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Surface Science 263 (1992) 541-546 forth-Holland

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Te~pcrature dcpcndent electronic properties of HgZnTe/CdTe superlattices Y. Guldner, J. Manassks, J.P. Vieren,

M. Voos

Laboratoire de Physique de la Mat&e C~~d~~~e~ D~~arte~ent de Phys~ue de I’Ecole Nor~~le Sup&ewe, 75005 Paris, France

24 rue Lhornond.

and J.P. Faurie

Received 20 May 1991; accepted for publication 26 August 1991

We present transport and far-infrared magneto-optical measurements in n-type HgZnTe-CdTe superlattices over a large temperature range (I.5300 K). The data show unambiguously that these superlattices are semimetallic at low temperature and are degenerate intrinsic semiconductors for T > 100 K, in good agreement with theory which predicts a semimetal-semiconductor transition induced by temperature.

We present new transport and far-infrared magneto-optical measurements in narrow-bandgap n-type Hg , _-xZn,Te-CdTe superlattices (SLs) with x < 0.1. These heterostructures, which consist of alternating zero-gap and wide-gap semiconductor layers, can exhibit a positive or a negative energy gap at the I7 point [l], depending on the layer thicknesses and on temperature. Hall and conductivity data obtained over a large temperature range (1.5-300 K) show that these superlattices are semimetallic at low temperature and are degenerate intrinsic semiconductors for T> 100 K, which constitutes a new interesting situation in semiconductor superlattice physics. The analysis of the data gives the Fermi level energy as well as the temperature dependent bandgap, in good agreement with the calculated band structure which predicts a semimetal-semiconductor transition induced by temperature in these heterostructures. We have measured the electron cyclotron resonances as a function of

temperature with the magnetic field B applied parallel and perpendicular to the growth axis. The observed magneto-optical intraband transitions are in very satisfying agreement with the calculated Landau levels and the Fermi level position. We show that the semimetal-semiconductor transition is characterized by an important reduction of the cyclotron mass measured with B perpendicular to the superlattice axis. The large variation of the conduction band anisotropy calculated near the transition accounts for this effect. We have studied three SLs grown by molecular beam epitaxy on (100) GaAs substrate with a 2 pm CdTe buffer layer [21 and consisting of 100 periods of Hg,_XZn,Te-CdTe. For each sample, the layer thicknesses, the alloy Zn composition x as well as the electron mobility and concentration at 25 K are listed in table 1. The SLs are n-type in the temperature range investigated in this work with electron mobilities in excess of 2 x 10”

0039~6028/92/$05.00 0 1992 - Elsevier Science Publishers B.V. and Yamada Science Foundation. All rights reserved

Table

I

Characteristics this work:

of the HgZnTe-C‘dTe

d,

thicknesses,

uperlattice~

and c/2 arc the HgZnTe

respectively,

are measured

uwd

and the (‘dTe

.Y i\ the Zn compwltion:

an

Iayel

II ant1 p

at 25 K

Sample

d, (A)

‘I, (A)

s,

.v

fi (cm’/V.\)

12(cm

‘1

10.5

20

0.053

2.1 x IO<

3.7x

s,

80

I7

o.os.3

2.1 x IO’

7.6 x IOli

s:

I60

70

0.070

7.4x

7.4 x IO”

IOi

IO”

cm’/(Vs) at low temperature. Such high carrier mobilities are usually measured in SLs with a small positive or negative gap at the I’ point [3]. The SL band structure is calculated by using a six-band envelope function model [4,51. For Hg,_lZn,Te alloys, we have assumed [6] the I;,-r, energy separation E”“m“X = 0 for x = O.l2 at T = 0 K and the temperature dependence of E’flm’.s is chosen identical to that established in HgCdTe alloys close to HgTe [7]. Fig. 1 shows calculated dispersion relations for S, in the plane of the layers (k,) and along the growth axis (k,)

500

I

/

1

Fig. I. Calculated

k,(x/d) hand structure

the plane of the layers (k,)

HH,

k,Wd)

o

of S, using

_

I t = 360 meV

and along the growth axis (XI)

in for

(a) T = 120 K and (b) T = I .S K. d = d, + tll is the superlattice period.

