Analysis and Design of Lead Salt PbSe/PbSrSe Single Quantum Well In the Infrared Region by IJASCSE

VIEWS: 24 PAGES: 6

There is a considerable interest in studying the energy spectrum changes due to the non parabolic energy band structure in nano structures and nano material semiconductors. Most material systems have parabolic band structures at the band edge, however away from the band edge the bands are strongly non parabolic. Other material systems are strongly parabolic at the band edge such as IV-VI lead salt semiconductors. A theoretical model was developed to conduct this study on PbSe/Pb 0.934 Sr0.066 Se nanostructure system in the infrared region. Moreover, we studied the effects of four temperatures on the analysis and design of this system. It will be shown that the total losses for the system are higher than the modal gain values for lasing to occur and multiple quantum well structures are a better design choice.

More Info
									                                                       IJASCSE, VOL 1, ISSUE 4, 2012
Dec. 31
 



     Analysis and Design of Lead Salt PbSe/PbSrSe Single
              Quantum Well In the Infrared Region

                                                              Majed F. Khodr
                                               Electronics and Communication Engineering
                                                 American University of Ras Al Khaimah
                                                          Ras Al Khaimah, UAE



 Abstract— There is a considerable interest in studying the              presence in parts per million (ppm). Laser emission at these
 energy spectrum changes due to the non parabolic energy                 critical wavelengths is related to several system parameters
 band structure in nano structures and nano material                     [1,2].
 semiconductors. Most material systems have parabolic
                                                                              In this work analysis and design are done on PbSe/Pb 0.934
 band structures at the band edge, however away from the
                                                                         Sr0.066 Se single quantum well (SQW) laser structure. The
 band edge the bands are strongly non parabolic. Other
                                                                         developed model is being used to perform energy level
 material systems are strongly parabolic at the band edge
                                                                         calculations, modal gain-current density relation, and threshold
 such as IV-VI lead salt semiconductors. A theoretical
                                                                         current–cavity length relation to determine the critical
 model was developed to conduct this study on PbSe/Pb 0.934
 Sr0.066 Se nanostructure system in the infrared region. Moreover,
                                                                         parameters of interest to the desired design structure. The
 we studied the effects of four temperatures on the analysis and         effects of band structure this material system and temperature
 design of this system. It will be shown that the total losses for the   are included in this model and studied extensively.
 system are higher than the modal gain values for lasing to occur
 and multiple quantum well structures are a better design choice.
                                                                                       II. ENERGY LEVEL CALCULATIONS
   Index      Terms—Semiconductor        device      modeling,             It is very well known that the energy levels in the bands can
 Nanotechnology, Modeling, Semiconductor lasers, Semiconductor           be calculated in the approximation of the envelope wave
 material                                                                function which can be determined to a good approximation by
                                                                         the Schrodinger-like equation [3,4]. By solving this equation
                         I. INTRODUCTION                                 for the finite well case, one can exactly determine the
    Recently, IV-VI lead salts quantum well lasers which                 quantized energy levels and their corresponding wave
 exhibit strong quantum optical effects, have been used to               functions for electrons in the conduction band and holes in the
 fabricate infrared (IR) diode lasers with wide single-mode              valence band. Because of the inversion symmetry around the
 tunability, low waste heat generation, and large spectral               center of the well, the solution wave functions can only be
 coverage up to about 10 µm. In this region, these IV-VI lasers          even or odd.
 may play a key role in IR spectroscopy applications such as               For a well material with parabolic bands in the growth
 breath analysis instruments, air pollution monitoring and IR            direction (z-direction), the effective masses in the
 integrated optics and IR telecommunication devices.                     Schrodinger-like equation are at the extreme of the bands and
                                                                         are independent of the energy. For a well material with non-
    In this work we focus on breath analysis as a promising              parabolic bands in the z-direction, two methods can be used to
 application and diagnostic tool that should perform well in             solve for the energy levels [4,5]. The first method uses the
 clinical settings where real time breath analysis can be                "effective mass" equation, also known as the Luttinger-Kohn
 performed to assess patient health [1]. Based on literature             (LK) equation and the second method is the "energy-
 reports, health conditions such as Breast cancer and Lung               dependent effective mass" (EDEM) method. The energy level
 Cancer have biomarker molecules in exhaled breath at                    shifts due to non-parabolicity effects differ depending on the
 wavelengths in the infra-red (IR) region. A new technique that          method and system parameters used. Throughout this work,
 may play a key role in detecting these biomarkers is Tunable            the effective mass of the barrier material is considered constant
 Laser Spectroscopy (TLS) [1]. PbSe/Pb 0.934 Sr0.066 Se quantum          and independent of energy.
 well laser structures, as part of TLS system, can be used to              The lead salts, such as PbSrSe, are direct energy gap
 generate these critical wavelengths that can be absorbed by the         semiconductors with band extreme at the four equivalent L
 various biomarkers molecules and hence detecting their


