Transcript n T - Noise Lab

CHAPTER 5
DEFECTS
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5.1 Introduction
The defects in semiconductors include:
(1)foreign interstitial (oxygen in silicon)
(2)foreign substitutional (dopant),
(3)vacancy,
(4)self interstitial,
(5)stacking fault,
(6)edge dislocation,
(7)precipitate.
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Schematic representation of defects in semiconductors. The
defect types are described in the text.
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MOSFET Regions Sensitive to
Metal Contamination
Metals degrade devices if: contaminate Si/SiO2
Interface, locate at high stress point.
MOSFET regions sensitive to metal contamination.
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Oxide failure percentage versus
oxide breakdown electric field
(a)

(b)
As a function of metal contamination for (a) Fe-contaminated Si and (b)
Cu-contaminated Si; the wafers were dipped in a 10 ppb or 10 ppm
CuSO4 solution and annealed at 400℃.
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5.2 GENERATION-RECOMBINATION
STATISTICS
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5.2.1 A Pictorial View
Electron energy band diagram for a semiconductor with deep-level impurities.
(a) electron capture, (b) electron emission, (c) hole capture, (d) hole capture.
Recombination=(a)+(c), generation=(b)+(d), electron trapping=(a)+(b)
hole trapping=(c)+(d)
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Whether an impurity acts as a trap or G-R
center depends on:
1. ET
2. the Fermi-level location in the bandgap
3. the temperature
4. the capture cross section of the impurity
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5.2.2 A Mathematical Description
If the G-R center is a donor, nT is neutral and pT is positively
charged.
If the G-R center is an acceptor, pT is neutral and nT is negatively
charged.
The time rate of change of n due to G-R mechanisms is given by
(nT+pT=NT)
(5.1)
For holes, we find the parallel expression
(5.2)
The capture coefficient Cn is defined by
(5.3)
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When electrons and holes are recombined or are
generated, n, p, nT, pT are all functions of time.
cnn is the density of electrons captured per second.
en has a unit of 1/s, cn has a unit of cm-3/s.
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Whenever an electron or hole is captured or emitted, the center
occupancy change rate is (a)+(d)-(b)-(c)= ((d)-(c))-((a)-(b))
(5.4)
In the Quasi-neutral regions n and p are reasonably constant
(5.5)
The Steady-state density as t  ∞ is
(5.6)
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For an n-type substrate p can be neglected, Eq.(5.5) becomes (5.7)
where τ1=1/(en+cnn+ep)
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Schottky Diode
A Schottky diode for (a) zero bias, (b) reverse bias at t=0, (c) reverse bias as t→∞.
The applied voltage and resultant capacitance transient are show in (d)
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During the initial emission period, the time dependence of nT
simplifies to ( for traps in n-Si en>>ep, and in the depletion region
n~0,  e  1 / e n )
(5.8)
The steady state trap density nT in the reverse-biased scr is
(5.9)
When bias is switched from reverse to zero, the time dependence
of nT during the capture period is
(5.10)
 C  1 / cn n
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5.3 CAPACITANCE MEASUREMENTS
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Capacitance Measurements
The capacitance of the Schottky diode is
(5.11)
Nscr=ND+-nTNscr=ND+
Nscr=ND+
Nscr=ND++pT+
for acceptor g-r center occupied by efor acceptor g-r center occupied by h+
for donor g-r center occupied by efor donor g-r center occupied by h+
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5.3.1 Steady-State Measurements
For shallow-level donors and deep-level acceptors l /C2 is given as
(5.12)
If we define a slope S(t) = -dV / d(1/C2), then
(5.13)
For en>>ep, nT(0)~NT, nT(∞)~0.
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5.3.2 Transient Measurements
(5.14)
(5.15)
1. Emission-Majority carriers
(5.16)
The capacitance increases with time for majority carrier emission, whether
the substrate is p or n type and the impurities are donors or acceptors.
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(5.17)
Plotting the capacitance difference
(5.18)
Under equilibrium conditions, dn/dt=0, hence
(5.19)
(5.20)
(5.21)
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Assume the emission and capture coefficients remains equal to
their equilibrium value under non-equilibrium conditions, then
(5.22)
(5.23)
With en=1/e and cn=vth, the emission time constant of electron
and hole as
(5.24)
(5.25)
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Electron energy diagram in equilibrium (1) and in the presence of an electric field
(2) showing field-enhanced electron emission: (a) Poole-Frenkel emission, (b)
phonon-assisted tunneling. The emission coefficient will be increased at high
electrical field.
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The electron thermal velocity is
(5.26)
(5.27)
(5.28)
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τeT2 versus 1 / T plots for Si diodes containing Au and Rh.
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τe can also be determined from plotting ln(S(∞)-S(t)) versus t.
(5.29)
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2. Emission-Minority carriers
For P+n diode under forward bias, holes are injected
into n-region, capture dominates emission, hence
(5.30)
For cp>>cn the acceptor g-r centers at t=0 nT≒0 and
Nscr≒ND. When switched to zero bias holes are emitted and
traps become negatively charged, then Nscr≒ND-nT.
The total negative charge in scr decreases and its width
increases with time, the capacitance decreases with time.
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The capacitance-time transients following majority carrier emission and
minority carrier emission.
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3. Capture – Majority Carrier
M-nSi is reverse biased for long enough time, traps are in the pT state.
When the bias is off (0V), for a filling time tf
(5.31)
For tf<τc and the device is reverse biased again
(5.32)
(5.33)
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(a) C - t response showing the capture and initial part of the emission process,
(b) the emission C - t response as a function of capture pulse width.
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(5.34)
(5.35)
4. Capture – Minority Carrier
The capture time during the filling time is:
(5.36)
The injected minority carrier density is varied by changing the
forward bias.
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5.4 CURRENT MEASUREMENTS
For transient current measurements, the integral of the I-t curve
gives the total trapped charge. At high temperatures, I large and
τ short; at low temperatures, I small and τ long. But the area
under I-t curve is the same. Measure I-t at high temperatures
and C-t at low temperatures give τ over ten orders of magnitude.
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The measured current includes emission current Ie, displacement
Id, and leakage current I1.
The emission current is
(5.37)
The displacement current is
(5.38)
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The lower limit of the Ie integral (Eq. 5-37) should have
been W(0V), for simplicity, it is set to 0. With dn/dt=ennT,
and dnT/dt=-ennT
(5.39)
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(5.40)
(5.41)
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Drain current ID and gate capacitance CG transients
of a 100μm × 150μm gate MESFET.
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5.5 CHARGE MEASUREMENTS
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Circuit for charge transient
measurements.
Circuit for charge transient measurements.
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Switch S is closed to discharge CF for t<0, at t=0 diode is
reverse biased and S is open, such that the diode current
charges the RFCF circuit and Vo changes with time.
(5.42)
(5.43)
For tF>>τe
(5.44)
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