CHAPTER
6
DIFFUSION, OXIDATION
AND
ION IMPLANTATION
This chapter will discuss some important processing techniques for device fabrication. These have been
discussed earlier by Ghandy [1] and Sze [2]. The present chapter introduces some newer techniques
such as laser annealing and presents some new research results on GaAs. While Diffusion and Oxidation are particularly important for Silicon-based devices, Ion Implantation is the preferred technique for
all semiconductor devices including III-V and II-VI compounds, since all semiconductor devices require a desired doping concentration and doping profile for optimum performance.
In the fifties doping was carried out during crystal growth and simple p-n junctions could thus be
made. In amorphous Si devices doping is still carried out during deposition as discussed in Ch 4.
Nowadays however the bulk single crystal wafer forms a high quality substrate for further processing,
which could include epitaxial growth followed by ion implantation. Till the seventies doping in Si was
carried out using high temperature diffusion. Since then ion implantation has become the workhorse
especially for shallow doping. Diffusion is still employed for deep junctions and a combination of the
2 processes may be used. Since the implantation of high energy ions results in damage to the crystalline
lattice, this must be followed by annealing in a furnace or by lamps as in a rapid thermal anneal (RTA)
process.
6.1 DIFFUSION
Diffusion is a process that involves the motion of atoms through a solid and is driven by a concentration
gradient. In crystalline semiconductors the motion of impurity atoms occurs by
(a)
(b)
(c)
(d)
substitutional
interstitial
substitutional-cum-interstitial mechanisms or
direct exchange and cooperative exchange.
These are shown schematically in Fig. 6.1. For substitutional diffusion there must exist a concentration of vacancies to which the impurity or host atom can jump. For interstitial diffusion the presence
of vacancies is not absolutely necessary while in the third case the impurity can move occupying both
substitutional and interstitial sites. Direct exchange and cooperative exchange have low probabilities
and are not considered further.
358 SEMICONDUCTOR MATERIALS & DEVICES
4
5
4
3
2
2
3
6
1
1
(a)
(b)
(c)
(d)
Fig. 6.1 Diffusion mechanisms: (a) substitutional (b) interstitial (c) substitutional-cum-interstitial
(d) direct exchange and cooperative exchange
6.2 FICK’S FIRST LAW
Atoms in a lattice in thermal equilibrium can be considered to vibrate about their lattice positions. With
increase in temperature these may acquire enough energy to overcome the potential barriers and thus
jump to adjacent substitutional or interstitial sites. In the presence of a concentration gradient, more
impurity atoms will jump in the direction of the gradient and than in the opposite direction and hence
constitute a flux of diffusing atoms. Thus diffusion is governed by Fick’s First law which states that the
flux F per unit area per unit time is proportional to the diffusion coefficient and the concentration
gradient:
dC
...(6.1)
dx
where C = dopant concentration per unit volume. This is Fick’s law in one dimension. The negative sign
indicates that the flux is from high to low doping concentration. The diffusion coefficient D depends on
the type of individual atom and is strongly dependent on temperature being given by
...(6.2)
D = D0 exp (−Ea/kT)
F = −D
DIFFUSION, OXIDATION
AND ION IMPLANTATION
359
where D0 = diffusion coefficient extrapolated to infinite temperature in units of cm2/s and Ea = activation energy in eV.
One of the standard methods for determining diffusion coefficients is by the radioactive tracer
technique. In this a radioactive species is coated on one end of a sample and diffused at a high temperature for a given time. The sample is then taken out and sliced into sections. The radioactive counts for
the different sections are then measured and the diffusion profile thus determined and fitted with a
gaussian or error function profile as determined by the diffusion condition. The experiment has to be
repeated over a range of temperatures to find D0 and Ea.
Interstitial Diffusion
z
1 ,
4
, 1 ,3
4 4
,
1 ,1 ,1
2 2 2
1 , 1 , 1
4
4 4
,
, 1
4
y
x
Atom sites
Interstitial sites
Fig. 6.2 Diamond structure showing 5 interstitial voids [1]
Examining the diamond structure of Si (Fig. 6.2) it is evident that there are 5 interstitial voids in an
unit cell. These are located at
(1/2, 1/2, 1/2), (1/4, 1/4, 1/4), (3/4, 3/4, 1/4), (1/4, 3/4, 3/4) and (3/4, 1/4, 3/4)
The tetrahedral radius of Si is 1.18 Å, computed as half the distance between nearest neighbours
(assuming a hard sphere model). It can also be shown that the diameter of the interstitial void is 1.18
Å and the size of the constriction between the voids is 1.05 Å.