 www.ijascse.in                                                                                                                  Page 11
                                                     IJASCSE, VOL 1, ISSUE 4, 2012
Dec. 31
                                                                      width is increased. Moreover, as this effect is higher for higher
                                                                      quantized energy levels. As for the fourth energy level the

 points of the Brillouin zone. Because the conduction and
 valence bands at the L points are near mirror images of each         model calculated the energy level including the effects of non
 other, the electron and hole effective masses are nearly equal.      parabolicity and it seems that this level does not exist
 Furthermore, the bands are strongly non parabolic [7]. Due to        assuming parabolic bands. Therefore it is important to include
 limitation in using the Lutting-Kohn equation [3], the energy-       the effects of non paraboliciyt to be able to calculate all the
 dependent effective mass method was adopted in this work for         energy levels for the system. Similar results can be obtained
 all calculations and analysis.                                       for the valence band.
    In order to solve for the energy levels, it is necessary to
 specify the potential barrier, the effective masses for the
 carriers in the well, and in the barrier for the particular single
 quantum well structure of interest. The system of interest in
 this work is PbSe/Pb 0.934 Sr0.066 Se. The energy gap and
 effective masses of Pb 1-x Sr x Se system dependence on
 temperature according to these relations [2 ]:




                                                              (1)
 and the empirical equation for the longitudinal mass:



                                                             (2)
                                                                       Fig. 1. The effects of non parabolicity on the conduction band energy levels
 where the barrier is Pb 0.934 Sr0.066 Se with Eg=0.46 eV and         at 300K.
 effective mass=0.142 m0, and the well is PbSe with its
 Eg=0.28 eV and effective mass=0.08 m0 at 300K. In this
 study we ignored the non-parabolicity effects of the barrier            The emitted wavelength values at 300K for the system are
 material. The difference in the energy gaps between the well         show in Fig. 2 where the effects of band non parabolicty are
 material and the barrier material is assumed to be equally           included and compared to those excluding the effects of band
 divided between the conduction and valence bands. The offset         non parabolicity. One notice that the emitted wavelength
 energy or the barrier potential for this system is 0.09 eV. This     values are higher including non-parabolicity and this
 assumption is made because measurements on the offset                difference is higher for smaller well widths and decreases as
 energy for this system have not been made.                           the well width increases. For applications that require critical
                                                                      wavelength calculation such as Breath Analysis Technique
    In addition, experimental data on similar IV-VI material          [1,8-12], it is important to include the effects of non
 QW structures showed that the conduction and valence band            parabolicity to be able to obtain the desired accurate results for
 offset energies are equal [7]. It was shown that, for a first        detecting the existence of volatile compounds at their
 approximation, the effective mass to be directly proportional        corresponding wavelengths.
 to the energy gap and the conduction and valence-band
 mobility effective masses in the well are equal and the                 Therefore, in what follows, the effects of non parabolicty
 calculated values are shown in terms of the free electron mass       are included in all calculation of the system. However, we
 [7]. In this study, the conduction and valence-band mobility         included in our calculations the first energy levels transitions
 effective masses in the well are assumed equal and the               between the conduction and valence bands.
 effective masses of the carriers outside the well are assumed
 constant.
 The energy level calculations for the system were calculated
 using the EDEM method. The conduction band energy levels
 calculation assuming parabolic and non-parabolic bands are
 shown in Fig. 1. As shown in the figure, the energy levels
 including the effects of non parabolicity are lower than those
 excluding the effects of non-parabolicity and this difference is
 higher for small well width values and decreases as the well


 www.ijascse.in                                                                                                                         Page 12
                                                  IJASCSE, VOL 1, ISSUE 4, 2012
Dec. 31



