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International Journal of ChemTech Research CODEN (USA): IJCRGG, ISSN: 0974-4290, ISSN(Online):2455-9555 Vol.9, No.08 pp 298-304, 2016

Effect of Temperature on Exciton Binding Energy in ZnSe/ Zn1-xMgxSe Quantum Well with Poschl-Teller Potential P.Sathiyajothi, A.Anitha and M. Arulmozhi* Department of Physics, Jayaraj Annapackiam College for Women (Autonomous) Periyakulam-625601, Theni District, Tamil Nadu, India. Abstract : Exciton binding energies with temperature in a quantum well with Poschl-Teller Potential formed by ZnSe/Zn1-xMgxSe are calculated theoretically. Using the temperature dependent value of the effective mass and barrier height, the sub-band energies of the electron, heavy hole and light hole are calculated by variational method. Binding Energy of light hole exciton and heavy hole exciton are calculated as a function of the wellwidth for different temperatures. We have obtained the result that the binding energy of exciton decreases with enhancing the temperature and increases with reducing the wellwidth upto 12 nm for heavy hole exciton and 10 nm for light hole exciton, beyond this wellwidth the exciton binding energy decreases. Keywords : Quantum well, Exciton, Binding energy, Poschl-Teller Potential, Temperature. Introduction In the last two decades, the low dimensional semiconducting systems have received much attention due to their potential application in optoelectronic devices such as displays1, light emitting diodes2, solar cells3 and photovoltaic devices4. Elabsy5 displays the variation of the binding energy of shallow donor in GaAs/Ga1-xAlxAs superlattice with respect to temperature. Abraham and John Peter6 have studied the exciton binding energy, interband emission energy and nonlinear optical properties in ZnMgSe quantum well with the effect of dielectric constant mismatch. Cingolani et al.7 have investigated the excitonic states in Zn1-xCdxSe/ZnSe as a function of wellwidth and composition of Cd experimentally. Krystek et al8 have reported the variation of energy and broadening parameter of the fundamental bandgap of ZnSe with different temperatures in the range 27 K to 370 K. Stachow et al.9 have showed that the energy gap of CdMnTe epilayers depends upon the temperature. Several authors10-11 have studied the effect of hydrostatic pressure on the binding energy of donor and acceptor in GaAs/GaAlAs quantum wells. Morales et al12 have made theoretical studies on simultaneous effect of hydrostatic stress and electric field on donor binding energy in GaAs/GaAlAs. Arulmozhi13 has studied the influence of temperature and pressure on the binding energy of hydrogenic donor in parabolic quantum well. Tevosyan et al14 have computed the energy levels and direct interband absorption in a spherical quantum dot with Poschl-Teller potential. Mora-Ramos et al15 have calculated the exciton binding energy in a cylindrical quantum dot with Poschl-Teller potential profile variationally. Effect of magnetic field on exciton binding energy in near triangular quantum well has been studied by Anitha and Arulmozhi16. II-VI semiconductors are extensively studied at nanoscale experimentally without doping17-19, with doping20-22 and with external perturbations23, 24. The purpose of the present work is to report the effect of temperature on binding energy of light and heavy hole exciton in quantum well with Poschl-Teller confining potential profile composed of ZnSe/Zn1-xMgxSe as a function of wellwidth. Theory The Hamiltonian of an exciton in effective mass approximation is given by25 (1) The subscripts h and e represent the hole and electron respectively. µ. The reduced effective mass of the exciton is hi* is the reduced effective mass of the heavy hole (i = h) or light hole (i = l) and the electron, (2) The potential profile for the electron and hole in Poschl-Teller potential15 are given by (3) where, V. The numerical values of χ and λ are chosen to be 1.0001. Since χ and λ are chosen to be same, a symmetric Poschl-Teller potential profile is considered. The trial wave function of the exciton in the Poschl-Teller potential0 is the barrier height, which depends on the composition x of Mg, 15 is taken to be (4) where, and . Substituting the available values from Ref.15, the final trial wave function (5) where A α are variational parameters, Ji, βi and 0 is the Bessel function of zeroth order with θ0=2.40483 (Ref.15), N is the normalization constant. The continuity conditions at ze = L/2 and zh = L/2 relates the normalization constant N and N1. We have computed expectation value of Hamiltonian as a function of the variational parameters using the Hamiltonian in (1) and the trial wave function in (5). The binding energy of exciton is then given by (6) where, E is the minimized value of with respect to the variational parameters. By applying external temperature to the system, the band gap of the material changes, ase and Eh are the ground state energies of electron and hole in bare quantum well respectively obtained variationally. 7 (7) where is the energygap at T=0, and are Varshni coefficients, respectively. The variation of effective mass, dielectric constant, barrier height according to the temperature is determined12 by (8) In this equation is an energy related to the momentum matrix element, is the spin-orbit splitting and is the temperature dependence of the energy gap. The variation of the barrier height with temperature is calculated by (9) Conduction band offset parameter and bandgap difference between quantum well and barrier layer material as a function of temperature and Mg concentration is given by ) (10) Variation of dielectric constant with temperature is expressed as (11) The numerical values for this calculation is taken from the references (Ref. 6, 8). Results and discussion Table 1 represents the physical parameters of ZnSe, taken from references6, 8, 27. The difference of total band gap between Zn1-xMgxSe and ZnSe is determined5 by the equation The conduction band and valence band discontinuity is taken to be 70% and 30% of this band gap difference respectively. Table 1: Physical parameters of ZnSe