If Em is the potential barrier height between interstitial positions, the number of jumps/s
ν = 4 ν0 exp (−Em/kT)
...(6.3)
13
14
where ν0 = vibrational frequency of lattice atoms = 10 – 10 /sec.
360 SEMICONDUCTOR MATERIALS & DEVICES
Considering diffusion in a concentration gradient (Fig. 6.3) in [100] direction it can be shown that
the flux density j is
j = −(ν d2/6) ΔN/Δx = −∂/∂x [D∂N/∂x)]
= −D (∂N/∂x)
if D is constant independent of the doping concentration.
d/ 3
d/ 3
[100]
N
1
2
x
Fig. 6.3 Diffusion in a concentration gradient [1]
Thus D = ν d 2/6 where d = tetrahedral spacing in the diamond lattice.
Therefore
j = (4 ν0 d 2/6) exp (−Em /kT) = D0 exp (−Em /kT)
...(6.4)
Substitutional Diffusion
For substitutional diffusion it is necessary to have a vacancy as a nearest neighbour. If the energy
necessary to create a vacancy is Es, the number of available vacancies is proportional to exp (−Es/kT).
In a diamond lattice each lattice site has 4 nearest neighbours and if the height of the potential barrier
is En the probability of jumps to nearest neighbours is proportional to exp (− En /kT). Thus the number
of jumps per unit time
j = (4 ν0 d 2/6) exp [−(En + Es)/kT] = D0 exp [−(En + Es)/kT]
...(6.5)
Table 6.1 Substitutional Dopants in Silicon
Impurity
P
As
Sb
B
Al
Ga
In
Type
n
n
n
p
p
p
p
10.5
0.32
5.6
10.5
8.0
3.6
16.5
3.69
3.56
3.95
3.69
3.47
3.51
3.9
950-1275
1080-1375
1105-360
1105-350
0.88
1.26
1.26
1.44
D0
(cm2/s)
Ea (eV)
Temp range (°C)
950-1235
Tetra. radius (Å)
1.10
1095-1380 1095-1380
Misfit factor
0.068
0
0.153
0.254
0.068
0.068
0.22
Sol. solub.(/cm3)
1021
2.1021
8.1019
6.1020
2.1019
4.1019
3.2.1019
1.18
1.36
The activation energies for substitutional diffusion are (3 – 4) eV for impurities, 0.6 – 2.4 eV for
interstitials and 5.5 eV for self-diffusion in Si. Thus substitutional diffusion is much slower than interstitial
DIFFUSION, OXIDATION
AND ION IMPLANTATION
361
diffusion and requires higher temperatures and longer times. The variation of D vs 1000/T for impurities
in Si is shown in Fig. 6.4(a).
The substitutional impurities belonging to Groups III & V are the ones used for doping since these
give rise to shallow acceptors and donors respectively. These single-charged donors are positively
charged while acceptors are negatively charged when ionized.
Impurity – Vacancy Interactions
The process of diffusion of substitutional impurities involves interaction with vacancies which can have
various charge states such as V+, V°, V−, V2− etc. These impurity atoms will interact with vacancies
depending on their charge state and each I-V combination will have its own activation energy. Thus
corresponding to each I − V+, I − V° , I − V− , I − V2− pair there will be intrinsic diffusion coefficients
Di+ , Di0 , Di− , Di2 − etc. Thus the overall intrinsic diffusivity will be given by
Di = Di+ + Di0 + Di− + Di2 −
For the case of extrinsic diffusion the variation of the Fermi level with doping has to be taken into
account as discussed by Ghandy [1]. This also affects the population of different charged vacancies. Si
vacancies exhibit the charge states V+, V− and V2− with locations in the energy band gap at EV + (0.06
– 0.16) eV, EC – 0.44 eV and EC – 0.11 eV respectively. Thus diffusing acceptors have only I − V+ type
interactions while donors interact with negatively charged species I − V− and I − V2−.
