51
CHAPTER 3 SRIM SIMULATIONS OF HEAVY ION IRRADIATION ON SiGe HBTs
3.1. Introduction The SRIM/TRIM program is the most commonly used simulation program for
calculating the stopping power and range of ions in solids. The SRIM stands for
Stopping and Range of Ions in Matter. The SRIM simulations are based on Monte
Carlo (MC) simulation method namely the binary collision approximation (BCA)
code [106]. The results obtained from the SRIM program will be the average result of
many simulated particle trajectories. Starting from 1983, several versions of SRIM
programs were released with minor or major corrections in the software program
[107, 108]. The SRIM 2011 is the modified software which is the combination of the
earlier versions of the SRIM and TRIM (TRansport of Ions in Matter) programs. The
advanced version of SRIM-2011 gives better accuracy in the calculations of stopping
power and range for different ions in different targets [109, 29].
The SRIM code simulates the transport of heavy ions of less than 2 GeV/amu
in matter. The BCA code is based on quantum mechanical treatment and thus SRIM
gives results after statistical calculations. The colliding ion and target atoms have
screened coulomb collision, exchange and correlation interactions between the
overlapping electron shells. Also the incident ion has long range interactions with the
target, creating electron excitations and Plasmon’s. These calculations require target’s
collective electronic structure and inter atomic bond structure, when the calculation is
set up. The charge state of the ion within the target is described using the concept of
effective charge, which includes a velocity dependent charge state and long range
screening due to the collective electronic sea of the target. The ions make
macroscopic moves between collisions and thus the collision results are averaged.
This procedure is common to most of the charged particle transport algorithms which
leads to increased efficiency. An ion treated in SRIM may be any heavy charged
particle, as heavy as a proton or greater. The SRIM code is a comprehensive ion
transport module because it treats targets that can be quite complex. The targets can
be made of up to eight layers, each layer being composed of a compound material.
SRIM estimates the final distribution of ions in different layers of target [29].
Chapter 3 52
The SRIM code is the simplified version of TRIM code, which is a
comprehensive ion-transport module and TRIM treats objects that can be quite
complex. The object can be made of up to eight layers, each layer being composed of
a compound material. TRIM estimates the final distribution of the ions (in three
dimensions) in the target material and TRIM is also able to estimate kinetic
phenomena that are induced by ion’s energy loss. These phenomena include
sputtering, target damage, the production of phonons and ionization. The SRIM
models the cascades that result from ion impact on target atoms. The SRIM package
can be used to generate tables of stopping powers, ranges of ions in matter and
straggling distributions. The SRIM also can be used to study ion implantation, ion
sputtering and ion beam therapy. The TRIM code was initially based on light ion
transport, but SRIM now treats ion transport in matter where both the ion and the
atoms in the matter include all elements up to uranium [29].
3.2. Binary-collision approximation method The computer simulations which treat the successive collisions as binary collisions
are called binary-collision approximation (BCA) methods [110]. The BCA codes are
implemented using Monte Carlo (MC) techniques [111]. In the MC technique, a
random number is used to determine the free flight path ‘l’ of an ion from an
exponential distribution
F(l) = e−l
λ�
λ → 3.1
where λ = 1Nσ(E)
is the mean free path, N is the density of the target and σ(E) is the
cross section for all the possible collisions under consideration. Each collision is
treated as a binary collision neglecting the rest of the environment. The binary
collisions are iterated until the ion has lost all of its energy. The implantation of ions
is simulated until the ions stop. A histogram of the penetration depth from the target
surface is used to give the range profile of the ions. The limitation of BCA is that it
does not take into account of the crystal structure or the dynamic composition changes
of the target material. However the materials used in semiconductor devices are
simple elements of the periodic table. Therefore the SRIM calculations are sufficient
to understand the damage mechanism inside the device structure.
