zn3P2 crystals. References [1] V.B. Lazarev, V.J. Sevcenco, J.H. Grinberg, V.V. Sobolev, Poluprovodnikovye soedineniia grupy AIIBV, Nauka, Moskva, 1978. (in Russian). [2] E.K. Arushanov, Prog. Cryst. Growth Charact. 3 (1980) 211. [3] E.K. Arushavov, Prog. Cryst. Growth Charact. 25 (1992) 131. [4] N.N. Syrbu, Optoelectronic Properties of II–V Compounds, Stiinta, Kishinev, 1983. (in Russian). [5] F.A. Fagen, J. Appl. Phys. 50 (1979) 6505. [6] A. Catalano, J. Cryst. Growth 49 (1980) 181. [7] J.F. Pawlikowski, N. Mirowska, P. Becla, P. Krolicfci, Solid State Electron. 23 (1980) 755. [8] N.C. Wyeth, A. Catalano, J. Appl. Phys. 51 (1980) 2286. [9] A. Catalano, M. Bhushan, Appl. Phys. Lett. 37 (1980) 567. [10] N.N. Syrbu, I.G. Stamov, A.Ju. Kamertcel, Fiz. Tekh. Poluprovodn. 26 (1992) 1191. [11] N.N. Syrbu, Fiz. Tekh. Poluprovodn. 26 (1992) 1069. [12] V.V. Sobolev, N.N. Syrbu, Phys. Status Solidi (B) 64 (1974) 423. [13] N.N. Syrbu, I.G. Stamov, V.I. Morozova, V.K. Kiosev, L.G. Peev, Proceedings of the International Symposium on Physics and Chemistry of II–V Compounds, Magilany, Poland, 1980, p. 237. [14] V.I. Morozova, N.N. Syrbu, I.G. Stamov, Patent SU, 795370, 1980. [15] N.N. Syrbu, V.I. Morozova, I.G. Stamov, Patent SU, 735133, 1980. [16] V.K. Duscenco, S.I. Radautsan, N.N. Syrbu, V.I. Morozova, L.G. Peev, Patent SU, 908201, 1980. [17] S.I. Radautsan, N.N. Syrbu, V.I. Morozova, I.G. Stamov, Patent SU, 730233, 1979. [18] N.N. Syrbu, V.I. Morozova, V.F. Baranov, L.G. Peev, Patent SU, 850342, 1980. [19] N.N. Syrbu, V.I. Morozova, Patent SU, 890886, 1981. [20] N.N. Syrbu, V.I. Morozova, J.G. Peev, M.E. Rusanovscii, Patent SU, 88657, 1981. [21] P.J. Lin-Chung, Phys. Status Solidi (B) 47 (1971) 33. [22] I.V. Kudreavcov, L.V. Tichonov, Izv. Vuz. Fiz. 121 (1971) 93. [23] D.M. Berca, N.N. Syrbu, Poluprovodnicovie pribori i materiali, Stiinta, Chisinau, 1973.
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Energetic band structure of Zn3P2 crystals I.G. Stamov a, N.N. Syrbu b,n, A.V. Dorogan b a b
Tiraspol State Corporative University, Lablocicin Street 5, 2069 Tiraspol, Republic of Moldova Technical University of Moldova, 168 Stefan cel Mare Avenue, 2004 Chisinau, Republic of Moldova
a r t i c l e i n f o
abstract
Article history: Received 16 August 2012 Received in revised form 14 September 2012 Accepted 15 September 2012 Available online 23 September 2012
Optical functions n, k, e1, e2 and d2e2/dE2 have been determined from experimental reflection spectra in the region of 1–10 eV. The revealed electronic transitions are localized in the Brillouin zone. The magnitude of valence band splitting caused by the spin–orbital interaction DSO is lower than the splitting caused by the crystal field DCR in the center of Brillouin zone and L and X points. The switching effects are investigated in Zn3P2 crystals. The characteristics of experimental samples with electric switching, adjustable resistors, and time relays based on Zn3P2 are presented. & 2012 Elsevier B.V. All rights reserved.
