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

2. I - + V 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 ~ 10-12 s v = F t / m = qE t / m
= (qt / m) E
= mE
m = electron mobility = qt / m

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

8. Ohm’s Law [m] = cm2 / Vs 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 Vx Ix 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 AnalysisVx Vy Bz Bz vx t W Ey L Ix Ex
A = tW Ix
Carriers experience force from :
Applied electric field, Fx = qEx
Applied magnetic field, Fy = qvxBz
Typical field ~ Tesla = 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): D C 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
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
Film
Substrate 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 Phonons (acoustic + optical)
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 , 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 , 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 W + + + + + + -eV + + + + + + + + + + + + + + + EF + + + +
Apply small ac signal (dV~ 10 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. Unwanted impurities or crystal defects → e.g., Fe, Au in InP, GaAs
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. Negative when an e- is captured Neutral when empty Acceptor-like
DLTS
Electron traps
Negative when an e- is captured
Neutral when empty
Acceptor-like
Hole traps
Positive when a hole is captured
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. DLTS W0 V C C0 EF t t WV0 Transient V C -eV EF -V t CV0 t WV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. Capacitance transient varies with temperature
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)