SRIM Simulations of Heavy Ion Irradiation on SiGe HBTs 53
3.3. Ion-solid interaction When an energetic heavy ion beam strikes the target, it immediately begins to transfer
its energy to the target system. The energy deposition process is commonly described
by the ‘stopping power’�− 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑�. It is also convenient to split up the particle stopping
power into two basic and dominant energy transfer mechanisms. The one arises from
“billiard” type atomic collisions with the target atoms (‘nuclear’ energy transfer, Sn)
and the other from excitation and ionization of the target electrons (‘electronic’
energy transfer, Se). The total stopping power is the sum of both components whose
reciprocal integral defines the total projectile range. The both stopping powers
increase with increasing energy, reach a maximum and thereafter fall away. The
accumulated electronic stopping power, however, reaches its maximum commonly
referred to as the ‘Bragg peak’ at energies which are orders of magnitude higher than
that for nuclear stopping. Generally, SRIM calculations are based on “Bethe Bloch
analytical theory” for electronic stopping and in case of compound targets the “Bragg
rule of additivity” from individual constituent atoms is assumed. The ion interactions
based on two basic dominant energy transfer mechanisms are briefly explained in the
following sub-sections.
3.3.1. Electronic energy loss When an energetic ion enters a solid, it immediately interacts with many electrons
simultaneously. In such an encounter, the electron experiences an impulse from the
attractive Coulomb force as the projectile ion passes its area. Sometimes this impulse
may be sufficient either for excitation or for ionization. The excitation or ionizations
are the result of the inelastic collisions. The energy which is transferred to the electron
comes from the energetic ion. Thus the velocity of the ion decreases as a result of ion
encounter with the sea of electrons in the target material. At any given time the ion
interacts with many electrons, so the net effect is to decrease its velocity continuously
until it is stopped. The swift heavy ions can move a few microns to tens of microns in
the target because a single encounter of ion with an electron does not deflect its path.
Therefore swift heavy ions pass through a definite range in a given material.
Chapter 3 54
In 1913, Bohr first proposed the theory of electronic energy loss Se of
energetic ions in solids [112]. He considered the target as a collection of harmonic
oscillators whose frequency was determined by optical absorption data. Bethe, Bloch
and others extended this work for the relativistic ions and solved the problem
quantum mechanically in the first Born approximation [112-115]. The electronic
energy loss Se of highly energetic ion in solid is stated as follows:
Se = �− dEdx�
e= 4e4Zp
2 Zt Nt
me v2 x �ln �2me v2
I� − ln �1 − v2
c2� −v2
c2� → 3.2
where, v and Zpe are the velocity and charge of the projectile ions, Zt and Nt are the
atomic number and number density of the target atoms, me is the electron rest mass
and e is the electronic charge. The parameter ‘I’ is the average excitation and
ionization potential of the target. The above equation is valid only for relativistic
projectile ions, where the velocity of the impinging ions is larger when compared to
the velocities of the orbital electrons in the target atom. In case of non-relativistic
projectile ions the term ln�2me v2
I� is significant and Se varies inversely with ion
energy or v2. Since the velocity of ion is low, it spends a greater time in the vicinity of
the electron and hence most of the ion energy is lost by greater impulse with the
electrons.
100 101 102 103 104 105 106 107 108 109 10100
500
1000
1500
2000
75 MeV B ion
Ener
gy lo
ss (k
eV/µ
m)
Electronic energy loss Lithium ion Boron ion Oxygen ion
Ion Energy (eV)
50 MeV Li ion
100 MeV O ion
Figure 3.1: Variation of electronic energy loss (Se) for different ions in silicon.
SRIM Simulations of Heavy Ion Irradiation on SiGe HBTs 55
The variation of Se with ion energy from 1eV to 1 GeV for lithium, boron and
oxygen ions in silicon target is shown in Figure 3.1. It is can be observed from the
graph that for low energy impinging ions (1 eV to 1 keV), Se is almost negligible. At
low energies, the velocity of ions is less than the Fermi velocity of the electrons in the
target atoms. Therefore the electrons in the target atoms move faster than the ion and
the collisions with ion are mostly adiabatic with direct energy loss to collisions. This
problem of energy loss due to low velocity of impinging ions is understood using a
model of slow heavy ion in a uniform electron gas. The outcome of this model is that
the electronic energy loss is found to be proportional to the ion velocity. After 1 keV,
Se starts increasing with increase in ion energy. After the Bragg peak, Se decreases
with increase in ion energy and in this region Se obeys Bethe-Bohr formula as given
in equation 3.2. The energy loss, ion energy and the range of different ions at Bragg
peak position are tabulated in Table 3.1.