                                                                             III. CONFINEMENT FACTOR CALCULATION
                                                                      A principal feature of the QW laser is the extremely high
                                                                   optical gain that can be obtained for very low current densities.
                                                                   Equally important, however, in determining laser properties
                                                                   are modal gain, determined by the optical confinement factor,
                                                                   and the ability to collect injected carriers efficiently [13].
                                                                   These latter factors prevent the improvement of laser
                                                                   performance for arbitrarily thin QW dimensions unless
                                                                   additional design features are added.
                                                                     These design improvements include the use of multiple
                                                                   QW's (MQW) and /or the separate confinement heterostructure
                                                                   (SCH) scheme where optical confinement is provided by a set
                                                                   of optical confinement layers, while carrier confinement
                                                                   occurs in another embedded layer. In this work the focus will
                                                                   be on SQW structure and the other design improvement are
                                                                   kept for future publications.
                                                                      The optical analysis of single quantum well lasers is
   Fig.2. The effects of non parabolicity on the emitted           conventional in that one solves for the TE modes in a three
 wavelengths at 300K.                                              region dielectric optical waveguide [14]. A planar SQW
    The emitted wavelengths as a function of five temperatures:    structure is commonly represented as a three layer slab
 77K, 200K, 150K, 250K, and 300K are shown in Fig. 3. For a        dielectric waveguide where the guiding layer corresponds to
 fixed well width, the emitted wavelengths decreases with          the active layer and the cladding layers correspond to the
 increasing temperature and increases with increasing well         passive layers [14]. If the structure is symmetrical (i.e., the
 width at the same temperature.                                    cladding layers have the same index of refraction), then the
                                                                   waveguide will always support at least one propagation mode
    This graph is important for investigators who are using this   [14]. The index of refraction for the well material PbSe is
 material system in tunable diode laser absorption spectroscopy    4.865 and the index of refraction for the barrier material
 to measure certain markers in exhaled breath which are            Pb 0.934 Sr0.066 Se is 4.38 and they are considered in this work
 correlated with certain diseases [8]. Examples include the        independent of wavelength and temperature [2].
 measurement of exhaled nitric oxide for Asthma at 5.2 m
 [9,10], Acetone for Diabetes at 3.4 m [11], Acetaldehyde for     The radiation confinement factor is one crucial parameter in
 Lung Cancer at 5.7 m [12].                                       the laser design which can be calculated using the general
                                                                   approximate solution that is valid for all well widths found by
                                                                   Botez [15, 16]. The analytical approximation given by Botez
                                                                   for calculating the optical confinement factor in a symmetrical
                                                                   waveguide for the TEo mode is:

                                                                             D2
                                                                        o  2                                              (3)
                                                                            D 2
                                                                   where
                                                                                w
                                                                        D  2 ( ) (nr2,b  nr2, w ) ,                      (4)
                                                                                   
                                                                   and  is the vacuum wavelength at the lasing photon energy
                                                                   and D is the normalized thickness of the active region.
                                                                      Plotting the confinement factor as a function of well width
                                                                   in Fig. 4 for the PbSe/ PbSe0.934Te0.066 SQW structure (at
                                                                   300K) shows that    o decreases with decreasing well width w.
                                                                   In this work, the variations of the index of refraction with
                                                                   emitted photon wavelength are not considered. Therefore, the
 Fig.3. The effects of temperature on the emitted wavelengths .
                                                                   index of refraction of the well material is fixed at nr , w =4.865
 The calculated values include the effects of non-parabolicity.