Choice of n-type impurities in Silicon
Impurity
Diffusion coefficient
Energy level
ED (eV)
Comments
P
High-same as B
0.044
Short diffusion time, shallow donor
Most widely used
As
Low
0.049
Slow diffuser - first diffusion;
Shallow donor. Small misfit factor –
Highest solubility. Toxic
Sb
Low-high EA
0.039
Slow diffuser - Shallow donor.
Preferred to As as less toxic.
Choice of p-type impurities in Silicon
Impurity
B
Diffusion coefficient
High-same as P
Energy level
EA (eV)
Comments
0.045
Short diffusion time, shallow donor
Highest solubility; Most widely used
Al
Moderate
0.065
Highly reactive with O – not commonly used
Ga
Moderate
0.065
Highly diffusion coefficient in SiO 2;
Used only for high power diodes
In
Slow diffuser; low
solubility
0.16
Deep acceptor partly ionized at 300K;
used as 7–8 μm IR detector
362 SEMICONDUCTOR MATERIALS & DEVICES
Table 6.2 Interstitial dopants in Silicon
Impurity
D0 (cm2/s)
Ea (eV)
Li
S
Fe
Cu
2.5 × 10−2
0.92
6.2 × 10−3
4 × 10−2
0.655
2.2
0.87
1.0
1.6
0.24, 0.37,
0.52 A
0.79 D
0.89 A
ED/EA (eV)
Ag
Au
O
Ni
0.21
1.3 × 10−2
0.1
1.12
2.44
1.4
1.4
0.76 D
0.57 A
0.16 D
0.21, 0.76
A
0.31,
0.56 A
2 × 10−3 1.1 × 10−3
Zn
The values of D0 and Ea for interstitial diffusion are given in Table 6.2. It is seen that the activation
energies are ~ 1 eV much lower than the values for substitutional diffusion. Further atoms with smaller
radii such as Li and Cu are fast diffusers. Thus elements such as Cu can easily give rise to undesired
contamination.
Interstitial diffusers belonging to Groups I, II, VI etc. are usually multiply charged and give rise to
multiple deep levels (Table 6.2). These have special applications e.g Li diffusion is used to fabricate
high resistivity material for Si (Li) detectors while Au, an amphoteric impurity, is used for control of
minority carrier life-time.
Many interstitial diffusers may also diffuse by a substitutional mechanism. Hence, an effective D
value must be used. On cooling a considerable fraction may end on substitutional sites e.g. 90 % Au
compared with 0.1% Ni.
Some interstitial diffusers may form compounds with Si and aggregate to form clusters which are
electronically inactive but harmful in causing junction breakdown.
O is a special case and has a very complex behaviour in Si. It can diffuse by a interstitial-cumsubstitutional mechanism and behaves as either a donor or acceptor. Thus during high temperature
processing O diffusion can cause type conversion. This is discussed later in Chapter 7.
6.3 FICK’S SECOND LAW
The time dependence of diffusion is given by Fick’s Second Law. This can be obtained from the basic
continuity equation for transport of atoms which is
b
∂N ∂t = − ∂j ∂x
Substituting
b
g
...(6.6)
g
j = − D ∂N ∂x , we get
Fick’s Second Law:
b g b
∂N ∂t = ∂ ∂x D ∂N ∂x
g
...(6.7)
This gives the time dependence of the diffusion process. In the special case when D is independent
of concentration N, this reduces to
e
∂N ∂t = D ∂ 2 N ∂x 2
j
...(6.8)
This equation is vital for obtaining the diffusion profile in a semiconductor as a function of time.
The profile depends on the initial and boundary conditions as will be illustrated through examples.
GaAs:
Impurity diffusion in GaAs is much more complex due to the presence of 2 sublattices and due to
DIFFUSION, OXIDATION
AND ION IMPLANTATION
363
the varied types of defects that are present. Since VAs and VGa are both neutral, Deff depends only in Di0 .
The high As vapour pressure also results in the presence of As vacancies.