Table 3.1: The energy loss, ion energy and range of different ions in silicon at Bragg peak position
Ion species The energy loss (in keV/µm)
Ion energy (MeV)
Range of ion (in µm)
Lithium
Boron
Oxygen
525.1
972.4
1663
1.6
2.25
5
3.93
3.06
4.06
The objective of this thesis work is to compare the ion irradiation effects with
ionizing radiation. The energy of the lithium, boron and oxygen ions are chosen such
that there is uniform ionization in the active region of the device. On this note,
starting with the smaller atomic number elements lithium ion with energy of 50 MeV
was selected for irradiation of SiGe HBTs. The ion energies chosen for irradiation
purpose should also be in compliance with working feasibility of the Pelletron
accelerator. The higher atomic number elements like boron and oxygen ions were
chosen with an increment in the ion energy of about 25 MeV. From the figure 3.1 it is
evident that 50 MeV lithium ions, 75 MeV boron ions and 100 MeV oxygen ions
predominantly ionize the SiGe HBT structure and few displacement damages also
may be created.
Chapter 3 56
3.3.2. Nuclear energy loss As the energetic ion comes to rest in the target, it makes sufficient number of
collisions with the lattice atoms. The elastic collision between the projectile ion and
individual target atom is known as nuclear energy loss (Sn). Therefore ion losses its
energy by two significant processes viz., electronic energy loss and nuclear energy
loss. The nuclear energy loss results in the creation of primary knock-on atoms
(PKA). When the energy of the incident ion is sufficient to displace the lattice atom,
then the displaced lattice atom is called PKA. The PKAs can in turn displace other
atoms creating secondary knock-on atoms, tertiary knock-on atoms, etc thus creating
a cascade of atomic collisions. The formation of PKAs leads to the distribution of
vacancies, interstitial atoms and other types of lattice defects. These PKAs will be
responsible for the uneven characteristics in a semiconductor material. The solution to
nuclear energy loss is arrived by considering two assumptions viz., screened coulomb
potential and impulsive approximation. The interaction potential V(r) between two
atoms Z1 and Z2 can be written in the form of a screened potential using χ as the
screening function:
V(r) = Z1Z2E2
r2 χ �rA� → 3.3
where ‘a’ is Thomas-Fermi screening radius for collision
a = 0.885𝑎𝑎𝑜𝑜
�𝑍𝑍11 2⁄ +𝑍𝑍2
1 2⁄ �2
3� → 3.4
where ‘ao’ is the Bohr radius. The values of ‘a’ lie between 0.1 and 0.2 Å for most the
interactions. In addition to Thomas-Fermi potential, the other potentials used to
calculate Sn are Lenz-Jensen, Moliere and Bohr potentials. The expression of Sn is
given as follows:
Sn = −�dEdX�
n= n2 ∫ Tdσn(E, T)Tmax
0 → 3.5
where n2 is the atomic density of the target, T is the energy transferred from an
incident ion of energy E to an atom of the target material. Tmax is the maximum value
of T and dσn is the differential cross-section. If the screening potential is
χ = a2R
→ 3.6
Then the final expression for nuclear energy loss is given by
Sn = N π2
2Z1Z2e2α M1
M1+M2 → 3.7
SRIM Simulations of Heavy Ion Irradiation on SiGe HBTs 57
As discussed earlier, in elastic collisions PKAs are created only if the energy
of the incident ion is more than the displacement threshold energy (Ed) of the target
atom (Ed = 21 eV for silicon). If Eʹ is the energy lost by the incident ion then the
initial PKA has energy of (Eʹ– Ed). If (Eʹ– Ed) > Ed, the PKA can in turn create
secondary PKA. In a complete analysis, each succeeding level of knock-on atom is
followed, counting each displacement until the cut-off energy Ed is reached. The
deposited energy depends on the mass and energy of the incident particle and also on
the mass of target material. The distribution of the energy deposited depends on the
type of the material and the damage structure may be different even for similar
distribution of energy deposition. According to the above condition, displacement
damages are created for energies greater than Ed. The number of displacement
damages for a particular depth is obtained with Kinchin-Pease formula [116] as given
below:
nd(χ) = 0.8V(E,x)2Ed
→ 3.8
where V(E, x) is the energy transferred to the recoil atoms at depth ‘x’ from the
surface of the target material. The total number of displacements in the irradiated
target material is given by:
Nd=0.8 ∫ V(E,x)dx∞
02ED
→ 3.9
The unit of displacement damage is the number of displacements per atom
(DPA). DPA is the relative measure of how much lattice damage has been created in
the target material for a given total dose. The value indicates the statistical average of
the fractional number of lattice atoms which have experienced lattice displacement. If
the DPA is 0.1 for a given total dose then 10% of the target atoms experienced
displacement after irradiation. The dependence of DPA versus depth if given by
DPA(x) = 0.8 V(E,x)2Ed N
Φ → 3.10
where N is the atomic density and Φ is the ion fluence (ions-cm-2). The variation in
nuclear energy loss (Sn) with increasing ion energy for lithium ion, boron ion and
oxygen ions is shown in figure 3.2. The maximum nuclear energy loss for lithium ion
in silicon occurs at energy 1.65 keV and Sn attains a maximum value of 39.93 eV.
