Network for Computational Nanotechnology (NCN) UC Berkeley, Univ.of Illinois, Norfolk State, Northwestern, Purdue, UTEP Homo-junction InGaAs Band-to-band Tunneling Diodes Cho, Woo-Suhl

Moore’s law and MOSFET scaling Transistor dimensions scale to improve performance, and reduce cost per transistor Increased packing density followed by Moore’s law Moore’s law* Downscaling of Transistors** Motivation * ** 2

Dramatic Increase of Power Consumption CMOS microprocessors have reached the maximum power dissipation level that BJT based chips had Motivation * R. R. Schmidt, and B. D. Notohardjono, “High-End Server Low-Temperature Cooling”, IBM J. Res. & Dev., vol.46, No. 6, p. 739, New device concept or idea required

Power consumption in MOSFETs Motivation * S. Borkar, “Getting Gigascale Chips: Challenges and Opportunities in Continuing Moore’s Law”, ACM Queue, vol. 1, No. 7, p. 26, Downscaling of MOSFETs -Leakage current usually fixed at I OFF =0.1μA/ μm -Increased transistor density per chip (>1 billion) Increase of power consumption & heat generation

Limitations of MOSFET Scaling Motivation log(I d ) VgVg V DD 5 Device with SS ≤ 60mV/dec is highly desired V DD Limitations of scaling -Almost non-scalable supply voltage V DD -Physical limit of Sub-threshold Swing (SS) I ON I OFF V T`

New Device Candidate: BTBT FETs Motivation S D EFEF EFEF +V g BTBT FETs Majority carrier transport through the barrier Band-to-band tunneling of cold electrons Boltzmann tails are ignored MOSFETs Minority carrier transport over the barrier Diffusion of hot electrons Depends on the thermal distribution of carriers SS ≥ 60mV/dec limit S D +V g 6 SS ≤ 60mV/dec possible Possible candidate to replace MOSFETs

BTBT FET BTBT Diode P + drain N + source Substrate Vertical structure -Sharp p-n interface can be more easily fabricated Experimental data exist 2 No Gate Bias: OFF STATE Source Drain Positive gate bias: ON STATE BTBT +V g Study of BTBT Diodes Motivation Buried Oxide P+P+ N+N+ Gate oxide S D I Gate 7 Horizontal structure -Difficult to get sharp interface -Need excellent channel control through gate contact Low on current Learn about the tunneling properties Test the potential of a given material as a TFET Test simulation model to design BTBT

Outline 8 Approach Basic Physics of Tunneling Diodes -Band-to-band Tunneling -I-V Characteristic of BTBT Diodes InGaAs Diodes -Junction Modeling and Effects of Junction Abruptness -Solution to Increase Tunneling Currents Band Gap Narrowing Effect and Modeling -Solution to Shift the Onset of Thermionic Current Effects of Doping Variation Excess Current Temperature Dependence Summary and Future Work

Outline 9 Approach Basic Physics of Tunneling Diodes -Band-to-band Tunneling -I-V Characteristic of BTBT Diodes InGaAs Diodes -Junction Modeling and Effects of Junction Abruptness -Solution to Increase Tunneling Currents Band Gap Narrowing Effect and Modeling -Solution to Shift the Onset of Thermionic Current Effects of Doping Variation Excess Current Temperature Dependence Summary and Future Work

Use full-band and atomistic quantum transport simulator based on the tight-binding model (OMEN) to model TDs -Ballistic transport using NEGF Reproduce and understand experimental data -Homogeneous InGaAS tunneling diodes (TDs) fabricated and measured at Penn State, a partner in the MIND center Simulation Approach and Objective 3 10 Approach

Outline 11 Approach Basic Physics of Tunneling Diodes -Band-to-band Tunneling -I-V Characteristic of BTBT Diodes InGaAs Diodes -Junction Modeling and Effects of Junction Abruptness -Solution to Increase Tunneling Currents Band Gap Narrowing Effect and Modeling -Solution to Shift the Onset of Thermionic Current Effects of Doping Variation Excess Current Temperature Dependence Summary and Future Work

Band-to-band Tunneling Basic Physics 12 Narrow band gap -Increase tunneling probability -Material property P+P+ N+N+ E FP E FN W High doping density -More degeneracy -High electric field -Small width barrier -Increase tunneling current P+P+ N+N+ E FN E FP W

Use of InGaAs Basic Physics Materials E g (eV) at 300K m*/m 0 Si Ge InAs In 0.53 Ga 0.47 As Small band gap material: Si  Ge  III-V (InAs) Indirect semiconductor  Direct semiconductor In 0.53 Ga 0.47 As: Lattice matched to InP 13 Indirect Direct EgEg

I-V Characteristics of BTBT Diodes Basic Physics I V 14 IVIVV P+P+ N+N+ E FN E FP EVEV ECEC P+P+ N+N+ E FN E FP EVEV ECEC Tunneling current IPIP VPVP P+P+ N+N+ E FN E FP EVEV ECEC Excess current (Gap state current) P+P+ N+N+ E FN E FP EVEV ECEC Thermionic current P+P+ N+N+ E FN E FP EVEV ECEC Zener current NDR

