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.