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Semimetallic electrical transport in PbTe-SnTe superlattices on KCl substrate
Solid State Communications, Vol. 58, No. 9, pp. 637-640, 1986. Printed in Great Britain.
0038-1098/86 $3.00 + .00 Pergamon Journals Ltd.
SEMIMETALLIC ELECTRICAL TRANSPORT IN PbTe-SnTe SUPERLATTICES ON KC1 SUBSTRATE S. Takaoka, T. Okumura and K. Murase Department of Physics, Faculty of Science, Osaka University, 1-1 Machikaneyama, Toyonaka 560, Japan and A. Ishida and H. Fujiyasu Department of Electronics, Faculty of Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu 432, Japan
(Received 20 January 1986 by W. Sasaki) The electrical resistivity and Hall coefficient (RH) in PbTe-SnTe superlattices on KC1 are measured between 4.2 and 300 K. Magnetic field dependence of RH shows a sign inversion of R E for a specimen of P b T e SnTe with 100-50 A at 5 K. This is due to coexistence of electrons and holes. PbTe-SnTe superlattices are of type II, where the valence band edge of SnTe is higher than the conduction band edge of PbTe. From the magnetic field dependence Of RH, the electron and hole concentrations are calculated and the band-offset between PbTe and SnTe is estimated. The possibility of the structural phase transition of these superlattices is also discussed. THE INVESTIGATIONS OF semiconductor superlattices (SL) have become one of the most interesting and active spheres of solid state physics in recent years. However, there have been few experimental and theoretical studies about the SL of I V - V I compound semiconductors [ 1 - 3 ] as compared with those of I I I - V compound. The SL of PbTe-SnTe has unique properties as follows [4]. (1)The minimum band gap is very narrow and especially becomes zero for P b l - x SnxTe (x = 0.35 and T = 0K). (2) The dielectric constant is very high and the ferro-olectric phase transition occurs for x > 0.40. Thus a carrier mobility is high due to large screening in spite of high impurity and (or) vacancy concentrations. (3) There are four conduction and valence bands extremes at L-points in the Brillouin zone (many valleys), while the I I I - V and I I - V I semiconductor has usually one extreme (single valley). Recently it has been found that the SL of P b T e Pb0.aSn0.2Te is of type I', that is, the conduction and valence band edges of PbTe are lower than those of Pbo.aSno.:Te, respectively, from the cyclotron resonance measurement [5]. If this result is extrapolated to PbTe-SnTe SL, it is expected that PbTe-SnTe SL is of type II, that is, the valence band edge of SnTe is higher than the conduction band edge of PbTe as shown in Fig. 1. A kind of semimetallic state occurs for an appropriate Fermi level. This is ascertained by Hall measurements in PbTe-SnTe SL on BaF2 with various
annealing times [6]. Further these SL show the superconducting behavior below several Kelvin [7], which is much higher than those of the well-known semiconductor superconductors such as SnTe, GeTe etc. [8]. It is also interesting whether these SL exhibit a ferroelectric phase transition, since SnTe shows a phase transition about 100K while PbTe does not at finite temperature [91. We have measured the electrical resistivity (O) and Hall coefficient (RE) of SL grown on KC1 with various layer thicknesses. Especially a large magnetic field dependence ofR H was observed at low temperature for some specimens of SL, which is due to coexistence of electrons and holes. The PbTe-SnTe SL were epitaxially grown on cleaved KC1 (1 00) substrates by a hot wall method with alternating growth chambers of PbTe and SnTe [1,6]. For SnTe layer growth, a stoichiometric SnTe source and a small amount of Pb source were used to reduce the metal vacancies. The period and typical electrical characteristics of present measured SL are listed in Table 1. The electrical resistivity and Hall coefficient were measured between 4.2 and 300K by conventional d.c. techniques. Gold wires of 50Arm diameter were soldered with indium to specimens as current and voltage probes. It is noted that these specimens were very delicate under thermal scanning from room temperature to liq. He temperature due to the differences of thermal expansion coefficients between SL and KC1 substrate as compared with those on BaF2. These SL on KC1 have advantage that the subbands from
637
638
PbTe-SnTe SUPERLATTICES ON KC1 SUBSTRATE
SnTe
PI)Te
(b) A A _ Fig. 1. Schematic illustration of energy profile of P b T e SnTe SL. C and V denote conduction and valence band edge, respectively. EF is Fermi level. Hatched area is energy gap. (a) ideal case. (b) with interdiffusion.