 www.ijascse.in                                                                                                             Page 13
                                                     IJASCSE, VOL 1, ISSUE 4, 2012
Dec. 31
                                                                        IV. MODAL GAIN AND CURRENT DENSITY CALCULATIONS

 and that of the cladding layer at   nr ,b =4.38 [2]. The effect of      Within the framework of Fermi's Golden Rule, the two
                                                                      major components of gain calculations are the electron and
 non-parabolicity on the confinement factor and thus on modal         hole density of states, and the transition matrix element
 gain is noticeably very small and therefore it can be neglected      describing the interaction between the conduction and valence
 for all well widths as it is shown in figure 4.                      band states. The derivation for the analytical gain expression
    This is expected because including the non-parabolicity           is given by the following expression [4,17]:
 effects for this system shifts the first energy levels toward the
                                                                                                                               2
 band extreme and thus, slightly increases the emitted photon
 wavelength  which decreases o as seen from Eq.(3). The
                                                                                            e 2  red          M QW ,n
                                                                             (o )                                           avg
                                                                                                                                       
 non-parabolicity effects are expected to be more obvious for                             o nr , wcm w2
                                                                                                       o                 o                  (5)
 higher quantized energy levels.                                                                        
                                                                            [ f c (o )  f v (o )] H (o  n )
                                                                                                       n 1
                                                                      and the radiative component of the carrier recombination is
                                                                      found from the spontaneous emission rate[3]:

                                                                                            e 2 nr , w  o  red
                                                                            Rsp ( o ) 
                                                                                                                                   2
                                                                                                                         M conv avg
                                                                                             m  o  c w
                                                                                                  2
                                                                                                  o
                                                                                                           2 3
                                                                                                                                                  (6)
                                                                                                              
                                                                            f c ( o )  [1  f v ( o )]   H ( o   n )
                                                                                                              n 1
                                                                      From this, the radiative current density is calculated by the
                                                                      following equation [3]:


                                                                            J  ew Rsp (o )o ,                                              (7)


 Fig.4. The effects of non-parabolicity on the confinement            where e is the charge of the electron,  mo is the electron free
 factor calculations at 300K.                                         mass, c is the speed of light, w is the well width, nr , w is the
    The effects of temperature on the confinement factor are
                                                                      index of refraction at the lasing frequency               o ,  o is the
 shown in Fig 5. The confinement factor increases with
                                                                                                                     2
 temperature at a fixed well width and this is due to the effects     permittivity of free space,     M QW ,n              is the transmission
 of temperature on the emitted wavelength as seen from Fig. 3                                                        avg

 and Eq 3.                                                            matrix element ,    red   is th reduced density of states,
                                                                       f c ,v (o ) are the Fermi-Dirac distribution functions, H(x) is
                                                                      the Heaviside function that is equal to unity when x> 0 and is
                                                                      zero when x<0, and  n is the energy difference between the
                                                                      bottom of the n-subband in the conduction band and the n-
                                                                      subband in the valence band.

                                                                         The excitation method that is of importance in this work is
                                                                      injection of carriers into the active region by passing current
                                                                      through the device. An increase in the pumping current leads
                                                                      to an increase in the density of injected carriers in the active
                                                                      region and with it, an increase in the quasi-Fermi levels [18,
                                                                      19].

                                                                         The gain, current density, and threshold current expressions
 Fig 5. The effects of temperature on the confinement factor as       for the non- parabolic bands is similar to that of the parabolic
 a function of well width. The effects of non-parabolcity are         case except in the reduced density of states and the quasi
 included in the calculations.                                        Fermi levels in the bands. More details about the model and
                                                                      theoretical derivations can be found in reference [18].

 www.ijascse.in                                                                                                                             Page 14
                                                    IJASCSE, VOL 1, ISSUE 4, 2012
Dec. 31




   In laser oscillators, the concern is with the modal gain rather
 with the maximum gain. The modal gain is obtained by
 multiplying the maximum gain values given in Eq.(5) by the
 confinement factor. The calculated maximum gain –current
 density values are shown in the inset of Fig. 6 at 300K and
 well width 7 nm.
   The model gain values are small for this SQW system as can
 be seen from Fig. 6.




