Magneto-optics in II–VI compound type III superlattices

540

Journal of Crystal Growth 101 (1990) 540—545 North-Holland

MAGNETO-OPTICS IN Il-VI COMPOUND TYPE III SUPERLATI1CES Y. GULDNER and J. MANASSES D~partementde Physique de l’Ecole Normale Supérieure, 24 Rue Lhomond, F-75231 Paris Cedex 05, France

Magneto-optical experiments on n-type Hg 1 _~Zn~Te—CdTesuperlattices yield the determination of the conduction band dispersion. Comparison with theoretical calculations demonstrates the semimetallic character of the superlattices and support a rather large value of the valence band offset. Similar experiments performed on a Hg1 — ,~Mn~Te—CdTesuperlattice at various temperatures show evidence of the exchange interaction in this new semimagnetic material.

1. Introduction Il—VT superlattices (SL) formed with CdTe and a zero-gap mercury based compound have been termed “Type III” heterostructures because of the unique inverted band structure of the zero-gap material. They can be either semiconducting or semimetallic [1], depending on the layer thicknesses and we show here that their band structure can be determined by far-infrared magneto-absorption experiments.. We report cyclotron resonance measurements on high electron mobility HgZnTe—CdTe SLs grown by molecular beam epitaxy in the (100) direction. The SL electron cyclotron resonance is measured as a function of 0, which is the angle between the direction of the magnetic field and the SL axis. The data are analysed by using an ellipsoidal conduction band approximation, from which the in-plane effective mass and the mass along the growth axis structure are deduced. Comparison of the results with band calculations clearly demonstrates the semimetallic nature of the SLs and support a large valence band offset value ( 300 meV) between Hg 1 Zn Te (x <0.1) and CdTe X x We also discuss far-infrared magneto-absorption experiments performed on a Hg0 96Mn0~Te— CdTe SL over a temperature range 1.5 to 10 K. The temperature dependence of ofthe electron cyclotron resonance and interband transitions shows evidence of the exchange interaction be -

0022-0248/90/$03.50 © 1990

—

tween the localized Mn d-electrons and the conduction band electrons in the semimagnetic SL. The results are interpreted from superlattice band-structure calculations which include the magnetization effects.

2. HgZnTe—CdTe superlattices We present here results obtained on two SLs (S1 and S2) grown on a (100) GaAs substrate with a 2 p~mCdTe buffer [2] and consisting of 100 periods of Hg1~Zn~Te—CdTe,the CdTe layers containing 15% HgTe [3]. For each sample, the layer thicknesses and the alloy Zn composition x, as well as the electron mobility ~t and concentration at 25 K are listed in table 1. The sample were prepared intentionally with thin CdTe barriers to study the carrier transport along the SL axis and were n type in the temperature range investigated5 (2—300 K), mobilities in excess of 2 x i0 cm2/V. S atwith lowHall temperature.

Table 1 Characteristics work; d1 and d2 of are the the HgZnTe—CdTe HgZnTe andsuperlattices CdTe layer thicknesses, used in this respectively, x is the Zn composition; n and ~sare measured at 25 K 2/V.s) n (cm3) Sample d1 (A) d2 (A) x p. (cm S 5 3.7x1015 S 5 2.6x1015 1 105 20 0.053 2.1x10 -_____________________________________________ 2 80 12 0.053 2.1x10

Elsevier Science Publishers B.V. (North-Holland)

Y. Guidner, J. Manassès

/ Magneto-optics in II— VI compound Type III superlattices

We first discuss the SL band structure and Landau levels. All the calculations are done by using a 6 X 6 envelope function Hamiltonian [4], taking for CdTe the band parameters given in ref. [4]. For HgZnTe, we obtained the F6—T~ energy

meV, the band is nearly isotropic around k = 0. On the contrary, for A = 300 meV and 450 meV, it is dispersionless for 0 < k~
separation by using x = 0.12 for the semimetal— semiconductor transition at 2 K [5], the other parameters being identical to those of HgTe. Fig. 1 shows the calculated band structure of S1 in the plane of the layers (kr) and along the SL growth axis (k2). Reported experimental and theoretical values of the valence band offset between CdTe and HgTe range between 0 and 500 meV [4,6,7] and, in the case of Hg1 ~Zn~Te—CdTe SL with low Zn content, we have performed the calculations for A = 40 meV (a), A = 300 meV (b) and A = 450 meV (c). The zero of energy is taken at the CdTe valence-band edge. E1, LH1 (HH1, HH2), respectively, denote the first light particles’ (heavy holes’) bands for the motion along the growth axis. For A = 40 meV (fig. la), the SL is a semiconductor, E1 being the conduction band and HH1 the highest valence band. For large valence band offset, the E1—HH1 separation decreases until finally E1 and HH1 meet and then cross in the k~direction for k2 = = k~.For A = 300 meV (fig. ib), HH1 is the conduction band and the superlattice is semimetallic with a nearly zero gap (E1 HH1 —2 meV) and k~= 0.lir/d. For A = 450 meV (fig. ic), E1 lies about 16 meV below HH1 and k~= 0.31r/d. The most significant change in the band structure when increasing A is the k~ dispersion of the SL conduction band. For A = 40 —