Keywords: Semiconductor compound Optical reflection spectra Kramers–Kronig relations Optical constants Band structure Switching effects Adjustable resistors
1. Introduction
2. Experimental method
The Zn3P2 compound that belongs to the AII-BV 2 group is crystallizing into a chalcopyrite structure with I42d–D15 4h spatial group. Information about material properties and crystal structure are presented in papers [1–4]. A lot of research data on elaborating solar energy converters using zinc phosphide have been reported [5–9]. Thin film device structures have been obtained on the basis of this compound [6,8]. Photoelectrical properties of surface barrier layered structures Me–Zn3P2 have been investigated [4,5] and practical recommendations for using these structures as a photorreceiver in near IR range have been given [6,9]. Optical properties of these structures have been studied in the papers [10–13]. Experimental optoelectronic device samples, such as ‘‘time relay’’, adjustable resistors, and memory elements, have been created on the basis of these crystals [14–17]. Results of investigation of switching effects in Zn3P2 crystals and optical spectra in the region of fundamental absorption as well as in the depth of the absorption band are presented in this paper. The contours of reflection spectra have been calculated using Kramers– Kronig relations and the optical functions n, k, e1, e2 and d2e2/dE2 in the region 1–10 eV have been determined. The revealed particularities are ascribed to electronic transitions in the frame of theoretical calculations of the energy band structure of these crystals.
Zn3P2 crystals grown in ampoules using the gas transportation method represent bulk pyramids with mirror surfaces of 8 mm 8 mm. If needed, the samples could be polished using mechanical and chemical methods. Reflection spectra in the region of fundamental absorption have been measured using a MDR-2 spectrometer and the optical spectra in the depth of absorption band were investigated using a SPECORD-M40. For low-temperature measurements the samples were mounted on the cold station of a LTS-22 C 330 optical cryogenic system.
n
Corresponding author. Tel.: þ373 222 37508. E-mail address: [email protected] (N.N. Syrbu).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.09.029
3. Experimental data and discussions 3.1. Optical properties of Zn3P2 crystals and Me–Zn3P2–Me structures Fundamental absorption of Zn3P2 single crystals in the region of 1.3–1.6 eV is changing in the range of absorption coefficients K¼ 103–105 cm 1. The measurements, carried out in the region of weak absorption have not revealed a sloping step region caused by direct transitions. Therefore, it was suggested [4,10–13] that the minimum of interband interval is caused by direct transitions. The energy value of the beginning of fundamental absorption is 1.30 eV at 296 K temperature and 1.32 eV at 77 K. The temperature coefficient of the absorption edge shifting equals 10 4 eV/K [1,4]. The change of absorption coefficient of Zn3P2 single crystals
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with different thicknesses measured at room temperature is shown in Fig. 1. The absorption of Zn3P2 polycrystalline thin films has been measured in the high energy region of K (103–105 cm 1) (Fig. 1, curve a). A pronounced interference pattern is revealed in films with thicknesses of 0.1–3 mm, which does not allow obtaining a thin absorption structure in this region. The interference pattern is not present in films with thicknesses thicker than 4 mm. This allows to measure the absorption coefficient up to 3 105 cm 1 (curve a). The fundamental absorption of single crystal samples and thin films are satisfactory correlating. Temperature decrease leads to the shift of fundamental absorption towards high energy regions (Fig. 1, curve c). The E1 (1.510 eV) line is evident at 80 K (curve b), which is better resolved near 1.550 eV at 10 K. An absorption line at 1.45 eV is revealed in the long wavelength part of the E1 maximum, which is resolved as a doublet (1.45 eV, 1.47 eV) in wavelength modulated spectra (DT/Dl). The line is likely caused by the phosphor vacancy in Zn3P2 crystals. It was observed that the line’s intensity weakly increased with annealing of Zn3P2 crystals in vacuum. The investigations of fundamental