CHAPTER 7
CARRIER LIFETIMES
1
7.1 INTRODUCTION
• Lifetime: Generation lifetime,
recombination lifetime.
• Occur in bulk: lifetime τg, τr..
• Occur in surface: surface velocity sg, sr.
• The measured lifetime are always effective
values consisting both components.
2
Recombination and Generation
(a) Forward-biased and (b) reverse-biased junction.
3
7.2 RECOMBINATION LIFETIME-SURFACE
RECOMBINATION VELOCITY
• Consider p-type semiconductor in this chapter.
• Consider minority electrons.
• Consider linear, quadratic, and third-order
terms.
4
RECOMBINATION LIFETIME-SURFACE
RECOMBINATION VELOCITY
(7.1)
(7.2)
n=no+Δn, p=po+Δp, no<<po, Δn=Δp.
(7.3)
(7.4)
5
Recombination mechanisms: (a) SRH, (b) radiative, (c) Auger.
6
(7.5)
(7.6)
(7.7)
(7.8)
(7.9)
7
(7.10)
low-level injection (ll):Δn<<po,
high-level injection (hl): Δn>>po.
(7.11)
(7.12)
(7.13)
8
Table 7.1 Recombination Coefficient
9
Recombination Lifetime Versus Majority Carrier
Density
Recombination lifetime versus majority carrier density for p-Si [Cp=1.1×10-30
cm6/s (dashed lines), Cp =10-31cm6/s (solid lines)] and for n-Si (Cn=2.8×10-31
cm6/s). Data from Ref. 10.
10
SRH (multi-phonon) recombination
(7.14)
(7.15)
(7.16)
(7.17)
(7.18)
(7.19)
11
sr Versus Injection Level η
sr Versus Injection Level η As a function of σps for Nit=1010cm-2,
pos=1016cm-3, ETs=0.4eV, σns =5×10-14cm2. Data from ref. 15
12
• For heavily doped Si, Auger recombination dominates
the carrier lifetime.
• For lightly doped Si, SRH (multi-phonon)
recombination dominates the carrier lifetime.
• Radiative recombination plays almost no role in Si,
but is important in direct bandgap material like GaAs.
13
7.3 GENERATION LIFETIME-SURFACE
GENERATION VELOCITY
• Each of the recombination process has a generation
counterpart.
SRH recombination --- Thermal generation
Radiative recombination --- Optical generation
Auger recombination --- Impact ionization
• When pn>ni2 recombination dominates,
when pn<ni2 generation dominates.
• The smaller the pn product, the higher is the
generation rate.
14
(7.20)
(7.21)
Usually, τg>τr. For Si τg≒(50~100)τr.
(7.22)
when psns<ni2
(7.23)
For ET≠Ei, sr > sg.
15
7.4 RECOMBINATION LIFETIME
-OPTICAL MEASUREMENTS
The continuity equation for uniform ehp
generation and zero surface recombination
n(t)/t = G – R = G – n(t)/ τeff
(7.24)
τeff(n) = n(t)/ [G(t) – dn(t)/d(t)]
(7.25)
In the Transient Photoconductance Decay (PCD)
method, with G(t) << dn(t)/d(t)
τeff(n) = – n(t)/ dn(t)/d(t)
(7.26)
16
In the steady-state method, with G(t) >> dn(t)/d(t)
τeff(n) = n(t)/ G
(7.27)
The excess carrier density for low level injection is given by
Δn(t)= Δn(0)exp(-t/τeff)
(7.28)
(7.29)
τB is the bulk recombination lifetime, D the minority carrier
diffusion constant under ll injection or the ambipolar diffusion
constant under hl injection, d the sample thickness.
17
For thick samples
τeff ~ τB.
For thin samples
τeff depends on
d and sr.
Effective lifetime versus wafer thickness as a function of surface
recombination velocity. D=30cm2/s.
18
(7.30)
Two limiting cases are of particular interest:
sr  0 gives tan(d/2)d/2 and
sr   gives tan(d/2) or d/2/2
(7.31)
• For Sr~0, plot 1/τeff vs. 1/d, the slope is 2sr, the intercept is 1/τB
• For Sr~∞, plot 1/τeff vs. 1/d2, the slope is πD2, the intercept is 1/τB.
