ECSE-6290 Semiconductor Devices and Models II Lecture 14

1. ECSE-6290Semiconductor Devices and Models IILecture 14 Shayla M. Sawyer Bldg. CII, Rooms 8225 Rensselaer Polytechnic Institute Troy, NY 12180-3590 Tel. (518)276-2164 FAX (518)276-2990 e-mail: ssawyer@ecse.rpi.edu

2. Lecture Outline • Important Concepts for Resonant Tunneling Diodes (RTDs) • RTDs vs. Tunnel Diodes • Advantages and Disadvantages of RTDs • Applications • RTD Physics and Phenomenon • RTD Equations and Parameters • Summary

3. RTD Concepts: Why Tunneling Devices? • Advantage of this quantum effect device • Works at room temperature • High switching speed • Low power consumption • Differing operating principles • Quantization • Quantum tunneling • Negative Differential Resistance (NDR) http://www.cse.unsw.edu.au/~cs4211/projects/presentations/james-pp.ppt#266,9,Resonant Tunnelling Diodes

4. RTD Concepts: Tunneling • Tunneling • Quantum mechanical phenomenon • Wave-particle duality • Calculate tunneling probability with Schrödinger’s equation • Complex barrier shapes by WKB approximation method • Requires finite barrier height and thin barrier width

5. RTD Concepts: Tunneling • Tunneling • Majority carrier effect • Not governed by conventional time transit concept • Governed by quantum transition probability per unit time proportional to exp[-2<k(0)>W] <k(0)> is the average value of momentum encountered in the tunneling path…..

6. RTD Concepts: Tunneling • Tunneling current Jt is calculated from the product of the number of available carriers in Region-A and empty states in Region-B Find tunneling probability

7. RTD Concepts: Tunneling • To determine tunneling probability use • Wavefunction for simple rectangular barrier height of U0 and width W is ψ =exp(±ikx) where

8. RTD Concepts: Tunneling • Solution to tunneling probability • Using WKB for other barrier shapes where wavefunction is ~

9. Tunneling vs. Resonant Tunneling http://w3.ualg.pt/~jlongras/OIC-NDRd.pdf

10. Tunneling vs. Resonant Tunneling http://w3.ualg.pt/~jlongras/OIC-NDRd.pdf

11. RTD Concepts: NDR • Negative Differential Resistance • DC biasing in the NDR region can be used for • Oscillation • Amplification • High speed switching http://www.answers.com/topic/gunn-diode?cat=technology

12. RTD Research (2010)

13. Two paths to THz • Light/optics (photonics) • Radio/microwave (electronics)

14. RTDs vs. Tunnel Diodes • Tunnel Diodes were discovered by Esaki in 1958 • Studied heavily (degenerately) doped germanium p-n junctions • Depletion layer width is narrow • Found NDR over part of forward characteristics

15. RTDs vs. Tunnel Diodes • (a) Fermi level is constant across the junction • Net tunneling current zero applied voltage is zero • Voltage applied: tunneling occurs • Under what conditions? • (b) Maximum tunneling current • (c) Tunneling current ceases • No filled states opposite of unoccupied states • (d) Normal diffusion and excess current dominates High doping Large capacitance Difficult device growth

16. RTDs vs. Tunnel Diodes • Tunneling Probability for tunnel diodes (triangular barrier) • Both effective mass and bandgap should be small • Electric field should be large

17. RTDs vs. Tunnel Diodes • Comparison of typical current voltage characteristics • Ip/Iv ratios • 8:1 for Ge • 12:1 GaSb • 28:1 for GaAs • 4:1 for Si • Limitation on ratio • Peak current (doping, effective tunneling mass, bandgap) • Valley current (distribution of energy levels in forbidden gap (defect densities)

18. RTDs vs. Tunnel Diodes • Advantages of RTDs • Not transit time limited • No minority carrier charge storage • Maximum operational oscillation projected in the THz range (at room temperature) • Better leakage current (can be used as a rectifier) • Lower doping than p-n (reduced capacitance) • Easier to fabricate and design than tunnel diodes • Multiple NDR peaks (multivalue logic and memory) • Disadvantages of RTDs • Does not supply enough current for high power oscillations

