Keywords: Auger recombination, leakage current, lead salts, quantum efficiency INTRODUCTION

Transcription

1 Researh Jurnal f Applied Sienes, Engineering and Tehnlgy (5: 67-6, 6 DOI:.96/rjaset..689 ISSN: ; e-issn: axwell Sientifi Publiatin Crp. Submitted: Otber 9, 5 Aepted: Otber 3, 5 Published: arh 5, 6 Researh Artile Quantum Effiieny Effets n dal Gain, Threshld Current and Threshld Current Density f PbSe/Pb.934 Sr.66 Se ultiple Quantum Well Struture ajed Khdr Department f Eletrnis and Cmmuniatins Engineering, Amerian University f Ras Al Khaimah, P.O. Bx, Ras Al Khaimah, United Arab Emirates Abstrat: In this study we studied the effets f internal quantum effiieny n PbSe/Pb.934 Sr.66 Se multiple Quantum well Struture. The alulatins were dne n the mdal gain, threshld urrent and threshld urrent density f the system. Inlusin f the theretial internal quantum effiieny inreased the threshld urrent and threshld urrent density values by almst times with n effets n the mdal gain values. Hwever, when the experimental internal quantum effiieny was inluded, the abve inrease was even mre. It was inluded that there is a leakage urrent abve the barrier whih is needed t aunt fr in any pratial appliatin. Keywrds: Auger rembinatin, leakage urrent, lead salts, quantum effiieny INTRODUCTION An attrative aspet f IV-VI lead salts semindutr materials is that they an be grwn with high rystalline quality n industry standard silin substrates (Lehtinen and Kuusela, 4; Razeghi et al., 3; Yang et al., 5; Kim et al., 7. Suh a grwth tehnlgy an be readily saled t enable lw unit st prdutin thus making pssible the mmerializatin f lw st sensrs fr the widest pssible distributin. This study fuses n the physis and engineering f IV-VI semindutr quantum well strutures mpsed f PbSe wells and Pb -x Sr x Se barrier materials. In this study, we use the referened mdel frm Khdr et al. (998 t study and alulate the effets f the internal quantum effiieny n the threshld urrent density J th. The internal quantum effiieny is influened by Auger rembinatin and may be readily demnstrated by nsidering the radiative and nn radiative life times. Als, quantum the internal quantum effiieny, alng with the gain and internal lsses, depends n the grwth temperature. Hene, these alulatins were dne at five different temperatures: 3, 5,, 5 and 77 K, respetively. ATERIALS AND ETHODS Within the framewrk f Fermi's Glden Rule, the tw majr mpnents f gain alulatins are the eletrn and whle density f states and the transitin matrix element desribing the interatin between the ndutin and valene band states. The derivatin fr the analytial gain expressin is given by the fllwing expressin (Khdr et al., 996, 998: e QW, n ( n m w [ f ( f ( ] r, w v n H ( avg n ( And the mpnent f the arrier rembinatin is fund frm the spntaneus emissin rate: R sp ( f ( e nr, w 3 m w [ f v ( ] n nv avg H ( n ( Frm this, the urrent density is alulated by the fllwing equatin: The system under investigatin is PbSe/Pb.934 Sr.66 Se ultiple Quantum Well (QW with PbSe as the well material with width f 7 nm and Pb.934 Sr.66 Se as barrier material with thikness f 7 nm, number f wells f 7, index f refratin f the well material is and that f the barrier material is e m J ew R sp ( : The harge f the eletrn : The eletrn free mass (3 This wrk is liensed under a Creative Cmmns Attributin 4. Internatinal Liense (URL: 67