absorption of crystals with different thicknesses, beginning with d ¼1 mm up to 2 mm at 10 K and even at T¼2 K temperatures, have not reveal characteristic absorption lines due to indirect transitions. The analysis of results shows that indirect transitions are not present in Zn3P2 crystals. The absorption edge is formed by direct transitions. The results of investigations of the interband absorption edge in this paper are correlating in those previously published [4,10–13]. The dependence K(:o) is strictly exponential and is described by the Urbach relations in the interval of K ¼1 104 cm 1. The temperature coefficient of the absorption edge shifting equals 10 4 eV/K. E2 (1.710 eV) and E3 (1.753 eV) maxima have been revealed in the high energy region of the wavelength modulated spectra DT/Dl at 80 K, which are caused by direct transitions in the G point from valence bands V2 and V3 to the C1 band (Table 1). E1 and E2 maxima are also evident in spectral dependencies of photoconduction Jf at 80 K, practically for the same energies as for DT/Dl spectra (Fig. 1). The switching effect has been revealed while studying spectral and electrical characteristics of Me–Zn3P2–Me structures, i.e. the transition of the crystal state from high-ohmic into a stable low-ohmic state [14,15]. This is observed when a voltage equal to Up is applied to crystal contacts. The switching effect was observed for a large number of materials into a wide range of specific resistance values [16,17]. When a voltage higher than Up is applied to the sample a transition into a low-ohmic state occurs, in which the delay time tz and the switching time tp (the duration of the sharp current increase) can be distinguished. The inverse transition into highohmic state is occurring during recovery. Fig. 2 shows the S-type
Fig. 1. Fundamental absorption of Zn3P2 thin films measured at 80 K (a) and of Zn3P2 single crystals measured at 80 K (b) and 10 K (c) as well as the spectral distribution of DT/Dl and the photoconduction Jf measured at 80 K.
Table 1 The energy of electronic transitions revealed from calculations of reflection spectra by means of Kramers–Kronig relations for Zn3P2 crystals. Indication
R (eV)
e2 (eV)
d2e2/dE2 (eV)
Transitions
e1, E1 E2 e2, E3 e3 e4 e5 e6 e6* e7 e8 e9 e10 e11 e12 e13 e14
1.462, 1.510 1.710 1.753 2.088 2.531 2.743 3.354
1.469 1.746
1.482 1.780
2.099 2.569
2.146 2.579 2.833 3.378 3.535 4.039 4.379 5.118 5.462 6.97 7.59 8.74 9.20
!15(V1)–!1(C1) !15(V2)–!1(C1) !15(V3)–!1(C1) L3(V1)–L1(C1) L3(V2)–L1(C1) L3(V3)–L1(C1)
4.079 4.336 5.089 5.460 6.86 7.54 8.67 9.14
3.345 3.486 4.027 4.265 5.010 5.465 6.86 7.54 8.69 9.14
X5(V1)–X1(C1) X5(V2)–X1(C1) X5(V1)–X3(C2) X5(V2)–X3(C2) !15(V1)–!25(C1) !15(V2)–!25(C1) !15(V3)–!25(C1) !15(V2)–!25(C2), !15(V1)–!25(C2)
Fig. 2. I–V characteristic of a Me–Zn3P2–Me structure with a sharp region of negative differential resistance (NDR) (A), and smooth differential resistance (SDR) (B). Numbers show the temperature at the surface of the sample.
I–V characteristics of Me–Zn3P2–Me structures with a sharp region of negative differential resistance (NDR) and a smooth one for SDR (B). Numbers show the temperature on the surface of the sample. The I–V parameters can be varied by selecting the outer circuit parameters (bias voltage, serial resistance). The S-type I–V characteristic is reversible in the region of negative differential resistance in each point. It is possible to pass multiple times all the I–V regions in any direction by changing the bias voltage and serial resistance. The hysteresis phenomenon was not observed. The temperature was increasing on the surface of the sample for Me–Zn3P2–Me structures with a smooth change of SDR (Fig. 2B). A thermocouple cooper–constantan was installed on the surface directly under the spring contact and an automatic recording of surface temperature was made. At the same time, the change of current value as a function of applied voltage J¼f(U) was recorded in a continuous regime. Fig. 2B shows the I–V characteristic for Me–Zn3P2–Me structure with indication of the surface temperature under the contact in various points of the curve. The increase of surface temperature was starting at the same time as the current increased in the NDR region. The temperature increased, practically, up to 150 K in short time.