four valleys are equivalent for (1 0 0) surface, while two kinds of subbands with light and heavy masses occur for (1 1 1) surface (SL on BaF2). In Fig. 2, the temperature dependences of p and R H at H = 10kG are shown for various periods of SL. The sharp drop of p with decreasing temperature at low temperatures is due to a superconductivity transition. In fact there is no sharp drop under a strong magnetic field. The details of the superconductivity transition of these SL are reported in [7]. As seen from Fig. 2, R H change their sign from p- to n-type with increasing PbTe layer width at constant SnTe layer width (d = 50 A). This is naturally explained if there exist electrons in PbTe layers and holes in SnTe layers and n-type conduction becomes dominant with increasing PbTe period. Particularly for the specimen of PbTe-SnTe ( 1 0 0 - 5 0 A ) , R H changes its sign from n- to p-type with increasing magnetic fields at 5 K as indicated in Fig. 3. This is a very clear evidence that electrons and holes coexist in this specimen, where the thermal excitation of carriers across the conduction and valence bands is very small at 5 K. The possibility of the conduction and valence band overlap caused by the valley spfitting by a shear strain due to mismatches between SL and substrate as observed in Indium doped Pb i - xSnx Te film on BaF2
Vol. 58, No. 9
[10] is also excluded, since four valleys at L-points are equivalent and do not split by the strain in the (1 0 0 ) film surface. Such a n - p inversion of R H with respect to magnetic field is observed only when the conditions, p > n and nb 2 > p, are satisfied, where p and n are the carrier concentration of holes and electrons, respectively and b =/ae/# h is the mobility ratio of electrons and holes. We determined the carrier concentrations of electron (n) and hole (p) and their mobilities from resistivity and magnetic field dependence of R H as follows. In the Drude model with two types of carriers (electron and hole), R H ( H ) and p are expressed as [I I ] (De + Dh) 1 R H ( H ) = (De + Dh) 2 + (Ae + Ah): 1
and
p
= - - , Oe + Oh
(1)
where Ae = ae/(1 + c~B~), De = O~BeAe,
o e = nePe , B e = --/.tell '
Ah
----
Oh/(1
"4-
aBe)
Dh = O~BhAh, Oh
=
pePh
B h = /lhH
a = 3K(K + 2)/(2K + 1) 2,
and K = 10 is the anisotropy of effective mass in each valley. The closed circles in Fig. 3 are the calculated one from equation (1). Thus determined carrier concentrations and their mobilities are as follows: n = 6.2 x 101Scm -3, p = 2 . 1 x l 0 1 S c m -a, p e = 6 . 2 x l 0 a c m 2 / V sec. and #h = 2.5 × 102 cm2/v.sec. The Fermi energies (EF) of electrons in PbTe well and holes in SnTe well are estimated from these carrier concentrations. We assume that the height of the well potential is sufficiently larger than the Fermi level and the two band model is applicable in each quantum well. In the (1 0 0 ) plane quantum wells in PbTe and SnTe layers, the relation between EF and the sheet carrier concentration (N) in the twoband model is given as
Table 1. Typical electrical characteristics o f P b T e - S n T e SL on KC1 at T = 77 K
PbTe-SnTe
p (~2 cm)
1/eRH (cm -a)
PH (cm2/Vs)
50-50 A 100-50 A 150-50 A 200--50 A 200-200 A
5.2 1.2 8.3 1.7 1.2
p p n n p
890 290 1300 7900 5200
× 10 -a x 10 -2 X 10 -3 x 10 -a x 10 -a
= = = = =
1.3 1.8 5.6 4.7 9.8
x 10 TM × 10 TM X 1017 × 10 t7 × 1017
Vol. 58, No. 9
PbTe-SnTe SUPERLATTICES ON KCI SUBSTRATE
,
21 (a)
,
PbTe-SnTe S.L.
639
J PbTe-SnTe
on
100-50A
15
,
(b)
,
PbTe-SnTe S.L. on KCI
o ~
¢w lit
lo-
>. I.-
t-i
o -- ~
PbTe-5nTe
°~oo-so,~,
~
M I,U) I/} M.I Or:
50 - 50A ~
¢*J
-
'00-200A
OIL
o
100
200
0
TEMPERATURE (K)
100 TEMPERATURE
200
300
(K)
Fig. 2. Temperature dependences of (a) electrical resistivity and (b)Hall coefficient at H = l0 kG of PbTe-SnTe SL on KC1. EF
.o N ( E F ) = na
(2)
f Pi(E)dE' i=1
0
where p i ( E ) = m___aa(1 + 2E/Eg) rt h2 O(E
pi(E) and E i are, respectively, density-of-states and -- El)
,
(100A-50A)
0
-o.s
LU
__U LL IJ-
N -1.o :Z
-1-! !