Similarly, for boron ion, at energy 3.25 keV, Sn attains a maximum value of 89.19 eV
Chapter 3 58
and for oxygen ion, at energy 6.0 keV, Sn attains a maximum value of 175.1 eV. The
limitation of this equation is that the value of Sn deviates considerably in energy
dependence. The error is more significant for Rutherford's scattering process for 1/E
dependence at high energy. The corrections to the Sn expression are made by
considering the Thomas-Fermi potential [98]. The electronic energy loss and nuclear
energy loss for different ions in silicon are tabulated in Table 3.2.
Table 3.2: The electronic energy loss and nuclear energy loss for different ions in silicon
Ion species with energy
Electronic energy loss dE/dX
(in keV/µm)
Nuclear energy loss dE/dX
(in keV/µm)
Range of ion (in µm)
50 MeV Lithium
75 MeV Boron
100 MeV Oxygen
94.71
277.8
721.2
5.323x10-2
1.503x10-1
4.028x10-1
310.24
166.07
95.23
100 101 102 103 104 105 106 107 108 109 10100
50
100
150
200
Ener
gy lo
ss (k
eV/µ
m)
Nuclear energy loss Lithium ion Boron ion Oxygen ion
Ion Energy (eV)
75 MeV B ion
50 MeV Li ion
100 MeV O ion
Figure 3.2: Variation of nuclear energy loss (Sn) for different ions in silicon.
3.4. 3-D simulation of ion interaction in SiGe HBT In SiGe BiCMOS integrated circuits, the different devices are interconnected with
thin layers of metals. There may be several layers of metals depending on the circuit
design and miniaturization of devices. A variety of multilevel (3 to 6 level) back-end-
of-the-line (BEOL) metallization schemes are employed in the SiGe integrated
SRIM Simulations of Heavy Ion Irradiation on SiGe HBTs 59
circuits. The SiGe IC's usually consists of small tungsten (W) studs between metal
layers (Cu or Al) and oxide (SiO2) inter-layers [117]. When the SiGe HBT is exposed
to energetic ion, the incident ion interacts with the metals and oxide layers before
entering the emitter region. A small amount of ion energy is lost in the metallization
schemes. After passing through the metallization layer, ion hits the N+ poly silicon
emitter region, emitter-base spacer oxide, SiGe base, n-type silicon collector and n–
sub collector. The active region of SiGe HBT can be considered from N+ poly silicon
emitter to n– sub collector and the approximate thickness of the active region is
around 20 μm. Therefore all the ions considered for irradiation studies will pass the
active region of the SiGe HBT. After crossing the active region of SiGe HBT, the ion
stops in the substrate region of the transistor. The magnitude of electronic energy loss
(Se) is more in the active region of the transistor when compared to the nuclear energy
loss (Sn). The magnitude of Sn increases at the end of ion range. The ionization and
displacement damages were simulated using SRIM-2011 software and the pictorial
representations are presented in the next section.