19
Determination of bulk lifetime, surface recombination velocity, and diffusion
coefficient from lifetime measurements.
20
The above discussions holds for samples with one dimension much
smaller than the other two dimensions. For samples with none of
the three dimensions (a, b, and c) very large, then for sr~ ∞
(7.32)
(7.33)
(7.34)
(7.35)
(7.36)
21
Calculated normalized excess
carrier density versus time as a
function of surface recombination
velocity. d=400μm, α=292 cm-1
(optical absorption coefficient).
22
7.4.1 Photoconductance Decay (PCD)
Schematic diagram for photoconductance decay measurements.
In PCD, the conductivity 
 = q (nn+ pp)
(7.37)
n=n0+n, p=p0+p under low level injection
n = p, the excess carrier density is related to the conductivity by
n=   / q (nn+ pp)
(7.38)
23
Schematic diagram for photoconductance decay measurements.
(7.39)
(7.40)
(7.41)
Where Δg =ΔσA/L.
24
For constant voltage method, choose R smaller than the
sample resistance, in ll case RΔg<<1 or ΔV<<Vo, then
(7.42)
For constant current method, R is very large, if rdkΔg<<1 or ΔV/
Vo/<<rdk /R, then
(7.43)
25
• For ΔV to be proportional to Δn, it is necessary that ll
injection must prevail, otherwise corrections must be
applied.
• The contacts should not inject minority carriers, nor
should they raise sample temperature.
• The electric field in the sample should be held at
E≦0.3/(μτr)1/2, μ is minority carrier mobility.
• The excitation light should be penetrating through the
sample.
26
PCD Measurement Schematic for
Contactless
(a) RF bridge measurement
(b) Microwave Reflectance
Measurement
27
Low Sr can be achieved by:
 Oxidized Si surface, Sr=20cm/s.
 Immersing Si in HF (Sr=0.25cm/s), in iodine/methanol
(Sr=4cm/s).
 Low temperature SiN remote plasma CVD deposition
(Sr=4-5cm/s).
 Inorganic sulfides passivation on GaAs (Sr=1000cm/s),
In the microwave reflection method
P / P = C 
(7.44)
28
7.4.2 Quasi-Steady-State Photoconductance
(QSSPC)
The sample is illuminated with a flash lamp with a ms
decay time, the sample is under quasi-steady-state
during the measurement as the light intensity varies from
the maximum to zero. The generation rate is
G = f / d
(7.45)
G(t) = 0 for t  0; G0exp(-t/flash) for t > 0
(7.46)
For eff < flash , the solution of Eq. (7.25) is
n(t)=eff/(1-eff /flash )G0(exp(-t/flash )-exp(-t/eff )
(7.47)
29
Effective Recombination Lifetime Versus
Injection Carrier Density
Obtained with the QSSPC technique. Adapted from ref. 37.
30
7.4.3 Short-Circuit Current / Open-Circuit
Voltage Decay (SCCD/OCVD)
For the short-circuit current,
(7.48a)
(7.48b)
For the open-circuit voltage
(7.49)
31
• The current decays exponentially with time, the time
constant depends on excess carrier density.
• The voltage decay is influenced by the junction RC time
constant. This effect is reduced by measuring the smallsignal voltage decay with a steady-state bias light to
reduce R.
• For samples with thickness much larger than the minority
carrier diffusion length, sr is no longer important
Isc, Voc ~ (exp(-t/τB))/(t1/2)
(7.50)
32
7.4.4 Photoluminescence Decay
(7.51)
• Direct band gap material has larger PL density than indirect band gap
material.
• It becomes complicate when self-absorption occurs .
(7.52)
• The first term is the non-radiative lifetime,γ is the photon recycling
factor.
• Self-absorption is not important for indirect semiconductor.
33
7.4.5 Surface Photovoltage (SPV)
Sample cross section for SPV
measurements. The optically
transparent, electrically conducting
contact to the left of the sample allow
light to reach the sample and the
voltage to be measured.
• The surface scr is induced by surface charges, not due to a bias
voltage.