It is thought that n-type impurities from Group VI such as S, Se and Te move along the As sublattice
and, as these have been found to be very slow diffusers, a di-vacancy mechanism has been proposed.
Impurities from Group IV such as Si, Ge & Sn can be amphoteric i.e., act as donors on Ga sites and
acceptors on As sites. These should be able to move on both sublattices but are also very slow diffusers.
The diffusion coefficients D0, Ea and ionisation energies of impurities in GaAs are given in Table 6.3
and in Fig. 6.4(a).
1300
10
10
-5
Li
-6
Au
2
Diffusion coefficient D (cm /s)
10
10
1100
10
10
O
Li
-5
10
1eV
2eV
3eV
4eV
5eV
900
GaAs
-4
10
Na
-9
1000
Cu
10
-6
-7
O
-8
Mn
10
10
-9
-10
Au
Be
C
-11
10
-12
10
10
-13
10
10
1200
Si
-8
-10
10
10
900
H
Slope for E a = 0
-7
10
T(°C)
1000
Cu
-4
10
10
T(°C)
1200 1100
-14
Cr
Te
-13
Sn
Ga
Sb
Si
10
-14
Ga
B
P
As
-15
0.6
In
-12
10
Al
In
-11
0.7
0.8
-1
1000/T (K )
10
Se
As
-15
0.65
0.85
S
Te
(a)
0.7
0.8
-1
1000/T (K )
0.9
Fig. 6.4 (a) Diffusion coefficients vs 1/T of impurities in Si and GaAs
Table 6.3 Impurities in GaAs
Impurity
Be
Mg
Zn
Cd
Type
p
p
P
p
Ionisation energy (eV)
D0 (cm2/s)
Ea (eV)
0.028
0.028
0.031
0.035
7.3 × 10−6
2.6 × 10−2
2.64
2.7
(Contd.)
364 SEMICONDUCTOR MATERIALS & DEVICES
Impurity
Type
Ionisation energy (eV)
D0 (cm2/s)
Ea (eV)
C
Si
Ge
Sn
Se
Te
Au
Cr
Cu
Mn
O
Li
n/p
n/p
n/p
n/p
n
N
P
deep
deep
p
deep
deep
0.006(D); 0.026(A)
0.0058(D); 0.035(A)
0.006(D),.07,.04 (A)
0.006 (D); 0.17(A)
0.006
0.03
0.09
0.63 (A)
multiple
0.095
0.40(D), 0.67(D)
5/3 × 10−1
3.8 × 10−2
3.0 × 103
D = 10−13 @ 1000° C
2.9 × 101
4.3 × 103
3 × 10−2
6.5 × 10−1
2 × 10−2
1.0
2.7
4.16
2.64
3.4
0.53
2.49
1.1
P-type dopants from Group II such as Be, Mg, Zn, Cd and Hg move in the Ga sublattice.
Only Zn diffusion, used for the formation of shallow p-type layers and p-n junctions, has been
studied in detail. Zn is a fast diffuser and moves by an interstitial-substitutional mechanism exhibiting
dependence on carrier concentration. Since the intrinsic carrier concentration of GaAs at 1000° C is less
than 1018/cm3 even for the lowest surface concentration of Zn, the diffusion is in the extrinsic region and
hence is concentration dependent.
The diffusion coefficient of Zn has been found to vary as N2. The diffusion profile is thus very steep
as shown in Fig. 6.4(b) The junction depth is strongly dependent on the surface concentration which in
turn is proportional to the square root of the partial vapour pressure of Zn. The diffusivity and hence the
20
T = 1000°C
3
Zinc concentration (atoms/cm )
10
10
10
19
18
10
17
0
50
100
Depth (mm)
(b)
150
Fig. 6.4 (b) Zn diffusion profiles in GaAs
200
DIFFUSION, OXIDATION
AND ION IMPLANTATION
365
junction depth is thus linearly proportional to the surface concentration. Relatively low temperatures
(600 – 800°C) suffice for the formation of p-n junctions using Zn but render control rather difficult. Cd
on the other hand is a much slower diffuser and hence capable of good control over junction depth.