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Fig. 2A shows the I–V characteristics that do not possess a stable region of negative resistance. A voltage breakdown occurred at a value of Up ¼7 V and the sample abruptly switched into a low-ohmic state. The transfer into low-ohmic state can also occur in a smooth regime (Fig. 2B). The S-type I–V characteristic with a smooth change of NDR can be transferred into a characteristic with a sharp voltage breakdown and a current increase through the structure. This was done by connecting to the Me–Zn3P2–Me structure a lower-ohmic serial resistance. A low load resistance Rtherm (RB 4Rtherm 4R) was connected to the sample when the transfer into low-ohmic state was investigated in order to prevent an irreversible thermal breakdown (RB, RH are the resistances of low- and high-ohmic states, respectively). The I–V characteristics of Me–Zn3P2–Me structures were symmetric relatively to the polarity of the applied voltage and were not dependent on the type of the contact material [15]. The electrode geometry does not influence the I–V characteristics. The replacement of fused contacts by spring contacts does not change the I–V characteristics [14,15]. These observations indicate on a bulk nature of the switching effect in Zn3P2 crystals. The sample resistance in the low-ohmic state was by 3–5 orders of magnitude lower as compared to the high-ohmic state. A linear increase of current with voltage was observed after the sample switching into a low-ohmic state. The sample was in a low-ohmic state if the value of the current through the sample was higher than 10 2 A. The high-ohmic state was restored at a current lower than this value. The conductivity in low-ohmic state was not dependent on the contact surface, which was an evidence of current pinching in a switched on state. Fig. 3A shows the switch resistance dependence on the dissipated power (a) and on the crystal temperature (b). Curve B in Fig. 3 shows the dependence of the switch resistance on the current through the sample. The switching character of zinc phosphide is essentially determined by the value of applied voltage. The delay time and the rate of the current increase were changing in dependence on the value of the applied voltage. Fig. 3 shows the change of the current that flows through Me–Zn3P2–Me structure in time for a crystal with d ¼640 mm thickness at various bias voltages. The delay time decreases with the voltage increase, while the rate of the current change increases. The delay time was changing inverse proportionally to the bias voltage. The delay time tends to zero and the dependence tz ¼f(U) undergoes almost an abrupt change in the region of high voltages (Fig. 3, curve 12, U¼105 V). Such structure is functioning as time relay [16–18]. An evident current increase and switching delay time decrease is observed as the voltage increases. At the same time, the current increase front is sharply changing and the rate of increasing is exponentially depending on the bias voltage. The switching voltage of zinc
Fig. 3. (A) Switch resistance dependence on the dissipated power (a) and temperature (b). (B) Switch resistance dependence on the current.
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phosphide single crystals increases proportionally to the sample thickness, while the current through the crystal during switching is practically unchanged and equal to 10 4 A at 300 K. The switching effect was observed both in case of continuous current and of alternative sinusoidal voltage of a 50 Hz frequency. The sample switching voltage was decreasing when a sinusoidal voltage was applied to the sample. This fact is in accordance with the final recovery time of high-ohmic state. The all other switching peculiarities were maintained. The current does not change in time at low shifting voltage, i.e. UoUp. The switching parameters can be controlled in a wide time interval by changing the resistance value, serially connected with the sample in a circuit, by changing the crystal thickness or the voltage value. The delay time and the current increasing time are decreased if the current is limited, although the switching time is decreasing. The Me–Zn3P2–Me structure is in a low-ohmic state if a current of about 10 5 10 4 A is flowing through the sample. The crystal turns back into a high-ohmic state after the voltage is switched off. As it was mentioned above, temperature influences the S-type I–V characteristics of Zn3P2 single crystals. As the temperature increases the switching occurs at lower voltages. The S-shape of L–V characteristics disappears at high temperatures and the samples possess a positive differential resistance in all the investigated voltage range. The dependence of the switching voltage on the inversed temperature in a half logarithmic scale represents a straight line. After switching, the I–V characteristic possesses a linear character and the sample resistance does not depend on temperature and light irradiation in a low-ohmic state. At the same time, crystals with electrical memory properties were revealed [18–20]. The sample can remain in low-ohmic switched state (memory state) for a long period of time without an applied bias voltage. The transfer into high-ohmic state for these samples is done by heating at the temperature 400 K. The influence of integral light irradiation on switching is similar to the change of sample temperature. The I–V characteristic was shifting towards low voltages part and the threshold voltage was decreasing as the light intensity increased, and the S-shape of the I–V characteristic disappeared at high intensities ( 10 lx). Two processes can be revealed in the case of high-state recovery: recovery of high resistance and recovery of the threshold voltage. The recovery of high resistance occurs practically instantly after the bias voltage is switched off for samples without electrical memory. However, if the bias voltage Up is switched on again after a short period of time 1 s, then the sample immediately occurs in a low-ohmic state without switching, i.e. switching occurs at lower threshold voltages Up0 . The recovery time of threshold voltage increases if the sample is maintained in the low-ohmic state for a longer period of time Fig. 4.
