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Far-infrared reflectivity of PbTe films on NaCl substrates
Solid State Communications, Vol. 18, pp. 773—776, 1976.
Pergamon Press.
Printed in Great Britain
FAR-INFRARED REFLECTIVITY OF PbTe FILMS ON NaCl SUBSTRATES H. Burkhard* and G. Bauer I. Physikalisches Institut der RWTH Aachen, Aachen, Germany and A. Lopez-Otero Institut für Physik, Johannes Kepler University, Linz, Austria (Received 2 September 1975 by M Cardona) In the wavenumber region 3—400 cm~reflectivity measurements of high quality single crystal n-PbTe epitaxial films on NaC1 substrates at T = 5, 77 and 300 K have been performed. From the analysis of the data a detailed information on the variation of the optical constants and particularly of TO phonon softening with decreasing lattice temperature ob3. In addition the is fretained for samples with n 0.3—3.0 x 10i7cm quency dependence of the carrier collision time was investigated. THE COMPOUND semiconductor PbTe has attracted considerable interest during recent years due to its outstanding dielectric properties.14 Neutron diffraction,4 far-infrared (FIR) reflectivity5’6 and capacitance2 measurements have given evidence for a softening of the transverse optic (TO) mode with decreasing lattice ternperature and thus for a strong temperature dependence of the static dielectric constant C~.Whereas in another IV—VI compound, in GeTe a ferroelectric transition from the NaC1 to the rhomboedral structure really occurs,7 PbTe retains its cubic structure even at very low temperatures and thus is paraelectric. In Pb 1_~Sn~Te, a structural transformation should occur at finite temperatures for Sn concentrations corresponding to x > 0.2.2.8 An explanation of the TO-phonon softening was recently given in termsthe of interband electron— of 0 However, softening behaviour phonon coupling.’ the TO branch will depend critically on the carrier concentration, since high carrier densities will essentially stabilize the cubic phase.9 All experiments concerning the softening of the TO mode reported so far however were performed with carrier concentrations in excess of 3 x 1017 cm3. Due to recent progress in PbTe crystal growing by a “hot wall” epitaxial technique,” now n-PbTe films with carrier concentrations as low as 4 x lOi6cm_3 are available, It is the purpose of this letter to report FIR measurements on PbTe films grown on NaCl substrates with carrier concentrations ranging from n = 0.38 to n = 2.8 x l0i7cm_3 and film thicknesses of 1—27 pm. Reflectivity measurements were performed at T = 5, 77 _____________
*
Present address: MPI für Festkorperforschung, Hochfeldmagnetlabor, Grenoble.
300 K using a Michelson-type and a Lamellar-type Fourier transform spectrophotometer in the wavenumber region from 3—400 cm~.In this spectral region detailed information on the phonons as well as on the plasma edge and. plasmon—phonon interaction can be obtained. Beside the low carrier concentration, reflectivity measurements with PbTe films offer an additional advantage. Bulk semiconductors having a high dielectric constant and a high carrier concentration exhibit a more or less total reflectivity. Thus nearly all characteristic properties like phonons, plasmon—phonon interaction and carrier damping are hidden, and one is usually faced with the problem of detecting changes of the reflectivity of a few per cent. Since the interesting spectral region for these measurements lies moreover in the FIR region it is difficult to perform measurements films, with high photometric accuracy. Using semiconductor multiple reflection and interference effects affect the measured reflectivity. Due to these effects, small dips in the reflectivity can be enhanced and by choosing the proper film thickness and carrier concentration a much more reliable determination of the optical constants and their frequency dependence is achieved~compared to bulk reflectivity measurements. Since bulk reflectivity measurements on n-PbTe have until now only been performed with a material having a carrier concentration n = 3 x l0’7cm3, yielding a TO phonon frequency of 18 cm~at helium temperatures, we investigated 11 PbTe films with n covering an order of magnitude (n = 0.38— 2.8 x l0’7cm3). In order to analyze the reflectivity R of an absorbing film on an absorbing substrate, R has been calculated taking into account multiple reflections within the film and interference effects for normal incidence. Using a 773
774
FAR-INFRARED REFLECTIVITY OF PbTe FILMS ON NaCl SUBSTRATES
t
____
02
_______
___
0 _________
~
~,— ~-32 32
.
_______
100_________
(c~).
