1 / 45

Electrical Characterization Techniques

Electrical Characterization Techniques. Hall Effect. C-V. DLTS. Electrical Parameters : Carrier concentration (ionized donors, acceptors) Carrier type (electrons or holes) Carrier mobility. Derive Ohm’s law: V = IR Consider a block of material

siran
Download Presentation

Electrical Characterization Techniques

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Electrical Characterization Techniques Hall Effect C-V DLTS • Electrical Parameters : • Carrier concentration (ionized donors, acceptors) • Carrier type (electrons or holes) • Carrier mobility

  2. Derive Ohm’s law: V = IR • Consider a block of material • What is the current, I, for an applied voltage, V ? I - + V

  3. Total Current, I n = # electrons per unit volume v = velocity of electrons in the material # electrons in volume AL, N = nAL time to travel distance L, t = L / v  I = Q/t = qN/t = q (nAL) / (L/v) = A nqv volume AL A L I - + V

  4. Electron Velocity, v What is the electron velocity, v ? Electric field in material, E = V/L Force on an electron, F = qE Electron acceleration, a = F/m L a E I - + V

  5. Electron Velocity, v Electrons accelerate until they collide with atoms in the material Assume electron loses all its energy (v=0) after each collision L E I - + V

  6. Mobility • Electron velocity, v = at • ~ 10-12s • v = F t / m • = qEt / m • = (qt / m) E • = mE m = electron mobility = qt / m

  7. Conductivity I = A nqv = A nq m E Current density, J = I / A = nqmE = sE s = conductivity = nqm = nq2t / m Resistivity, r = 1 / s

  8. Ohm’s Law I = A nqm E = A nqm V/L Rearranging gives V = I (L/Anqm) Resistance, R = L / Anqm = L/sA = rL/A Units: [R] = W [r] = W cm [s] = (W cm)-1 [m] = cm2 / Vs

  9. Conductivity Measurement Jx = Ix / A = Ix / tW Ex = Vx / L s = Jx / Ex = Ix L / Vx tW Ix Vx t W L A = tW • Usually use symmetric samples (L = W): • s = Ix / Vxt • Measure Ix, Vx, t  Can determine s • s = nqm Can determine n if mobility is known (or vice versa) • Need another technique to determine n or m

  10. Hall Effect : Simple Analysis • Discovered by Hall in 1879 on Au foils • Reference (review article): • D.A. Anderson and N. Apsley, “The Hall Effect in III-V Semiconductor Assessment”, Semicond. Sci. Technol. 1, 187 (1986)

  11. Hall Effect : Simple Analysis Vx Vy Bz Bz vx t Ey W L Ix Ex A = tW Ix • Carriers experience force from : • Applied electric field, Fx = qEx • Applied magnetic field, Fy = qvxBz • Typical field ~ 0.05 - 1 Tesla = 500 - 104 Gauss • Carriers are deflected • producing an electric field, Ey = Vy / W • (Hall voltage) • Electric field builds up that counteracts magnetic field force • Sign of Hall voltage gives dominant carrier type

  12. Hall Effect At equilibrium, qEy + qvxBz = 0 Ey = - vxBz vx = Jx / nq Jx = Ix / tW Vy t / BzIx = - (nq)-1 Ey = Vy / W Define Hall coefficient, RH = - (nq)-1 =Vy t / BzIx Measure Hall coefficient Then n = - (RHq)-1 Measure conductivity (at B=0) Then m = s / nq Or m = - RHs

  13. Van der Pauw Technique C D B A • Gives RH, s for arbitrary sample shapes • Assumptions : • Contacts are at circumference of sample • Contacts are much smaller than sample area • Sample is uniformly thick • Sample has no holes • Sample thickness << contact spacing • References : • L.J. van der Pauw, Philips Research Reports 13, 1 (1958) • L.J. van der Pauw, Philips Research Reports 20, 220 (1961)

  14. Van der Pauw Technique C D B A • Conductivity measurement (when B = 0) : • Apply IBC,measure VDA, define RBC-DA = VDA/IBC • Apply IAB,measure VCD, define RAB-CD = VCD/IAB • van der Pauw analysis : • r=(s)-1 = (p/ln2) t [(RBC-DA +RAB-CD)/2] F(RAB-CD /RBC-DA ) • Previous simple analysis gave : • r=(s)-1 = t Vx / Ix 4.53 correction factor

  15. Van der Pauw Technique Correction factor, F from Schroder, Fig. 1.7, p. 15 RAB-CD / RBC-DA • Usually use symmetric samples (F ~ 1): C D B A

  16. Van der Pauw Technique D C A B • Hall effect measurement : • Apply B perpendicular to surface • Apply IBD • Measure DRBD-AC = VAC(B) / IBD – VAC(0)/IBD • Then RH = ( t / B) DRBD-AC • Previous simple analysis gave : • RH = ( t / B ) (Vy / Ix)

  17. Application to Thin Films thin film substrate • Want to measure n, m of thin film not substrate • Conductance of substrate must be very low compared to film • No current flow in substrate • Use semi-insulating (S.I.) substrates • S.I. substrate created by doping with an impurity producing deep traps (acceptors) • e.g., Cr in GaAs • Fe in InP

  18. Film Thickness • What is the film thickness, t ? • Depletion layers form at surfaces and interfaces due to defects • Fermi level is pinned at EF • Chandra et al., Solid State Electronics 22, 645 (1979) • t = d – Ls- Li Substrate Film d Ls Li EF