Fig. 4. Switching time into low-ohmic state dependence on bias voltage U¼ 50 V(1), 55 V(2), 60 V(3), 65 V(4), 70 V(5), 75 V(6), 80 V(7), 85 V(8), 90 V(9), 95 V(10), 100 V(11), 105 V(12).
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3.2. Optical properties of Zn3P2 crystals in the depth of absorption line Reflection spectra were measured in the depth of fundamental absorption band in the energy interval of 1–6 eV at 80 K, as well as in the interval of 6–10 eV at 300 K (Fig. 5). The absorption coefficient and optical functions n, k, e1, e2, d2e1/dE2 and d2e2/dE2 were calculated from reflection spectra by means of Kramers– Kronig relations (Figs. 6 and 7). The maximum e1 is observed at 80 K in the fundamental absorption region of reflection spectra, which practically coincides with E1 peak in DT/Dl spectra (Fig. 1). e2–e14 are revealed in the fundamental reflection spectra (E 1.5– 10 eV). These maxima are also evident in optical functions n, k, e1, e2 and d2e2/dE2 (Figs. 5 and 6). The peculiarities in reflection spectra and optical functions are due to direct electronic transitions in special points of the Brillouin zone. The revealed values of electronic transitions in experimental reflection spectra and in calculations of optical functions have been interpreted in the frame of theoretical calculations of Zn3P2 crystals in the points of high symmetry of Brillouin zone [21]. The Brillouin zone represents a rectangular prism with 14 special points [22]. Theoretical calculations of dispersion relations in actual points of the Brillouin zone as well as calculations of the selection rules for Zn3P2 have been previously reported [23]. The actual points of Brillouin zone (points of zero energy slope), the dispersion relations, and the selection rules in these points have been determined. The zero energy slopes in !, Z, M, R, X, A points is realized in two directions from three Kx, Ky, Kz available. The zero slope is realized in all the three directions in the !, M, R points without taking into account the spin–orbital interaction. The zero energy slope is realized in all the directions in the ! point taking into account the spin. The analysis of dispersion relations shows that they have a most common view in G, V, U, S, D points. According to the selection rules, the transitions in R, X, Y, T, S and S points are not polarized. The selection rules in the center of the Brillouin zone prove that the transitions possess different energetic intervals for
Fig. 6. Spectral dependence of optical functions e1, e2 and d2e2/dE2.
Fig. 7. Energy band structure of Zn3P2 crystals [21].
Fig. 5. Spectral dependence of reflection coefficient R, absorption coefficient K, phase of the reflected beam F and optical functions n, k.