02
1 Ir cm’ = 3 cm400 300
200
Vol. 18, No. 7
Fig. 1. Reflectivity of PbTe epitaxial film on NaC1 substrate vs wavenumber at T= 300 K. Dots: experimental data. Full line: calculated with equations (1) and (2). Parameters of the fit are given in the figure.
0
50
00
50
200
260
300cn~1 350
Fig. 2. Reflectivity vs wavenumber of ad = 27.0 pm thick PbTe film on NaCl at T = 300 K. Dots: experimental data. Full line: calculated with parameters: v = 520 cm~,e~= 34.5, & = 350, ~TO = 32, F = 3 cm’~, damping parameter v,. as shown in the inset (full line); dashed line: parameters as above but damping parameter
complex refractive index ñ 1 = n1 i/c1 (1 = 1 3) of all three media (vacuum or helium gas, film, substrate) involved the reflectivity is given by —
R123
=
. . .
{R~2~ +R23e~+ 2(Re r12 Re r23
Im r12 Im r23) cos a
+ 2(Re r12 Im r23
+
Re r23 Im r12) sin a} —1
(1)
wherere,, = (nj —n1)/(n, + ni), a = 4irnvd, and 13 = 4irkvd, and Re( ), and Im( ) denote real and2imaginary parts, re= R spectively d is the film thickness (1r111 11). Since the optical constants of the substrate NaC1 are well known in the interesting wavenumber region at 5 as well as 300 K we have used these values and have assumed for the films a dispersion oscillator model including contributions from the phonons and the free carriers: 2 ~-
~
— —
~oo
+
w~.0~WTO ~2
2 —
iwf
—
w(w
+ iWr)
—
~
(.
‘
~~1•
•
08
_____
.
I r 5K
57A5
• —~
——
I 0
-
2 2crr~ 5 cm’ io cm’
____________________
10
20
Cfl~’
30
______
Fig. 3. Reflectivity of a PbTe film on NaCl at T = 5 K. 2~ PbTe full, dashed film thickness: and dash 4.25 dotted pm.lines: Dots:calculated experimental with the data,
‘~ ~‘
where c~.idenotes the2/m*eo frequency, WTO frequency, the TO phonon the plasma F the frequency, w~ = ne phonon damping and ~ the free carrier damping and L~e= e 0 e0. o.~was determined from the d.c. Hall data and the known values of the effective mass. d was measured during and after the growth of the films with an accuracy of 5%. In order to fit the measured reflectivity data we have varied ~TO~ F and w~.. Figure 1 shows the reflectivity as a function of wavenumber for a 1.3 pm thick PbTe film on NaC1 at T = 300 K together with the results of the calculation according to equations (I) and (2). The parameters used for PbTe are indicated in this figure. The phonon damping was taken to be constant whereas the carrier damping parameters varied and turned out to be frequency —
1.0
R
—
—
______________________________
I
+ Im r12 Im r23) cos a + 2(Re r12 Im r23 3+ R Re r23 Im r12) sin a}- {e~ 12R23e~ + 2(Re Ti2 Re r23
v1. as shown in the inset (dashed line).
