1. Defects Maria Berdova maria.berdova@aalto.fi
Postgraduate Course in Electron Physics I

2. Outline Types of Defects Generation-Recombination Statistics
Mathematical Description
Detection Methods
Postgraduate Course in Electron Physics I

3. Types of defects 1) Foreign interstitial (e.g. Oxygen in silicon)
3) Vacancy
4) Self interstitial
2) Foreign substitutional (like dopant atom)
5) Stacking fault
When a particle is missing at one or more lattice sites we get a vacancy. When a particle forces its way into a hole between lattice sites, we get an interstitial impurity.  Substitutional impurities result from replacing the particle that should occupy a lattice site with a different particle, such as substituting a K+ ion for a Na+ ion in NaCl. Dislocations are one-dimensional defects caused by holes that are not large enough to be a vacancy.
6) Edge dislocation
7) Precipitate
Postgraduate Course in Electron Physics I

4. Defects Vacancy Stacking fault Interstitial
Interstitial
Stacking fault
Postgraduate Course in Electron Physics I

5. Metallic impurities Degradation of gate integrity
Degradation of the device (at high stress point and in junction space charge region)
Postgraduate Course in Electron Physics I

6. Effect of contamination
Fe in Si, and Cu in Si
Postgraduate Course in Electron Physics I

7. Defects Shallow defects Deep defects
Energy levels close to the valence or conduction band
Acting as dopants
Deep defects
Energy level away from the band edges
Short range part of the potential determines energy level
Normally non-wanted defects
E  ~ 150 meV (from the conduction band or valence band edges)
Postgraduate Course in Electron Physics I

8. Generation-Recombination Statistics
Trapping
Trapping
Traps or G-R centers
Deep level impurities
(metal impurities, crystal
imperfections)
Postgraduate Course in Electron Physics I R G

9. Mathematical Description
G-R center is occupied by hole or by electron, which are recombined or generated
Time dependence of electron or hole density
(electron/hole time rate of change due to G-R mechanisms)
Center occupancy rate
thermal velocity
Postgraduate Course in Electron Physics I
electron capture cross-section
of the G-R center

10. Mathematical Description
Solution
nT(0) is the density of G-R centers occupied by electrons at t = 0
the steady-state density
n-type substrate

11. Schottky diode a) nT = NT Capture dominates emission b) t ≤𝟎
G-R centers are
initially occupied by electrons
𝒕>𝟎 electrons are
emitted from G-R centers
Near the edge of scr the mobile electron density tails of from qnr to scr – captures compete with emissions
Postgraduate Course in Electron Physics I

12. Mathematical Description
from zero bias to reverse bias
Emission period
Capture period
from reverse bias to zero bias
Postgraduate Course in Electron Physics I

13. Capacitance measurements
Capacitance of the Schottky diode
Nscr - ionized impurity density in the SCR
time dependence of nT (t ) or pT (t )
capacitance at t = 0 and t = ∞
time – varying capacitance
Postgraduate Course in Electron Physics I

14. Capacitance measurements
the steady-state density
Plot 1/C2 vs V
nT(t) is “-” charged when occupied by electrons. With time, as electrons are emitted and the traps become neutral, (ND − nT(t)) increases and 1/C2 decreases
S (t) – slope
Postgraduate Course in Electron Physics I

15. Capacitance measurements
Transient Measurements
time-varying W is detected
as time-varying capacitance
C0 is the capacitance of a device with no deep-level impurities at reverse bias -V
nT(t) is “-” charged when occupied by electrons. With time, as electrons are emitted and the traps become neutral, (ND − nT(t)) increases and 1/C2 decreases
Postgraduate Course in Electron Physics I

16. Capacitance measurements
Emission—Majority Carriers:
During the reverse bias pulse, majority carriers are emitted as a function of time
nT(t) is “-” charged when occupied by electrons. With time, as electrons are emitted and the traps become neutral, (ND − nT(t)) increases and 1/C2 decreases
As majority carriers are emitted from the traps , W decreases and C increases until steady state is attained
Postgraduate Course in Electron Physics I

17. Capacitance measurements
Reverse biased capacitance change
The capacitance increases with time for majority carrier emission whether the substrate is n- or p-type and whether the impurities are donors or acceptors.
nT(t) is “-” charged when occupied by electrons. With time, as electrons are emitted and the traps become neutral, (ND − nT(t)) increases and 1/C2 decreases
Intercept on the ln-axis gives ln[nT(0)Co/2ND]
Postgraduate Course in Electron Physics I

18. Emission minority carriers
During the forward-bias phase, holes are injected into the n-substrate and
capture dominates emission.
(p+n junction)
forward bias
reverse bias
Lower half of the band gap pulses minority carrier
charge changes from neutral to negative
Postgraduate Course in Electron Physics I

19. Capture—Majority Carriers
The density of traps able to capture majority carriers
tf is ”filling” time
tf>>τc
tf <<τc
1. Reverse bias
2. Zero bias
Postgraduate Course in Electron Physics I

20. Capture—Majority Carriers
The reverse-bias capacitance depends on the filling pulse width
τc can be determined by varying tf
Postgraduate Course in Electron Physics I

21. Capture—Majority Carriers
ln(∆Cc) versus tf has a slope of 1/τc = σnvthn
an intercept on ln(∆Cc) axis of ln{[NT − nT (0)]C0/2ND} obtained by varying the capture pulse width during the capacitance transient measurement
Postgraduate Course in Electron Physics I