2 w n r, w QW, n avg Res. J. Appl. Si. Eng. Tehnl., (5: 67-6, 6 : The internal quantum effiieny : The speed f light : The well width : The index f refratin at the lasing frequeny ω : The permittivity f free spae, : The transmissin matrix element : The ued density f states, f, v ( : The Fermi-Dira distributin funtins, H(x : The Heaviside funtin that is equal t unity when x> and is zer when x< and n : The energy differene between the bttm f the n-subband in the ndutin band and the n-subband in the valene band. The exitatin methd that is f imprtane in this study is injetin f arriers int the ative regin by passing urrent thrugh the devie. An inrease in the pumping urrent leads t an inrease in the density f injeted arriers in the ative regin and with it, an inrease in the quasi-fermi levels. In laser sillatrs, the nern is with the mdal gain rather with the maximum gain. The mdal gain is defined as the gain experiened by the traveling laser mde. It is btained by multiplying the maximum gain values given by Eq. ( by the nfinement fatr. The ptial nfinement fatr depits the verlap f the ptially guided wave with the quantum well. In rder fr laser sillatin t ur, the mdal gain g md ( at the lasing phtn energy must equal the ttal lsses α ttal given by the fllwing equatin: ttal QW f s ln L R R (4 QW : The nfinement fatr fr the partiular struture : The free arrier absrptin f : The sattering lss due t waveguide s imperfetins R =.4, the threshld urrent density (J th rrespnds t the mdal gain value that satisfies the sillatin nditin Eq. (4 and an be btained frm the mdal gain-urrent density plts. The influene f Auger rembinatin n the quantum effiieny may be readily demnstrated by nsidering the radiative lifetime r and Auger lifetime a. The radiative rembinatin rate Rr varies with injeted arrier density as: R r = Bn (5 n p The radiative lifetime is given by: r = n/r r = /Bn (6 B : The radiative nstant The nnradiative Auger rembinatin rate R a varies as: R a = Cn 3 (7 C: The Auger effiient. The Auger lifetime bemes: a = /Cn (8 The verall lifetime is: = a r /( a + r (9 And the quantum effiieny is: = /(+ r / a ( Substitute fr r and a frm Eq. (6 and (8: = /(+Cn/B ( The temperature dependene f α ttal is ntained in the first tw terms. The lss due t radiatin frm the The temperature dependene f is ntained in ends f the laser is given by the third term in Eq. 4, B, C and n. where L is the laser avity length and R, R are the end Fr PbSe, the radiative B effiient is - m 3 /s faet refletivity s. and Auger effiient C is 8-8 m 6 /s (Hanna et al., The urrent needed t mpensate fr the ttal lss 5. Beause the temperature dependene f B is α ltal is alled the threshld urrent (I th and is alulated believed t be small, B will be taken as nstant with by the usual frmula: temperature. As fr Auger effiient C the value given is apprximately nstant between 3 and 7K and I th J th Area J thl width (5 then drps t a value abut -8 m 6 /s (Hanna et al., 5. The remaining temperature-dependent quantity Assuming the avity width has a nstant value f is the arrier density at threshld n th. The values f nth μ m and the mirrr refletivities fixed at R =.4 and at the five temperatures f interest in this study are 68

3 Res. J. Appl. Si. Eng. Tehnl., (5: 67-6, 6 alulated and aunted fr in the sftware prgram, hene the theretial internal quantum effiieny values were btained using Eq. (. On the ther hand, the experimental values f nth at the five temperatures f interest in this study were btained frm Fig. (Findlay et al., 998, hene the experimental internal quantum effiieny values were btained using Eq. (. The temperature dependene f the gain is first intrdued by taking the quantum effiieny = at all temperatures. Then we inluded and alulated the effets f internal lsses and quantum effiieny n the behavir f the mdal gain, threshld urrent and threshld urrent density f the system. RESULTS AND DISCUSSION dal gain (/m T=5K T=K T=5K T=3K Current density 3 (A/m The behavir f the mdal gain vs. urrent density values assuming = at five different temperatures: 77, 5,, 5 and 3 K, respetively is shwn in Fig.. The effets f quantum effiieny an be seen in Fig. and as shwn in this figure, the urrent density inreases almst times with n effet n the mdal gain values. Frm these figures ne ntie that the transpareny urrent J (interept at gain = inreases with inreasing temperature. rever, the slpe f the gain versus urrent density plt dereases with inreasing temperature. These tw quantities are imprtant in alulating the harateristi temperature T fr the system. The alulated threshld urrent values are shwn in Fig. 3 assuming = and Fig. 4 with quantum effiieny values inluded. Inlusin f the quantum effiieny inreases the threshld urrent value by almst flds. Als, we inluded the experimental quantum effiieny btained frm Findlay et al. (998. Frm these figures, ne nties that the threshld urrent urves have a minimum threshld urrent value at a ritial avity length. The regin abve the ritial thikness value rrespnds t the lw mdal gain regime (r lw lsses regime. Hwever, the regin belw the ritial avity length value rrespnds t the high mdal gain regime (r high lsses regime. The threshld urrent value fr the experimental quantum effiieny is muh higher than that value fr the theretial quantum effiieny due t leakage urrent ver the barrier. The threshld urrent density urves fr = and are shwn in Fig. 5 and 6, respetively. As seen in these figures, these values inrease with temperature inrease at any fixed avity length. Als, it an be ntied that the threshld urrent density values drps fast at small avities and remains nstant after sme ritial avity length arund m. The effets f quantum effiieny are lear in that it inreases the threshld urrent density values. We inluded the experimental quantum effiieny values t alulate the urrent density values at 3K and the results are Fig. : The mdal gainassuming unity quantum effiieny dal gain (/m T=K T=3K Current densit 3 (A/m T=5K T=5K Fig. : The mdal gain values inluding the effet f quantum effiieny Thershld urrent (ma T=3K T=K T=5K T=5K Cavity length (µm Fig. 3: Threshld urrent assuming unity quantum effiieny shwn in Fig. 6. Frm this figure ne nties that the threshld urrent density values using the experimental quantum effiieny values are higher than the theretially assumed nes. Similar t threshld urrent, this indiates that there is an additin fatr affeting the urrent density value and it uld be due 69

