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Roger Lake and Cristian Rivas

UCR. Full Quantum Simulation, Design, and Analysis of Si Tunnel Diodes, MOS Leakage and Capacitance, HEMTs, and RTDs. Roger Lake and Cristian Rivas Department of Electrical Engineering, University of California, Riverside, California 92521-0204

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Roger Lake and Cristian Rivas

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  1. UCR Full Quantum Simulation, Design, and Analysis of Si Tunnel Diodes, MOS Leakage and Capacitance, HEMTs, and RTDs Roger Lake and Cristian Rivas Department of Electrical Engineering, University of California, Riverside, California 92521-0204 Eric Jonsson School of Engineering, University of Texas at Dallas, Richardson, TX 75083-0688 rlake@ieee.org

  2. OUTLINE • Nanoelectronic Engineering Modeling Software (NEMO) status • Examples of NEMO supporting experimental programs: QMOS, HEMTs, and RTDs. • Versatility • Full Band modeling of Si tunnel diodes • Theoretical extension • Comparison with experimental measurements • Verification • Conclude

  3. NEMO Status • Developed during the years 1993 to 1997 and delivered to the U. S. Government. • Raytheon owns the software and is not currently distributing it. • CFDRC is negotiating with Raytheon to commercialize NEMO. • NASA JPL has extended NEMO to 3D QDots. • For URLs and references see Proceedings.

  4. OUTLINE • Nanoelectronic Engineering Modeling Software (NEMO) status • Examples of NEMO supporting experimental programs: QMOS, HEMTs, and RTDs. • Versatility • Full Band modeling of Si tunnel diodes • Theoretical extension • Comparison with experimental measurements • Verification • Conclude

  5. NEMO Design / Analysis Examples • NEMO was used extensively at TI and Raytheon to support experimental device programs: • Quantum MOS (QMOS) • HEMT / RTD circuits for ADCs and TSRAM • RTDs for THz sources and detectors.

  6. Quantum Charge Single Band Calculations Design / Analysis Example • QMOS Si / SiO2 • Extraction of m* of SiO2 Band Diagram n-Si / SiO2 / Al Brar, Wilk, and Seabaugh, APL, 69, 2728 (1996).

  7. C-V Single Band Calculations Design / Analysis Example • QMOS Si / SiO2 • n-Si / SiO2 / Al • C-V Experimental Data Brar, Wilk, and Seabaugh, APL, 69, 2728 (1996).

  8. Single Band Calculations Experimental Data Design / Analysis Example • I-Vs • tox = 1.65 nm - 3.51 nm • I = 10-13 - 102 A/cm2 • mox = 0.3 m0 • QMOS Si / SiO2 • n-Si / SiO2 / Al Brar, Wilk and Seabaugh, APL, 69, 2728 (1996).

  9. Design 4/2/98 Experimental Device 4/1/98 4 nm Si0.5Ge0.5 intrinsic Multiple Single Band Calculation 8nm Si0.5Ge0.5 n+ / p+ Data Rommel et al., APL, 73, 2191 (10/98) NDR 5/98 Design / Analysis Example • QMOS Si / SiGe • MBE grown Tunnel Diode No reproducible NDR

  10. Coupled 2-Band Calculation NEW DATA OLD DATA Gate recess etch process had gone South Design / Analysis Example • HEMT In0.48Al0.52As / In0.47Ga0.53As on InP • Gate tunnel current

  11. Design / Analysis Example • HEMT In0.48Al0.52As / In0.47Ga0.53As on InP • Gate tunnel current • Temperature Dependence

  12. Design /Analysis Example • HEMT In0.48Al0.52As / In0.47Ga0.53As on InP • Non-alloyed ohmic contacts

  13. Design /Analysis Example • Goal: Simplify epi • 1. Remove the superlattice • 2. Remove the doped In0.52Al0.48As. • HEMT In0.48Al0.52As / In0.47Ga0.53As on InP • Non-alloyed ohmic contacts • Coupled 2-Band coherent tunneling calculations: • Metal to channel • Digital superlattice to channel • Gate Barrier to channel

