Cd1-xMnxTe double-barrier heterostructures with zero external field

Accepted Manuscript Spin-resonant tunneling in CdTe/Cd1-xMnxTe double-barrier heterostructures with zero external field

R. Dilber Pushpitha, L. Bruno Chandrasekar, J. Thirumalai, K. Gnanasekar, R. Chandramohan PII:

S1386-9477(18)30337-0

DOI:

10.1016/j.physe.2018.11.017

Reference:

PHYSE 13359

To appear in:

Physica E: Low-dimensional Systems and Nanostructures

Received Date:

07 March 2018

Accepted Date:

13 November 2018

Please cite this article as: R. Dilber Pushpitha, L. Bruno Chandrasekar, J. Thirumalai, K. Gnanasekar, R. Chandramohan, Spin-resonant tunneling in CdTe/Cd1-xMnxTe double-barrier heterostructures with zero external field, Physica E: Low-dimensional Systems and Nanostructures (2018), doi: 10.1016/j.physe.2018.11.017

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ACCEPTED MANUSCRIPT

Polarisation efficiency peaks of LH and HH, two resonant peaks are obtained for HH; Dwell time of LH and HH corresponding to lowest resonance energy for 4% Mn doped CdTe/CdMnTe double barrier heterostructure with barrier width of 10nm.

ACCEPTED MANUSCRIPT

Spin-resonant tunneling in CdTe/Cd1-xMnxTe double-barrier heterostructures with zero external field R.Dilber Pushpitha1, L.Bruno Chandrasekar2, J. Thirumalai1*, K.Gnanasekar2, R.Chandramohan3 1Department

of Physics, Srinivasa Ramanujan Centre, SASTRA Deemed to be University, Kumbakonam, India.

2Department 3

of Physics, The American College, Madurai, India.

Department of Physics, Sree Sevugan Annamalai College, Devakottai, India. * Telephone:0435-242154 ; E-mail: [email protected]

Abstract:

Spin-dependent

resonant

tunneling

in

CdTe/CdMnTe

double-barrier

heterostructures was theoretically investigated. The transfer-matrix method was employed to study the spin transport properties under zero applied field. The effect of Dresselhaus spinorbit coupling was considered in the symmetrical heterostructure. The influences of the barrier width and height on the polarization efficiency, barrier transparency and dwell time of light and heavy holes were observed and discussed. Keywords: resonant tunneling, transfer matrix, resonance polarization, dwell time, symmetric heterostructures 1. Introduction Spin is an intrinsic property of particles that can be manipulated alone or with charge to exploit the electrical and magnetic properties of materials. Spintronics is a developing branch of science with the scope of research supporting construction of billion dollar quantum computing devices as well as exploring the fundamental nuances of spin. Such devices have perform with high speed, low power consumption and novel operational modes compared to their conventional counterparts. Important technological applications of spintronics include spin-filters, spin-polarized diodes, spin-field effect transistors, spin-polarized lasers, magnetic bipolar transistor, hot-electron spin transistors, spin-light emitting diodes and spin lasers [16]. Spin-dependent carrier transport in various materials must be explored for efficient device

construction. One mechanism of transport, spin-dependent tunneling is often caused by spin orbit coupling (SOC), the coupling of spin with the orbital degree of freedom in carriers. Structural inversion asymmetry in confined potentials can induce Rashba SOC and the lack of bulk inversion symmetry in semiconductors causes Dresselhaus SOC. However, in 1

ACCEPTED MANUSCRIPT symmetrical semiconductor heterostructures, the k3 Dresselhaus effect contributes to the effective Hamiltonian causing spin splitting in the transmission resonance and therefore we study only the Dresselhaus SOC in the symmetric double-barrier structure considered here [7, 22]. Initially, ferromagnetic and nonmagnetic heterostructures were employed in such devices; semiconductor interfaces gained importance because they rectify conductivity mismatches in earlier devices. The difficulty of integrating magnetic materials with semiconductors rather

than with metals led to the development of an alternative approach in which a fraction of constituent ions of a semiconductor are replaced with magnetic ions, yielding diluted magnetic semiconductors (DMS), which facilitate integration. Spin-dependent quantum confinement,

enhanced

magneto-optical

effects,

spin-polarons

and

carrier-induced

ferromagnetism are among the phenomena observed in DMS materials [8]. Because Mn- or Fe-based dilute magnetic spin super-lattices were first proposed by Ortenberg [9], many reports have described Mn-based DMS heterostructures. In addition spin-dependent transport through