• The incident light wavelength is varied, the sample back is kept in
dark.
• Some minority carriers diffuse toward the illuminated surface, building
a SPV which is proportional to Δn(W).
34
• SPV method is used to determine the minority carrier diffusion
length.
• To simplify data extraction, we need
 Undepleted wafer much thicker than Ln
 The scr width smaller than Ln
 α(d-W)>>1>> αW, α the absorption coefficient
 Sample diameter > sample thickness
(7.53)
The diffusion equation solution is
(7.54)
35
The Δn(W) is related to the voltage by
(7.55)
which yields
(7.56)
Vspv is proportional to Δn for Vspv<0.5kT/q
In constant surface photovoltage method, Vspv=const, Δn(W) is
constant, for different wave lengths with different α, adjust the
photon flux density to obtain constant Vspv, this yields
36
(7.57)
Plot Φ vs. 1/α, the intercept is Ln and the slope is related to s1.
In constant photon flux density method,
(7.58)
Plot 1/ Vspv vs. 1/α, the intercept is Ln.
37
(a) Constant voltage, (b) constant photon flux SPV plots for Si samples.
38
The condition W<<Ln is usually true for single-crystal Si, yet, for
GaAs and amorphous Si this condition is not satisfied, then the
intercept is given as
(7.59)
The relation between λ and α is important for the accuracy of SPV
method
For Si, λ=0.7~1.1μm.
(7.60)
For GaAs, λ=0.75~0.87μm.
(7.61)
For InP, λ=0.8~0.9μm.
(7.62)
For Si.
(7.63)
39
7. 4. 6 Steady-State Short-Circuit Current
The sample should be a pn junction or Schottky diode.The Jsc is
measured with varying wavelength.
Measurement schematic for (a) the short-circuit current diffusion length
measurement method, (b) for the ELYMAT double surface method.
40
(7.64)
For an n+p diode the second term is negligible.
(7.65)
Adjust Φ such that Jsc is kept constant.
(7.66)
Where C1=Jsc/q(1-R)Ln, plot Φ vs. 1/α.
(7.67)
Or write
Where X=q(1-R) Φ/Jsc, plot 1/α vs. (X-1).
41
Electrolytical metal tracer method:
IF: short penetration depth, moderate diffusion length,negligible back
surface recombination.
IR: penetrating light, low front surface recombination.
(7.68a)
(7.68b)
A is the area, sf is the front surface recombination velocity.
42
7.4.7 Free Carrier Absorption
(a)
(b)
(a) Schematic free carrier absorption arrangement,
(b) schematic for lifetime mapping.
43
Pump beam energy hυ>Eg, probe beam energy hυ>Eg. The
transmitted photon flux is
(7.69)
d is the sample thickness, αfc is free carrier absorption coefficient, R
the reflectance. For n-type semiconductor Kn~10-18cm2/μm2, Kp~(22.7)10-18cm2/μm2.
fc=Kn2n
(7.70)
44
The change in a transmitted pulsed beam is
(7.71)
The change in the absorption coefficient is
(7.72)
Δn is related to the minority carrier lifetime.
The fractional change in transmitted flux is
(7.73)
45
Knowing the laser generation rate G’=(1-R)(cm-2s-1) and the
sample thickness d, the effective lifetime is
eff = dn/G’
(7.74)
Free carrier absorption
lifetime map
The black body emits over a wide wavelength range with a peak
at
peak = 3000/T m
(7.75)
46
7.4.8 Electron Beam Induced Current (EBIC)
E/Eehp=Nehp+γ(Ebs/Eehp)
(7.76)
Ebs is the mean backscattering electron energy, Eehp~3.2Eg,
=3.64eV for Si. γis the backscattering coefficient. The electron
penetration depth is
ρis the semiconductor density. The generation volume is pear
shaped for Z<15. for 15<Z<40 a sphere, for Z>40 a semispherical.
(7.77)
47
Electron Beam Induced Current
Assume a sphere volume of (4/3) π(Re/2)3, the generation rate is
(7.78)
For Si with a beam current of 10-10A. Eehp=3.64eV, E=104eV, G=3X1024
ehp/cm3.s IEBIC can be collected by a junction. The beam position and
energy can be changed. G’=IbNehp/q.