22. Current Measurements
The carriers emitted from traps can be detected as a capacitance, a charge, or a current.
The integral of the I -t curve represents the total charge emitted by the traps.
high temperatures
is short
is high
time constant
current
low temperatures
increases
decreases
Area under I -t curve remains constant
C-t measurements at low temp
& I-t measurements at high temp
time constant data
Postgraduate Course in Electron Physics I

23. Current Measurements Emission current Displacement current
Junction leakage current I1
Postgraduate Course in Electron Physics I

24. Drawbacks of Current Measurements
Leakage current might be sufficiently high
The instrumentation must handle the large current transients during the pulse
The amplifier should be non-saturable, or the large circuit transients must be eliminated from the current transient of interest
No distinction between majority and minority carrier emission
Postgraduate Course in Electron Physics I

25. Current Measurements is applied
When difficult to make capacitance measurements
Low capacitance of small-geometry MOSFETs
When possible to detect the presence of deep-level impurities by pulsing the gate voltage and monitoring the drain current as a function of time
In devices in which the channel can be totally depleted
Postgraduate Course in Electron Physics I
Drain current ID and gate capacitance CG transients of a 100 μm × 150 μm gate MESFET.

26. Charge Measurements
Switch S is closed to discharge the feedback capacitor CF
At t = 0 the diode is
reverse biased
S is opened
Current through the diode
Postgraduate Course in Electron Physics I

27. Charge transient Measurements
With the input current into the op-amp approximately zero, the diode current must flow through the RFCF feedback circuit, giving the output voltage
Choosing the feedback network such that tF>>τe
Postgraduate Course in Electron Physics I

28. Deep-level Transient Spectroscopy (DLTS)
The measurements use a two stage carrier capture and emission process
Quantitative (deduce absolute concentrations of electrically active defects)
Sensitive (In 20 Ω-cm silicon detection of cm-3 electrically active defects)
Trap Energy Level
Carrier Capture and Emission Rates
Trap density
Spatial Distribution of Defects
Postgraduate Course in Electron Physics I

29. Deep-level Transient Spectroscopy (DLTS)
Pulse applied to change occupancy of deep states
Pulse from reverse to zero for majority carrier traps
Into forward bias to inject minority carriers capacitance changes as carriers are emitted from states (can also use current)
ƒ Rate depends on temperature and binding energy
Postgraduate Course in Electron Physics I
J. Appl. Phys. 45, 3023 (1974)

30. Deep-level Transient Spectroscopy (DLTS)
Conventional DLTS
Rate window concept to deep level impurity characterization
Conventional DLTS varies the temperature
and produces a peak when the emission rate
matches a ‘standard’ rate (the rate window)
determined by the positions of t1 and t2
The magnitude of the peak ΔC gives the concentration of deep states:
signal changes as a function of temperature when a single trap is present
Postgraduate Course in Electron Physics I

31. Deep-level Transient Spectroscopy (DLTS)
‘Tutorial Day: DLTS’ 16th July 2011 Tony Peaker
By repeating the temperature scan with different settings of t1 and t2 the system filters out different rates (rate windows) and so each Tmax corresponds to the temperature at which the trap emits carriers at that rate window. So by making an Arrhenius plot (plotting log en vs. 1/T) it is possible to determine the energy of the state from the slope
Postgraduate Course in Electron Physics I

32. Arrhenius plot of emission rates
Xn is an entropy factor
plot log (en /T 2) vs 1/T
en /T 2
slope gives -Ea
intercept A is used to obtain Xnσn(∞)
Postgraduate Course in Electron Physics I

33. DLTS: Conclusion Advantages Disadvantages Highly sensitive
- Defect concentrations to 1010 cm-3
Requires electrically active defects
Contact less, non-destructive relatively easy measurement
Levels identification requires comparison with other techniques
Identification of impurities is not always straightforward
Inability to characterize high resistivity substrates (capacitance transient)

34. Thermally stimulated capacitance and current
Capacitance steps or current peaks are observed as traps emit their carriers
Appl. Phys. Lett. 22, 384 (1973)
The trap density is from the area under the TSC curve or from the step height of the TSCAP curve
From zero bias to reverse bias
Postgraduate Course in Electron Physics I

35. Positron annihilation spectroscopy
The spectroscopy of gamma (γ ) rays emerging from the annihilation of positrons and electrons
positron wave-function can be localized in the attractive potential of a defect
annihilation parameters change in the localized state (e.g. positron lifetime increases in a vacancy)
lifetime is measured as time difference between appearance of start and stop quanta
defect identification and quantification possible
If voids are available, positrons will reside in them and annihilate less rapidly than in the bulk of the material, on time scales up to ~1 ns.
Postgraduate Course in Electron Physics I
AMERICAN JOURNAL OF UNDERGRADUATE RESEARCH, VOL. 2, NO. 3 (2003)

36. Positron annihilation spectroscopy
- Positron lifetime is measured as time difference between 1.27 MeV quantum (β+ decay) and MeV quanta (annihilation process)
- PM…photomultiplier; SCA…single channel analyzer (constant-fraction type); TAC…time to amplitude converter; MCA… multi channel analyzer
Postgraduate Course in Electron Physics I

37. Positron annihilation spectroscopy
Reinhard Krause-Rehberg,
Martin-Luther-University Halle-Wittenberg, Germany
Postgraduate Course in Electron Physics I
(Polity et al., 1997)

38. Thank you
Postgraduate Course in Electron Physics I