semi合集-English.pdf - 第7454页
SEMI MF1535-1104 © SEMI 2004 12 Figure R1-2 Recombination Lifeti me as a Function of Injec tion Level
SEMI MF1535-1104 © SEMI 2004 11
Figure R1-1
Derivation of
0
and
from Plots of Recombination Lifetime versus Injection Level
Table R1-1 Parameters Used for Calculation of Recombination Lifetime versus Injection Level
Parameter Elemental Iron (Fe) Iron-Boron (Fe-B)
Temperature, K 300 300
Boron density (p
0
), cm
3
1 × 10
15
1 × 10
15
n
0
, cm
3
1.16 × 10
5
1.16 × 10
5
Iron density, atoms/cm
3
5 × 10
11
5 × 10
11
Defect energy, eV (above valence band edge) 0.400 0.100
n0
, s
3.64 0.400
p0
, s
30.3 3.33
n
1
, cm
3
1.96 × 10
7
179
p
1
, cm
3
5.91 × 10
12
6.48 × 10
17
R1-5 This linearity is illustrated in Figure R1-1 for
recombination through the elemental iron defect center
in both n- and p-type silicon and through iron-boron
pairs in p-type silicon. The parameters for the
calculations are listed in Table R1-1; in each case it is
assumed that all of the iron is in the defect state listed.
Note that for elemental iron in p-type silicon,
0
=
n0
, for
the iron-boron pair,
0
>>
n0
; and for elemental iron in n-
type silicon,
0
=
p0
.
R1-6 Injection level spectroscopy, which has been
proposed
3
as a method for identifying impurity levels,
relies on the relationship between
0
and
as a
function of the density of the impurity center for
specific doping conditions. This method is particularly
useful for studying iron in p -type silicon because of the
facts that (1) it is possible to treat the sample to ensure
that essentially all of the iron is in either the elemental
or paired state,
19
and (2) the injection level dependence
19 Zoth, G., and Bergholz, W., “A Fast, Preparation-Free Method to
Detect Iron in Silicon,” J. Appl. Phys. 67, 6764–6771 (1990).
is markedly different for the two species (see Fig. R1-
2).
R1-7 However, it should be noted that if several
contaminants are present at the same time at similar
concentrations, the measured ratio of
0
to
may
represent some average of the values for the various
contaminants because this technique is not impurity
specific as is deep-level transient spectroscopy or other
spectroscopic techniques involving filling and emptying
of defect centers in the space-charge layer.
SEMI MF1535-1104 © SEMI 2004 12
Figure R1-2
Recombination Lifetime as a Function of Injection Level
SEMI MF1535-1104 © SEMI 2004 13
RELATED INFORMATION 2
TEMPERATURE DEPENDENCE OF CARRIER RECOMBINATION
LIFETIME
NOTICE: This related information is not an official part of SEMI MF1535. It was derived from
information developed during the original preparation of the standard in ASTM Committee F-1 in 1994.
This related information was approved for publication by full letter ballot procedures.
R2-1 The temperature dependence of the carrier
recombination lifetime as determined under low-
injection conditions has been proposed
4
as a means for
identifying metallic impurities in silicon. However, this
is possible only for low injection and then only under
very restricted conditions.
R2-2 In the low-injection limit, the (S-R-H) carrier
recombination lifetime is given by Equation R1-2. In a
nondegenerate semiconductor, the carrier densities, n
0
,
p
0
, n
1
, and p
1
, are all exponential functions of
temperature. The equilibrium electron and hole
densities, n
0
and p
0
, respectively, are given as follows:
kT
Nn
cF
c
exp
0
and
kT
Np
Fv
v
exp
0
(R2-1)
where:
N
c
= the density of states in the conduction band, in
states/cm
3
,
N
v
= density of states in the valence band, in
states/cm
3
,
F
= Fermi energy, or the equilibrium electrochemical
potential, in eV,
c
= conduction band edge, in eV,
v
= valence band edge, in eV,
k =
Boltzmann's constant ( = 8.6173 × 10
5
eV/K),
and
T = temperature, in K.
Similarly, the electron (n
1
) and hole ( p
1
) densities when
the Fermi energy is at the defect center energy
T
are
given as follows:
kT
n
kT
Nn
FT
cT
c
expexp
01
and
kT
p
kT
Np
TF
Tv
v
expexp
01
(R2-2)
R2-3 From Equation R1-2, it is clear that the low-
injection (or small-signal) carrier recombination
lifetime,
0
, can be calculated readily in terms of the
electron and hole capture time constants,
n0
and
p0
, as
the sum of four terms:
00
10
00
00
00
10
00
00
0
np
n
np
n
np
p
np
p
pp
nn
(R2-3)
In the temperature region between the freeze-out region
and the intrinsic region where the majority carrier
density is equal to the net dopant density, the
denominator of these terms is constant. If, in addition,
the capture time constants are assumed not to depend
on temperature, the slope of the ln
0
versus 1/T curve
yields the defect center energy,
T
, in those temperature
regions where the defect centers are partially filled (that
is, when a term in p
1
or n
1
dominates the small-signal
recombination lifetime). Although this assumption is
usually not rigorously correct, the variation of capture
time constant with temperature is usually much less
strong than the exponential dependence of the carrier
densities.
R2-4 Three examples, elemental iron in both n- and p-
type silicon and iron-boron pairs in p-type silicon, serve
to illustrate these considerations. In each case the iron
density is assumed to be 5 × 10
11
atoms/cm
3
and the
dopant density is assumed to be 1 × 10
15
atoms/cm
3
, for
p-type silicon this dopant density corresponds to a
resistivity
10–15 ·cm and for n-type silicon it
corresponds to a resistivity 3–5 ·cm. The
temperature range considered is from 250 to 1000 K
over which the dopant atoms may be assumed to be
fully ionized. Elemental iron is a donor center which,
as shown in Table R1-1, lies well above the valence
band edge in the bottom half of the forbidden energy
gap. The iron-boron pair is also a donor center but it
lies much closer to the top of the valence band.
Consequently, in each case p
1
>> n
1
, the difference
being greater for the iron-boron pair.
R2-4.1 Elemental Iron in p-Type Silicon (see Figure
R2-1) — Below room temperature, p
0
>> p
1
>> n
1
>>
n
0
, so
0
=
n0
. Between about 150°C and about 200°C,
p
1
> p
0
> n
0
and the term p
1
is the largest single term.
However, because there is not much difference between
p
1
and p
0
, the slope of the
0
curve never quite reaches
that of the p
1
term, and thus the energy of the elemental
iron center cannot be determined accurately from the
curve. At still higher temperatures, n
0
becomes