oscillator fit. Parameters: v~= 580 cm~,~ = 33, ~e = 1350, ~TO = 18.2 cm’, F = 1 cm~. dependent for an optimum fit. In contrast to the situation found in bulk reflectivity, the film-substrate reflectivity in the region above the plasma edge is very sensitive to changes in the damping parameter WT• Thus we obtain particularly useful information on the frequency dependence of the electron collision time (l/Wr) over a wide spectral region. Also in the region near the TO phonon frequency, where the bulk reflectivity scarcely deviates from 1, the film-substrate reflectivity still shows easily observable structures. The parameters used in the fit-program thus can be determined very accurately. Figure 2 shows the reflectivity of a rather thick PbTe sample (d = 27 pm) which exhibits
Vol. 18, No. 7
FAR-INFRARED REFLECTIVITY OF PbTe FILMS ON NaC1 SUBSTRATES
775
Table 1. Parameter values ofoscillator fit T coo
LXe 1~TO(cm~)
F (cm’)
300K
5K
34.5 350±30 32 3—lO(d < 1 pm) 60—300
33 1300±50 18 2(d < 1pm) 5(d < 1 pm)
3(d > 2pm)
pronounced interference oscillations in the region above the plasma edge. Since the amplitude of these oscillations is very sensitive to the damping parameter, thick samples (d> 10pm) are well suited to determine wr(w) as well as the refractive index (position of the extrema) whereas thin samples are better suited for a determination of the TO phonon modes. The inset of Fig. 2 shows the variation of the carrier damping parameter as a function of frequency. Its behaviour cannot be understood in terms of the photon—plasmon-ionized impurity (defect) process suggested recently by Mycielski’3 for PbSe having however higher carrier concentrations. Figure 3 shows the reflectivity of a PbTe film (d = 4.25 pm) in the region 3—30 cm~at T = 5 K. Again due to interference effects the reflectivity shows an enhanced structure associated with the phonon. Due to the occurence of steep minima in the film-substrate
l(d > 2pm) 2(d > 2pm)
In Table 1 we have summarized the results obtained from the fitting of the reflectivity curves for 5 and 300 K. As was expected, samples with carrier thicknesses below 2pm show somewhat higher carrier as well as phonon damping parameters. It turned out that the TO mode frequency does not depend on n in the carrier concentration range investigated to within 1.5 cm~.The parameters characterizing the PbTe films are summarized in Table 1. We have demonstrated that reflectivity measurements of thin films on absorbing substrates are a powerful tool for the investigation of nearly total reflecting semiconductors. The TO phonon frequency in PbTe softens by decreasing the temperature from 300 to 5 K and obeys a Curie law. The frequency dependence of the carrier collision time was given for a wide range. A more detailed description of this work including also an investigation of PbTe films on BaF 2 substrates is in progress.
reflectivity the position of the TO mode can be determined easily to be 18.2 cm~from the fit using equations (1) and (2). In addition the influence of the carrier damping on the reflectivity spectra is shown. At 77 1. K Acknowledgements We thank and P. Grosse and H.and Heinrich for helpful discussions R. Siedling using the same sample we determined ~TO = 23 cm The temperature dependence of 1~TOthus obeys a Curie- R. Kohnen for technical assistance. law ~2 —
REFERENCES 1. 2.
DALVENR.,InfraredPhys. 9,141(1969). BATE R.T., CARTER D.L. & WROBEL J.S., Proc. mt. Conf Phys. Semicond. p.7!. Cambridge, MA 1970; Phys. Rev. Lett. 25, 159 (1970).
3.
PAWLEY G.S., COCHRAN W., COWLEY R.A. & DOLLING G.,Phys. Rev. Lett. 17, 759 (1966).
4. 5.
COCHRAN W., COWLEY R.A., DOLLING G., ELCOMBE M.M.,Proc. R. Soc. (London) 293, 433 (1966). KINCH M.A. & BUSS D.D., Solid State Commun. 11, 319 (1972).
6.
BUSS D.D. & KINCH M.A.,J. Nonmetals 1, 111(1973).
7. 8.
GOLDAK J., BARRETT C.S., INNES D. & YONDELIS W., J. Chem. Phys. 44,3323 (1966). DOLLING G. & BUYERS W.J.L., J. Nonmetals 1, 159 (1973).
9.
LUCOVSKY G., MARTIN R.P. & BURSTEIN E.,J. Nonmetals 1, 137 (1973).
10. 11.
KAWAMURA H., KATAYAMA S., TAKANO S. & HOTTA S., Solid State Commun. 14,259(1974); KAWAMURA H., TAKANO S., HOTTA S., NISHI S., KATO K., KOBAYASHI K.L.I. & KOMATSUBARA K.F.,Proc. mt. Conf Phys. Semicond. p.551. Stuttgart (1974). LOPEZ-OTERO A., App!. Phys. Lett. 26, 470 (1975); LOPEZ-OTERO A. & HAAS L.D., Thin Solid Films 23, 1(1974).
776
FAR-INFRARED REFLECTIVITY OF PbTe FILMS ON NaC1 SUBSTRATES
Vol. 18, No. 7
12.
BAUER G., BURKHARD H. & LOPEZ.OTERO A. VerhandlDPG(Vm) 10, 391 (1975); Using a similar principle Pb0 82Sn0 18Te—Pb08Sn02Te film-substrate structures were investigated in the 50—250 cm’ region at T = 300 K; TENNANT W.E. & CAPE J.A., App!. Phys. Lett. 26, 694 (1975).
13.
