2. Contribution to the Analysis of High-Speed Single Quantum Well Laser Response: Effect of Leakage Current Petar Matavulj PhD Thesis

3. Petar Matavulj – PhD Thesis Nobel Prize in Physics 2000. Zhores I. Alferov  For developing semiconductor heterostructures used in high-speed- and opto-electronics  Laser diodes First Nobel Prize in Optoelectronics.

4. Petar Matavulj – PhD Thesis Main Purpose Versatile analysis of laser diode response considered  in all operating conditions  including wide group of relevant physical processes Forming concrete model  Physical model  Efficient numerical tool  exact and fast  user-friendly for usual electrical engineers

5. Petar Matavulj – PhD Thesis Analyzed device optimization for special applications  application in optical communications o Finding extreme value of bandwidth and threshold current Main Purpose

6. Petar Matavulj – PhD Thesis SQWL Considered L QW = 8nm L SCH = 76,150,300nm L R = 2.5  m L L = 300  m intrinsic cladding P = 10 18 cm -3 N = 5x10 17 cm -3 0 = 980nm

7. Petar Matavulj – PhD Thesis Why QWL?  Lower threshold current for one order of magnitude  Lower threshold current dependence of temperature  Differential gain higher double  Up to 50% higher bandwidth Superior for applications in optical communicatons. Better energy efficiency. Faster laser diode.

8. Petar Matavulj – PhD Thesis What Kind of Analysis? In three operating conditions  DC response  L-I curve (current-voltage characteristic), I th – threshold current  AC response  frequency response, f -3dB – bandwidth (cut-off frequency)  Transient response  real diode response change,  onD – time on delay, ER – extinction ratio Complex group of physical processes  Effect of leakage current o analyzed first time

9. Petar Matavulj – PhD Thesis SQWL Response Modeling  Forming closed system of rate equations and its solving  Development of complete procedure for solving system of equations for used physical model  Approximation of exact physics up to the limit for numerical computing Complex and unnecessary for determined characteristic parameter optimization. Simple, efficient and enough exact. Used method.

10. Petar Matavulj – PhD Thesis Rate Equations  One-level rate equations o DHL Two equations; for electrons N QW and photons S.

11. Petar Matavulj – PhD Thesis Rate Equations  Two-level rate equations o QWL Three equations; for 3D electrons N S, for 2D electrons N QW and for photons S.

12. Petar Matavulj – PhD Thesis Rate Equations  Three-level rate equations o QWL Four equations; for 3D electrons N S, for quazi-2D electrons N G, for 2D electrons N QW and for photons S. Gateway states important for fast processes gateway states

13. Petar Matavulj – PhD Thesis Modeling Inside Application in optical communications Fast responses, energy efficiency (QWL) Three-level rate equations Including effect of leakage current carrier leakage right layer – SCH 2 layer Extended system of rate equations - five equations (for 3D electrons in left SCH 1 layer, for 3D electrons in right SCH 2 layer, For quazi-2D electrons in gateway states, for 2D electrons in QW and for photons )

14. Petar Matavulj – PhD Thesis Modeling Inside Encompassed Physical model enough exact

15. Petar Matavulj – PhD Thesis Modeling Inside Numerical tool Efficient (fast) and user-friendly for usual electrical engineers. SPICE (the best choice) Integration optoelectronic with classical electronic components. Construction of equivalent electric circuit from defined system of rate equations Solving stability and convergence problems in formed SPICE program

16. Petar Matavulj – PhD Thesis Modeling Inside Built Numerical tool reliable and suitable for interactive work

17. Petar Matavulj – PhD Thesis Result Overview Response analysis  Two-level rate equations o Nagarajan (1991.) – frequency response o Nguyen (1995.) – TLLM, frequency response and transient response (leakage current not include)  Three-level rate equations o McDonald (1995.) – frequency response (first time analyzed three-level system, improved Nagarajan’s model) Response SPICE analysis ( three operating conditions)  One-level rate equations (DHL) o Tucker (1981.) – first SPICE model for semiconducter laser

18. Petar Matavulj – PhD Thesis  Two-level rate equations o Gao (1990) – first equivalent electric circuit of QWL (two-port model) o Lu (1995.) – SPICE model of SQWL, improved Tucker’s model o Bewtra (1995.) – SPICE modeling of QWL thermal characteristics  Three-level rate equations o Tsou (1997.) – the most complex SPICE model of SQWL up to now  incorporate parasitic subcircuit o Rossi (1998.) – first SPICE model of multimode MQWL  simulated laser with output emission 0 =1.55  m  main drawback is very simple form of equivalent circuit Result Overview

19. Petar Matavulj – PhD Thesis Result Overview - Conclusion Effect of leakage current hasn’t modeled Complete model which include carrier leakage, is formed (2001).