  19. Film Thickness • For GaAs with n ~ 1015 cm-3 • Ls ~ 1 mm, Li ~ 1 mm • Need thick films, d > 2 – 3 mm

  20. Compensation • Conductivity and Hall effect measure net free carrier concentration • n = ND+- NA- • Or p = NA-- ND+ • Mobility can determine the compensation ratio : • q = NA- / ND+ • Walukiewicz et al., J. Appl. Phys. 51, 2659 (1980) n

  21. Compensation compensation ratio, q = NA- / ND+ Walukiewicz et al., J. Appl. Phys. 51, 2659 (1980)

  22. Compensation • Mobility is affected (reduced) by scattering mechanisms between the free carriers (electrons and holes) and the sample • Scattering mechanisms: • Phonons (acoustic + optical) • Impurity atoms (neutral + ionized) • Alloy disorder • Scattering from surfaces and interfaces • Defect scattering

  23. Temperature-Dependent Hall Effect/Conductivity • Can determine scattering mechanisms by using temperature-dependent measurements At low T, ionized impurity scattering dominates At high T, phonon scattering dominates From Ibach & Luth, Fig. 12.13, p. 291

  24. Temperature-Dependent Hall Effect/Conductivity • Can determine scattering mechanisms by using temperature-dependent measurements At low T, ionized impurity scattering dominates At high T, phonon scattering dominates From Ibach & Luth, Fig. 12.12, p. 291

  25. Temperature-Dependent Hall Effect • Can determine donor or acceptor energy levels • n ~ exp [ – (EC – ED)/kT ] • Donors become increasingly ionized as T increases • slope of Arrhenius plot (log n vs 1/T)  EC – ED

  26. C-V • Gives n = ND+ as a function of depth • Requires a device: Schottky diode, p-n junction • e.g., apply metal contacts to semiconductor sample to form Schottky diode • Apply reverse bias voltage, V W + + + + + -eV + + + + + + + + + + + + + + + + EF

  27. C-V • Apply small ac signal (dV~ 10 mV @ 1 MHz) on top of dc reverse bias • Depletion width varies (dW) with ac signal (dV) • Causes donor ionization over width dW • Measure capacitance change • Can determine n = ND+ W + + + + + + + -eV + + + + + + + + + + + + + + EF + + + + + -e(V+ dV) + + + + + + + + + + + + + + + EF dW

  28. C-V C = eA/W dQ = - e ND+ A dW C = - dQ/dV = eA ND+ dW/dV • ND+ = 2 • eeA2 [ d(1/C2)/dV ] • Can determine ND+ from slope of 1/C2 versus V 1/C2 slope = 2/ [eeA2 ND+] V • Can convert voltage scale to depth scale by W = eA/C

  29. C-V from Schroder, Fig. 2.2, p. 67

  30. C-V • Usually assume n = ND = ND+ : • All donors become ionized • Minority carriers are neglected • All majority carriers in depletion region are removed

  31. C-V Interface characterization (MOSFETs)

  32. C-V • Disadvantage : • Maximum depth is limited by electrical breakdown at high reverse bias • C-V Profiling : • Can perform C-V measurement while performing a chemical etch • Reference : • T. Ambridge et al., J. Appl. Electrochem. 5, 319 (1975)

  33. Electrochemical C-V Profiling • Replace metal contact with electrolytic solution • Destructive method

  34. DLTS • Deep level transient spectroscopy • Reference : • D.V. Lang, J. Appl. Phys. 45, 3023 (1974)

  35. DLTS • What are traps ? • Unwanted impurities or crystal defects • → e.g., Fe, Au in InP, GaAs • → Introduces discrete energy levels in the bandgap, usually near midgap • → Trap electrons or holes + + + + + + + + EF ET Electron traps

  36. DLTS • Electron traps • Negative when an e- is captured • Neutral when empty • Acceptor-like • Hole traps • Positive when a hole is captured • Neutral when empty • Donor-like + + + + + + + + EF Electron traps ET

  37. DLTS • Requires Schottky diode or p-n junction • e.g., apply metal contacts to sample to form Schottky diode • Apply reverse bias pulse and measure capacitance transient • Gives : • NT vs W • NT energy levels

  38. W0 DLTS V C 0 C0 EF t t WV0 Transient V C -eV EF -V t CV0 t WV Steady-state V C -eV EF CV -V t t

  39. DLTS V C CV -V t CV0 t • DC = CVNT / 2ND • Capacitance transient gives trap concentration, NT

  40. DLTS WV0 V C -eV EF CV -V t CV0 t • Capacitance transient is characteristic of the emission of electrons from the traps: • DC(t) = DC exp (-ent) emission rate en ~ exp [ - (Ec – ET)/ kT ]

  41. DLTS • DC(t) = DC exp (-ent) • en ~ exp [ - (Ec – ET)/ kT ] • Capacitance transient varies with temperature From Schroder, Fig. 5.12, p. 291

  42. DLTS DC(t) = DC exp (-ent) From Schroder, Fig. 5.12, p. 291 • Define a “rate window” using two times, t1 and t2 • C(t2) – C(t1) is maximum when • (t1-t2)/ln(t1/t2) = 1 / en(T) • e.g., C(t2) – C(t1) is maximum at 260 K in above figure

  43. DLTS • Vary the temperature and measure DC with t1 & t2 fixed • Produces peak when (t1-t2)/ln(t1/t2) = 1 / en(T) • en ~ exp [ - (Ec – ET)/ kT ] • Each kind of trap has different ET and therefore en • Produces a distinct peak for each trap • Called the DLTS spectrum From D.V. Lang, JAP 45, 3023 (1974)

  44. DLTS • Vary the rate window • Peak moves to new position From D.V. Lang, JAP 45, 3023 (1974)

  45. DLTS • Slope of Arrhenius plot (log en vs 1/T) gives trap energy level, ET From D.V. Lang, JAP 45, 3023 (1974)

More Related