MYCIELSKI J.,Proc. IntConf Phys. Semicond. p.1137. Stuttgart (1974).
Pergamon Press.
Printed in Great Britain
FAR-INFRARED REFLECTIVITY OF PbTe FILMS ON NaCl SUBSTRATES H. Burkhard* and G. Bauer I. Physikalisches Institut der RWTH Aachen, Aachen, Germany and A. Lopez-Otero Institut für Physik, Johannes Kepler University, Linz, Austria (Received 2 September 1975 by M Cardona) In the wavenumber region 3—400 cm~reflectivity measurements of high quality single crystal n-PbTe epitaxial films on NaC1 substrates at T = 5, 77 and 300 K have been performed. From the analysis of the data a detailed information on the variation of the optical constants and particularly of TO phonon softening with decreasing lattice temperature ob3. In addition the is fretained for samples with n 0.3—3.0 x 10i7cm quency dependence of the carrier collision time was investigated. THE COMPOUND semiconductor PbTe has attracted considerable interest during recent years due to its outstanding dielectric properties.14 Neutron diffraction,4 far-infrared (FIR) reflectivity5’6 and capacitance2 measurements have given evidence for a softening of the transverse optic (TO) mode with decreasing lattice ternperature and thus for a strong temperature dependence of the static dielectric constant C~.Whereas in another IV—VI compound, in GeTe a ferroelectric transition from the NaC1 to the rhomboedral structure really occurs,7 PbTe retains its cubic structure even at very low temperatures and thus is paraelectric. In Pb 1_~Sn~Te, a structural transformation should occur at finite temperatures for Sn concentrations corresponding to x > 0.2.2.8 An explanation of the TO-phonon softening was recently given in termsthe of interband electron— of 0 However, softening behaviour phonon coupling.’ the TO branch will depend critically on the carrier concentration, since high carrier densities will essentially stabilize the cubic phase.9 All experiments concerning the softening of the TO mode reported so far however were performed with carrier concentrations in excess of 3 x 1017 cm3. Due to recent progress in PbTe crystal growing by a “hot wall” epitaxial technique,” now n-PbTe films with carrier concentrations as low as 4 x lOi6cm_3 are available, It is the purpose of this letter to report FIR measurements on PbTe films grown on NaCl substrates with carrier concentrations ranging from n = 0.38 to n = 2.8 x l0i7cm_3 and film thicknesses of 1—27 pm. Reflectivity measurements were performed at T = 5, 77 _____________
*
Present address: MPI für Festkorperforschung, Hochfeldmagnetlabor, Grenoble.
300 K using a Michelson-type and a Lamellar-type Fourier transform spectrophotometer in the wavenumber region from 3—400 cm~.In this spectral region detailed information on the phonons as well as on the plasma edge and. plasmon—phonon interaction can be obtained. Beside the low carrier concentration, reflectivity measurements with PbTe films offer an additional advantage. Bulk semiconductors having a high dielectric constant and a high carrier concentration exhibit a more or less total reflectivity. Thus nearly all characteristic properties like phonons, plasmon—phonon interaction and carrier damping are hidden, and one is usually faced with the problem of detecting changes of the reflectivity of a few per cent. Since the interesting spectral region for these measurements lies moreover in the FIR region it is difficult to perform measurements films, with high photometric accuracy. Using semiconductor multiple reflection and interference effects affect the measured reflectivity. Due to these effects, small dips in the reflectivity can be enhanced and by choosing the proper film thickness and carrier concentration a much more reliable determination of the optical constants and their frequency dependence is achieved~compared to bulk reflectivity measurements. Since bulk reflectivity measurements on n-PbTe have until now only been performed with a material having a carrier concentration n = 3 x l0’7cm3, yielding a TO phonon frequency of 18 cm~at helium temperatures, we investigated 11 PbTe films with n covering an order of magnitude (n = 0.38— 2.8 x l0’7cm3). In order to analyze the reflectivity R of an absorbing film on an absorbing substrate, R has been calculated taking into account multiple reflections within the film and interference effects for normal incidence. Using a 773
774
FAR-INFRARED REFLECTIVITY OF PbTe FILMS ON NaCl SUBSTRATES
t
____
02
_______
___
0 _________
~
~,— ~-32 32
.
_______
100_________
(c~).