(7.79)
48
(a) Conventional EBIC implementation, (b) depth modulation by electron
beam energy.
In figure (b),
(7.80)
For high Sr,
(7.81)
49
7.5 RECOMBINATION LIFETMEELECTRICAL MEASUREMENTS
pn junction I-V curve showing the space-charge and quasi-neutral
region currents.
50
7.5.1 Diode Current-Voltage
The forward current of a diode has two parts:
J = J0,scr(exp(qV/nkT)-1) + J0,qnr(exp(qV/kT)-1)
J0,scr = qniW/scr;
J0,qnr = qni2F (Dn/NALn + Dp/NDLp)
(7.82)
J0,qnr  qni2F Dp/NDLp
(7.83)
for a p+n diode τp can be calculated
51
PN Junction Cross Sections
(a) Recombination mechanisms in the n-substrate for d<Lp, (b) Denuded zone
on precipitated substrate, (c) Epitaxial layer on substrate, and (d) SOI wafer
52
The correction factor:
F=
(SrLp/Dp)cosh(d/Lp) + sinh(d/Lp)
(7.84)
cosh (d/Lp)+ (SrLp/Dp)sinh(d/Lp)
For the ex[itaxial device in Fig. 7.17(c)
F
(1+NA2/NA1)exp(Dp/Lp)+(1-NA2/NA1)exp(-Dp/Lp)
(1+NA2/NA1)exp(Dp/Lp)-(1-NA2/NA1)exp(-Dp/Lp)
(7.85)
Jr=-qniW/g-qni2F(Dn/NALn+Dp/NDLp)

(7.86)
-qniW/g-qni2FDp/NDLp
53
Reverse Leakage Current Versus SCR Width for
Measured and Corrected Capacitance
54
7.5.2 Reverse Recovery (RR)
(a) Reverse recovery circuit schematic, (b) current and voltage waveforms for
abruptly switched current, (c) current and voltage waveforms for ramped currents.
55
(7.87)
(7.88)
(7.89)
Qs is the charge remained at t=ts. Usually, Qs/Irτr is a constant.
For power diodes, the current can not change abruptly, there is a
current slope during turn off. The life time is calculated as:
(7.90)
56
Storage time versus (1+ If/Ir). Reprinted after Kuno (Ref. 87) by
permission of IEEE.
57
7.5.3 Open-Circuit Voltage Decay (OCVD)
Open-Circuit voltage decay (a) circuit schematic, (b) voltage waveform.
The carrier concentration at the junction edge is
(7.91)
58
The corresponding voltage is
(7.92)
The diode voltage is Vd=Vj+Vb. Vb, the Dember Voltage, is
caused by μn and μp difference.
(7.93)
Vb has to be taken into consideration at hl, but is negligible at ll.
For substrate thickness d>>Ln, and ll the diode voltage is
(7.94)
59
Open-circuit voltage decay waveform.
60
The slope of the above curve is
(7.95)
For t>4τr ,
(7.96)
At hl, the life time is
(7.97)
61
7.5.4 Pulsed MOS Capacitor
Method 1
Pulsed MOS capacitor recombination
lifetime measurement. The device
behavior at various voltages is shown in
(a), (b), (c), and the C-VG and VG-t curves
in (d).
62
(7.98)
(7.99)
For tp>τr, the capacitance change is CACBCC .
For tp<<τr, the capacitance change is CACBCA .
(7.100)
Change the pulse width and measure the CC,
plot ln((1/CA2)-(1/CC2)) vs. tp, τr is obtained from the slope.
63
Method 2
The C-VG and C-t behavior of and MOS-C pulsed into deep depletion.
64
The thermal generation
components of a deep-depleted
MOS capacitor.
1. Bulk scr generation τg, 2. lateral surface scr generation sg, 3. surface
scr generation under the gate sg’, 4. qnr generation Ln, 5. back surface
generation sc.
