1. Intoduction to VCSEL Device Simulation Mou Zongying 07-06-2004

2. VCSEL Device Simulation Introduction Basic concepts of Laser and semiconductor Physical model of VCSEL device Computing optical mode Numerical simulation Simulation results

3. Introdction VCSEL: vertical-cavity surface-emitting laser (semiconductor laser device, diode laser) Telecomunications, Pumping source Wave length : from infrared to visible etched mesa VCSEL 980nm Buried tunnel junction(BTJ) VCSEL 1300nm,1550nm Material: ALGaAs(GaAs),InGaAsP(InP) Simulators are needed to explore the design parameter for an optimum solution—low cost and short time for a design cycle

4. Basic Concepts of Laser  Laser

5. Requirements for Laser Action Population inversion

6. Basic Concepts of Semiconductor There are three types of conductors. Insulaters.Metals.Semicondctors

7. Energy Band for Solid Metals. Overlapping energy bands or vary small gap. Electrons in conduction band Semiconductors. Small energy gap <2ev. Some electrons in conduction band Insulators. Large energy gap. No electrons in conduction band

8. Physical Model of VCSEL Diode laser devices – history Physical Model of VCSEl Schematic of two kinds of VCSEL. Etched Mesa.BTJ Maxwell´s equation Laser device simulation

9. Diode Laser Devices First working device appeared in 1962, at low temperature Structure containing several semiconductor layers In 1969, at room temperature After 1990, employed BTJ which causes a transverse waveguiding--stable transverse mode profile and small threshold current

10. Physical Model of VCSEL Time Dependent Model (Finite Difference Time Domain) in 1995 Stationay Model (Finite Difference Method) in 1995 Microscopic VCSEL Model in 1998 Isothermal Electric model in 1999 Method of Lines in 2001

11. Etched Mesa VCSEL Etched Mesa VCSEL(electron micrograph) Schematic Etched Mesa VCSEL. DBR( distributed Bragg Resonator)

12. Etched Mesa VCSEL

13. BTJ VCSEL Schematic Buried Tunnel Junction VCSEL

14. Etched Mesa and BTJ VCSEL Schematic cross section of two types of VCSEL

15. Maxwell´s Equation Maxwell´s eq. and material eq.

16. Maxwell wave equation for J=0

17. Maxwell wave equation Separate Eigenvalue problem Frequency Normalization

18. Laser Device Simulation Dielectric fuction Mechanism:. Direct interband absorption. Indirect interband absorption. Free carrier absorption. Interconduction band and intervalence band absorption

19. Laser Device Simulation Photon rate eq. Where S k is the photon number R k is spontaneous emmission w k ‘‘ is the net modal rate change

20. Computing Optical Mode Open Cavity. Only the innerboundary Structure determines the optical mode. Outerboundary is an absorber (no backscattering)

21. Computing Optical Mode Variational function

22. Computing Optical Mode Rotation symmetric

23. Computing Optical Mode  Variational function for axi-symmetric case

24. Computing Optical Mode Boundary condition

25. Numerical Simulation Jacobi-Davidson QZ iteration method Biconjugate gradient stabilished method (BiCGstab) is used to solve Jacobi correction equation and speed up the convergence Software: LUM12 mode solver package

26. Simulation Result The intensity of  k (z) for the fundermental longitudinal VCSEL mode (Etched Mesa)

27. Simulation Result Foundmental mode (BTJ)

28. Simulation Result Higher mode (BTJ)

29. 3D Numerical Simulation Edge finite elements for solving 3D- Maxwell equation. Shape function are vectors. Unknows now along the edge. Natural elements for Maxwell´s equation. Restriction: domain has to be convex