3.4.1. Ionization of SiGe HBT structure The simulation of ionization damage in SiGe HBT structure after 50 MeV Li, 75 MeV
B and 100 MeV O ion irradiation are shown in figures 3.3 to 3.5 respectively. It is
evident from the figures that there is significant amount of ionization after oxygen ion
irradiation when compared to lithium and boron ion irradiation. The amount of
ionization after boron ion irradiation is more when compared to lithium ion
irradiation. The LET increases with increasing atomic number of the impinging ions
and consequently the ionization also increases with increasing LET of the incident
ions. The incident ion looses more energy in metals when compared to other elements
contained in SiGe HBT structure. In the metallization schema, the higher atomic
number metal used is tungsten. Therefore the ion looses more energy in tungsten
when compared to copper and SiO2 insulating layers. The three spikes observed in the
figures correspond to the three metal layers. Depending on the atomic number and the
energy of ion, electronic energy loss decreases drastically and becomes zero at the end
of ion range.
Chapter 3 60
Figure 3.3: SRIM simulations showing ionization (eV/Ȧ-ion) damage in 50 MeV lithium ion irradiated SiGe HBT.
Figure 3.4: SRIM simulations showing ionization (eV/Ȧ-ion) damage in 75 MeV boron ion irradiated SiGe HBT.
Figure 3.5: SRIM simulations showing ionization (eV/Ȧ-ion) damage in 100 MeV oxygen ion irradiated SiGe HBT.
3.4.2. Displacement damage in SiGe HBT structure The simulation of displacement damage in SiGe HBT after 50 MeV Li, 75 MeV B
and 100 MeV O ions are shown in figures 3.6 to 3.8 respectively. It can be seen from
the figure that displacement damages increases with increase in the atomic number of
the incident ion. The displacement damages are created by non-ionizing energy loss
(NIEL) process and NIEL increases with increasing atomic number of the incident
ions. The amount of displacement damage is more for oxygen ions when compared to
lithium and boron ions. Similarly, the amount of displacement damage is more for
boron ions when compared to lithium ions. The ions loose more energy in metals of
higher atomic number. The high electron density of metals will reduce the effect of
defects in metals. As the ions cross the metallization layer in the SiGe HBT structure
very few displacement damages are created in the active region of SiGe HBT. The
vacancies and interstitials are produced due to nuclear energy loss and maximum
numbers of defects are created in the substrate region, at the end of ion range.
SRIM Simulations of Heavy Ion Irradiation on SiGe HBTs 61
Figure 3.6: SRIM simulations showing displacement damage (displacement/Ȧ -ion) in 50 MeV lithium ion irradiated SiGe HBT.
Figure 3.7: SRIM simulations showing displacement damage (displacement/Ȧ -ion) in 75 MeV boron ion irradiated SiGe HBT.
Figure 3.8: SRIM simulations showing displacement damage (displacement/Ȧ -ion) in 100 MeV oxygen ion irradiated SiGe HBT.
The displacement per atom (DPA) is calculated by SRIM program using equation
3.10. The DPA is plotted versus ion range in SiGe HBT structure for 50 MeV Li ion,
75 MeV B ion and 100 MeV O ions are shown in Figures 3.9 to 3.11. It can be seen
from the figures that the ion range decreases with increase in atomic number of the
incident ion. The number of recoil atoms (DPA) is negligible in the active region of
SiGe HBT. Since the range of ions will pass through the active region of SiGe HBT,
displacement damages are created in the substrate region. The DPA’s are drastically
increases at the end of ion range and the amount of DPA is more for higher atomic
number ions when compared to lower atomic number ions.
Chapter 3 62
0 100 200 300 4000
1x10-3
2x10-3
3x10-3
4x10-3
5x10-3
6x10-3
DPA
(Vac
anci
es/A
-ion)
Target depth (µm)
50 MeV Lithium ion Ions Recoils
Figure 3.9: Displacement per atom (DPA) in 50 MeV Li ion irradiated SiGe HBT.
0 100 200 300 4000
1x10-2
2x10-2
3x10-2
DPA
(Vac
anci
es/A
-ion)
Target depth (µm)
75 MeV Boron ion Ions Recoils
Figure 3.10: Displacement per atom (DPA) in 75 MeV B ion irradiated SiGe HBT.
0 100 200 300 4000
1x10-2
2x10-2
3x10-2
4x10-2
5x10-2
6x10-2
DPA
(Vac
anci
es/A
-ion)
Target depth (µm)
100 MeV Oxygen ions Ions Recoils
Figure 3.11: Displacement per atom (DPA) in 100 MeV O ion irradiated SiGe HBT.