CdTe/CdMnTe,

CdTe/CdMgTe/CdMnTe/CdMgTe/CdTe

and

ZnSe/ZnMnSe

symmetrical and asymmetrical heterostructures in the presence of external field has been studied widely [10-18]. However to the best of our knowledge, no reports have yet (i) studied spin transport in CdTe/CdMnTe heterostructures with zero field and (ii) compared the characteristics of spin-polarized heavy holes (HH) and light holes (LH). Reports have described the increases in tunneling lifetime with increasing external fields; these results are disadvantageous for swift processesing. Electron transport is widely studied but hole transport is equally important for applications including complementary metal-oxide semiconductors. Thus, we study spin-polarized resonant tunneling in CdTe/CdMnTe doublebarrier structures with zero applied field for LH and HH. The report is arranged as follows: The Theory with formalism is given in section 2; the Results are discussed in section 3; and the Conclusion follows. 2. Theory We consider charge carriers moving along the z-direction with effective mass (m) through a symmetric double-barrier heterostructure with barrier widths 𝑧2 ‒ z1 = z4 ‒ z3 and well width z3 ‒ z2 as shown in fig.1. In the well region, the motion of the charge carrier with an in-plane wave vector (𝑘 ∥ ) is described by the Hamiltonian, 2

𝐻𝑤𝑒𝑙𝑙 =‒

2 2 ℏ 𝑘∥ ℏ ∂ + 2𝑚 2𝑚∂𝑧2

2

(1)

2

ACCEPTED MANUSCRIPT The charge carrier motion is described by the function Ψ𝜎(𝑟) = 𝜒𝜎𝑢𝜎(𝑧)exp (𝑖𝑘 ∥ 𝜌) where,

(2)

𝜒𝜎 is the spin-dependent spinor [19] and the solution of the time-independent

Schrödinger equation gives the solution (𝑗)

(𝑗)

(𝑗)

𝑢 𝜎 (𝑧) = 𝐴 𝜎 exp [𝑖𝑘𝑧𝑧] + 𝐵 𝜎 exp [ ‒ 𝑖𝑘𝑧𝑧]

(3)

𝑘𝑧 is the component of the wave vector in z-direction. In the barrier region, the Hamiltonian is given as [20] 2

𝐻𝑏𝑎𝑟𝑟𝑖𝑒𝑟 =‒

2 2 ℏ 𝑘∥ ℏ ∂ + 2𝑚 2𝑚∂𝑧2

2

(4)

+ 𝑉(𝑧) + 𝐻𝐷

Here, V(z) is the heterostructure potential and 𝐻𝐷 represents the Dresselhaus Hamiltonian. The basic form of 𝐻𝐷 is given as [20] 𝐻𝐷 = 𝛾[𝜎𝑥𝑘𝑥 ‒ 𝜎𝑦𝑘𝑦]

2

∂

∂𝑧

(5)

2

(

)

0 1 γ is the Dresselhaus spin-orbit splitting constant;the Pauli spin matrices are 𝜎𝑥 = 1 0 and

(

)

0 𝜎𝑦 = 𝑖

‒𝑖 0 . The non-diagonalized Dresselhaus Hamiltonian becomes the diagonalized

Dresselhaus Hamiltonian using the spinor, 𝜒𝜎 =

1

( ‒ 𝜎𝑒1 )

(6)

‒ 𝑖𝜃

2

σ is +1 for spin-up and ‒1 for spin-down directions and θ is the polar angle of the wave vector k in the x-y plane given by 𝑘 = (𝑘 ∥ cos 𝛷, 𝑘 ∥ 𝑠𝑖𝑛 𝛷,kz) [21]. +

The diagonalized Dresselhaus Hamiltonian is formed as U HDU where U is the unitary matrix formed from the spinor 𝜒𝜎. The charge carrier motion is given as (𝑗)

(𝑗)

(𝑗)

𝑢 𝜎 (𝑧) = 𝐴 𝜎 exp [𝑞𝜎𝑧] + 𝐵 𝜎 exp [ ‒ 𝑞𝜎𝑧]