for 7‘ = 120 K and 7‘ = 1.5 K. The energy origin is taken at the CdTe valence band edge and the valence band offset is 360 mcV. E, (HH,) denotes the first electron (heavy hole) band considering the dispersion along k,. For T = 120 K, E, is the conduction band, HH, the highest valcncc band and the 1’ point energy gap es1 = E, - HH , is positive (31 meV). The in-plane electron and hole masses near k, = 0 arc very small ( < lOF’nz,,) and nearly proportional to ls1 as far as tSl is small [ 11. E, is light along k,. so that the conduction band is nearly isotropic around k = 0 and its density of states is weak. On the contrary, HH, is almost dispersionlcss along k, and is extremely nonparabolic in the plane of the layers. As a consequence, when the temperature increases and the hole and electron thermal distribution spreads over a few meV into the HH, and E, bands, it is clear that the density of states is much larger for HH, than for E,. When the temperature is decreased, ~‘1 is reduced until E, and HH, meet for T = 30 K and then cross in the k; direction for k, = k,, leading to ls1 negative and a semimetallic band structure. For instance. fig. Ib shows the calculated band structure fol 7‘ = 1.5 K. ~‘1 is negative ( -6.5 meV) and HH, displays an electron in-plane dispersion while E, has an hole in-plant dispersion. The conduction band in the semimetallic regime is flat for 0 < kc SO K with a positive temperature coefficient cy = 0.35 meV/K. Quite similar results are obtained for S, and S, where E” and es! arc negative at 1.5 K (~‘2 = - 15.5 meV, tS’ = - 13.5 meV) and become positive for T > 50 K. Low magnetic field transport measurements (Hall effect and conductivity) give the carricl density II and the electron mobility as a function of the temperature in the range 10-300 K. The density II is found to be nearly independent of T at low temperature. from which the donor concentration Nd - N:, = 2 X 10” cm-” is obtained. Fig. 2a shows the carrier density II normalized by 7-j” as a function of the inverse temperature for S, and S,. It is clear that the condition 12> N,, ~

Y Guldner et al. / T-dependent electronic properties of HgZnTe / CdTe super-lattices

n”

E

the conduction band is shown in fig. 2b. Note that E, is positive in the entire temperature range which corresponds to a degenerate situation. The degenerate intrinsic regime arises from the extremely high density of states of the valence band previously discussed. Assuming a linear temperature variation of the gap ls1 = l s1 + aT and an average density of states mass rnyos for the valence band, the intrinsic electron concentration is given by [91:

la)

‘E

A! N ?f_ g,(j' n :

b-5'

s3

300/T

30

I

I

543

II

(6)

Xexp( - EFky”).

200 T (K) Fig. 2. (a) Experimental carrier density normalized by T3’2 versus inverse temperature for S, and S,. (b) Fermi energy E, versus temperature for samples S,, S, and S,. 0i

100

N, is fulfilled for T > 100 K so that the SLs are intrinsic over a broad temperature range (100-300 K) as it can be expected in very-narrow-gap semiconductors with a low doping level. It is wellknown that in the intrinsic regime, the temperature dependence n(T) can be used to determine the zero-temperature extrapolation of the SL gap [S]. Here we have to take into account that our SLs are degenerate intrinsic semiconductors in the temperature range 100-300 K. From the cyclotron mass measurements described later, the dispersion of the conduction band is known and the electron density of states too. A first-order estimate of the Fermi energy E, measured from the bottom of the conduction band is given by the expression [9]: n(T)

= 2( $m:os)3’2F,,2(

E,,kT).

(1)

Here F,,,(X) is the Fermi-Dirac integral and the density of states conduction mass mFos is obtained from the cyclotron resonance data. The variation E,(T) measured from the bottom of

(2)

The Fermi energy level being constant between 200 and 300 K, a linear variation of ln(nT-3/2) with reciprocal temperature is expected in this temperature region. The slope of the solid line drawn for S, in fig. 2a gives directly E, + ELI = 9 meV and therefore E:] = - 11 meV. A similar analysis done in S, and S, gives the zero-temperature extrapolation of the gap es2 = - 10 meV and $ = -8 meV. These results are in surprising agreement with the semimetallic band structure calculated at low temperature using a valence band offset of 360 meV (see fig. lb) if one takes into account the crude approximations of our model (parabolic bands, linear temperature variation of the SL gap,. . . ). Note that it is possible to obtain a determination of the temperature coefficient (Yfrom the variation E,(T) shown in fig. 2b and the cyclotron mass m, measured at high temperatures. In first approximation, the in-plane conduction mass at the energy E, in a narrow-gap semiconductor is given by m, = m:(l + EF/eS1), where the mass rn: at k, = 0 is proportional to ~‘1. Assuming that the cyclotron mass is measured at the Fermi energy, one obtains m, = 10P2m, and m, = 1.8 x lo-*m,, at 100 K and 200 K, respectively (fig. 3a), from which one deduces immediately cx= 0.35 meV/K in good agreement with the gap variation calculated for T > 50 K. Far-infrared transmission was measured versus B at fixed photon energy on samples S ,, S, and