0
I
5 10 MAGNETIC FIELD (kG)
15
Fig. 3. Magnetic field dependence of Hall coefficient with PbTe-SnTe ( 1 0 0 - 5 0 A ) SL at 5 K. Solid line is an experimental one and closed circles are calculated from equation (1).
energy level of subband and EF is measured from the band edge of bulk crystal [12], md = m t x / ( 2 K + 1)/3, mz = m t x 3 K / ( 2 K + 1), mr: the transverse effective mass at the band edge, Eg: the energy gap in bulk crystal, n a = 4 : number of valleys, d: the width of quantum well and i is the quantum number of subband. From the carrier concentrations of electrons and holes of PbTe-SnTe (100-50 A) SL, E F of electrons in PbTe layer and holes in SnTe layer are estimated from equation (2) as EF = 80.5 meV for PbTe and EF = 191.3 meV for SnTe. In the calculation we used the band parameters of bulk PbTe and SnTe and carrier concentration from the curve fitting in Fig. 3 as follows: Eg = 190meV, rn t = 0.023mo and N = n x 150A = 9.3 x 109cm -2 for PbTe and Eg = 300meV, m t = 0.036mo a n d N = p x 1 5 0 A = 3.3 x 1012 cm -2. It is noticed that the only first subbands are occupied in both PbTe and SnTe layers. From those EF, we evaluate that the band offset (A) between the conduction band edge of PbTe and the valence band edge of SnTe is (191.3 meV + 80.5 meV) = 271.8meV, where the band bending effect due to the charge transfer among PbTe and SnTe layers is neglected, because the static dielectric constant is very high (~ 103)
640
PbTe-SnTe SUPERLATTICES ON KC1 SUBSTRATE
and a typical screening length is several thousands angstrom, which is much larger than the period of the present SL. The band offset predicted from the indium impurity level standard is about 350 meV [5]. From the optical absorption measurement of PbTe-Pbo.~8Sno.22Te SL, the conduction band edge of Pb0.TaSno.22Teis found to be about 70meV higher than that of PbTe [13]. If we extrapolate this result to PbTe-SnTe SL, the band offset is evaluated to be 320 meV. The present estimation of A is somewhat smaller than those from other methods. Actually, there is considerable interdiffusion between PbTe and SnTe layers [6] and pure SnTe and PbTe layers does not exist in the present SL, as schematically shown in Fig. l(b). This effect reduces the potential wells as compared with pure PbTe-SnTe SL profile shown in Fig. l(a). Thus the present evaluated A is underestimated. As seen in Fig. 2, R n show maxima between 50 and 100K. On the other hand, RH of bulk Pbl_xSnxTe (0.4 < x < 1.0) show minima at the phase transition temperature [14, 15]. The tendency of temperature dependences is opposite to that of SL and their magnitudes are not so large as those of SL. With lowering temperature, p of PbTe, SnTe and their alloys monotonically [16] decrease and/or show small humps at the phase transition temperatures [8, 14]. The SL of PbTeSnTe ( 5 0 - 5 0 A and 200-200A) show resistivity enhancements at low temperature region and those of (100-50 A and 150-50 A) show large and broad humps, which could not be simply attributed to the phase transition as observed in bulk Pbl-xSnxTe, since the temperature region of such anomalies is higher than the phase transition temperature of bulk specimen (< 100 K). In the SL of PbTe-SnTe, we have to consider the following complicated situations. With decreasing temperatures from 300 to 4.2K, the tin composition which gives zero-gap in Pbl_xSnxTe changes from x = 0.6 to 0.35 [16]. Then the position at E u = 0 shifts to "PbTe layer" in SL. Further, t h e four equivalent valleys split into a singlet and triplet valleys below the phase transition temperatures [17]. These effects cause the carrier redistributions among the singlet and triplet valleys both in PbTe and SnTe layers. The interband carrier excitation between the conduction and valence bands at small gap Pbl-xSn~Te region can not be neglected at relatively high temperatures. As the precise quantitative informations about these effects are not yet obtained at present stage, such temperature dependences of p and R n of SL cannot be explained satisfactorily. However the structural phase transition and the coexistence of electrons and holes separated by small gap Pbl_xSnxTe region as shown in Fig. l(b) will have important influences upon the anomalous temperature behaviors of p and R~.