20. Petar Matavulj – PhD Thesis Complete Model Extended system of three-level rate equations  Five equations (four for electrons and one for photons) Derived complete equivalent electric circuit of SQWL  Six main box-subcircuit and six binding box-subcircuit Formed stabile and convergent SPICE program  Give possibilities for simulation SQWL in all three operating conditions

21. Petar Matavulj – PhD Thesis Extended System of Three-level Rate Equations – Included Physical Processes

22. Petar Matavulj – PhD Thesis Extended System of Three-level Rate Equations – Included Physical Processes  Carrier diffusion from both SCH layers in gateway states and vice versa (  D,  G )  Carrier leakage beyond QW (  )  Carrier capture and emission from QW  All recombination processes  monomolecular (A S,A QW ), bimolecular (B S,B QW ) and Auger recombinations (C S,C QW )  Nonlinearity of gain  nonlinear gain (  ) and nonlinear dependence of material gain ( g ~ ln() )  Parasitic effects of bindings in equivalent circuit – parasitic subcircuit

23. Petar Matavulj – PhD Thesis Extended System of Three-level Rate Equations

24. Petar Matavulj – PhD Thesis Extended System of Three-level Rate Equations

25. Petar Matavulj – PhD Thesis Complete Equivalent Electric Circuit of SQWL carriers in adequate layersarm currents ; Extended system of three-level rate equations photon emissionoutput voltage Equivalent system of current equations

26. Petar Matavulj – PhD Thesis Complete Equivalent Electric Circuit of SQWL Equivalent system of current equations Kirchhoff ‘s laws Complete equivalent electric circuit of SQWL

27. Petar Matavulj – PhD Thesis Complete Equivalent Electric Circuit of SQWL photon emission QW gateway states SCH layers parasitic subcircuit

28. Petar Matavulj – PhD Thesis Complete Equivalent Electric Circuit of SQWL– Subcircuit for Left SCH 1 Layer

29. Petar Matavulj – PhD Thesis Complete Equivalent Electric Circuit of SQWL – Subcircuit for Right SCH 2 Layer

30. Petar Matavulj – PhD Thesis Complete Equivalent Electric Circuit of SQWL – Subcircuit for Gateway States

31. Petar Matavulj – PhD Thesis Complete Equivalent Electric Circuit of SQWL – Subcircuit for QW

32. Petar Matavulj – PhD Thesis Complete Equivalent Electric Circuit of SQWL – Subcircuit for Output Photon Emission

33. Petar Matavulj – PhD Thesis Complete Equivalent Electric Circuit of SQWL – Parasitic Subcircuit

34. Petar Matavulj – PhD Thesis SPICE Program Complete equivalent electric circuit Selection of SQWL parameters variable parameters SPICE program Solving stability and convergence Incorporation in SPICE

35. Petar Matavulj – PhD Thesis Response Analysis – DC Response L-I Curve 76 150 300 50m v 100m v 150m v 0m v 0mA1mA2mA 3mA  =0 L SCH (nm) Injection current - I SNSN

36. Petar Matavulj – PhD Thesis Response Analysis – DC Response Threshold Current - I th I th (mA) 1.29 1.13 1.02 0mV 4mV 8mV 0.9mA1.1mA1.3mA1.5mA  =0 Injection current - I SNSN

37. Petar Matavulj – PhD Thesis Response Analysis – DC Response Threshold Current - I th (  ) 76 150 300

38. Petar Matavulj – PhD Thesis Response Analysis – AC Response Frequency Response – Parasitic Subcircuit Frequency SNSN 1GHz3GHz10GHz15GHz 0V0V 250  V 500  V L SCH =300nm;  =0 I B =2mA I B =15mA parasitic subcircuit without with

39. Petar Matavulj – PhD Thesis Response Analysis – AC Response Frequency Response - Comparison L SCH =76nm S N (  V) Frequency (GHz) I B =15mA 0.60.8126810 40 25 50 75 100 125 150 175 200 225 250 420204040 0 L SCH =300nm  =0  =0.9  =0

40. Petar Matavulj – PhD Thesis Response Analysis – AC Response Bandwidth - f -3db (  ) L SCH (nm) 76 150 300 0.00.10.20.30.40.50.60.70.80.91.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5  f -3dB (GHz) I B =2mA 0.785 > 0.9

41. Petar Matavulj – PhD Thesis Response Analysis – AC Response Bandwidth - f -3db (  ) L SCH (nm) 76 150 300 0.00.10.20.30.40.50.60.70.80.91.0 0 2 4 6 8 10 12 14  f -3dB (GHz) I B =15mA 0.09 0.74 > 0.9

42. Petar Matavulj – PhD Thesis 2 10 2.53.55 Response Analysis – Tran Response Laser Start - Animation IP=IP= mA 15

43. Petar Matavulj – PhD Thesis IP=IP=2,2.5,3.5,5,10,15mA input current impulse Response Analysis – Tran Response Laser Start

44. Petar Matavulj – PhD Thesis Response Analysis – Tran Response Normalized Response I B /I th =0 I B /I th =15 L SCH (nm) 76 300

45. Petar Matavulj – PhD Thesis Response Analysis – Tran Response Influence of Carrier Leakage I B =0mA I B =15mA  0 0.5

46. Petar Matavulj – PhD Thesis Response Analysis – Tran Response Laser Time on Delay -  onD (  ) 76 150 300 L SCH (nm) 0.00.10.20.30.40.50.60.70.80.91.0   onD (ns) I B =0mA, I P =5mA  >0 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

47. Petar Matavulj – PhD Thesis Response Analysis – Tran Response Extinction ratio - ER(  ) 76 300 L SCH (nm) IB=IB= 76 300 2 15 mA

48. Petar Matavulj – PhD Thesis New model – Complete model of SQWL  Complete equivalent electric circuit of SQWL Analysis of leakage current effects – first time  Influence of leakage current is important in all operation condition of SQWL and can’t be neglected. Conclusion – Thesis Contribution

49. Petar Matavulj – PhD Thesis Conclusion – Thesis Contribution Influence of Leakage Current  Increasing threshold current if carrier leakage increase for large thickness of SCH layers.  Carrier leakage always reduce SQWL bandwidth, especially for larger thickness of SCH layers and higher bias currents. Critical leakage factor.  Increasing laser time on delay if increase carrier leakage, especially for larger thickness of SCH layers; ER don’t depend of carrier leakage.