Spectral Gain-Carrier Density Distribution of SQW GaAs/AlGaAs Laser

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1 Wasit Jurnal fr Science & Medicine 11 4 (1): ( 1-11 ) Spectral Gain-Carrier Density Distributin f SQW GaAs/AlGaAs Laser *Adawiya J. Haider & *Safaa A. Oudah Al-Qaysi & **Awatif Sabir Jassam *Schl f Applied Sciences, University f Technlgy, Baghdad, IRAQ ** The University f Mustansiriya, Cllege f Pharmacy. الخالصة توزيع طيف حامالت الش حن لجهد البئر المفرد ل ليزر. GaAs/AlGaAs هذذذذلا البحذذذذل جذذذذرا كلذذذذي موديذذذذج الذاذذذذج لليذذذذزر بئذذذذر الجهذذذذد لات الجذذذذدار المفذذذذرد ذذذذو L z مذع تييذر اذمل الجذدار المذمذم (Fermi- Glden) قاكذد ييرمذا الذلهبا GaAs/AlGaAsبأاتخدام (1,75)= Ǻ, ك ذذد درجذذا حذذرار K ك ذذد يجذذو طاقذذا م ط ذذا, ΔE 3=T c =.1 ev هذذل الحاذذذذذابات ا جذذذذذزت بأاذذذذذتخدادم مذذذذذولجين الباذذذذذيط و موديذذذذذج ا اذذذذذت طاج الم ززك ذذذذذد ذ ايذذذذذا ح ذذذذذن.N=3.348*1 18 cm -3 Abstract: In this wrk, the mdal gain f SQW GaAs/AlGaAs has been calculated using the Fermi-Glden Rule with varying the quantum well thickness L z =(1,75) Ǻ, at a temperature f T=3 K, at a bandgap discntinuity f ΔE c f.1 ev, this calculatin was achieved using tw mdels, the simplified and the plarizatin enhancement mdel at a carrier injectin cnditin f N=3.348*1 18 cm -3. Keywrds: SQW GaAs/AlGaAs laser, Mdal gain, Spectral gain. 1

2 I. Intrductin: Quantum well (QW) semicnductr lasers have attracted cnsiderable interest because f their significant superirity in perfrmance ver cnventinal duble heterstructure (DH) lasers; [1] they are attractive fr research because they are bth physically very interesting and technlgically imprtant. QW technlgy allws the crystal grwer fr the first time t cntrl the range, depth, and the arrangement f the quantum mechanical ptential wells. In the last decade, the imprtance f the quantum well laser has steadily grwn until tday it is preferred fr mst semicnductr laser applicatins, []. They ffer the advantages f lwer threshld current density, lwer temperature sensitivity, high mdulatin speed; imprved cherency wit reduced lasing linewidth and superir mde stability, and high efficiency, etc, [1]. Their grwing ppularity is because, in almst every respect, the quantum well laser is smewhat better than cnventinal lasers with bulk active layers. One bvius advantage is the ability t vary the lasing wavelength merely by changing the width f the quantum f the QW. A mre fundamental advantage is that the QW lasers delivers mre gain per injected carrier than cnventinal lasers, which results in lwer threshld currents, [,3]. A principal feature f the QW laser is the extremely high ptical gain that can be btained in the QW fr very current densities. This arises partly frm greater ppulatin inversin at a given carrier density because f the lwer quantized density f states, but mstly frm the high carrier density in the QW because f its small width, [4]. In general, the QW lasers have the extremely high ptical gain because f their high carrier cnfinement. The ptical cnfinement factr f the QW lasers is relatively lw due t their thin active regin. T predict the lasing behavir, we must evaluate the mdal gain f the QW lasers. The mdal gain f QW lasers is determined by their ptical cnfinement factr and their ability t cllect injected carriers efficiently, [6]. In this paper, the primary gal was t apply the tw mdels f calculating the mdal gain fr SQW GaAs/AlGaAs laser (simplified and plarizatin enhancement mdels) with varying the well widths L z at a bandgap discntinuity f ΔE c f.1 ev, and at a temperature f T=3 K.