Vol. 58, No. 9
In summary, the transport properties of PbTe-SnTe SL on KC1 are investigated and it is confirmed that this SL is of type II. The band-offset between PbTe and SnTe is estimated and the obtained value is comparable with those from other ways. However, the temperature dependence of p and R n in SL are greatly different from those of host material (PbTe, SnTe and their alloy) and cannot be well elucidated. Further investigations of these SL are necessary to make clear such anomalous behaviors.
Acknowledgements - This work was supported in part by Grant-in-Aid for Special Project Research No. 106 from Ministry of Education, Science and Culture. One of the authors (S.T.) acknowledges the support from the 15th Kurata Foundation and another (K.M.) from the 22nd Science and Technology Grants of Toray Science Foundation. REFERENCES 1. 2.
3. 4. 5. 6. 7.
8. 9. 10.
11. 12. 13. 14. 15. 16. 17.
M. Kinoshita & H. Fujiyasu, J. Appl. Phys. 51, 5845 (1980). M. Kinoshita, S. Takaoka, K. Murase & H. Fujiyasu, Proc. 2nd Symposium on MBE, p. 61, (Edited by Ueda, Japan Soc. Appl. Phys.) Tokyo, (1982). M. Kriechbaum, K.E. Ambrosch, E.J. Fantner, H. Clemens & G. Bauer, Phys. Rev. B30, 3394 (1984). G. Nimitz & B. Schlicht, Narrow-Gap Semiconductors, p. 1, Springer-Verlag, (1983). K. Murase, S. Shimomura, S. Takaoka, A. Ishida & H. Fujiyasu, Superlattices and Microstructures 1,177 (1985). A. Ishida, M. Aoki & H. Fujiyasu, J. Appl. Phys. 58, 1901 (1985). K. Murase, S. Ishida, S. Takaoka, T. Okumura, H. Fujiyasu & M. Aoki, Proc. 6th Int. Conf.
Electronic Properties of Two-Dimensional Systems, Sept. 9-15, 1985, p. 621, Kyoto. K. Murase, Ferroelectrics 35, 67 (1981). D.V. Gubser & R.A. Hein, Solid State Commun. 15, 1039 (1974). S. Takaoka, T. Hamaguchi, S. Shimomura & K. Murase, Proc. 17th Int. Conf. Phys. Semiconductors, Aug. 6-10, 1984, p.621, San Francisco. S. Takaoka, T. Itoga & K. Murase, Jpn. J. Appl. Phys. 23,216 (1984). F. Stern & W.E. Howard, Phys. Rev. 163, 816 (1967). A. Ishida & H. Eujiyasu, Jpn. J. Appl. Phys. 24, L956 (1985). K.L.I. Kobayashi, Y. Katayama, K. Narita & K.F. Komatsubara, Proc. 14th Int. Conf. Phys. Semiconductors, Sep. 4 - 8 , 1978, p. 441, Edinburgh. S. Nishi, Ph.D. Thesis, Osaka University (1980). J.R. Dixon & R.F. Bis, Phys. Rev. 176, 176 (1968). S. Takaoka & K. Murase, J. Phys. Soc. Japan 51, 1857 (1982).
0038-1098/86 $3.00 + .00 Pergamon Journals Ltd.
