Mechanical Stress Effect on Gate Tunneling Leakage of Ge MOS Capacitor Younsung Choi Electrical Engineering University of Florida

Gate Tunneling Current Summary Outline Background Ge MOS Device Gate Tunneling Current Summary

Background What is strain? Strain is differential deformation in response to an applied stress. Uniaxial: one directional (1D) deformation Biaxial: two directional (2D) deformation Hydrostatic: volume deformation of a solid (average energy level shift in the conduction and valence bands) Shear: twisted deformation of a solid (subband splitting in the conduction and valence bands without changing the average energy level) Hydrostatic strain Shear strain

Background Why is strain important? Strain increases carrier mobility in MOSFETs, resulting in faster speed of a MOSFET operation. Thompson et al., Uniaxial-Process-Induced Strained-Si: Extending the CMOS Roadmap, IEEE Trans. On Electron Devices, 53, 1010, 2006 Strain affects a MOSFET operation characteristics such as its threshold voltage, gate tunneling current. Lim et al., Comparison of threshold voltage shifts for Uniaxial and Biaxial Tensile-stressed n-MOSFETs, IEEE Elec. Device Letters, 25, 731,2004 Lim et al., Measurement of conduction band deformation potential constants using gate direct tunneling current in n MOSFET under mechanical stress, APL, 89, 073509,2006

Background Why do we need Ge? Promising as an alternative channel material due to its high carrier mobility Why have we used Si for a long time? => based on the synergy between the silicon itself and its thermal oxide, SiO2. For decades, thermal SiO2 has provided the best possible surface passivation and it is a superb gate insulator. Non-SiO2 Gate Insulator with Ge MOSFET =>direct electron tunneling through very thin SiO2

Ge MOS Device L valley of Ge Conduction Band How to calculate Ge MOS Electrostatics Ge MOS Electrostatics with solving self-consistently the Schrodinger and Poisson equations Stress Effect on Ge Quantization

L valley of Ge Conduction Band For electrons in Ge, the conduction band minima are located at L valley Uniaxial Tension along <110> direction [111],[11-1] [1-11],[-111] Shear Strain ∆EShear Hydrostatic Strain ∆EHydro Unstrained Four-fold degenerate L-valleys in the Ge conduction band.

How to calculate? 1-D Effective Mass Hamiltonian : the strain Hamiltonian : the effective mass associated the electron motion perpendicular to the interface Electron Concentration along quantum box Electro static potential with Poisson equation

Ge MOS Electrostatics Vg = 1V Vg = 1V Vg = 0.5V Vg = 0.5V HfO2 Ge Sub. Conduction Band Edge vs Distance HfO2 Ge Sub. Vg = 1V Vg = 0.5V Vg = 1V Vg = 0.5V

Stress Effect on Ge Quantization Energy Band Splitting Electron Repopulation [111],[11-1] [-111],[1-11] Band Splitting Electron Repopulation

Gate Tunneling Current What is Gate Tunneling Current? Tunneling Probability Calculation with a modified Wentzel-Kramers-Brillouin (WKB) approximation Stress Effect on Gate Tunneling Current

What is Gate Tunneling Current? Gate tunneling is a phenomenon in which channel charge carriers tunnel into the oxide layer when the gate bias is applied. Z (001) EL(σ) EC Direct Tunneling Current Y.T. Hou et al., Direct tunneling hole currents through ulrtathin gate oxides in MOS devices, JAP, 91, 258 EV Metal Gate Ge Substrate HfO2

Tunneling Probability Calculation with a modified WKB approximation TWKB : the usual WKB tunneling probability valid for smoothly varying potentials TR : the correction factor for reflections from boundaries of the oxide K(E) : the imaginary wave number within the oxide gap energy vGe(E) & vGe(E+qVOX) : the group velocities of carrier incident and leaving the Oxide layers vOX(EOXi) & vOX(EOXo) : the magnitude of the imaginary group velocities of Carriers tunneling in and out of the oxide layer

Stress Effect on Gate Tunneling Current ∆τ[111],[11-1] ∆τ[-111],[1-11] ∆n/n & ∆τ/τ (%) VG=0.6V VG=1V ~+2% ~-3% -1% ~+1.3% ~-2% -0.7% Line Model Symbol Exp.Data ∆ФB(σ)<0 E(σ)[111],[11-1] E(σ)[1-11],[-111] Relative Change of Tunneling Current with Uniaxial Tension along (110) direction Barrier Lowering of [111],[11-1] valleys => Tunneling Current Enhancement

Summary Ge Electrostatics with solving self-consistently the Schrodinger and Poisson equations Tunneling Probability with the modifeied WKB approximation Gate Tunneling Leakage Current Change with Uniaxial Stress was obsereved. => Barrier Height Lowering leads to Enhancement of Tunneling Current

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