19. Applications • Nine-State Resonant Tunneling Diode Memory • Eight double barriers Al/In0.53Ga0.47As/InAs grown by MBE A.C. Seabaugh et al., IEEE Electron Dev. Lett., EDL-13, 479, (1992)

20. Applications • High frequency, low power dissipation • Trigger circuits • AlAs/GaAs RTDs 110 GHz • Pulse Generator • 1.7 ps switching transition times with InAs/AlSb RTDs • Oscillators • 712 GHz with InAs/Alsb T.C. Sollner, GaAs IC Symposium, 15, (1990)

21. Physics and Phenomenon • RTD consists of • Emitter region: source of electrons T(E) • Double barrier structure: inside is the quantum well, with discrete energy levels • Collector region: collect electrons tunneling through the barrier T(C)

22. Physics and Phenomenon • Double barriers formed • Quantum well quantizes energy • Assumes infinite barrier height • Actual barrier height (ΔEc) ~0.2-0.5eV giving quantized levels of ~0.1eV

23. Physics and Phenomenon • Carriers tunnel from one electrode to the other via energy states within the well • Wavefunctions of Schrodinger equation must be solved for emitter, well, and collector • Tunneling probability exhibits peaks where the energy of the incoming particle coincides with quantized levels

24. Physics and Phenomenon • Probability of tunneling when electron energy does not align with quantized state • Probability of tunneling when electron energy does align with quantized state • Resonant tunneling current is given by

25. Physics and Phenomenon • Model of sequential tunneling (emitter to well and well to collector uncorrelated events) • Carriers from emitter to well determining mechanism for current flow • Requires • Available empty states at same energy level (conservation of energy) • Same lateral momentum (conservation of momentum)

26. Physics and Phenomenon • Energy of carriers in subband: lateral momentum only (En is quantized) • Free electron energy in the emitting electrode is given by • Electrons in the emitter with energy given by second equation will tunnel into energy level given in first equation

27. Physics and Phenomenon • If E1 is above EF there is little of electrons for tunneling • As bias is increased E1 is pulled below EF and toward EC of the emitter, tunneling starts to increase with bias

28. Physics and Phenomenon • Conservation of lateral momentum requires that the last terms of these equations are equal • Along with the conservation of energy, this results in the requirement that Implies that as long as emitter Ec is above En resonant tunneling is possible(but not the case when momentum is taken into account)

29. k Physics and Phenomenon • From the below figure k at the well becomes large • Minimum value of k even with kx=0 is k • For k outside the fermi sphere, there is no electron available for tunneling • So the tunneling event is prohibited For the emitter

30. Physics and Phenomenon • So maximum tunneling current, En, should line up between EF and EC (low temperatures En should line up with Ec) • At higher bias, Ec is above En and there are no electrons available to tunnel: tunneling drops significantly • This results in the Negative Differential Resistance

31. Physics and Phenomenon • I-V characteristic (a) Near zero bias E1 is above EF (b) Bias increased, E1 is pulled below EF tunnel current increases with bias to a maximum (Jp) (c) Bias increased E1 is lower than EC causing NDR

32. Physics and Phenomenon • I-V characteristic (d) Resonant tunneling through second quantized energy state, E2 (e) E2 is below Ec causing second NDR

33. Physics and Phenomenon • Peak Voltage Vp~ • For a symmetrical junction • Half bias is developed across each barrier • Ratio of local peak current (Jp) to valley current (Jv) is a critical measure of NDR • Current can be maximized with lighter effective mass ~

34. Physics and Phenomenon • High peak current density is required for high frequency • Small valley current is required for switching applications • Tradeoff: barrier thickness, peak valley ratio

35. Equations and Parameters: Tunneling Probability of tunneling no coincidence of incoming energy and quantized levels coincidence of incoming energy and quantized levels Resonant tunneling current Available electrons (per unit area)