S, using a molecular gas laser (A = 41-25.5 pm) in the temperature region 1.5-200 K. The measurements were carried out in both the Faraday geometry (0 = 0) and the Voigt geometry (H = 90 o ), where 0 is the angle between the SL axis and the applied magnetic field. The cyclotron masses deduced from the intraband transitions observed in S, at photon wavelength A = 11X pm are plotted in fig. 3 as a function of the temperature for H = 0 (fig. 3a) and 0 = 90 o (fig. 3b). For 0 = 0, the SL Landau level energies are calculated by using the six-band envelope function model [4] and fig. 4 shows the S, Landau level at 1.5 K and 150 K. The selection rules for intraband transitions in the Faraday geometry are An = _t 1, where II is the Landau level index. The transitions actually observed in the SLs depend on the Landau level occupation and the Fermi level energy deduced from the transport measurements is indicated by the dashed line in fig. 4. The thermal broadening of width kT on both

/ ?-A-I 1-o

Y0

0.5_!*Q

1

./‘-*

Cal

_I___

E” \

8=90”

,

.

(6) 0.5, 0

50

100

150

I 200

T (K) Fig. 3. Cyclotron

masses corresponding

band

observed

transitions

in S,

to the different

at A = 118 /em

intra-

in the (a)

Faraday and (b) Voigt geometry (dots). The solid lines are the theoretical masses calculated from the Landau level encrgics at fl = 0 and from the band structure in the text

at 0 = 90 o as described

0

1

3

0

1

B :TI Fig. 4. Calculated 1 = 360 meV configuration. shaded

Landau

Icvcl encrgich at /‘; = 0 in S, using

in the (a) semiconducting The

dashed

area represent\

3

et:,

line

is the

the thermal

and (b) semimetallic Fermi

hroadening

level and the

h-T on both

\ider of E,

sides of E, is shown by the shaded region. The solid lines in fig. 3a are the calculated cyclotron masses deduced from the theoretical energy of the intraband transitions. In these calculations, we have taken into account, for each temperature, the initial and final Landau level occupations, except for the 0 + 1’ transition at low tcmperature, and the solid lines are limited to the temperature domain where the corresponding transitions can occur. At low temperature, the two resonances correspond to the - 1 + 0 and 0 + I’ transitions which are the two first intraband transitions available in the semimetallic configuration. The observation of the 0 --j I’ transition is rather puzzling, the Landau level II = 0 being unoccupied at the resonant field. It is tentatively explained by the existence of an electron accumulation layer at the interface between the SL and the CdTe buffer layer. Such an electron accumulation would result from charge transfer from CdTc towards the SL, as previously observed in [ lOO]-oriented HgCdTe-CdTe heterojunctions 1101. As a consequence, the Fermi energy would lie deeper into the conduction band near this interface where a higher cyclotron resonance (for instance 0 + 1’) can occur. Note that an electron accumulation could also exist at the front SL surface and give similar results. In the intermediate temperature range 30-60 K, the SL is semiconducting and the lighter cyclotron mass

Y Guldner et al. / T-dependent electronic properties of HgZnTe / CdTe superlattices

is attributed to 1 -+ 2 or 1 3 0 transitions which are both allowed in the Faraday geometry. Considering the variation E,(T) given in fig. 2b, the final levels 0 and 2 are more and more occupied when the temperature is raised and the associated transmission minimum vanishes for T > 60 K. The heavier cyclotron mass corresponds to 0 -+ l’, which is consistent with E, lying between 0 and 1’ around B = 1 T. Finally in the high temperature domain (T> 100 K), a single transmission minimum is observed which corresponds to the mixing of different intraband transitions. As shown in fig. 3a, the main transitions observed as T is increased are successively 0 + l’, 2 --f 3 and 1’ ---)2’. For instance, at T = 150 K, II = I’ is fully occupied at the resonant field B = 1.2 T (fig. 4) and the observed transitions are therefore 1’ -+ 2’ and 2 --) 3 (fig. 3a). The overall agreement between the magneto-optical data and the calculations is quite satisfying in the entire temperature region investigated in these experiments and supports the calculated Landau levels and band structures using A = 360 meV, with a semimetal-semiconductor transition occuring at 30 K in S,. A similar agreement is obtained in S, and S, with a transition occurring at - 50 K. In the Voigt configuration (@= 90 o 1, the most striking feature observed in the m,(T) dependence is the drop of N 25% appearing around 30 K in S, (fig. 3b) and 40 K in S, and S,. The cyclotron resonance field is B = 1 T at A = 118 ,um and the cyclotron orbit size is then larger than the SL period. The electrons are forced to tunnel through the interfaces and the cyclotron mass depends on conduction dispersion relations along both k, and k,. The m, drop corresponds to a significative reduction of the conduction mass m, along k, when the temperature varies from I.5 to 40 K, in very good agreement with the calculated band structures (fig. 1) which show a large variation of the conduction band anisotropy when the SL undergoes a semimetal-semiconductor transition. Indeed, when the temperature is raised from 1.5 K, the crossing point between E, and HH, at k, = k, moves towards kZ = 0 and the conduction band becomes lighter and lighter of the along k,. The calculated temperature semimetal-semiconductor transition (k, = 01, in-