  14. (a) Design /Analysis Example • Approach • Coupled 2-band DC calculations of I-V and C-V • Design InAs / AlAs RTD LOs for THz recivers

  15. RTD Rs Ls -R C Z • Calculate small signal R = (dI/dV)-1 -Lqu = -R tqu • Use R & C in circuit model RCL Model • Calculate max frequency Design /Analysis Example • Approach • Coupled 2-band DC calculations of I-V and C-V • Design InAs / AlAs RTD LOs for THz recivers

  16. OUTLINE • Nanoelectronic Engineering Modeling Software (NEMO) status • Examples of NEMO supporting experimental programs: QMOS, HEMTs, and RTDs. • Versatility • Full Band modeling of Si tunnel diodes • Theoretical extension • Comparison with experimental measurements • Verification • Conclude

  17. Questions: What is the effect of confinement in the contacts? Can we model this device using modern quantum device modeling techniques? -Peak current? -Excess current? LT-MBE Grown Si Tunnel Diode • Delta-doped Sb and B on either side of the tunnel junction • SIMS data for as-grown and after 1 min. RTA. • Indirect, Interband, Phonon Assisted Tunneling • Main current from 4 X4 valleys. 2 x 1020 Sb 2.5 x 1020 B

  18. Atomic scale physics Practical devices Atomic Layers STM Micrograph Full quantum calculation of current, voltage, and capacitance. Theoretical Approach • Non-equilibrium Green function formalism • Fermi’s Golden Rule in Green function form. • 2nd neighbor sp3s* • 1st neighbor sp3s*d5. • Read in SIMS doping profile. • Perform a semiclassical calculation of the charge and potential profile. • Calculate direct and phonon-assisted tunnel current. • TA and TO phonons. • The phonon wavevector is fixed at the G-X valley minimum wavevector of 0.82 2p/a <100> • Approximate the overlap of the Bloch states with a constant deformation potential. • Numerically calculate the overlap of the wavefunction envelopes between the X-conduction-band and G-valence band states. • Include a finite lifetime in the calculation of the spectral function of the contacts ==> bandtails.

  19. Is the component of the spectral function injected from the right contact. Imaginary potential used for calculating the surface Green funcitons contained in Transport Equation • Phonon assisted tunneling current Interband (100) phonons:

  20. g00(E, k) rgf gs(E, k) site 0 Partitioning of Device into “Contacts” & “Tunnel Region” • Exact bulk surface Green function is calculated in the flat band region to left and then “moved in” using the recursive Green function algorithm. • Finite lifetime included in left and right contacts. X G

  21. Effect of Confinement in Contacts • 3 Current calculations: TA phonon-assisted, TO phonon-assisted, and direct tunneling (X2 - G). • Direct tunneling current ~ 5 orders of magnitude < phonon-assisted tunneling current. • Structure most notable in NDR region. t= 165 fs

  22. Effect of Confinement in Contacts t= 165 fs • Comparison of bulk contacts vs. quasi-2D contacts.

  23. C A V B Excess current mechanism Band Tails and the Excess Current • Effect of band tails in the contacts on the tunnel current • ALL of the current above is tunnel current. • NONE is p-n diode current

  24. SIMS Data Gap States? The features around 0.5 - 0.6V from gap states. Calculations As Grown RTA 700o C Comparison with the Data • Hump current observed in experiments ==> midgap states in tunnel region.

  25. Band parameters • Imaginary wavevectors in gap? Light Hole Electron Determine Tunneling (From old parameter set) Verification • Doping profile • Activation • Deformation potentials • Gap states.

  26. Conclusion • NEMO status • NEMO in Design / Analysis role - versatility • First modern full-band treatment of phonon-assisted, indirect, interband tunneling. • Qualitative agreement with I-V - peak and excess current. • Experimental unknowns - verification • Doping profile and activation ==> tunnel barrier thickness • Gap states • Complex wavevectors in gap

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