Maria Berdova Postgraduate Course in Electron Physics I [email protected] 1

Postgraduate Course in Electron Physics I

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Maria Berdova

Defects

[email protected]

mailto:[email protected]


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*Outline

*Types of Defects

*Generation-Recombination Statistics

*Mathematical Description

*Detection Methods


Types of defects1) Foreign interstitial (e.g. Oxygen in silicon)

2) Foreign substitutional (like dopant atom)

3) Vacancy

4) Self interstitial

5) Stacking fault

6) Edge dislocation7) Precipitate

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Defects Vacancy

Interstitial

Stacking fault

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Metallic impurities

*Degradation of gate integrity

*Degradation of the device (at high stress point and in junction space charge region)


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Effect of contamination

Fe in Si, and Cu in Si


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*Defects*Shallow 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)


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Generation-Recombination Statistics

*Traps or G-R centers

*Deep level impurities

(metal impurities, crystal

imperfections)

R G

Trapping Trapping


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Mathematical Description

(electron/hole time rate of change due to G-R mechanisms)

G-R center is occupied by hole or by electron, which are recombined or generated

Time dependence of electron or hole density

thermal velocity

electron capture cross-sectionof the G-R center

Center occupancy rate

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nT(0) is the density of G-R centers occupied by electrons at t = 0

the steady-state density

n-type substrate

Solution


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Schottky diodea) nT = NT

Capture dominates emission

b) t

G-R centers are

initially occupied by electrons

electrons are

emitted from G-R centersNear the edge of scr the mobile electron density tails of from qnr to scr – captures compete with emissions


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Emission period

Capture period

from reverse bias to zero bias

from zero bias to reverse bias


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Capacitance measurements

• Nscr - ionized impurity density in the SCR

• time dependence of nT (t ) or pT (t )

Capacitance of the Schottky diode

capacitance at t = 0 and t = ∞time – varying capacitance


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Capacitance measurementsthe steady-state density

S (t) – slope

Plot 1/C2 vs V


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Capacitance measurementsTransient Measurements

C0 is the capacitance of a device with no deep-level impurities at reverse bias -V

time-varying W is detected as time-varying capacitance

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Capacitance measurementsEmission—Majority Carriers:

*During the reverse bias pulse, majority carriers are emitted as a function of time

As majority carriers are emitted from the traps , W decreases and C increases until steady state is attained



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*Capacitance measurements*Reverse biased capacitance change

Intercept on the ln-axis gives ln[nT(0)Co/2ND]

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.


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Emission minority carriersDuring the forward-bias phase, holes are injected into the n-

substrate andcapture dominates emission.

forward bias

reverse bias charge changes from neutral to negative

(p+n junction)

Lower half of the band gap pulses minority carrier


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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


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τc can be determined by varying tf

The reverse-bias capacitance depends on the filling pulse width


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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


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Current MeasurementsThe 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

low temperatures

time constant

increases

is short

decreases

current

is high

Area under I -t curve remains constant

C-t measurements at low temp& I-t measurements at high temp

time constant data

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Current Measurements

Emission current

Displacement current

Junction leakage current I1


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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


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Current Measurements is applied

Drain current ID and gate capacitance CG transients of a 100 μm × 150 μm gate MESFET.

• 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


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Charge Measurements

Switch S is closed to discharge the feedback capacitor CF

At t = 0 the diode isreverse biasedS is opened

Current through the diode


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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


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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 1010 cm-3 electrically active defects)

• Trap Energy Level• Carrier Capture and Emission Rates• Trap density• Spatial Distribution of Defects



*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)

* Rate depends on temperature and binding �energy

J. Appl. Phys. 45, 3023 (1974)29


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The magnitude of the peak ΔC gives the concentration of deep states:

Conventional DLTSRate window concept to deep level impurity characterizationConventional 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

signal changes as a function of temperature when a single trap is present

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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

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Arrhenius plot of emission rates

Xn is an entropy factor

• plot log (en /T 2) vs 1/T e

n /

T 2

• slope gives -Ea

• intercept A is used to obtain Xnσn(∞)

DLTS: Conclusion

• 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)

Advantages Disadvantages

34Postgraduate Course in Electron Physics I

Thermally stimulated capacitance and current

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Capacitance steps or current peaks are observed as traps emit their carriers

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


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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

AMERICAN JOURNAL OF UNDERGRADUATE RESEARCH, VOL. 2, NO. 3 (2003)


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- Positron lifetime is measured as time difference between 1.27 MeV quantum (β+ decay) and 0.511 MeV quanta (annihilation process)- PM…photomultiplier; SCA…single channel analyzer (constant-fraction type); TAC…time to amplitude converter; MCA… multi channel analyzer


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(Polity et al., 1997)

Reinhard Krause-Rehberg, Martin-Luther-University Halle-Wittenberg, Germany


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*Thank you

Documents

Maria Berdova Postgraduate Course in Electron Physics I [email protected] 1