65
The mechanism 2 is involved when pulsing from accumulation,
pulsing from inversion is usually used to obtain low surface
generation. The capacitance dependence on VG and Qn is
(7.101)
Solving for VG and differentiate wrt t gives
(7.102)
For pulsed capacitor, dVG/dt=0, that gives
(7.103)
66
The dQn/dt is the thermal generation rate, which can be written as
(7.104)
As=2πrW is the area of the lateral scr region.
AG=2πr2 is the gate area. Ln’ is effective diffusion length contains bulk
and surface effects.
where  = d/Ln
(7.105)
When dQn/dt = -qni2Dn/NALn’ is substituted into Eq.(7.103)
C= Ci/(1-t/t1)1/2
(7.106)
67
Generation rates as function of temperature for Si with τg=1 ms, sg=1cm/s,
s'g=0.1cm/s,L'n=10-2cm, sc=100cm/s, W=3 μm, r=0.5mm, NA=1016 cm-3,
Dn =37(300/T)1.2 cm2/s, d=750 μm, and ni =9.15×1019(T/300)2exp(-0.5928/kT).
68
7.6 GENERATIN LIFETIME
7.6.1 Gate-Controlled Diode
The gate-controlled diode. D is the n+p diode, G the circular gate, and
GR the circular guard ring.
69
The generation currents are:
1. Diode scr current IJ
2. Gate induced scr current IGIJ
3. Surface under the gate IS
Gate-controlled diode in (a) accumulation, (b) depletion, (c) inversion; (d) shows
the current-voltage characteristic with points A, B, and C corresponding to (a),
(b), and (c). Reprinted with permission after Schroder, Ref. 107.
70
At point B 0<φs<VD1+2φF, the scr width is
(7.107)
For φs>VD1+2φF, the scr width pins to
(7.108)
The junction scr width is
(7.109)
71
Experimental gate-controlled diode
current-voltage characteristic.
(7.110)
(7.111)
72
7.6.2 Pulsed MOS Capacitor
Zerbst plot
The MOS is pulsed into deep depletion and the
C-t is measured. The generation rate is
(7.112)
Winv=(4KsεoφF/qNA)1/2
73
Pulsed MOS Capacitor
Zerbst plot
τg,eff is defined by considering only the Scr generation rate
(7.113)
74
(a) C-t response and
(b) Zerbst plot. Reprinted with permission after Kang and Schroder, Ref. 118.
75
(7.114)
The relation between scr width and C is
(7.115)
The relation for Zerbst plot is
(7.116)
The slope contains the information of τg and sg.
The intercept is related to sg’, Ln, and Sc.
76
Because
(7.117)
The Zerbst plot vertical axis is proportional to the ehp generated
charge or current, and the horizontal axis is proportional to the scr
width.
The C-t transient time is quite long, the relaxation time tf is
(7.118)
77
Generation lifetime measurement schematic for SOI devices.
(7.119)
(7.120)
78
(7.121)
Current versus inverse capacitance plot for the device whose Zerbst plot is
shown in Fig. 7.28 Reprinted with permission after Kang and Schroder, Ref. 118.
79
Jscr = [Cox/(Cox-C)]J = qni(W-Winv)/q,eff+qniseff
(7.122)
W = Ks0Ag(1/C-1/Cox)
(7.123)
g,eff =
qni(W-Winv)
(7.124)
dJscr/dW
80
Linear sweep method
Inversion, saturation, and deep-depletion MOS-C curves.
R=dVG/dt is the
sweep rate
(7.125)
(7.126)
81
When the device enters saturation, Csat changes neither with VG nor
with t, the left side of the above Equation becomes 0.
(7.127)
Linear ramp plot for the device whose Zerbst plot is shown in Fig. 7.28.
Reprinted with permission after Kang and Schroder, Ref. 118.
82
Corona-oxide-semiconductor (COS) method
+ or – charge from a corona source is deposited on the
semiconductor surface
Corona-pulsed deep-depletion measurement apparatus.
83
(7.128)
(7.129)
(7.130)
∵ dVFB/dt=0,
∴
(7.131)
For QG = -Qs = constant
(7.132)
84
(7.133)
From dQn/dt, one finds
(7.134)
COS generation lifetime plot.
85