(7)

𝑞𝜎 is the wave-vector in the barrier region, expressed as, 𝑞𝜎 =

𝑞0

(8)

1 + 𝜎 𝛾2𝑚 𝑘 ℏ2 2 ∥

𝑞0 is the wave-vector in the barrier region without considering spin-orbit interactions. The value of 𝑞0 in the barrier region is [21] 𝑞0 =

2𝑚𝑏𝑉 ℏ

2

‒ 𝑘𝑧

(

)

𝑚 𝑚 2 𝑏 2 𝑏 ‒ 𝑘 ∥ 𝑚𝑤 ‒ 1 𝑚𝑤

(9)

3

ACCEPTED MANUSCRIPT 𝑚𝑏 and 𝑚𝑤 are the effective masses of the carrier in the barrier and well region respectively. The condition for the Eigen function Ψ𝜎(𝑟) and its derivative

1 ∂Ψ𝜎(𝑟) 𝑚𝜎 ∂𝑧

to be continuous at

the interfaces yields

() 𝑉

𝐴𝜎

𝑉

𝐵𝜎

() 𝐼

= 𝑆4.𝑆3.𝑆 .𝑆1 2

𝐴𝜎

(10)

𝐼

𝐵𝜎

() 𝐼

where the transfer matrix relation of the coefficients in the first

() () 𝑉

𝐴𝜎

𝑉

𝐵𝜎

𝐴𝜎 𝐼

𝐵𝜎

() 𝑉

and last region

𝐴𝜎

𝑉

𝐵𝜎

is

𝐼

=𝑆

𝐴𝜎 𝐼

𝐵𝜎

, where S represents the transfer matrix and is 𝑆 = 𝑆4.𝑆3.𝑆 .𝑆1

( )

2

( ( ))(( ) ( ) ( ( ))(( ) ( ) ( ( ))(( ) ( ) ( ( ))(( ) 1

1 𝑆4 = 2

1

1

1 𝑆3 = 2

1

1

1 𝑆2 = 2

1

1

1 𝑆1 = 2

1

𝑚𝑏2 𝑞𝜎2

‒ 𝑚𝑏2 𝑞𝜎2

𝑚𝑤 𝑖𝑘𝑧

‒ 𝑚𝑤 𝑖𝑘𝑧

𝑚𝑏1 𝑞𝜎1

‒ 𝑚𝑏1 𝑞𝜎1

𝑚𝑤1 𝑖𝑘𝑧

‒ 𝑚𝑤 𝑖𝑘𝑧

𝑒𝑥𝑝(𝑖𝑘𝑧(𝑧4 ‒ 𝑧5)) 𝑖𝑘𝑧 𝑒𝑥𝑝(𝑖𝑘𝑧(𝑧4 ‒ 𝑧5)) 𝑚𝑤

𝑒𝑥𝑝( ‒ 𝑖𝑘𝑧(𝑧4 ‒ 𝑧5)) ‒ 𝑖𝑘𝑧 𝑒𝑥𝑝( ‒ 𝑖𝑘𝑧(𝑧4 ‒ 𝑧5)) 𝑚𝑤

( )

𝑒𝑥𝑝(𝑞𝜎1(𝑧3 ‒ 𝑧4))

𝑞𝜎1

𝑚𝑏2

𝑒𝑥𝑝( ‒ 𝑞𝜎1(𝑧3 ‒ 𝑧4)) ‒ 𝑞𝜎1 𝑒𝑥𝑝( ‒ 𝑞𝜎1(𝑧3 ‒ 𝑧4)) 𝑚𝑏2

( )

𝑒𝑥𝑝(𝑞𝜎1(𝑧3 ‒ 𝑧4))

𝑒𝑥𝑝(𝑖𝑘𝑧(𝑧2 ‒ 𝑧3)) 𝑖𝑘𝑧 𝑒𝑥𝑝(𝑖𝑘𝑧(𝑧2 ‒ 𝑧3)) 𝑚𝑤

)

𝑒𝑥𝑝( ‒ 𝑖𝑘𝑧(𝑧2 ‒ 𝑧3)) ‒ 𝑖𝑘𝑧 𝑒𝑥𝑝( ‒ 𝑖𝑘𝑧(𝑧2 ‒ 𝑧3)) 𝑚𝑤

( )

