# CHAPTER 5 DEFECTS.

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CHAPTER 5 DEFECTS

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.

Schematic representation of defects in semiconductors
Schematic representation of defects in semiconductors. The defect types are described in the text.

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.

Oxide failure percentage versus oxide breakdown electric field
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℃.

5.2 GENERATION-RECOMBINATION STATISTICS

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)

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

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) For holes, we find the parallel expression The capture coefficient Cn is defined by (5.1) (5.2) (5.3)

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.

In the Quasi-neutral regions n and p are reasonably constant
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)

For an n-type substrate p can be neglected, Eq.(5.5) becomes
(5.7) For an n-type substrate p can be neglected, Eq.(5.5) becomes where τ1=1/(en+cnn+ep)

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)

The steady state trap density nT in the reverse-biased scr is
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, ) (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)

5.3 CAPACITANCE MEASUREMENTS

Capacitance Measurements
The capacitance of the Schottky diode is (5.11) Nscr=ND+-nT- for acceptor g-r center occupied by e- Nscr=ND for acceptor g-r center occupied by h+ Nscr=ND for donor g-r center occupied by e- Nscr=ND++pT+ for donor g-r center occupied by h+

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.

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.

Plotting the capacitance difference
(5.17) Plotting the capacitance difference (5.18) Under equilibrium conditions, dn/dt=0, hence (5.19) (5.20) (5.21)

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)

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.

The electron thermal velocity is
(5.26) (5.27) (5.28)

τeT2 versus 1 / T plots for Si diodes containing Au and Rh.

τe can also be determined from plotting ln(S(∞)-S(t)) versus t.
(5.29)

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.

The capacitance-time transients following majority carrier emission and minority carrier emission.

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)

(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.

4. Capture – Minority Carrier
(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.

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.

The displacement current is
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)

The lower limit of the Ie integral (Eq
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)

(5.40) (5.41)

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

5.5 CHARGE MEASUREMENTS

Circuit for charge transient measurements.

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)