4 Thershld urrent (ma T=3K T=K Fig. 4: Threshld urrent values inluding the theretial and experimental quantum effiieny Thershld urrent density (A/m Fig. 5: Threshld urrent density assuming unity quantum effiieny Thershld urrent density (A/m Fig. 6: Threshld urrent density inluding the theretial and experimental quantum effiieny t leakage urrent ver the barrier. Leakage urrent alulatins will be addressed in future publiatins. Res. J. Appl. Si. Eng. Tehnl., (5: 67-6, T=K T=3K Cavity length (µm T=5K T=5K T=3K, Exp Cavity length (µm T=K T=3K T=5K T=5K Cavity length (µm T=5K T=5K T=3K, Exp 6 CONCLUSION The effets f temperature and quantum effiieny n the threshld urrent density and threshld urrent values f PbSe/Pb.934 Sr.66 Se multiple Quantum well Struture were alulated. Inlusin f quantum effiieny inreased the threshld urrent values by almst times. Als, it was ntied that the threshld urrent density values drpped fast at small avities and remained nstant after sme ritial avity length arund m. When experimental quantum effiieny values were used, the threshld urrent values were higher than thse fund using the theretial quantum effiieny values. This indiates that there is an additinal fatr affeting the urrent density values and it uld be due t leakage urrent ver the barrier, whih we will aunt fr in future wrk. REFERENCES Findlay, P.C., C.R. Pidgen, R. Ktitshke, A. Hllingwrth, B.N. urdin, C.J. Langerak, A.F. Van der eer, C.. Ciesla, J. Oswald, A. Hmer, G. Springhlz and G. Bauer, 998. Auger rembinatin dynamis f lead salts under pisend free-eletrn-laser exitatin. Phys. Rev. B, 58: prb/abstrat/.3/physrevb Hanna,.C., R.J. Ellingsn,. Beard, P. Yu, O.I. ii and A.J. Nzik, 5. Quantum dt slar ells: High effiieny thrugh multiple exitn generatin. Preeding f the DOE Slar Energy Tehnlgies Prgram Review eeting DOE/GO Z/. htm. Khdr,.F., B.A. asn and P.J. Cann, 996. Effets f band Nn-parabliity n the gain and urrent density in EuSe/PbSe.78 Te. /EuSe IV-VI semindutr quantum well lasers. IEEE J. Quantum Elet., 3(: ieee.rg/xpl/artiledetails.jsp?relad=true&arnumb er=4887. Khdr,.F., B.A. asn and P.J. Cann, 998. Optimizing and engineering EuSe/PbSe.78Te./EuSe multiple quantum well laser strutures. IEEE J. Quantum Elet., 34(9: ber=79577&url=http%3a%f%fieeexplre.iee e.rg%fxpls%fabs_all.jsp%3farnumber%3d Kim, C.S., C.L. Canedy, E.H. Aifer,. Kim, W.W. Bewley et al., 7. leular beam epitaxy grwth f antimnide type-ii W high-pwer interband asade lasers and lng-wavelength infra phtdides. J. Va. Si. Tehnl. B, 5: jurnal/jvstb/5/3/.6/

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