I

A+l0O

I

A,.4OmeV

A

1

/

A~45Omê1

L+~0

/1c

-

L+5O

HH1 /

1

m~ is extremely small near k~= 0 (m~ 2 x 3m 10 0), as a result of the small HH1—E1 separation. The dashed line in figs. lb and lc shows the in-plane dispersion relation calculated for k~ = k~.One can see the m~depends on the growthdirection wavevector because m~cc HH1—E1 which is a function of k2. From fig. 1, it is clear that the measurement of the conduction band anisotropy will provide a very good determination of the nature of the SL (semiconductor or semimetallic). Similar calculations are done for S2 and the resulting calculated band structures for A = 40, 300 and 450 meV are shown in figs. 2a, 2b and 2c. We have performed magnetotransmission experiments at 1.6 K, using a molecular gas laser (A = 41—255 ~Lm). The transmission signal was measured at fixed infrared photon energies E, while B could be varied up to 12 T. Fig. 3a shows transmission spectra of S1 at A = 118 ~smfor 0 = 0 (Faraday geometry), 450 and 900 (Voigt geometry). For 0 = 0, two well-developed resonance lines occur at low magnetic field (<1 T). These two lines are shifted towards higher magnetic fields when 0 is increased and a cos 0 dependence is observed for 0 between 00 and 450~ We plotted the energy positions of the transmission minima as a function of B in fig. 3c. At 0 = 00, the two observed transitions extrapolate to E 0 at B = 0 and are therefore attributed to electron cyclotron I

Ar3O~fl~

A+50

541

k~(L/d) 0

T—..-~

k1(i/d) 11

HH1 1*42 ~

k5(v’~) 0

“.—

_______ k~(x/d) 11

~i1 HH

~

k~(IJd) 0

k1~/d)

Fig. 1. Calculated band structure of S~in the plane of the layers (kr) and along the growth axis (ks) for A 40 meV (a), A meV (b) and A = 450 meV (c). The dashed lines in (b) and (c) represent the in-plane dispersion for k~= k~.

300

542

Y. Guidner, J. Manassès A.1OC

/ Magneto-optics in II— VI compound

r

I

,40 1eV

2

1

0

Fig. 2. Calculated band structure of

~2

k1(ii/d)

A~450meV

/1

~

1 1

iffi2.~ k~(w/d) 0

~L+lOO

I

p300meV

HH ~

I

Type III superlattices

\

L+5O

HH

I

k1(~/d) 1 1

1 I

k5(i/d) 0

____________ k~(1~/d)1

along k~and k~for A =40 meV (a), A =300 meV (b) and A = 450 meV (c). The dashed lines are the in-plane dispersion for k~= k~.

resonances, considering the n-type nature of the sample. To interpret these results, we have calculated the SL Landau levels when a magnetic field is applied along the growth axis (0 = 00) [4]. The solid line in fig. 3c is the calculated cyclotron resonance using A = 300 meV. The agreement with the experimental points is quite satisfying; thus, the low magnetic field transition can be reasonably attributed to the SL electronic cyclotron resonance. The measured cyclotron mass at low magnetic field (<0.2 energies is m~ = 2.5 T) x 10and3mfor vanishing photon 0, in good agreement with the calculated dispersion relations near k~= 0. One can see in fig. 3c that the energy of the transition is not a linear function of the magnetic field, reflecting the strong non-parabolicity of the /“~ OrO

/ I ~ / ~—8~45 / 7 A:118~i.m ~~ \I/

in-plane dispersion relation. In the Voigt geometry 0 = 900, the cyclotron resonance line occurs around 1 T for A = 118 ~tm corresponding to a cyclotron orbit radius of 250 A, so that electrons are forced to tunnel through several interfaces. In fig. 2b, we have plotted the measured cyclotron mass m~versus 0 for A = 118 p~m.We assume an ellipsoidal dispersion relation for the conduction band near k = 0 so that the cyclotron mass is given at20 low magnetic[8] field m~the = (m~m5)/ + m~sin20) wherebym~is in-plane (m~cos mass at the photon energy and m the mass along the growth axis. The solid line in fig. 3b, which is the calculated cyclotron mass using m~= 0.065m0, is in very good agreement with experimental points. The measured mass-anisotropy ratio