each polarization. In the E:c polarization at K ¼0 the transitions between the !1,2,3,4-!4,3,2,1 states are allowed, while transitions between the !1,2,3,4-!10,9,10,9 states are allowed in E?c polarization [1,4,22]. In the R point, the transitions between the R1,2-R1,2 states are allowed by the selection rules in E:c polarization, while transitions between the R1,2-R1 þR2 states are allowed in E?c polarization. In the X(L) point of the Brillouin zone, the transitions between the X(L)1,2-X(L)1,2 states are allowed in E:c polarization, while transitions between the X(L)1,2-X(L)1 þX(L)2 states are allowed in E?c polarization [22]. The theoretical calculations of the energy band structure using the pseudo-potential method for Zn3P2 crystals have been carried out by Lin-Chung in a wide energy range and in different points of the Brillouin zone [21]. The crystal lattice of Zn3P2 and Cd3P2 has been considered in theoretical calculations as an analog of the fluorite lattice. The Zn and Cd atoms are introduced as vacancies periodically arranged in the
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crystal lattice. The Zn3P2 band structure calculated by Lin-Chung along several symmetry directions is presented in Fig. 7. The maximum of the valence band and the minimum of the conduction band are situated in the center of the Brillouin zone, in the ! point. The spin–orbital interaction and other relativistic effects have not been taken into account in calculations. The maximum of the valence band in the ! point is triple degenerated. The calculated value of the bandgap is Eg ¼1.886 eV. Taking into account the potential of the crystal field and the spin–orbital interaction in real crystals will lead to splitting of the valence bands. The maximum of the valence band !15 will split into three bands due to the removal of degeneracy. The maxima E1 at 1.510 eV, E2 at 1.710 eV, and E3 at 1.753 eV have been revealed in the region of the bandgap in DT/Dl spectra (Fig. 1, Table 1). The E1–E2 maxima are separated by each other by an energetic interval of 200 meV, while the distance between the E1 – E3 maxima is of 43 meV. The value of spin–orbital slitting of the valence band in Zn3P2 crystals was estimated in the approximation of covalent bonds it being equal to Dso ¼0.06 eV, while estimations in the approximation of singly and doubly ionized Zn ions give the value of Dso ¼0.15 and 0.30 eV, respectively. The splitting due to the crystal field should be of the order of 0.01 eV by analogy with known anisotropic crystals. Taking into account these data, we suppose that E1, E2, and E3 maxima are due to transitions G15(V1)–G1(C1), G15(V2)–G1(C1), and G15(V3)–G1(C1), respectively. Therefore, one can conclude from our experimental data that the valence band splitting caused by the crystal field V1 V2(V3) equals 43 meV, while that caused by the spin–orbital interaction is equal to 200–243 meV. The next energetic intervals are situated in the L point of Brillouin zone as the energy increases. The e3 (2.146 eV), e4 (2.579 eV), and e5 (2.833 eV) maxima determined from experimental data are caused by the electronic transitions L3(V1)–L1(C1), L3(V2)–L1(C1), and L3(V3)–L1(C1), respectively. Consequently, the valence band splitting in the L point of the Brillouin zone caused by the spin–orbital interaction equals DSO ¼0.433 eV, and that caused by the crystal field is equal to DCR ¼0.254 eV. The value of valence band splitting due to spin–orbital interaction DSO is higher as compared to the magnitude of the crystal field splitting DCR in the L point as well as in the G point of the Brillouin zone. The experimentally revealed energetic interval e7 (4039 eV) is caused by the transitions X5(V1)–X1(C1), and the energetic interval e8 (4.379 eV) is due to the transitions X5(V2)–X1(C1). The energetic distance between the bands X5(V1) and X5(V2) equals 0.340 eV. These states are split due to spin–orbital interaction. The energetic intervals e9 (5.118 eV) are caused by the electronic transitions X5(V1)–X3(C2), and e10 (5.460 eV) are due to electronic transitions X5(V2)–X3(C2). In this case, the X5(V1)–X5(V2) splitting equals 0.342 eV. Therefore, this splitting value corresponds to the splitting value of the same bands determined from the difference of transitions e7 e8 (0.340 eV). Consequently, the energetic distance between the bands X1(C1) and X3(C2) equals 1.079 eV. The higher energetic transitions e11, e12, e13 and e14 occur most probably in the center of Brillouin zone and are caused by the transitions G15(V1)–G25(C1), G15(V2)–G25(C1), G15(V3)–G25(C1) and G15(V2)–G25(C2), respectively. The order of these transitions is difficult to be determined because the number of bands and the splitting value of the G25 state were not theoretically estimated.