02
1 Ir cm’ = 3 cm400 300
200
Vol. 18, No. 7
Fig. 1. Reflectivity of PbTe epitaxial film on NaC1 substrate vs wavenumber at T= 300 K. Dots: experimental data. Full line: calculated with equations (1) and (2). Parameters of the fit are given in the figure.
0
50
00
50
200
260
300cn~1 350
Fig. 2. Reflectivity vs wavenumber of ad = 27.0 pm thick PbTe film on NaCl at T = 300 K. Dots: experimental data. Full line: calculated with parameters: v = 520 cm~,e~= 34.5, & = 350, ~TO = 32, F = 3 cm’~, damping parameter v,. as shown in the inset (full line); dashed line: parameters as above but damping parameter
complex refractive index ñ 1 = n1 i/c1 (1 = 1 3) of all three media (vacuum or helium gas, film, substrate) involved the reflectivity is given by —
R123
=
. . .
{R~2~ +R23e~+ 2(Re r12 Re r23
Im r12 Im r23) cos a
+ 2(Re r12 Im r23
+
Re r23 Im r12) sin a} —1
(1)
wherere,, = (nj —n1)/(n, + ni), a = 4irnvd, and 13 = 4irkvd, and Re( ), and Im( ) denote real and2imaginary parts, re= R spectively d is the film thickness (1r111 11). Since the optical constants of the substrate NaC1 are well known in the interesting wavenumber region at 5 as well as 300 K we have used these values and have assumed for the films a dispersion oscillator model including contributions from the phonons and the free carriers: 2 ~-
~
— —
~oo
+
w~.0~WTO ~2
2 —
iwf
—
w(w
+ iWr)
—
~
(.
‘
~~1•
•
08
_____
.
I r 5K
57A5
• —~
——
I 0
-
2 2crr~ 5 cm’ io cm’
____________________
10
20
Cfl~’
30
______
Fig. 3. Reflectivity of a PbTe film on NaCl at T = 5 K. 2~ PbTe full, dashed film thickness: and dash 4.25 dotted pm.lines: Dots:calculated experimental with the data,
‘~ ~‘
where c~.idenotes the2/m*eo frequency, WTO frequency, the TO phonon the plasma F the frequency, w~ = ne phonon damping and ~ the free carrier damping and L~e= e 0 e0. o.~was determined from the d.c. Hall data and the known values of the effective mass. d was measured during and after the growth of the films with an accuracy of 5%. In order to fit the measured reflectivity data we have varied ~TO~ F and w~.. Figure 1 shows the reflectivity as a function of wavenumber for a 1.3 pm thick PbTe film on NaC1 at T = 300 K together with the results of the calculation according to equations (I) and (2). The parameters used for PbTe are indicated in this figure. The phonon damping was taken to be constant whereas the carrier damping parameters varied and turned out to be frequency —
1.0
R
—
—
______________________________
I
+ Im r12 Im r23) cos a + 2(Re r12 Im r23 3+ R Re r23 Im r12) sin a}- {e~ 12R23e~ + 2(Re Ti2 Re r23
v1. as shown in the inset (dashed line).
oscillator fit. Parameters: v~= 580 cm~,~ = 33, ~e = 1350, ~TO = 18.2 cm’, F = 1 cm~. dependent for an optimum fit. In contrast to the situation found in bulk reflectivity, the film-substrate reflectivity in the region above the plasma edge is very sensitive to changes in the damping parameter WT• Thus we obtain particularly useful information on the frequency dependence of the electron collision time (l/Wr) over a wide spectral region. Also in the region near the TO phonon frequency, where the bulk reflectivity scarcely deviates from 1, the film-substrate reflectivity still shows easily observable structures. The parameters used in the fit-program thus can be determined very accurately. Figure 2 shows the reflectivity of a rather thick PbTe sample (d = 27 pm) which exhibits
Vol. 18, No. 7
FAR-INFRARED REFLECTIVITY OF PbTe FILMS ON NaC1 SUBSTRATES
775
Table 1. Parameter values ofoscillator fit T coo
LXe 1~TO(cm~)
F (cm’)
300K
5K
34.5 350±30 32 3—lO(d < 1 pm) 60—300
33 1300±50 18 2(d < 1pm) 5(d < 1 pm)
3(d > 2pm)