𝑒𝑥𝑝(𝑞𝜎1(𝑧1 ‒ 𝑧2)) 𝑞𝜎1 𝑒𝑥𝑝(𝑞𝜎1(𝑧1 ‒ 𝑧2)) 𝑚𝑏1

)

𝑒𝑥𝑝( ‒ 𝑞𝜎1(𝑧1 ‒ 𝑧2)) ‒ 𝑞𝜎1 𝑒𝑥𝑝( ‒ 𝑞𝜎1(𝑧1 ‒ 𝑧2)) 𝑚𝑏1

( ) 𝑉

)

)

The barrier transparency is given by 𝐴𝜎2 [22] and the polarization efficiency of the charge carriers is [23]

4

ACCEPTED MANUSCRIPT

𝑃=

2

2

2

2

|𝐴𝑉𝜎| ‒ |𝐴𝑉𝜎|

|𝐴𝑉𝜎| + |𝐴𝑉𝜎|

(11)

The dwell time 𝜏𝜎 is the average time spent in the barrier region, overall incoming particles, irrespective of transmission and reflection. It is calculated for LH and HH using the following expression [11,25] 2

𝑧

𝜏𝜎 = 𝑚/ℏ𝑘𝑧∫𝑧4|Ψ𝜎(𝑟)| 𝑑𝑧

(12)

1

3. Results and Discussion A symmetrical double-barrier heterostructure of CdTe/Cd1-xMnxTe is considered with 𝑘 ∥ 8

= 3 × 10 𝑚

‒1

to study the spin-dependent transport properties of LH and HH. The 3

parameters used in the calculation are given:𝑧3 ‒ 𝑧2 = 6 𝑛𝑚 and 𝛾 = 12 𝑚𝑒𝑉𝑛𝑚 . The effective masses of LH and HH are 0.18 𝑚0 and 0.60 𝑚0 respectively, both less than electron masses which indicates higher mobility. The band gaps of DMS depend on the Mn concentration resulting in an offset at the well-barrier junction. The band gap offset falls partially in valence and conduction bands. The total band gap offset is calculated by [13,2425], Cd1 ‒ xMnxTe CdTe ‒ = 1.59𝑥 𝑒𝑉 𝐸 𝑔 𝑔

(13)

𝐸

The total offset is not shared equally but in a 7:3 ratio by the conduction and valence bands respectively, as inferred from many experimental works and supported by theoretical predictions [28-30]. Thus, the offset of the band gap in the valence band gives the valenceCd1 ‒ xMnxTe CdTe ‒ )[11]. 𝐸 𝑔 𝑔

band barrier height which is 30% of (𝐸

As the Mn concentration

increases in the CdTe/Cd1-xMnxTe double-barrier heterostructure, the height of the barrier also increases. Fig 2 shows the polarization efficiency of LH and HH for different barrier widths of 6, 8, and 10 nm. The Mn concentration in the barrier region is 4%. The plots help to infer the energies of the maximum and minimum polarizations. The polarization efficiency of HH is greater than that of LH; both are increased with increasing barrier width. The barrier transparencies of LH and HH are shown in Fig. 3‒5.

The spin-up and spin-down holes have equal

probabilities of transmission unlike electrons where spin-down electrons dominate transmission. The imbalanced ratio of the transmission probabilities for spin-up and -down 5