36. Equations and Parameters:Energy levels • Energy of carriers in subband: lateral momentum only • Free electron energy in the emitting electrode

37. Equations and Parameters:Parameters • Peak voltage for a symmetrical barrier • Current density

38. Summary • Tunneling and negative differential resistance are key characteristics of RTDs • These devices are used for amplification, oscillation, and high speed switching • RTDs are not transit time limited (no minority carrier storage charge) • Tunneling occurs when incoming energy of electrons coincide with quantized states in quantum wells (resonance) • Diminished current due to lack of available electrons in line with quantized states causes NDR • Thermionic emission dominates in the valley

39. ECSE-6290Semiconductor Devices and Models IILecture 14 Prof. Shayla M. Sawyer Bldg. CII Room 8225 Rensselaer Polytechnic Institute Troy, NY 12180-3590 Tel. (518)276-2164 FAX (518)276-2990 e-mail: ssawyer@ecse.rpi.edu

40. HFET Lecture Outline • Introduction and Review • Principle and Operation • Carrier Transport • HFET Material Systems • Configurations • Summary

41. Introduction and Review • Field Effect Transistor: Why the name? • The channel is controlled capacitively by an electric field • Advantages? • Low power • Less temperature dependence • FET family tree • Other names for Heterojunction FET • SDHT, HEMT, TEGFET, MODFET…

42. Principle of Operation • Purpose of heterostructure is to add flexibility to design based on doping and material variations in various layer • Control the flow and distribution of charge carriers • Modulation doped heterojunction consists of a semiconductor that is heavily doped with impurities and a semiconductor that is intrinsic or lightly doped with impurities of the opposite type • Band bending causes a narrow layer of electrons at the interface (electron transfer across the junction) • Additional advantage: Compound semiconductor’s smaller effective mass than in Si

43. Principle of Operation

44. Principle of Operation • Can add another undoped AlGaS spacer layer between the doped AlGaS layer and the undoped GaAs where the 2DEG lies • leads to reduction in electron density but increase in electron mobility • Also can use a delta doped charge sheet in the barrier layer and place it close to the channel interface instead of uniform doping • Advantage: reduction of traps contributing to anomalous behavior of current collapse at low temperature • Advantage: close proximity of dopant to channel also gives a lower threshold voltage

45. Principle of Operation • Barrier layer AlGaAs is doped while the channel layer GaAs in undoped • Enhances mobility and effective velocity of electrons • Channel layer is analogous to the inversion channel in SiO2/Si MOS, electrons are quantized in a two dimensional systems at the heterointerface (2DEG) (2D electron gas) • Sheet of high mobility electrons can be modulated by the field effect from a gate electrode

46. Carrier Transport Properties • Major issues • Mobility of the carriers • Effective velocity of carriers in the channel • Trade-offs • Aspect ratio with submicron gates

47. Carrier Transport Properties • Mobility: Selective doping • Have donor energy levels in the wider bandgap material lie above the conduction band edge of the lower bandgap materials • Electrons from ionized donors accumulate in the conduction band states with large electron affinity • Requirement that Fermi level be constant

48. Carrier Transport Properties • Mobility: Selective doping • Separation of ions from conduction electrons • These conduction electrons are now in undoped GaAs which means no impurity scattering • When is the scattering mechanism dominant?

49. Carrier Transport Properties • Carrier velocity • Peak velocity vs. effective carrier velocity • Effective carrier velocity is the averaged velocity of carriers in a FET structure • Since the field in the channel is not constant, the value is less than the peak velocity • Peak velocity: At high fields where non-equilibrium transport is important, carrier velocities are higher than the values shown on curves

50. Carrier Transport Properties • Carrier velocity • Carrier velocity affects the electron transit time under the gate • Also affects the cutoff frequency fT • Drain voltage at which velocity saturation occurs is lower in the HFET than in MESFET • HFET can operate at very low supply voltages and logic swings