pronounced interference oscillations in the region above the plasma edge. Since the amplitude of these oscillations is very sensitive to the damping parameter, thick samples (d> 10pm) are well suited to determine wr(w) as well as the refractive index (position of the extrema) whereas thin samples are better suited for a determination of the TO phonon modes. The inset of Fig. 2 shows the variation of the carrier damping parameter as a function of frequency. Its behaviour cannot be understood in terms of the photon—plasmon-ionized impurity (defect) process suggested recently by Mycielski’3 for PbSe having however higher carrier concentrations. Figure 3 shows the reflectivity of a PbTe film (d = 4.25 pm) in the region 3—30 cm~at T = 5 K. Again due to interference effects the reflectivity shows an enhanced structure associated with the phonon. Due to the occurence of steep minima in the film-substrate
l(d > 2pm) 2(d > 2pm)
In Table 1 we have summarized the results obtained from the fitting of the reflectivity curves for 5 and 300 K. As was expected, samples with carrier thicknesses below 2pm show somewhat higher carrier as well as phonon damping parameters. It turned out that the TO mode frequency does not depend on n in the carrier concentration range investigated to within 1.5 cm~.The parameters characterizing the PbTe films are summarized in Table 1. We have demonstrated that reflectivity measurements of thin films on absorbing substrates are a powerful tool for the investigation of nearly total reflecting semiconductors. The TO phonon frequency in PbTe softens by decreasing the temperature from 300 to 5 K and obeys a Curie law. The frequency dependence of the carrier collision time was given for a wide range. A more detailed description of this work including also an investigation of PbTe films on BaF 2 substrates is in progress.
reflectivity the position of the TO mode can be determined easily to be 18.2 cm~from the fit using equations (1) and (2). In addition the influence of the carrier damping on the reflectivity spectra is shown. At 77 1. K Acknowledgements We thank and P. Grosse and H.and Heinrich for helpful discussions R. Siedling using the same sample we determined ~TO = 23 cm The temperature dependence of 1~TOthus obeys a Curie- R. Kohnen for technical assistance. law ~2 —
REFERENCES 1. 2.
DALVENR.,InfraredPhys. 9,141(1969). BATE R.T., CARTER D.L. & WROBEL J.S., Proc. mt. Conf Phys. Semicond. p.7!. Cambridge, MA 1970; Phys. Rev. Lett. 25, 159 (1970).
3.
PAWLEY G.S., COCHRAN W., COWLEY R.A. & DOLLING G.,Phys. Rev. Lett. 17, 759 (1966).
4. 5.
COCHRAN W., COWLEY R.A., DOLLING G., ELCOMBE M.M.,Proc. R. Soc. (London) 293, 433 (1966). KINCH M.A. & BUSS D.D., Solid State Commun. 11, 319 (1972).
6.
BUSS D.D. & KINCH M.A.,J. Nonmetals 1, 111(1973).
7. 8.
GOLDAK J., BARRETT C.S., INNES D. & YONDELIS W., J. Chem. Phys. 44,3323 (1966). DOLLING G. & BUYERS W.J.L., J. Nonmetals 1, 159 (1973).
9.
LUCOVSKY G., MARTIN R.P. & BURSTEIN E.,J. Nonmetals 1, 137 (1973).
10. 11.
KAWAMURA H., KATAYAMA S., TAKANO S. & HOTTA S., Solid State Commun. 14,259(1974); KAWAMURA H., TAKANO S., HOTTA S., NISHI S., KATO K., KOBAYASHI K.L.I. & KOMATSUBARA K.F.,Proc. mt. Conf Phys. Semicond. p.551. Stuttgart (1974). LOPEZ-OTERO A., App!. Phys. Lett. 26, 470 (1975); LOPEZ-OTERO A. & HAAS L.D., Thin Solid Films 23, 1(1974).
776
FAR-INFRARED REFLECTIVITY OF PbTe FILMS ON NaC1 SUBSTRATES
Vol. 18, No. 7
12.
BAUER G., BURKHARD H. & LOPEZ.OTERO A. VerhandlDPG(Vm) 10, 391 (1975); Using a similar principle Pb0 82Sn0 18Te—Pb08Sn02Te film-substrate structures were investigated in the 50—250 cm’ region at T = 300 K; TENNANT W.E. & CAPE J.A., App!. Phys. Lett. 26, 694 (1975).
13.
MYCIELSKI J.,Proc. IntConf Phys. Semicond. p.1137. Stuttgart (1974).