ACCEPTED MANUSCRIPT charge carriers can be utilized for spin-filter applications [26]; while ratio imbalance is not observed in our case, the difference in resonance energy still indicates potential for such applications. The energy difference between spin-up and -down holes is negligible in LH, whereas considerable energy separation is achieved in HH. The energy separation is almost independent of the barrier width. The energy separation between spin-up and -down holes increases with the external magnetic field and becomes saturated at high magnetic field strengths in the work by Mnasri et al. [9]. Without application of an external field, the energy separation is greater for HH and negligible for LH, which suggests that CdTe/CdMnTe heterostructures could be used for spin-polarization applications of HH, while not for those of LH. For HH the barrier transparency peaks are sharper than those for LH; the sharpness increases with increasing barrier width in both cases. This yields a definite energy value with which holes could be incident on the material to achieve 100% transmission. Gnansekar et al. investigated the spin transport of holes through CdTe/CdMnTe symmetrical and asymmetrical heterostructures with an external field. 100% polarization was achieved for holes with a modulated weak magnetic field. Regarding barrier transparency, spin-up and – down holes had negligible and nearly 100% transmission respectively, above the critical magnetic field [11]. In our observation, both spin-up and spin-down LH have 100% transmission; HH have considerable transmission with no field but varying transmissions through different potential fields. The HH peak at lower resonance energies shows < 100% transmission. The same material responds differently for the same carrier at two different energies; this interesting behaviour merits further research. The resonance energy of LH lies between the two observed resonance energies of HH. This displays the availability of two quantum confinements for HH in the considered material. Fig.6 shows the polarization efficiency, barrier transparency and dwell times of LH and HH for the ‘Mn’ concentration of 7%. As the Mn concentration increases, the barrier height increases. This causes an increase in the polarization efficiency for both LH and HH. Moreover, the resonance peaks also shift to higher energy levels. The influence of Mn doping on the resonance energy levels is evident by comparing all the figures. The influence of magnetic field on the spin-dependent transport of LH and HH has been reported by Bruno et al. [31]. In comparison, the results obtained without an applied field are not negligible. For an applied magnetic field, B = 1 the barrier transparency and polarization efficiency are studied for the case of barrier width of 8 nm and 𝑥 = 0.04 and reported in Fig 7.

6

ACCEPTED MANUSCRIPT When a magnetic field is applied, the 𝑉𝑧 term in equation (4) includes the Giant Zeeman effect given by 𝑉𝐺𝑍 =

‒1 𝑁 𝛽𝑥𝑒𝑓𝑓 3 0

〈𝑆𝑧〉𝜎𝑚𝑗

(14)

where 𝑁0 is the number of crystalline elementary cells per unit volume, 𝛽 is the value of the sp-d exchange integral, 𝑥𝑒𝑓𝑓 is the effective functional occupancy of the Mn ions on Cd sites 5

and 〈𝑆𝑧〉 is the thermal average of the z component of Mn 3𝑑 spin.

( )[718.2𝑒

2 𝑥 𝑥𝑒𝑓𝑓 = 5 1100

‒𝑥 0.02307

‒𝑥 (0.01615 ) + 19.66]

+ 1988

( )

〈𝑆𝑧〉 =‒ 𝑆0𝐵𝑠

𝑔𝑆𝜇𝐵𝐵

(15) (16)

𝑘𝐵𝑇𝑒𝑓𝑓

Where 𝑇𝑒𝑓𝑓 = 𝑇 + 𝑇0 and 𝐵𝑠(𝑥) is the Brillouin zone function. 35.37𝑥

𝑇0(𝑥) = 1 + 2.752𝑥 (17) On comparison with Fig 3-5 and 7 the field induced shift in the resonance energy of the carriers; the shift is large for HH and small for LH. The shift is due to the alteration of barrier height by the applied field. The polarization efficiency is enhanced while the barrier transparency peak becomes narrow, sharp and suppressed. The application of the magnetic field separates the spin-up and -down holes, but the tunneling probability through the barrier is affected for this particular value of the magnetic field. In the case of HH, the transparency becomes null in the energy range corresponding to the first peak. There is considerable transparency in the second peak, but is less compared to the case without field.

The dwell times of spin-up and spin-down electrons are different; spin-down electrons stays longer within the barrier, as observed by Yang et al., in the presence of a magnetic field [27]. As with our observation from Fig 3‒5, the dwell times for spin-up and -down HH are not equal; that of spin-down holes is greater than that of the spin-up holes. This is because the spin-up holes experience the barrier while the spin-down holes experience the well and vice versa. This causes the different dwell times of holes with different orientations in the heterostructure. This property arising from the nature of the energy band of the material used, could be exploited in spin-filters to draw holes with either spin orientation at different time

7

ACCEPTED MANUSCRIPT intervals. No reports are available to compare the dwell times for LH and HH; further theoretical and experimental investigations are required.