Outline 15 Approach Basic Physics of Tunneling Diodes -Band-to-band Tunneling -I-V Characteristic of BTBT Diodes InGaAs Diodes -Junction Modeling and Effects of Junction Abruptness -Solution to Increase Tunneling Currents Band Gap Narrowing Effect and Modeling -Solution to Shift the Onset of Thermionic Current Effects of Doping Variation Excess Current Temperature Dependence Summary and Future Work

Fabricated device Simulated device Device Structure and Doping Profile Penn State: InGaAs Diode A InGaAs lattice matched to InP BTBT Diode N A =10 20 /cm 3, N D =5×10 19 /cm nm 20nm N+N+ x In 0.53 Ga 0.47 As P+P+ 3nm N A =8×10 19 N D =4×10 19 I Measured I-V I-V chracteristics of BTBT diodes

Abrupt doping Linear doping 20nm 10nm 3nm D (N + ) S (P + ) N A =8×10 19 /cm 3 N D =4×10 19 /cm 3 x 20nm 10nm 3nm D (N + ) S (P + ) N D =4×10 19 /cm 3 x Doping Profiles at the Junction 17 N A =8×10 19 /cm Junction Modeling

Only Zener tunneling branch is shown Step junction uses R s closer to the estimated value (20Ω) Effect of Junction Abruptness 18 Junction Modeling

I-V Characteristics: Experiment vs Simulation Step junction is used Zener current matched -Too low series resistance: R S =13.5Ω vs. Estimated value: R S =20Ω 7 I-V Characteristics: Experiment vs Simulation 19 Poor reproduction of forward- biased region -Low peak and valley currents -Thermionic current turns on at large bias Investigate potential explanations for the observed disagreements Junction Modeling

Outline 20 Approach Basic Physics of Tunneling Diodes -Band-to-band Tunneling -I-V Characteristic of BTBT Diodes InGaAs Diodes -Junction Modeling and Effects of Junction Abruptness -Solution to Increase Tunneling Currents Band Gap Narrowing Effect and Modeling -Solution to Shift the Onset of Thermionic Current Effects of Doping Variation Excess Current Temperature Dependence Summary and Future Work

Causes of BGN: High Doping Effects High doping level ≥ /cm 3 -D.O.S depends on the impurity concentration -Overlapping impurity states form an impurity band ~200meV BGN Band Gap Narrowing 21 Impurity Bands ECEC EVEV ΔE D Donor Impurity Band ΔE D E ECEC ρ DOS (E) Random distribution of impurities -Potential fluctuation of the band edges -Impurity states tails into the forbidden gap

BGN Calculation Model Jain-Roulston model* Band Gap Narrowing 22 Advantages 1.Compact model calculated based on many-body theory 2.Compute BGN as function of doping concentrations (N), and material parameters (A, B, C) 3.Compute band shifts in major and minor bands separately for all materials 4.No need for experimental fitting parameters S. C. Jain, and D. J. Roulston, Solid-State Electronics, vol. 34, No. 5, p. 453, 1990 S (P + ) D (N + ) Before BGN EgEg After BGN E g1 E g2 S (P + ) D (N + ) ΔE V(min) ΔE C(min) ΔE V(maj) ΔE C(maj) P+P+ N+N+ EFEF

BGN calculation for In 0.53 Ga 0.47 As Band Gap Narrowing 23 p-In 0.53 Ga 0.47 As ΔE g ΔE c ΔE V n-In 0.53 Ga 0.47 As ΔE g ΔE c ΔE V N A =8e19/cm -3 N D =4e19/cm -3 Most shift occurs at conduction band Not negligible shift in minor band Less BGN than n-type material * S. C. Jain, J. M. McGregor, and D. J. Roulston, and P.Balk, Solid-State Electronics, vol. 35, No. 5, p. 639, * James C. Li, Marko Sokolich, Tahir Hussain, and Peter M. Asbeck, Solid-State Electronics, vol. 50, p. 1440, 2006.

Inclusion of BGN in Tight-Binding Band Gap Narrowing S (P + ) D (N + ) In 0.53 Ga 0.47 As before BGN 0.75eV In 1-x1 Ga x1 As-In 1-x2 Ga x2 As after BGN E g1 E g2 In 1-x1 Ga x1 As In 1-x2 Ga x2 As S (P + ) D (N + ) 11 1.Calculate new compositions of In and Ga from the reduced band gaps 2.Calculate tight-binding parameters from the empirical parameters of InAs and GaAs, and Bowing parameters 3.Shift band edges 24 23nm 10nm S (P+) D (N+) eV e V In 0.64 Ga 0.36 As In 0.71 Ga 0.29 As

1 Penn State: InGaAs Diode The effect of BGN 25 Closer to the experimental data: Effect of BGN 1.An increase of the series resistance 2.An increase of tunneling current including the peak current 3.An earlier turn-on of the thermionic current Discrepancies: 1.Mismatch in NDR region, and low valley current 2.A shift of the thermionic current