~20

7J ~ I ,‘ Ii / fII/

:~

(I

30

a

k

A~118~Lm

E 2.102

I,

—

-

:4

B(T)

9(0)

B(T)

Fig. 3. (a) Typical transmission spectra of S~for A =118 p.m and T=1.6 K. (b) Cyclotron mass versus 0 for A =118 p.m and T=1.6 K; the dots represent the experimental points and the solid line the calculated values in the ellipsoidal approximation. (c) Energy of the observed transmission minima versus B (dots). The solid line is the calculated SL cyclotron resonance for A = 300 meV.

Y. Guidner, J. Manassés

/ Magneto-optics in II— VI compound Type III superlattices

543

m~/m~is 25 for A = 118 rim. Note that this ratio decreases from 40 to 14 when increasing the photon energy from 5 to 30 meV. Comparison of these results with the band structure calculations shown in fig. 1 clearly supports the semimetallic nature of the superlattice. Indeed calculations done

the HgMnTe—CdTe SLs, a strong effect of the exchange interaction on the Landau level energy is expected which can be evidenced by the temperature dependence of the electron cyclotron resonance. We report here results obtained on a Hg096

in the semiconductor configuration for A = 40 meV (fig. la) lead to an anisotropy ratio of — 1 at A = 118 ~tm. The anisotropy is found to be 10 for A = 300 meV and — 20 for A = 450 meV, which is very close to the experimental value. Similar experiments performed on sample S2 lead to a agreement mass—amsotropy 6 at 118structure ~sm, in good with theratio calculated band shown in fig. 2c (A = 450 meV). The higher field line observed in fig. 3 is most

Mn0 04Te—CdTe SL grown by molecular beam epitaxy on a (100) GaAs substrate with a 2 ~im CdTe (111) buffer layer [16]. The SL consists of 100 periods of 167 A thick Hg0 96Mn0~Telayers interspaced by 22 A thick CdTe barriers and is n type with electron density n = 6s at x 1016 4 cm2/V. 25 K.cm ~ and mobility ~u = 2.7 x i0 The SL band structure and Landau level calculations are done by using a 6 x 6 envelope function Hamiltonian [4,17]. The I~—F 8 energy separation is taken to be 130 meV in Hg0 96Mn004 Te at low temperature. For the Hg0 96Mn004Te layers, the model is modified to take into account the exchange interactions 2 ±between ions andlocalized the F d electrons bound to the Mn 6 and F8 s- and p-band electrons. The s—d and p—d interactions are introduced in the molecular field approximation through two additional parameters, r and A, where r = a/fl is the ratio between the T~ and T~exchange integrals, a and /3, respectively [18,19]. Here A is the normalized magnetization defined by A = -~$xN~/S~), where N0 is the number of unit cells per unit volume of the crystal, x is the Mn composition (x = 0.04), and
—

probably due to electron accumulation near the interface resulting from the charge transfer which occurs from the CdTe buffer layer towards the SL [9]. It can be identified as the cyclotron resonance of the resulting two dimensional electron gas at the interface or as a cyclotron resonance between higher Landau levels of the SLs. Such a transition was previously observed in the HgCdTe—CdTe heterojunctions grown in the (100) direction under the same conditions [10]. Finally, from measurements of the conduction band dispersion in type III HgZnTe—CdTe SLs, we have demonstrated that the conduction band is highly anisotropic in the investigated samples, showing that they are semimetallic and that the valence band offset is large (A 300 meV), in agreement with the XPS measurements [7] and with recent magneto-optical studies done in p-type HgTe—CdTe SLs [11].

—

—

3. HgMnTe—CdTe superlattices Much work has been directed toward semimagnetic SLs in search of low-dimensionality electronic and magnetic effects [12—15].The type III system Hg1 ~Mn~Te—CdTeis unique because the two-dimensional electron confinement is in the semimagnetic layers, and this system should be particularly interesting to probe the exchange interaction between the localized Mn magnetic moments and the SL conduction band electrons. In

Magnetization A given in meV/T at various magnetic fields and temperatures for bulk Hg0 96Mn0 ~Te T K B T

______________________________________ 1.5 4.2 10.0

0.5 —2.3 —1.4 —0.5

3 —1.3 —1.1 —0.5

5 —1.0 —0.9 —0.45

7 —0.8 —0.7 —0.45

10 —0.6 —0.6 —0.4

___________________________________________

544

Y. Guidner, J. Manassès

/ Magneto-optics in II— VI compound

A+100

~+l00

I

Type III superlattices I

I

I

I

I

I

I

I

I

I

I

A: 300mev

A+50

‘N.