The idea can be extended to

compare the group delays between the LH and HH. The case of CdTe/CdMnTe with the barrier height of 𝑥 = 0.04 and barrier width of 10 nm seems to hold well for HH spin-filter applications with different and relatively specific resonance energies for spin-up and -down holes with 100% polarization efficiency and maximum barrier transparency. 4. Conclusion The spin-transport properties of HH and LH in the CdTe/Cd1‒xMnxTe double-barrier heterostructure are presented as functions of the barrier width and height. Both dimensions of the barrier strongly influence the polarization efficiencies of LH and HH. The energy of the resonance polarization is shifted by varying the barrier height alone for both LH and HH. Two resonance energies for HH are observed; the resonance energy of LH lies between these values. The maximum barrier transparency of spin-up and spin-down holes is observed in both cases indicating potential spin-injection applications. The application of a magnetic field causes considerable changes. Barrier dwell time differ for holes with opposite spin states. The dwell time variation on the order of 102 is observed between the LH and HH, which insists extension of research regarding concepts like Group delay. The presented work can be extended for the effect of external fields incorporating Zeeman splitting term into the heterostructure potential. References: 1. M.Holub, P.Bhattacharya, J.Phys.D:Appl.Phys.40 (2007) R 179. 2. I.Zutic, J.Fabian, S.Dassarma, Rev.Modern Phys.76 (2004) 323. 3. Anatoly Yu. Smirnov, Lev G. Mourokh, Phys. Rev. B 71 (2005) 161305. 4. D. Loss and D. P. DiVincenzo, J. Magn. Magn.Mater.200(1999) 202. 5. Prashant Sharma, Piet W. Brouwer, Phys. Rev. Lett. Vol 91 (2003) 166801. 6. Jiangchao Han, YulinFeng, Kailun Yao, G. Y. Gao, Appl. Phys. Lett. 111 (2017) 132402. 7. J.Gong, X.X.Liang, S.L.Ban, J.Appl.Phys. 102 (2007) 073718. 8.K.Gnanasekar, K.Navaneethakrishnan, Mod. Phy.Lett. B 18 (10) (2004) 419-426. 9. G.Papp, S.Borza, F.M.Peeters, J. Appl. Phys. 97 (2005) 113901. 10. S.Mnasri, S.Abdi-Ben Nasrallah, A.Bouazra, N.Sfina, M.Said, J.Appl.Phys.110 (2011) 034303. 11. K.Gnanasekar, K.Navaneethakrishnan,Europhys.Lett. 73(5) (2006) 786. 8

ACCEPTED MANUSCRIPT 12. Yong Guo, Ci-En Shang, Xin-Yi Chen, Phys.Rev.B 72 (2005) 045356. 13.L.BrunoChandrasekar, K.Gnanasekar, M.Karunakaran, R.Chandramohan, Eur.Phys.J.Plus. 132 (2017) 279. 14. L.BrunoChandrasekar, Superlattices andMicrostructures, 112 (2017) 451. 15. G.Papp, S.Borza, F.M.Peeters, J.Appl.Phys.97 (2005) 113901. 16. Y.Guo, H. Wang, B-L Gu, Yoshiyuki Kawazoe, J.Appl.Phys.88 (2000) 6614. 17. Y.Ming, J.Gong, R.Q.Zhang, J.Appl.Phys.110 (2011) 093717. 18.J.Radovanovic, V.Milanovic, Z.Ikonic, D.Indjin, J.Appl.Phys,99 (2006) 073905. 19. J-D Lu, Jian-Wen Li, Appl.Surface.Sci. 256 (2010) 4027. 20. Jian-Duo Lu, Xiong-Ping Xia, Lin Yi, Yu-Hua Wang, Phys.Lett.A 374 (2010) 3341. 21. V. I. Perel’, S. A. Tarasenko, I. N. Yassievich ,S. D. Ganichev, V. V. Bel’kov, W. Prettl, Phys.Rev.B 67 (2003) 201304. 22. M.M. Glazov, P.S. Alekseev, M.A. Odnoblyudov, V.M.Christyakov, S.A.Tarasenko, I.N.Yassievich, Phy. Rev. B 71 (2005) 155313. 23.Jian-Duo Lu, Bin Xu, Shun-Jin PEng, Mat.Sci.Semicon.Process. 27 (2014) 785. 24. F. Long, P. Harrison, and W.E. Hagston, J. Appl. Phys. 79 (1996) 6939. 25. S.G. Jayam, K. Navaneethakrishnan, Int. Mod. Phys. B 16, 3737 (2002). 26. MoumitaDey, Santanu K. Maiti, International. J. Modern. Phy.B. 30 (2016) 1650184. 27. Ping-Fan Yang, Yong Guo, Appl. Phy. Lett. 108 (2016) 052402. 28. P. Chen, J. E. Nicholls, J. H. C. Hogg, T. Stirner, W. E. Hagston, Phy. Rev. B 52 (7), 4732, 1995. 29. X F Wang, I C da Cunha Lima, A Troper, Semicond. Sci. Technol. 14, 829–835, 1999. 30. K. Hieke, W. Heimbrodt, Th. Pier, H.-E. Gumlich, W.W. Riihle, J.E. Nicholls, B. Lunn, J. Cryst. Growth, 159, 1014, 1996. 31. L.BrunoChandrasekar, K.Gnanasekar, M.Karunakaran, R.Chandramohan, Eur. Phys. J. Plus, 132 279, 2017.