Outline 26 Approach Basic Physics of Tunneling Diodes -Band-to-band Tunneling -I-V Characteristic of BTBT Diodes InGaAs Diodes -Junction Modeling and Effects of Junction Abruptness -Solution to Increase Tunneling Currents Band Gap Narrowing Effect and Modeling -Solution to Shift the Onset of Thermionic Current Effects of Doping Variation Excess Current Temperature Dependence Summary and Future Work

What can shift the thermionic current? * Effect of doping variation 1.Influence of the donor concentration 2.Influence of the acceptor concentration 27

(1) Variation of the donor concentration N D Higher tunneling current for higher N D -Increase in tunneling window ( ) No shift of the thermionic current onset -No variation of potential barrier ( ) 8 P+P+ N+N+ EFEF 28 Effect of Doping Variation P+P+ N+N+ EFEF P+P+ N+N+ EFEF N A =8e19/cm 3 Experiment data N D =8e19/cm 3 N D =4e19/cm 3 N D =2e19/cm 3

P+P+ N+N+ EFEF (2) Variation of the acceptor concentration N A 9 29 Effect of Doping Variation P+P+ N+N+ EFEF P+P+ N+N+ EFEF Small increase in tunneling current for higher N A -Increase in tunneling window ( ) Earlier turn-on of the thermionic current for lower N A -Lowered potential barrier ( ) -No strong influence 8 N D =4e19/cm 3 Experiment data N A =4e19/cm 3 N A =8e19/cm 3 N A =1.2e20/cm 3

What can increase the valley current? 30 * Excess current 1.Existence of excess current via gap states 2.Influence of excess current I V IVIV V Excess current (Gap state current) Thermionic current Zener NDR Tunneling current IPIP VPVP

Source of Excess Current (I x ) Excess Current P+P+ N+N+ E FN E FP A B C V EgEg qV EVEV ECEC E Tail states ECEC EVEV Conduction band Valence band ρ DOS (E) E x Tunneling + Energy loss mechanism through gap states* Gap States are mostly originated from the band edge tails -A: Tails of acceptor levels extending to the forbidden gap -B: Tails of donor levels extending to the forbidden gap * A. G. Chynoweth, W. L. Feldmann, and R. A. logan, Phys. Rev, vol. 121, p. 684,

(1) Existence of I x : Intrinsic I-V data Excess Current σ 32 No series resistance is included Purely thermionic current beyond the valley in the simulation data Lower slope of the experiment data (σ≈⅓ of q/kT) at the valley confirms the existence of I x Assume that there is a dominant I x around the valley

Excess Current Calculation Excess Current Exponential nature of the excess current* Linear increase of the currents beyond the valley * D. K. Roy, Solid-State Electron., vol. 14, p.520,

(2) The Effect of Excess Current Excess Current of excess current (BGN is included) *Effects of excess current (BGN is included) 1.Increased current around and beyond the valley 2.Closer match to the experiment results 34

Effect of BGN Penn State: InGaAs Diode V=0.95V Efl Efr V P =0.35V Efl Efr V=-0.4V Efl Efr Efl Efr V V =0.64V 35 (I x included)

(3) The Effect of Temperature Temperature Dependence of temperature *Effects of temperature 1.20meV more BGN occurs at room temperature 2.Increase of peak and NDR region currents 36

Outline 37 Approach Basic Physics of Tunneling Diodes -Band-to-band Tunneling -I-V Characteristic of BTBT Diodes InGaAs Diodes -Junction Modeling and Effects of Junction Abruptness -Solution to Increase Tunneling Currents Band Gap Narrowing Effect and Modeling -Solution to Shift the Onset of Thermionic Current Effects of Doping Variation Excess Current Temperature Dependence Summary and Future Work

Investigate the performances of homogeneous InGaAs III-V band-to- band-tunneling (BTBT) diodes Study the tunneling properties of a given material and its potential as a BTBT Field-Effect Transistors (TFETs) Use full-band and atomistic quantum transport solver based on tight-binding to simulate BTBT diodes Coherent tunneling (no e-ph) Compare the simulation results to experimental data from Penn State BGN provides good agreement with experimental data for tunneling currents: Zener and peak currents Excess current increase current around and beyond valley Current in NDR region is not well captured Solution: T-dependence, e-ph scattering OBJECTIVE RESULTS APPROACH Summary

Conclusion & Future works To investigate tunneling device, high doping effects such as BGN, and current via gap states should be considered 39 Electron-phonon scattering should be included to examine the effect on the increase of the current in the NDR region The approach can be applied to the analysis of other tunneling devices, such as the broken gap heterostructure diodes, and TFETs Need the verification of the approach by analyzing another fabricated device Exploring some other scattering mechanisms that may explain the mismatches between the experiments and simulation results

40 Acknowledgement Prof. Klimeck Prof. Lundstrom and Prof. Garcia Dr. Mathieu Luisier All NCN Students and Group Members Thank you!