                                                                     Fig.7: Modal gain calculations as a function of current density
                                                                     at four different temperatures assuming non parabolic bands.

                                                                        In order for laser oscillation to occur, the modal gain at the
                                                                     lasing photon energy   l must equal the total losses  total .
                                                                     The laser oscillation condition is given as:
                                                                          g mod (l )  o max (l )   total ,           (8)

                                                                     The threshold current needed to compensate for the total loss
                                                                     is calculated by the usual formula [19]:

                                                                          I th  J th  Area  J thL  width                 (9)

                                                                     The threshold current density     J th that corresponds to the
 Fig 6 Modal gain as a function of current density at 300K. the
                                                                     modal gain value that satisfies the oscillation condition can be
 inset showes the maximum gain as a function of current
                                                                     obtained from the modal gain-current density plots. The
 density.
                                                                     threshold current calculations are performed assuming the
    The behavior of the modal gain vs. current density values at     width has a constant value of 20  m, the cavity length L as an
 five different temperatures: 77K, 150K, 200K, 250K, and 300         independent variable L and the mirror reflectivities fixed at
 K and including the effects of non-parabolicity are shown in        R1=0.4 and R2=0.4 . The estimate total loss for the system
 Fig. 7. From this figure one notice that the transparency           under investigation at cavity length of 600 m was found to be
 current J0 (intercept at gain =0) increases with increasing         approximately 46 (1/cm), which is higher than the modal gain
 temperature. Moreover, the slope of the gain versus current         values shown in Fig. 7. Therefore, a modification to the design
 density plot decreases with increasing temperature. These two       of the system is needed were multiple quantum well structures
 quantities are important in calculating the characteristic          are required.
 temperature T0 for the system.
                                                                     The modal gain-current density relation can be deduced from
 The threshold current values and characteristic temperature         that of a single quantum well by multiplying the modal gain
 calculation are left for future publication.                        and the current density by the number of wells. Whether the
                                                                     SQW or the MQW is the better structure depends on the loss
                                                                     level. At low loss, the SQW laser is always better because of
                                                                     its lower current density where only one QW has to be
                                                                     inverted.
                                                                     At high loss, the MQW is always better because the
                                                                     phenomena of gain saturation can be avoided by increasing the
                                                                     number of QW's although the injected current to achieve this
                                                                     maximum gain also increases by the increase in the number of
                                                                     wells. Owing to this gain saturation effect, there exists an
                                                                     optimum number of QW's for minimizing the threshold current
                                                                     for a given total loss [13].

 www.ijascse.in                                                                                                              Page 15
                                                                IJASCSE, VOL 1, ISSUE 4, 2012
Dec. 31
                                                                                    [16] D. Botez, "Near and far-field analytical approximations for the
                                                                                         fundamental mode in symmetrical waveguide DH lasers," RCA Rev.,
                                                                                         39, 577 (1978).
                    V. SUMMARY AND CONCLUSION                                       [17] R. H. Yan, S. W. Corzine, L. A. Coldren and I. Suemune, "Corrections
                                                                                         to the expression for gain in GaAs," IEEE J. Quantum Electron., 26, 213
    In this work we analyzed PbSe/Pb 0.934 Sr0.066 SQW structure                         (1990).
 by calculating the quantized energy levels, confinement factor,                    [18] M. F. Khodr, B. A. Mason, P. J. McCann, "Optimizing and Engineering
                                                                                         EuSe/PbSe0.78Te0.22/EuSe Multiple Quantum Well Laser Structures”
 maximum gain and modal gain current density relationships.                              IEEE Journal of Quantum Electronics, 34, 1604 (1998)
 The effects of band non parabolicty was studied and it was                         [19] M. F. Khodr "Effects of non-parabolic bands on nanostructure laser
 shown that non parabolicity will have small effect on                                   devices”” Proceedings of SPIE, 8102, (2011)
 quantized energy levels that are close to the band edge and it
 will have a larger effect on those far above the band edge. The
 confinement factor values for the first energy levels were very
 small as expected for SQW structures with minimum or no
 effects of non parabolicty. The effects of temperature on the
 behavior of the system was analyzed and studied at four
 different temperatures: 77K, 150K, 250K, and 300K. It was
 concluded that for low loss values, SQW is a good choice to
 be used.