Physical parameters

Absolute values

Mass of Electron (me)

0.16 m0

Mass of heavy hole (mh)

0.6 m0

Mass of light hole (ml)

0.145 m0

Dielectric Constant ()

8.8

Spin-Orbit splitting ()

0.43 eV

Energy gap at 0 K () g

2.8 eV

Varshni co-efficient (α)

7.3x10-4 eV/0K

Varshni co-efficient (β)

2950K

Linear temperature co-efficient (C)

1.71x10-4 K-1

where m0 is the free electron mass. Fig.1 shows that the variation of binding energy of heavy hole exciton as a function of well width L for different temperatures T for a barrier height corresponding to the Mg composition x = 0.3. When L is reduced, the binding energy increases. If the L is reduced further, they reach a maximum value and then start to decrease rapidly. The peak value of binding energy is observed at L = 12 nm, for all values of T. The behavior of binding energy of light hole exciton as a function wellwidth L for different temperatures is shown in Fig. 2. The peak value of binding energy is observed at L = 10 nm, for all values of T. It is also noted that the binding energy of heavy hole exciton is more than that of the light hole exciton. So the hh-exciton is more bound than the lh-exciton, which is due to mhh* > mlh*. In both cases, the decrease in wellwidth produces a spreading of the wave function, which causes a lowering in the binding energy. The contribution of confinement is dominant for smaller wellwidth and make the electron unbound, and tunnels through the barrier. This behavior is similar to those reported in Ref. 15 for a quantum dot of same profile. But a decrease in binding energy for narrow wells is observed in quantum wells. Fig.1. Variation of the binding energy of hh-exciton as a function of wellwidth for different temperatures Fig.3 shows that the variation of binding energy of heavy hole exciton as a function of temperature for different wellwidths, for a barrier height corresponding to the Mg composition x = 0.3. As temperature increases, the binding energy decreases4. Fig.2. Variation of the binding energy of lh-exciton as a function of wellwidth for different temperatures Fig.3. Variation of the binding energy of hh-exciton as a function of temperature for different wellwidths The behavior of binding energy of light hole exciton as a function of temperature for different wellwidths is shown in Fig. 4. For a given quantum well thickness, there is a decrease in the binding energy of the exciton, when the temperature is increased, because increasing the temperature, decreases the values of both the effective mass and the barrier height. Fig.4. Variation of the binding energy of lh-exciton as a function of temperature for different wellwidths Conclusions Binding energies of hh-exciton and lh-exciton in the presence of temperature in a quantum well with Poschl-Teller potential are calculated variationally. A maximum value of binding energy occurs at a critical well width (12 nm for hh-exciton and 10 nm for lh-exciton), same for all values of temperature. For a fixed wellwidth, the binding energy decreases as temperature increases. For same wellwidth and temperature, the binding energy of hh-exciton is more than that of lh-exciton. Acknowledgements The authors thank the University Grants Commission (UGC), New Delhi, India for the financial support through Major Research Project (No. F. 42-836/2013 (SR) dated 22.03.2013) and the authorities of Jayaraj Annapackiam College for Women (Autonomous), Periyakulam, Theni District, Tamilnadu, India for the encouragements. References

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