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4. Conclusions The investigated spectral dependences of the fundamental absorption at 80 K and 10 K show that the minimum of interband intervals is formed by direct transitions in Zn3P2 crystals. The absorption coefficient and the optical functions n, k, e1, e2, d2e1/dE2 and d2e2/dE2 were calculated by means of Kramers–Kronig relations from experimentally measured reflection spectra in the region of 1–10 eV. The energies of direct electronic transitions were determined and their localization in actual points of the Brillouin zone was carried out according to the theoretical calculations of the energy band structure. The splitting value of the valence bands caused by the crystal field DCR in the high symmetry points of the Brillouin zone G, L and X is lower as compared to that caused by the spin–orbital interaction DSO. The switching effect is observed in bulk Zn3P2 single crystals and in thin Zn3P2 films with a multiplicity 106. The switching mechanism is electrometric. The linear current increase is caused by the injection of charge carriers. Electrical switches, adjustable resistances, and time relays have been manufactured on the basis on Zn3P2 crystals. Time relays with active region based on Zn3P2 crystals work both with continuous and sinusoidal or pulsed current. In contrast to the currently existing switches with adjustable delay, the switch investigated in this work does not need application of an inverse bias for returning into the initial state. The returning into the high-ohmic state is performed by disrupting the circuit. The delay time is determined by the amplitude and frequency of the applied sinusoidal or pulsed voltage, and it is linearly decreasing as the amplitude and frequency increase. Recording and optical data storage devices can be manufactured on the basis of Zn3P2 crystals. References [1] V.B. Lazarev, V.J. Sevcenco, J.H. Grinberg, V.V. Sobolev, Poluprovodnikovye soedineniia grupy AIIBV, Nauka, Moskva, 1978. (in Russian). [2] E.K. Arushanov, Prog. Cryst. Growth Charact. 3 (1980) 211. [3] E.K. Arushavov, Prog. Cryst. Growth Charact. 25 (1992) 131. [4] N.N. Syrbu, Optoelectronic Properties of II–V Compounds, Stiinta, Kishinev, 1983. (in Russian). [5] F.A. Fagen, J. Appl. Phys. 50 (1979) 6505. [6] A. Catalano, J. Cryst. Growth 49 (1980) 181. [7] J.F. Pawlikowski, N. Mirowska, P. Becla, P. Krolicfci, Solid State Electron. 23 (1980) 755. [8] N.C. Wyeth, A. Catalano, J. Appl. Phys. 51 (1980) 2286. [9] A. Catalano, M. Bhushan, Appl. Phys. Lett. 37 (1980) 567. [10] N.N. Syrbu, I.G. Stamov, A.Ju. Kamertcel, Fiz. Tekh. Poluprovodn. 26 (1992) 1191. [11] N.N. Syrbu, Fiz. Tekh. Poluprovodn. 26 (1992) 1069. [12] V.V. Sobolev, N.N. Syrbu, Phys. Status Solidi (B) 64 (1974) 423. [13] N.N. Syrbu, I.G. Stamov, V.I. Morozova, V.K. Kiosev, L.G. Peev, Proceedings of the International Symposium on Physics and Chemistry of II–V Compounds, Magilany, Poland, 1980, p. 237. [14] V.I. Morozova, N.N. Syrbu, I.G. Stamov, Patent SU, 795370, 1980. [15] N.N. Syrbu, V.I. Morozova, I.G. Stamov, Patent SU, 735133, 1980. [16] V.K. Duscenco, S.I. Radautsan, N.N. Syrbu, V.I. Morozova, L.G. Peev, Patent SU, 908201, 1980. [17] S.I. Radautsan, N.N. Syrbu, V.I. Morozova, I.G. Stamov, Patent SU, 730233, 1979. [18] N.N. Syrbu, V.I. Morozova, V.F. Baranov, L.G. Peev, Patent SU, 850342, 1980. [19] N.N. Syrbu, V.I. Morozova, Patent SU, 890886, 1981. [20] N.N. Syrbu, V.I. Morozova, J.G. Peev, M.E. Rusanovscii, Patent SU, 88657, 1981. [21] P.J. Lin-Chung, Phys. Status Solidi (B) 47 (1971) 33. [22] I.V. Kudreavcov, L.V. Tichonov, Izv. Vuz. Fiz. 121 (1971) 93. [23] D.M. Berca, N.N. Syrbu, Poluprovodnicovie pribori i materiali, Stiinta, Chisinau, 1973.