a
Hg1- x Cdx Te MCT
f
As a II-VI compound, group III and VII elements act as donors while Group I and V elements are
expected to behave as acceptors in MCT. Si is found to behave as a donor on Group II site. In addition
due to low defect formation energies, native defects play an important role VHg acting as acceptor and
VTe as donor. The diffusivity of impurities in MCT are given in the Table 6.4
Table 6.4 Behaviour of Dopants in Hg1−xCdxTe
Element
Ga
In
Ag
Cu
Au
Li
Al
Si
P
As
Br
Type
Donor
Donor
Acceptor
Acceptor
Acceptor
Acceptor
Donor
Donor
Acceptor
Acceptor
Donor
Diffusion
Fast
Fast
Fast
Fast
Fast
Fast
Slow
Slow
Slow
Slow
Slow
6.4 DIFFUSION PROFILES
For device fabrication it is important to be able to tailor diffusion profiles according to requirements.
The profiles depend on the initial and boundary conditions. The two most important conditions are
Constant Source and Instantaneous Source Diffusion. In the first case the silicon wafer surface is
exposed to an impurity source of constant concentration for the entire diffusion period while in the
second case a fixed amount of dopant is deposited on the semiconductor surface and is subsequently
diffused into the wafer.
(a) Constant Source Diffusion
In Fig. 6.5(a) the initial condition is N(x, 0) = 0 since the dopant concentration on the surface is initially
zero.
The boundary conditions are
...(6.9)
N (0, t) = N0 and N (∝, t) = 0
where N0 = the surface concentration which is constant independent of time. The second boundary
condition states that at large distances from the surface the impurity concentration is zero.
Inserting these conditions into Fick’s second equation and solving (see Appendix 6.1 given at the
end) the doping profile obtained is
...(6.10)
N (x, t) = N0 erfc [x/2 (Dt)1/2]
366 SEMICONDUCTOR MATERIALS & DEVICES
where D = diffusion coefficient, t = time of diffusion and erfc = 1 – erf so that
⎡
12
erfc ⎡ x 2 ( Dt ) ⎤ = ⎢1 − 2
⎢⎣
⎥⎦ ⎢
⎣
(p)
12
x 2 D (t )1 2
∫
0
⎤
exp − z 2 dz ⎥
⎥
⎦
( )
...(6.11)
N0
t4 > t3 > t2 > t1
Nc
t1
0
t2
t4
t3
Distance x
(a)
Concentration (log scale)
Concentration (log scale)
This profile is shown in Fig. 6.5(a) from which it is evident that the surface concentration is
constant at N = N0 while the diffusion depth increases with time. This profile is called the Complementary Error Function Profile. Values for the function are available in tables for numerical computation.
t0 = 0
t4 > t3 > t2 > t1
Nc
t4
t1
t2
t3
Distance x
(b)
Fig. 6.5 (a) Error function profile for Constant Source diffusion (b) Gaussian profile for
Instantaneous Source diffusion
In practice the Si wafer is exposed to a vapour source during the entire duration. The surface
concentration is the value in equilibrium with surrounding gas, the ultimate limit being set by the solid
solubility of the dopant. Emitter doping in a transistor is typically carried out under Constant Source
conditions to give high surface doping concentration and low resistivity.
(b) Instantaneous Source Diffusion
In this case a finite quantity of dopant is placed on the surface and diffusion is carried out from this
fixed amount of dopant. Assuming that all the impurity atoms are consumed the doping profile obtained
is given by
...(6.12)
N(x, t) =[Q/π Dt)1/2] exp {−(x2/4 Dt)}
2
where Q = amount of dopant placed on the surface before diffusion in atoms/cm (Appendix 6.1). The
profile is a Gaussian one and is depicted in Fig. (6.5b). Its main feature is that the surface concentration
decreases with time but as diffusion proceeds the area under the curve remains constant. Both profiles
can be approximated by exponentials at concentration levels 2 or more less than the surface concentration. Here the dopant concentration is normalized in terms of the surface concentration and the distance
in terms of x/2(Dt)1/2. Instantaneous source diffusion is used to obtain low surface concentration and
high diffusion depth e.g. for the base layer of a junction transistor.
