**1. Introduction**

The work of Essaki & Tsu [1] caused a big interest to the study of superlattices made from alternating layers of two semiconductors. The development of molecular beam epitaxy (MBE) was successfully applied to fabricate different quantum wells and superlattices. Among them III-V superlattices [Ga1-xAlxAs-GaAs [1-2] - type I], III-V superlattices [InAs/ GaSb [3] - type II] and later II-VI superlattice [HgTe/CdTe [4] - type III]. The latter is a stable alternative for application in infrared optoelectronic devices than the Hg1-xCdxTe alloys. Es‐ pecially in the region of second atmospheric window (around 10 μm) which is of great inter‐ est for communication.

HgTe and CdTe crystallize in zinc –blend lattice respectively. The lattice-matching within 0.3 % yield to a small interdiffusion between HgTe and CdTe layers at low temperature near 200 °C by MBE. HgTe is a zero gap semiconductor (due to the inversion of relative positions of Γ6 and Γ8 edges [5]) when it is sandwiched between the wide gap semiconductor CdTe (1.6 eV at 4.2 K) layers yield to a small gap HgTe/CdTe superlattice which is the key of an infrared detector.

A number of papers have been published devoted to the band structure of this system [6] as well as its magnetooptical and transport properties [7]. The aim of this work is to show the correlation between calculated bands structures and magneto- transport properties in n type HgTe/CdTe nanostructures superlattices. The interpretation of the experimental data is con‐ sistent with the small positive offset Λ=40 meV between the HgTe and CdTe valence bands.

© 2013 Nafidi; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Nafidi; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Theoretical calculations of the electronic properties of n-type HgTe/CdTe superlattices (SLs) have provided an agreement with the experimental data on the magneto-transport behav‐ iour. We have measured the conductivity, Hall mobility, Seebeck and Shubnikov-de Haas effects and angular dependence of the magneto-resistance [8]. Our sample, grown by MBE, had a period d=d1+d2 (124 layers) of d1=8.6 nm (HgTe) /d2=3.2 nm (CdTe). Calculations of the spectres of energy E(d2), E(kz) and E(kp), respectively, in the direction of growth and in plane of the superlattice; were performed in the envelope function formalism. The energy E(d2, Γ, 4.2 K), shown that when d2 increase the gap Eg decrease to zero at the transition semiconduc‐ tor to semimetal conductivity behaviour and become negative accusing a semimetallic con‐ duction. At 4.2 K, the sample exhibits n type conductivity, confirmed by Hall and Seebeck effects, with a Hall mobility of 2.5 105 cm2 /Vs. This allowed us to observe the Shubnikov-de Haas effect with n = 3.20 1012 cm-2. Using the calculated effective mass (m\*E1(EF) = 0.05 m0) of the degenerated electrons gas, the Fermi energy (2D) was EF=88 meV in agreement with 91 meV of thermoelectric power α. In intrinsic regime, α T-3/2 and RHT3/2 indicates a gap Eg =E1- HH1= 101 meV in agreement with calculated Eg(Γ, 300 K) =105 meV The formalism used here predicts that the system is semiconductor for d1/d2 = 2.69 and d2 < 100 nm. Here, d2=3.2 nm and Eg (Γ,4.2 K) = 48 meV so this sample is a two-dimensional modulated nano-semiconduc‐ tor and far-infrared detector (12 μm<λc<28 μm).

with a valence band offset Λ between heavy holes bands edges of HgTe and CdTe of 40

Correlation Between Band Structure and Magneto- Transport Properties in n-type HgTe/CdTe Two-Dimensional...

The general dispersion relation of the light particle (electron and light hole) subbands of the

<sup>2</sup> (ξ+ <sup>1</sup> <sup>ξ</sup> )+ kp² 4k1k2 (r+ 1

where the subscripts 1 and 2 refer to HgTe and CdTe respectively. kz is the superlattice wave vector in the direction parallel to the growth axis z. The two-dimensional wave vector

E is the energy of the light particle in the superlattice measured from the top of the Γ<sup>8</sup> va‐ lence band of bulk CdTe, while εi (i =1 or 2) is the interaction band gaps E(Γ6) - E(Γ8) in the bulk HgTe and CdTe respectively. At given energy, the two–band Kane model [10] gives the

where m\* = 0.03 m0 is the electron cyclotron mass in HgTe [5]. For a given energy E, a super‐ lattice state exists if the right-hand side of Eq. (1) lies in the range [-1,1]. That implies -π/d ≤

ℏ²(k1²+kp²)

The band structure computation consists of solving Eq. (1) which represents the dispersion relations (i.e. finding the values of energy E which are roots of the Eq. (1) for a given value

<sup>3</sup> P² ℏ² (k1²+kp²) = (E-Λ) ( E - Λ + |ε<sup>1</sup> |) for HgTe

2P² 3|ε<sup>1</sup> <sup>|</sup> <sup>=</sup> <sup>1</sup>

The heavy hole subbands of the superlattice are given by the same Eq. (1) with :

 ℏ²(k2 2 +kp²)

m\*HH =0.3 m0 [5] is the effective heavy hole mass in the host materials.

r, *and* r =1 with{-

*E* − *ε*<sup>2</sup>

<sup>3</sup> P² <sup>ℏ</sup>² (k2²+kp²) = E ( E -ε2) for CdTe } (3)

2 m\*HH = E - Λ for HgTe

2 m\*HH = E for CdTe

<sup>r</sup> -2) sin(k1d1)sin(k2d2) (1)

http://dx.doi.org/10.5772/52101

139

*<sup>E</sup>* <sup>+</sup> <sup>|</sup> *<sup>ε</sup>*<sup>1</sup> <sup>|</sup> <sup>−</sup> *<sup>Λ</sup>* (2)

2m\* (4)

(5)

meV determined by the magneto-optical absorption experiments [9].

kp(kx, ky) describes the motion of particles perpendicular to kz. Here,

*<sup>k</sup>*<sup>2</sup> and r=

*<sup>ξ</sup>* <sup>=</sup> *<sup>k</sup>*<sup>1</sup>

²+kp²) in each host material:

P is the Kane matrix element given by the relation:

superlattice is given by the expression [6]:

wave vector (ki

2

2

kz≤-π/d in the first Brillion zone.

ξ = k1 k2

cos kz(d1+d2) = cos (k1d1) cos (k2d2)- <sup>1</sup>

In conclusion, we will show that the HgTe/CdTe nano-superlattice is a stable alternative for application in infrared optoelectronic devices than the alloys Hg1-xCdxTe.