SEMIMETALLIC ELECTRICAL TRANSPORT IN PbTe-SnTe SUPERLATTICES ON KC1 SUBSTRATE S. Takaoka, T. Okumura and K. Murase Department of Physics, Faculty of Science, Osaka University, 1-1 Machikaneyama, Toyonaka 560, Japan and A. Ishida and H. Fujiyasu Department of Electronics, Faculty of Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu 432, Japan
(Received 20 January 1986 by W. Sasaki) The electrical resistivity and Hall coefficient (RH) in PbTe-SnTe superlattices on KC1 are measured between 4.2 and 300 K. Magnetic field dependence of RH shows a sign inversion of R E for a specimen of P b T e SnTe with 100-50 A at 5 K. This is due to coexistence of electrons and holes. PbTe-SnTe superlattices are of type II, where the valence band edge of SnTe is higher than the conduction band edge of PbTe. From the magnetic field dependence Of RH, the electron and hole concentrations are calculated and the band-offset between PbTe and SnTe is estimated. The possibility of the structural phase transition of these superlattices is also discussed. THE INVESTIGATIONS OF semiconductor superlattices (SL) have become one of the most interesting and active spheres of solid state physics in recent years. However, there have been few experimental and theoretical studies about the SL of I V - V I compound semiconductors [ 1 - 3 ] as compared with those of I I I - V compound. The SL of PbTe-SnTe has unique properties as follows [4]. (1)The minimum band gap is very narrow and especially becomes zero for P b l - x SnxTe (x = 0.35 and T = 0K). (2) The dielectric constant is very high and the ferro-olectric phase transition occurs for x > 0.40. Thus a carrier mobility is high due to large screening in spite of high impurity and (or) vacancy concentrations. (3) There are four conduction and valence bands extremes at L-points in the Brillouin zone (many valleys), while the I I I - V and I I - V I semiconductor has usually one extreme (single valley). Recently it has been found that the SL of P b T e Pb0.aSn0.2Te is of type I', that is, the conduction and valence band edges of PbTe are lower than those of Pbo.aSno.:Te, respectively, from the cyclotron resonance measurement [5]. If this result is extrapolated to PbTe-SnTe SL, it is expected that PbTe-SnTe SL is of type II, that is, the valence band edge of SnTe is higher than the conduction band edge of PbTe as shown in Fig. 1. A kind of semimetallic state occurs for an appropriate Fermi level. This is ascertained by Hall measurements in PbTe-SnTe SL on BaF2 with various
annealing times [6]. Further these SL show the superconducting behavior below several Kelvin [7], which is much higher than those of the well-known semiconductor superconductors such as SnTe, GeTe etc. [8]. It is also interesting whether these SL exhibit a ferroelectric phase transition, since SnTe shows a phase transition about 100K while PbTe does not at finite temperature [91. We have measured the electrical resistivity (O) and Hall coefficient (RE) of SL grown on KC1 with various layer thicknesses. Especially a large magnetic field dependence ofR H was observed at low temperature for some specimens of SL, which is due to coexistence of electrons and holes. The PbTe-SnTe SL were epitaxially grown on cleaved KC1 (1 00) substrates by a hot wall method with alternating growth chambers of PbTe and SnTe [1,6]. For SnTe layer growth, a stoichiometric SnTe source and a small amount of Pb source were used to reduce the metal vacancies. The period and typical electrical characteristics of present measured SL are listed in Table 1. The electrical resistivity and Hall coefficient were measured between 4.2 and 300K by conventional d.c. techniques. Gold wires of 50Arm diameter were soldered with indium to specimens as current and voltage probes. It is noted that these specimens were very delicate under thermal scanning from room temperature to liq. He temperature due to the differences of thermal expansion coefficients between SL and KC1 substrate as compared with those on BaF2. These SL on KC1 have advantage that the subbands from
637
638
PbTe-SnTe SUPERLATTICES ON KC1 SUBSTRATE
SnTe
PI)Te
(b) A A _ Fig. 1. Schematic illustration of energy profile of P b T e SnTe SL. C and V denote conduction and valence band edge, respectively. EF is Fermi level. Hatched area is energy gap. (a) ideal case. (b) with interdiffusion.