Figure caption Fig1. Representation of the heterostructures Fig 2.Polarization efficiency of holes for various barrier widths Fig 3.Barrier transparency (a-c) and dwell time (d-f) of LH for various barrier widths Fig 4.Barrier transparency (a-c) and dwell time (d-f) of HH for various barrier width 9

ACCEPTED MANUSCRIPT Fig 5.Barrier transparency (a-c) and dwell time (d-f) of HH for various barrier width Fig 6.Polarization efficiency (a), barrier transparency (b-d) and dwell time (e-g) of LH and HH with x = 0.07 Fig 7.Polarization efficiency and barrier transparency of LH, HH-first peak and HH-second peak with applied magnetic field; barrier width = 8nm; x = 0.04; B = 1 T

10

ACCEPTED MANUSCRIPT

Fig.1 – Representation of the heterostructures

11

ACCEPTED MANUSCRIPT

Barrier width = 6 nm

Polarization efficiency

1

0.5

0

0.5

1

0

2

4

6

8

10

12

14

16

12

14

16

12

14

16

Ez (meV)

Barrier width = 8 nm

Polarization efficiency

1

0

1

0

2

4

6

8

10

Ez (meV)

Barrier width = 10 nm

Polarization efficiency

1

0

1

0

2

4

6

8

10

Ez (meV)

LH HH

Fig.2 – Polarization efficiency of holes for various barrier widths

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Fig.3 – Barrier transparency and dwell time of LH for various barrier widths

Fig.4 – Barrier transparency and dwell time of HH for various barrier width

Fig.5 – Barrier transparency and dwell time of HH for various barrier width

Polarization efficiency

1

0

1

0

2

4

6

8

10

12

14

16

Ez (meV)

Fig.6 - Polarization efficiency, barrier transparency and dwell time of LH and HH with x = 0.07 13

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Polarization efficiency

1

0

1

10

10.5

11

11.5

12

Ez (meV)

Polarization efficiency

1

0

1

70

72

74

76

78

80

Ez (meV)

Polarization efficiency

1

0

1

110

110.5

111

111.5

112

112.5

113

113.5

114

Ez (meV)

Figure 7 Polarization efficiency and barrier transparency of LH, HH-first peak and HHsecond peak with applied magnetic field; barrier width = 8nm; x = 0.04; B = 1 T

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ACCEPTED MANUSCRIPT FIGURE Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7

CAPTION

Representation of the heterostructures Polarization efficiency of holes for various barrier widths Barrier transparency and dwell time of LH for various barrier widths Barrier transparency and dwell time of HH for various barrier width Barrier transparency and dwell time of HH for various barrier width Polarization efficiency, barrier transparency and dwell time of LH and HH with x = 0.07 Polarization efficiency and barrier transparency of LH, HH-first peak and HH-second peak with applied magnetic field; barrier width = 8nm; x = 0.04; B=1T

ACCEPTED MANUSCRIPT

Research Highlights

    

Spin dependent resonant tunneling of light and heavy holes in CdTe/Cd1-xMnxTe double barrier heterostructure in the absence of external field is studied. Considerable energy separation for spin-up and spin-down holes in the absence of external field is observed. Two resonance energy states are reported for heavy holes and the resonance energy of the light holes lies in between them. Increase in spin polarization efficiency with increasing barrier width is observed. Shift in resonance energy for different barrier heights is reported.