 REFERENCES
 [1]    C. B. Roller, K. Namjou, J. Jeffers, M. Camp, P. J. McCann, and J.
        Grego, “Nitric oxide breath testing using tunable diode laser absorption
        spectroscopy: Application in respiratory inflammation monitoring”
        Applied Optics,vol. 41, 6018 (2002).
 [2]    W. Shen, H.F. Jiang, K. Wang, G.Yu, H.Z. Wu, and P.J.McCann, “
        Band gaps, effective masses and refractive indices of PbSrSe thin films:
        Key properties for mid-infrared optoelectronic devices applications”, J.
        of Appl. Phys., vol. 91, 192-198, (2002)
 [3]    M. F. Khodr "Effects of non-parabolic bands on nanostructure laser
        devices”” Proceedings of SPIE, 7039, 70390T (2008)
 [4]    C. Weisbuch and B. Vinter, [Quantum Semiconductor Structures:
        Fundamentals and Applications], Academic Press Inc., Califorina,
        1991.
 [5]    Welch DF, Wicks GW, Eastman LF, “Calculation of the
        conduction band discontinuity for Ga0.47In0.53As/Al0.48 In0.52As
        heterojunction,” J Appl Phys 1984;55(8): 3176–9.
 [6]    C. K. Williams, T. H. Glisson, M. A. Littlejohn, and J.R. Hauser, “
        Ballistic transport in GaAs,” IEEE Electron Device Lett. EDL-4, 161
        (1983).
 [7]    D. L. Partin, "Lead salt quantum effect structures," IEEE J. Quantum
        Electron., 24, 1716 (1988).
 [8]    P.C. Kamat, C.B.Roller, K.Namjou, J D. Jeffers, A. Faramarzalian, R.
        Sal as, and P.J.McCann, “Measurment of acetaldehyde in exhaled
        breath using a laser absorbtion spetcrometer ,” in Applied Physics, Vol
        46, No.19, pp. 3969-3975.
 [9]    D.H. Yates,” Role of Nitric Oxide in Asthma,” Immunology and cell
        Biology, 79, 178-190 (2001).
 [10]   C. Roller, K. Namjou, J. Jeffers, W. Potter, P.J.Mccan, and J. Grego,”
        Simultaneous NO and CO2 Measurment in Human Breath with a single
        IV_VI mid-infrared Laser,” Optics Letters, Vol. 27, No 2, pp-107-109,
        (2002).
 [11]   E. Owen, V. E. Trapp, C. L. Skutches, M. A. Mozzoli, R.D. Hoeldtke,
        G.Boden, and G. A. Reichard, “ Actetone Metabolism During Diabetic
        Ketoacidosis,” Diabetes 31, 242 (1982).
 [12]   D. Smith , T. Wang, J. Sule-Suso, P.Spanel, A. E. Haj, “ Quantification
        of acetaldehyde releases by lung cancer cells in vitro using selected ion
        flow tube mass spectrometry,” Rapid Commun. Mass Spectrom. 17, 845
        92003)
 [13]   Y. Arkawa and A. Yariv, "Quantum well lasers-gain, spectra,
        dynamics," IEEE J. Quantum Electron., 22, 1887 (1986).
 [14]   P. K. Cheo, Handbook of Solid-State Lasres, Marcel Dekker, Inc., New
        York 1989.
 [15]   D. Botez, "Analytical approximation of the radiation confinement factor
        for the TE0 mode of a double heterojunction laser," IEEE J. Quantum
        Electron., 14, 230 (1978).

 www.ijascse.in                                                                                                                                      Page 16

								
To top