four valleys are equivalent for (1 0 0) surface, while two kinds of subbands with light and heavy masses occur for (1 1 1) surface (SL on BaF2). In Fig. 2, the temperature dependences of p and R H at H = 10kG are shown for various periods of SL. The sharp drop of p with decreasing temperature at low temperatures is due to a superconductivity transition. In fact there is no sharp drop under a strong magnetic field. The details of the superconductivity transition of these SL are reported in [7]. As seen from Fig. 2, R H change their sign from p- to n-type with increasing PbTe layer width at constant SnTe layer width (d = 50 A). This is naturally explained if there exist electrons in PbTe layers and holes in SnTe layers and n-type conduction becomes dominant with increasing PbTe period. Particularly for the specimen of PbTe-SnTe ( 1 0 0 - 5 0 A ) , R H changes its sign from n- to p-type with increasing magnetic fields at 5 K as indicated in Fig. 3. This is a very clear evidence that electrons and holes coexist in this specimen, where the thermal excitation of carriers across the conduction and valence bands is very small at 5 K. The possibility of the conduction and valence band overlap caused by the valley spfitting by a shear strain due to mismatches between SL and substrate as observed in Indium doped Pb i - xSnx Te film on BaF2
Vol. 58, No. 9
[10] is also excluded, since four valleys at L-points are equivalent and do not split by the strain in the (1 0 0 ) film surface. Such a n - p inversion of R H with respect to magnetic field is observed only when the conditions, p > n and nb 2 > p, are satisfied, where p and n are the carrier concentration of holes and electrons, respectively and b =/ae/# h is the mobility ratio of electrons and holes. We determined the carrier concentrations of electron (n) and hole (p) and their mobilities from resistivity and magnetic field dependence of R H as follows. In the Drude model with two types of carriers (electron and hole), R H ( H ) and p are expressed as [I I ] (De + Dh) 1 R H ( H ) = (De + Dh) 2 + (Ae + Ah): 1
and
p
= - - , Oe + Oh
(1)
where Ae = ae/(1 + c~B~), De = O~BeAe,
o e = nePe , B e = --/.tell '
Ah
----
Oh/(1
"4-
aBe)
Dh = O~BhAh, Oh
=
pePh
B h = /lhH
a = 3K(K + 2)/(2K + 1) 2,
and K = 10 is the anisotropy of effective mass in each valley. The closed circles in Fig. 3 are the calculated one from equation (1). Thus determined carrier concentrations and their mobilities are as follows: n = 6.2 x 101Scm -3, p = 2 . 1 x l 0 1 S c m -a, p e = 6 . 2 x l 0 a c m 2 / V sec. and #h = 2.5 × 102 cm2/v.sec. The Fermi energies (EF) of electrons in PbTe well and holes in SnTe well are estimated from these carrier concentrations. We assume that the height of the well potential is sufficiently larger than the Fermi level and the two band model is applicable in each quantum well. In the (1 0 0 ) plane quantum wells in PbTe and SnTe layers, the relation between EF and the sheet carrier concentration (N) in the twoband model is given as
Table 1. Typical electrical characteristics o f P b T e - S n T e SL on KC1 at T = 77 K
PbTe-SnTe
p (~2 cm)
1/eRH (cm -a)
PH (cm2/Vs)
50-50 A 100-50 A 150-50 A 200--50 A 200-200 A
5.2 1.2 8.3 1.7 1.2
p p n n p
890 290 1300 7900 5200
× 10 -a x 10 -2 X 10 -3 x 10 -a x 10 -a
= = = = =
1.3 1.8 5.6 4.7 9.8
x 10 TM × 10 TM X 1017 × 10 t7 × 1017
Vol. 58, No. 9
PbTe-SnTe SUPERLATTICES ON KCI SUBSTRATE
,
21 (a)
,
PbTe-SnTe S.L.
639
J PbTe-SnTe
on
100-50A
15
,
(b)
,
PbTe-SnTe S.L. on KCI
o ~
¢w lit
lo-
>. I.-
t-i
o -- ~
PbTe-5nTe
°~oo-so,~,
~
M I,U) I/} M.I Or:
50 - 50A ~
¢*J
-
'00-200A
OIL
o
100
200
0
TEMPERATURE (K)
100 TEMPERATURE
200
300
(K)
Fig. 2. Temperature dependences of (a) electrical resistivity and (b)Hall coefficient at H = l0 kG of PbTe-SnTe SL on KC1. EF
.o N ( E F ) = na
(2)
f Pi(E)dE' i=1
0
where p i ( E ) = m___aa(1 + 2E/Eg) rt h2 O(E
pi(E) and E i are, respectively, density-of-states and -- El)
,
(100A-50A)
0
-o.s
LU
__U LL IJ-
N -1.o :Z
-1-! !
0
I
5 10 MAGNETIC FIELD (kG)
15
Fig. 3. Magnetic field dependence of Hall coefficient with PbTe-SnTe ( 1 0 0 - 5 0 A ) SL at 5 K. Solid line is an experimental one and closed circles are calculated from equation (1).