545

dicated by the arrow on fig. 3b, is in satisfactory agreement with observed data. A similar agreement is obtained in S, and S3. We have carefully investigated the cyclotron resonance in the photon energy range 5-30 meV and the temperature region 1.5-60 K, and we have observed no plasma shift of the cyclotron resonance in the Voigt geometry. For T > 50 K, a monotonic increase of m,(T) is observed at 6 = 90 o which corresponds essentially to the opening of the SL bandgap when the temperature is raised, and, as a consequence, to the increase of the in-plane mass. The solid line in fig. 3b shows the variation m,(T) calculated for S, in the semiconducting regime using an approximate dispersion relation for the conduction band which takes into account the band nonparabolicity. The agreement with the experimental data is quite satisfying. We have discussed transport and far-infrared magnetotransmission measurements performed in n-type HgZnTe-CdTe SLs over a large temperature range. The temperature-dependent electron concentration together with the conduction band density of states deduced from cyclotron resonance data, shows unambiguously that these SLs are degenerate in the entire temperature region and are degenerate intrinsic semiconductors for T > 100 K, which constitutes a new interesting situation in semiconductor superlattice physics. The analysis of the data gives the Fermi level energy, the negative bandgap of the SLs at T = 0 as well as the temperature coefficient of the bandgap. Band structures calculated using a valence band offset A = 360 meV between CdTe and Hg,_,YZn,Te (x < 0.1) account perfectly for these data and show the existence of a semimetal-semiconductor transition which is induced by temperature. We have shown that the semimetal-semiconductor transition is characterized by an important reduction of the cyclotron mass measured when B is perpendicular to the SL axis. The observed magneto-optical intraband transitions are in very satisfying agreement with the calculated Landau levels and the Fermi level energy. Finally, we have shown that the temperature-dependent band structure of these Hg-based SLs presents very unique features quite different from those of III-V heterostructures.

This work was partly supported by a joint research programme CNRS/NSF and by the NATO research grant no. 9.13/890519. The Laboratoire de Physique dc la Mat2re condensCe de I’Ecole Normal SupCrieure is associated to CNRS and to University Paris 6.

References [II N.F. Johnson,

P.M. Hui and H. Ehrenreich, Phys. Rev. Lett. 61 (198X) lYY.3. and J.P. Faurie. Superlattices [21 X. Chu, S. Sivananthan Microstruct. 4 (1988) 173. (.?I J.R. Meyer, C.A. Ifoffman, F.J. Bartoli. J.W. Han, J.W. Cook, Jr.. J.F. Schetzina, X. Chu, J.P. Faurie and J.N. Schulman, Phys. Rev. B 3X (IYXX) 2204.

[4] J.M. Berroir. Y. Guldnrr, J.P. Vieren, M. Voos and J.P. Faurir, Phys Rev. B 34 (lYX6) 891. [5] J.M. Berroir. Y. Guldner. J.P. Vieren. M. Vooa. X. <‘hu and J.P. Faurie, Phys. Rev. Lett. 62 (IYXY) 2024. 161B. Toulouse, R. Granger, S. Rolland and R. Triboulet. J. Phya. 4X (1YX7) 247. and Semimetals. Vol. [71 M.H. Weiler, in: Semiconductors If>, Eds. R.K. Willardson and AC. Beer (Academic Press, New York, lY8l) p. I IY. [Xl C.A. Hoffman, J.R. Meyer. F.J. Bartoli. J.W. IIan. J.W. Cook, Jr.. J.F. Schetzina and J.N. Schulman, Phys. Rev. B 3’) (1089) 520x. Statistics. Vol. 3. Ed. [VI J.S. Blakemore, in: Semiconductor H.K. Henisch (Pergamon. New York. lYh2) p. 103. [I()1 Y. Guldner, G.S. Boebinger, J.P. Vieren. M. Voos and J.P. Faurie, Phys. Rev. B 3h (1987) 2Y.58.