3.5. Variation of LET and NIEL of heavy ions in SiGe HBT The variation of linear energy transfer (LET) and non-ionizing energy loss (NIEL)
versus the depth in SiGe HBTs for different ions are shown in figures 3.12 to 3.14. In
these figures the thicknesses of different regions shrink in the logarithmic scale. The
energy loss in SiGe HBT is calculated using the similar structure as mentioned in the
previous section. The figures show the energy loss of a single ion in different layers of
transistor and the depth travelled by the ion in the transistor. The range of the ions
decreases with the increase in atomic number of the incident ions. Therefore the ion
range in SiGe HBT decreases in the order 50 MeV Li3+ ion, 75 MeV B5+ ion and 100
MeV O7+ ions. It can be seen that around three orders of magnitude differences in the
SRIM Simulations of Heavy Ion Irradiation on SiGe HBTs 63
LET and NIEL for different ions studied in the present work. The comparison of LET
and NIEL for different heavy ions in SiGe HBT is plotted in a single graph and is
shown in Figure 3.15. The variation in the LET and NIEL of heavy ions in
metallization layers is clearly visible in the expanded view. It is evident from the
figure that there is no significant energy loss in metallization layer of SiGe HBT. The
displacement damages are profoundly created at the end of ion range and very few
displacement damages are created in the active region of SiGe HBT.
1 10 100 10001x10-5
1x10-4
1x10-3
1x10-2
1x10-1
1x100
1x101
SiSiO2
Ener
gy lo
ss (M
eV-c
m2 /m
g)
Depth (um)
LET of Li ion NIEL of Li ion
Figure 3.12: SRIM simulations of LET and NIEL for 50 MeV Li ion irradiated SiGe HBT.
1 10 100 10001x10-5
1x10-4
1x10-3
1x10-2
1x10-1
1x100
1x101
Depth (µm)
Ener
gy lo
ss (M
eV-c
m2 /m
g)
LET of B ion NIEL of B ion
SiSiO2
Figure 3.13: SRIM simulations of LET and NIEL for 75 MeV B ion irradiated SiGe HBT.
1 10 100 10001x10-5
1x10-4
1x10-3
1x10-2
1x10-1
1x100
1x101
Depth (um)
Ener
gy lo
ss (M
eV-c
m2 /m
g)
LET of O ion NIEL of O ion
SiSiO2
Figure 3.14: SRIM simulations of LET and NIEL for 100 MeV O ion irradiated SiGe HBT.
1 10 100 1000 10000
1x10-51x10-41x10-31x10-21x10-11x1001x101
10 11 12 131x10-51x10-41x10-31x10-21x10-11x1001x101
LET of O ion NIEL of O ion
LET
NIEL
LET of B ion NIEL of B ion
LET
NIEL
LET of Li ion NIEL of Li ion
SiSiO2SiO2 CuEner
gy lo
ss (M
eV-c
m2 /m
g)
Depth (µm)
SiO2 Cu W
Figure 3.15: Comparison of LET and NIEL for different heavy ions in SiGe HBT
3.6. Conclusions The SRIM software is used to calculate the Se and Sn for different high energy ions in
SiGe HBT structure. The 50 MeV Li3+ ion, 75 MeV B5+ ion and 100 MeV O7+ ions
were selected for irradiation studies on SiGe HBTs. The ratio of LET and NIEL of
Li3+:B5+:O7+ ions is 1:3:7½. The ratio of range of ions Li3+:B5+:O7+ is 3¼:1¾:1 and
Chapter 3 64
the range of ions is above 20 μm which is the active area of SiGe HBT. The ion
energies are chosen such that the ionization is uniform in the active region of SiGe
HBT. The 3 dimensional simulations of ionization and displacement damages in SiGe
HBTs are also discussed in this chapter. The amount of ionization and displacement
damages due to different ions in SiGe HBT structure is compared by observing the
simulated graphs. The SRIM program is also used to estimate the LET and NIEL of
different ions in different layers of SiGe HBTs. The results of heavy ion irradiation on
50 GHz and 200 GHz SiGe HBTs are presented in next chapters.
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