HH 2 ________

~~_~10

A+50

/

~

K

Cl)

I

I—

—

H I

1

~

kz(1T/d)

0

kx(TI’/d)

t~B

1

Fig. 4. Calculated band structure along k~,and k~of the

a350

~.v1

-

>

,,

300

I

--

--

~

I

~

,~/

I

~ 105 0K ._4.2K 1

~

-

I

0

I

2

I

I

4

5

I

I I

A:41~Lm I I I 10

B (tesla) Fig. 6. Far-infrared magnetotransmlssion spectra at A = 41 p.m

(T + T0). T0 is found to be — 5 K for x = 0.04 [21]. The exchange integral N0f3 — 1 eV and r — —1 [19]. The magnitude of A which satisfies the modified Brillouin function for x = 0.04 is given in table 2 for various magnetic fields and temperatures between 1.5 and 10 K. The resulting band structure along k~ and k2, calculated for zero magnetic field using a valence band offset A = 300 meV, is shown in fig. 4 and one can note that the SL is semimetaffic. Fig. 5 shows the SL conduction Landau levels calculated for T = 1.5, 4.2 and 10 K, using the bulk Hg0 96Mn 0~Temagnetization. Note that as T decreases, the magnetization

I

I

0

Hg0~Mn0 ~Te—CdTe superlattice.

I

I

-

-

for temperatures from 1.5 to 10 K. The arrows correspond to resonance position. The marker above ~the B calculated indicates cyclotron the magnitude of the calculated shift in the —1 .-~ o cyclotron resonance transition.

A is increased (See table 2) and all the conduction levels increase in energy. Magneto-absorption experiments were done with temperature range 1.5—10 K, using a molecular gas laser (A = 41—255 jim). Fig. 6 shows transmission spectra obtained at A = 41 ~im between 1.5 and 10 K. The main absorption minimum corresponds to the 1 0 transition (fig. 5) which is the ground electron cyclotron resonance. For each temperature, the calculated field position of the line is indicated by the arrows in fig. 6 and one —

—

most can and see Landau striking the point agreement calculations is —0.6 that the is—1temperature, quite experiments 01.5 good. transition shifts vanation K. There to that lower being arelevel two Bz.~B with contributions increasing Tbetween between to the temperaandThe the 10 ture-dependent shift: the temperature dependence of the Hg0 96Mn0~Teenergy gap and the temperature dependent Mn magnetization. In bulk HgTe, as T increases from 1.5 to 10 K, the magnitude of —

—*

I

6

B (T) Fig. 5. Calculated conduction Landau levels for different temperatures using A = 300 meV.

the energy gap diminishes by less than 3 meV. The effect in Hg096 Mn 004Te is expected to be similar. Such a small shift in energy gap is calculated to have only a slight effect on the cyclotron reso-

Y. Guidner, J. Manassès

/ Magneto-optics in II— VI compound

nance transition at most —0.05T. The observed shift of the I 0 transition is an order of magnitude larger than could be due to the temperature dependence of the energy gap alone and the Mn magnetization can account for the enhanced temperature dependence of the cyclotron resonance line. As T increases over our experimental range, the Mn magnetization decreases dramatically at lower magnetic fields (see table 2). This has a direct effect on the Landau levels in the superlattice, as shown in fig. 5. In particular, the N = I level is depressed more than the N = 0 level, increasing the cyclotron resonance energy as temperature is increased. In bulk semimagnetic semiconductors, the exchange interaction has been observed by magneto-absorption primarily in the spin and combined (cyclotron plus spin) resonances. The observation of the exchange interaction in cyclotron resonance is a result of the increased band mixing in a superlattice [17]. To summarize the results, we observe cyclotron resonance in a Hg0 56Mn004Te—CdTe superlattice, —

545

References

—~

—

which is in good agreement with band structure calculations in the envelope function approximation with a valence band offset A — 300 meV. The temperature dependence of cyclotron resonance transitions evidences the effect of the exchange interaction in the semimagnetic semiconductor superlattice. The magnetization observed in the superlattice is consistent with the bulk Hg0 96Mn004 Te magnetization, due to the thick Hg0 96Mn004Te layers and thin CdTe barriers in our superlattice.

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Acknowledgements [19]

We wish to thank J.M. Berroir, J.P. Vieren and M. Voos from the Ecole Normale Supérieure, X. Chu and J.P. Faurie from University of Illinois at Chicago, C. Dupas from the Institut d’Electronique Fondamentale at Orsay and G.S. Boebinger from AT & T Bell Laboratories for contributing

to this work.

Type III superlattices

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