3 Eg(eV) n II. Theretical Cncept: Using the structure f the SQW GaAs/AlxGa 1-x As with x=. fr the barrier layer and a layer thickness f (d=.μm), x=.6 fr the cladding layer (d=1μm) and (d=.1μm) fr the active regin, a detailed structure is shwn in Fig.(1) d(m) d(m) Fig.(1) Schematic diagram f the laser structure shws refractive index change fr the prpsed structure, energygap change fr the prpsed structure. The present mdel calculates the laser gain n the basis f band-t-band transitins, the fllwing assumptins are used in this mdel: 1. the wells in the cnductin and valence bands are apprximated by infinitely deep square wells,. the bandgap discntinuity is (ΔE c /ΔE v =.67/.33), 3. transitins t light and heavy hle subbands, 4. transitins frm subbands with the same quantum numbers. Fr each quantized level, there is a cntinuum f energies arising frm the lateral kinetic energy f the carriers in the plane f the QW. Assciated with each discrete level, the resulting sheet density f states fr energies abve the minimum level is, [1]: 3

4 Adawiya J. Haider at all all states mc QW ( E) H( E E nc) n1,... (1) where: E nc is the energy f subband n f the cnductin band, m c is the effective mass f the electrn at the bttm f the cnductin band. Since ρ QW is cnstant in each subband, the density f electrns N e and hles N h can be calculated analytically and the result will be, [3]: m c EFc Enc N e kt ln1 exp n Lz kt,.... () m v EFv Env N h kt ln1 exp n Lz kt,.... (3) where: E Fc is Fermi energy f the cnductin band, E Fv is Fermi energy f the valence band, L z is the layer thickness, f the QW, m v is the effective mass f the electrn at the tp f the valence band. The ptical gain is calculated using standard perturbatin thery Fermi's Glden Rule, (neglecting the effect f intraband scattering). Fr the simplified mdel the gain spectrum can be evaluated using the fllwing equatin, []: b j, n r, jn c v g( E) g ( E) M f f, (4) here, the gain prefactr is given by: g ( E) e / m n E c..(5) 1 E, jn and M b is the average, energy independent, mmentum matrix element fr the diple transitin in the bulk semicnductr, i.e.: M b ( /3) M,.(6) Since the gain anistrpy favrs lasing in TE mdes, we calculate the gain nly fr this plarizatin. The spectrally dependent gain cefficient fr the quantum well regin is, [7]: g( E) q E m c L M z i, j m C r A f 1 f H E E c v 4,...(7)

5 where: M =bulk mmentum transitin matrix element, ε =free-space permittivity, m=free electrn mass, c =vacuum speed pf light, N=effective refractive index, i,j= cnductin, valence quantum numbers (at Γ), m r =spatially weighted reduced mass, C =spatial verlap factr between states i and j, A =anistrpy factr fr transitin i, j, f c =Fermi ppulatin factr fr cnductin electrns, f v =Fermi ppulatin factr fr valence hles, H= Heaviside step functin, E =transitin energy between states i and j. Fr TE transitin, with the electric field vectr in the plane f the QW, its values are, [] 3 A 1 cs ( ) 4 heavy hle..(8) 1 5 3cs ( light hle) 4 and fr TM transitins, with the electric field nrmal t the QW, its values are, []: 3 A sin ( ) heavy hle (9) 1 4 3sin i ( light hle) The angular factr is cs θ =E /E and shws decreasing anistrpy between nearby heavy and light hle transitins as the phtn energy increases deeper int the band. The bulk averaged mmentum matrix element between cnductin and valence states is, [8]: m Eg Eg M 6mc E g / 3,...(1) where: T Eg E T 4,...(11) Eg = direct bandgap, E = bandgap cnstant, T = perating temperature, Δ s- = split-ff band separatin, mc = cnductin band effective mass. 5

6 mdal gain(cm - 1) mdal gain(cm - 1) III. Results and Discussin: The results btained by using the abve equatins are fr SQW GaAs/AlGaAs laser. The mdal gain has been calculated using the Fermi's-Glden Rule that is the prduct f the material gain cefficient times the ptical cnfinement factr evaluated at the curve's spectral peak. Fig.(a,b) represents the simplified gain mdel in which the spectral bradening effects as well as effects resulting frm the anistrpy f the QW have been ignred. This curve is assciated with a carrier density f N= cm -3 at 3 K. Nte the sharp features arising frm the lw-energy heavy-hle transitin, and the higher energy light-hle transitin. The gain crss-ver between the n=1 heavy and light-hle transitin energies. The first figure was pltted against the transitin wavelength, while the secnd was pltted against the transitin energy m E(eV) Fig.() Plt f the mdal gain versus the transitin wavelength, the transitin energy, at T=3 K, L z =1 Ǻ. The relatin between the mdal gain fr the same injectin cnditin, N= , versus the wavelength transitin and the transitin energy, respectively, is shwn in Fig.(3a, b), with TE and TM plarizatin enhancement, in which the feedback cnditin fr lasing usually selects TE ver TM plarizatin even when the gain is plarizatin-independent. The anistrpy factr in the QW prvides an enhancement f the scillatr strength fr TE plarizatin at phtn energies near the gain peak as ppsed t TM plrizatin, where the scillatr strength diminshed. Thus fr QW structure, stability f lasing in the TE mde is imprved further, and TM plarizatin need nt t be cnsidered. 6

