2. 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 UCR rlake@ieee.org

3. 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

4. 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.

5. 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

6. 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.

7. Design / Analysis Example QMOS Si / SiO 2 –Extraction of m* of SiO 2 Brar, Wilk, and Seabaugh, APL, 69, 2728 (1996). Band Diagram n-Si / SiO 2 / Al Quantum Charge Single Band Calculations

8. Design / Analysis Example QMOS Si / SiO 2 –n-Si / SiO 2 / Al –C-V Brar, Wilk, and Seabaugh, APL, 69, 2728 (1996). Experimental Data C-V Single Band Calculations

9. Design / Analysis Example QMOS Si / SiO 2 –n-Si / SiO 2 / Al I-Vs –tox = 1.65 nm - 3.51 nm –I = 10 -13 - 10 2 A/cm 2 –m ox = 0.3 m 0 Experimental Data Brar, Wilk and Seabaugh, APL, 69, 2728 (1996). Single Band Calculations

10. 4 nm Si 0.5 Ge 0.5 intrinsic Design 4/2/98 Multiple Single Band Calculation NDR 5/98 Data Design / Analysis Example QMOS Si / SiGe –MBE grown Tunnel Diode 8nm Si 0.5 Ge 0.5 n+ / p+ Experimental Device 4/1/98 No reproducible NDR Rommel et al., APL, 73, 2191 (10/98)

11. Design / Analysis Example HEMT In 0.48 Al 0.52 As / In 0.47 Ga 0.53 As on InP –Gate tunnel current NEW DATA Coupled 2-Band Calculation Gate recess etch process had gone South OLD DATA

12. Design / Analysis Example HEMT In 0.48 Al 0.52 As / In 0.47 Ga 0.53 As on InP –Gate tunnel current –Temperature Dependence

13. Design / Analysis Example HEMT In 0.48 Al 0.52 As / In 0.47 Ga 0.53 As on InP –Non-alloyed ohmic contacts

14. Design / Analysis Example HEMT In 0.48 Al 0.52 As / In 0.47 Ga 0.53 As on InP –Non-alloyed ohmic contacts Goal: Simplify epi –1. Remove the superlattice –2. Remove the doped In 0.52 Al 0.48 As. Coupled 2-Band coherent tunneling calculations: –Metal to channel –Digital superlattice to channel –Gate Barrier to channel

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

16. Design / Analysis Example Design InAs / AlAs RTD LOs for THz recivers Approach –Coupled 2-band DC calculations of I-V and C-V –Calculate small signal R = (dI/dV) -1 –Use R & C in circuit model RCL Model Z RsRs C -R LsLs RTD -L qu = -R  qu –Calculate max frequency

17. 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

18. 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 X 4 valleys. 2.5 x 10 20 B 2 x 10 20 Sb 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?

19. Atomic scale physics Practical devices Full quantum calculation of current, voltage, and capacitance. STM Micrograph Atomic Layers Non-equilibrium Green function formalism Fermi’s Golden Rule in Green function form. 2nd neighbor sp 3 s* 1st neighbor sp 3 s*d 5. 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  -X valley minimum wavevector of 0.82 2  /a 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  -valence band states. Include a finite lifetime in the calculation of the spectral function of the contacts ==> bandtails. Theoretical Approach

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

21. 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. g 00 (E, k) site 0 g s (E, k) rgf X 

22. Effect of Confinement in Contacts 3 Current calculations: TA phonon-assisted, TO phonon- assisted, and direct tunneling (X 2 -  ). Direct tunneling current ~ 5 orders of magnitude < phonon- assisted tunneling current. Structure most notable in NDR region.  = 165 fs

23. Effect of Confinement in Contacts Comparison of bulk contacts vs. quasi-2D contacts.  = 165 fs

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

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

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

27. 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