energy level of subband and EF is measured from the band edge of bulk crystal [12], md = m t x / ( 2 K + 1)/3, mz = m t x 3 K / ( 2 K + 1), mr: the transverse effective mass at the band edge, Eg: the energy gap in bulk crystal, n a = 4 : number of valleys, d: the width of quantum well and i is the quantum number of subband. From the carrier concentrations of electrons and holes of PbTe-SnTe (100-50 A) SL, E F of electrons in PbTe layer and holes in SnTe layer are estimated from equation (2) as EF = 80.5 meV for PbTe and EF = 191.3 meV for SnTe. In the calculation we used the band parameters of bulk PbTe and SnTe and carrier concentration from the curve fitting in Fig. 3 as follows: Eg = 190meV, rn t = 0.023mo and N = n x 150A = 9.3 x 109cm -2 for PbTe and Eg = 300meV, m t = 0.036mo a n d N = p x 1 5 0 A = 3.3 x 1012 cm -2. It is noticed that the only first subbands are occupied in both PbTe and SnTe layers. From those EF, we evaluate that the band offset (A) between the conduction band edge of PbTe and the valence band edge of SnTe is (191.3 meV + 80.5 meV) = 271.8meV, where the band bending effect due to the charge transfer among PbTe and SnTe layers is neglected, because the static dielectric constant is very high (~ 103)
640
PbTe-SnTe SUPERLATTICES ON KC1 SUBSTRATE
and a typical screening length is several thousands angstrom, which is much larger than the period of the present SL. The band offset predicted from the indium impurity level standard is about 350 meV [5]. From the optical absorption measurement of PbTe-Pbo.~8Sno.22Te SL, the conduction band edge of Pb0.TaSno.22Teis found to be about 70meV higher than that of PbTe [13]. If we extrapolate this result to PbTe-SnTe SL, the band offset is evaluated to be 320 meV. The present estimation of A is somewhat smaller than those from other methods. Actually, there is considerable interdiffusion between PbTe and SnTe layers [6] and pure SnTe and PbTe layers does not exist in the present SL, as schematically shown in Fig. l(b). This effect reduces the potential wells as compared with pure PbTe-SnTe SL profile shown in Fig. l(a). Thus the present evaluated A is underestimated. As seen in Fig. 2, R n show maxima between 50 and 100K. On the other hand, RH of bulk Pbl_xSnxTe (0.4 < x < 1.0) show minima at the phase transition temperature [14, 15]. The tendency of temperature dependences is opposite to that of SL and their magnitudes are not so large as those of SL. With lowering temperature, p of PbTe, SnTe and their alloys monotonically [16] decrease and/or show small humps at the phase transition temperatures [8, 14]. The SL of PbTeSnTe ( 5 0 - 5 0 A and 200-200A) show resistivity enhancements at low temperature region and those of (100-50 A and 150-50 A) show large and broad humps, which could not be simply attributed to the phase transition as observed in bulk Pbl-xSnxTe, since the temperature region of such anomalies is higher than the phase transition temperature of bulk specimen (< 100 K). In the SL of PbTe-SnTe, we have to consider the following complicated situations. With decreasing temperatures from 300 to 4.2K, the tin composition which gives zero-gap in Pbl_xSnxTe changes from x = 0.6 to 0.35 [16]. Then the position at E u = 0 shifts to "PbTe layer" in SL. Further, t h e four equivalent valleys split into a singlet and triplet valleys below the phase transition temperatures [17]. These effects cause the carrier redistributions among the singlet and triplet valleys both in PbTe and SnTe layers. The interband carrier excitation between the conduction and valence bands at small gap Pbl-xSn~Te region can not be neglected at relatively high temperatures. As the precise quantitative informations about these effects are not yet obtained at present stage, such temperature dependences of p and R n of SL cannot be explained satisfactorily. However the structural phase transition and the coexistence of electrons and holes separated by small gap Pbl_xSnxTe region as shown in Fig. l(b) will have important influences upon the anomalous temperature behaviors of p and R~.
Vol. 58, No. 9
In summary, the transport properties of PbTe-SnTe SL on KC1 are investigated and it is confirmed that this SL is of type II. The band-offset between PbTe and SnTe is estimated and the obtained value is comparable with those from other ways. However, the temperature dependence of p and R n in SL are greatly different from those of host material (PbTe, SnTe and their alloy) and cannot be well elucidated. Further investigations of these SL are necessary to make clear such anomalous behaviors.
Acknowledgements - This work was supported in part by Grant-in-Aid for Special Project Research No. 106 from Ministry of Education, Science and Culture. One of the authors (S.T.) acknowledges the support from the 15th Kurata Foundation and another (K.M.) from the 22nd Science and Technology Grants of Toray Science Foundation. REFERENCES 1. 2.
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