7 mdal gain(cm - 1) Mdal gain (cm -1 ) mdal gain(cm - 1) mdal gain(cm - 1) 4 35 TM TE 4 35 TM TE m E(eV) Fig.(3) Plt f the TE and TM mdal gain versus, the transitin wavelength, the transitin energy. Fig.(4a,b) plt the mdal gain fr the same injectin cnditin N= cm -3, versus the transitin wavelength and transitin energy, respectively. Frm the simplified mdel and the TE plarizatin enhancement, the planar symmetry f the electrnic wavefunctins in a QW structure results in a plarizatin dependence f the stimulated ptical transitins, which results in a difference between the diple e-lh and e-hh simplified with plarizatin simplified --- with plarizatin m Fig.(4) Plt f the mdal gain versus the transitin wavelength, the transitin energy at Lz=1 Ǻ. E (ev) The relatin between the mdal gain fr the same injectin cnditin, N= cm -3, versus the wavelength transitin and the transitin energy, respectively using L z =75 Ǻ, T=3 K is shwn Fig.(5a,b). The transitin energy and wavelength are varied due t the fact that varying the quantum well thickness will result in a change in transitin energy. Als, reducing the active regin thickness will result in an increase in bth the simplified mdal gain, and the TE enhanced plarized mdal gain. 7

8 mdal gain(cm - 1) mdal gain(cm - 1) 1 simplified,lz=75a with plarizatin 1 simplified,lz=75a with plarizatin m E(eV) Fig.(5) Plt f the mdal gain versus the transitin wavelength, the transitin energy, Lz=75 Ǻ. a flw chart fr the calculatin f the gain prfile is shwn in Fig.(6). Start Set initial values n 1, n, L, L z, N e, N h Calculate E 1c, E 1v, λ Calculate the Quasi-Fermi Level Calculate N e and N h using eq.(), eq.(3) N Cnverged Yes Calculate the gain prfile using Fermi-Glden Rule, eq.(4), and eq.(7). End Fig.(6) Flw chart fr slving the QW gain prfile and the current 8

9 IV. Cnclusins: We have studied the spectral gain carrier distributin f SQW GaAs/AlGaAs, the mdal gain f using the Fermi-Glden Rule with varying the quantum well thickness Lz =(1,75) Ǻ, at a temperature f T=3K, at a bandgap discntinuity f ΔEc f.1 ev, this calculatin was achieved using tw mdels, the simplified and the plarizatin enhancement mdel at a carrier injectin cnditin f N=3.348*118 cm-3. V. References: [1] W.L.Li,Y.K.Su,and D.H.Jaw, "the Influence f Refractive Index Dispersin n The Mdal Gain f a Quantum Well Laser", IEEE Jurnal f Quantum Electrnics, Vl.33,N.3, March [] Peter S. Zry, "Quantum Well Lasers", 1993, Academic Press, Inc. [3] Dr.W.Kechner, "Slid-state laser engineering", Sixth Editin, Springer Series, 6. [4] S. R. Chinn, P.S.Zry, A.R.Reisinger, "A Mdel fr GRIN-SCH-SQW Dide Laser", IEEE Jurnal f Quantum Electrnics, Vl. 4, N.11, pp , Nvember [5] O.Svelt, "Principles f Lasers", Plenum Press, New Yrk, [6] F.Gity, V.Ahmadi, M.Nshiravani, "Numerical Analysis f Vid-Induced Thermal effects n GaAs/AlxGa1-xAs High Pwer Single-Quantum-Well Laser Dides", Slid-State Electrnics, Vl.5, pp , 6. [7] J. Hader, J.V. Mlney, S.W.Khch, "Temperature Dependence f Radiative and Auger Lss in Quantum Wells", IEEE Jurnal f Quantum Electrnics, Vl.44, N., February, 8. [8] R. Muller, "A Theretical Study f the Dynamical Behavir f Single Quantum-Well Semicnductr Lasers", Vl.91, Optics Cmmunicatin, pp , 199. [9] A. Yariv, "Optical Cmmunicatin in Mdern Cmmunicatin", Oxfrd university Press, Recived... ( 9/6 /1 ) Accepted (/9/1 ) 9

A Theoretical Study of the Dynamical Behavior of SQW GaAs/AlGaAs Laser

A Theoretical Study of the Dynamical Behavior of SQW GaAs/AlGaAs Laser En. & Tech. Jurnal,Vl.8, N., 1 Behavir f SQW GaAs/AlGaAs Laser Dr. Azhar I. Hassan* Received n: 15//9 Accepted n: /9/1 Abstract In this wrk, the peak mdal ain and the radiative and Nnradiative current