In IC processing a 2-step diffusion process is commonly used in which a pre-deposition diffused
layer is first formed under constant source conditions (with diffusion coeffcient D1 for time t1) followed
DIFFUSION, OXIDATION
AND ION IMPLANTATION
367
by a drive-in diffusion under instantaneous source conditions (with diffusion coeffcient D2 for time t2).
The temperatures T1 and T2 determine D1 and D2 and hence are implied variables.
If (D1t1)1/2 >> (D2t2)1/2 an error function profile results whereas if (D1t1)1/2 << (D2t2)1/2 the profile
is gaussian but in general the diffusion profile is determined by both diffusion conditions. Then the
profile is given by
U
{ (
(
) ) (1 + U )} dU
N ( x , t1 , t 2 ) = ( 2 N 01 p ) ∫ ⎡exp −b 1 + U 2 ⎤
⎢⎣
⎥⎦
0
2
...(6.13)
where
U = (D1t1/D2t2)1/2 and β = [x/2 (D1t1 + D2t2)1/2]2
It can be shown that the final surface concentration is N02 = (2 N01/π) tan−1 U
...(6.14)
The 2 step process can be used to avoid surface damage by having a short pre-deposition process
and thus approximate a erfc profile. A slow oxidation process can be used simultaneously to grow a
protective oxide layer.
In many processes successive diffusions are carried out such that the layer diffused first is subject
to many temperature cycles e.g. the base impurities are subject to the thermal conditions during emitter
diffusion. In such cases the total effect of these cycles is given by the effective Dt product
(Dt)eff = ∑ (D1t1 + D2t2 + D3 t3)
...(6.15)
where t1, t2, t3 are the successive diffusion times and D1, D2, D3 are the corresponding diffusion
coefficients.
6.5 EXTRINSIC DIFFUSION
So far diffusion has been considered for the case when the diffusion coefficient is constant i.e. independent
of the doping concentration. This is true when the doping concentration is below the intrinsic carrier
concentration at the diffusion temperature. e.g. at 1000 °C, ni = 5 × 1018/cm3 for Si and 5 × 1017/cm3
for GaAs. Such a condition is shown in Fig. 6.6. For successive diffusions eqn. (6.15) is valid in
this case.
100
D/Dl(T)
10
1
Extrinsic
diffusion
Intrinsic
diffusion
0.1
0.01
0.1
1.0
n/n j (T)
10
Fig. 6.6 Intrinsic and extrinsic diffusion regions (after Sze [2])
100
368 SEMICONDUCTOR MATERIALS & DEVICES
However, if the doping concentration is larger than the intrinsic value ni the regime is called the
extrinsic diffusion regime. The diffusion coefficient becomes concentration dependent and interactions
between charged defects makes the diffusion profile more complex. In this case, the generalized form
of Fick’s First Law has to be used:
j = − ∂ ∂x ⎣⎡ D∂N ∂x ⎦⎤
6.6 CONCENTRATION-DEPENDENT DIFFUSION
If the dopant diffusion is dominated by the vacancy mechanism, the diffusion coefficient is expected to
be proportional to the vacancy concentration which is given by
CV = Ci exp [(EF – Ei)/ kT]
...(6.16)
where Ci = intrinsic vacancy concentration, EF and Ei are the Fermi level and the intrinsic Fermi level
respectively. At low doping concentrations (n < ni) the Fermi level is at the intrinsic Fermi level and
hence CV = Ci independent of the doping concentration. The diffusion coefficient is hence independent
of the doping concentration. At high doping levels (n > ni), the Fermi level moves towards the conduction band edge and hence CV increases as does the diffusion coefficient as shown in Fig. 6.6.
When the diffusion coefficient is not independent of the doping concentration C it can be
written as [2]
...(6.17)
D = DS [C/CS]γ
where DS = diffusion coefficient at the surface, CS = doping concentration at the surface and γ is a
positive integer. In this case the diffusion equation can be solved numerically the results being shown
in Fig. 6.7 as a function of normalised distance. γ = 0 corresponds to the case of D = constant. It is found
that the diffusion profiles are much steeper at low concentrations (C << CS) for concentration-dependent diffusion coefficients. The junction depths for values of γ = 1, 2 & 3 are given below:
...(6.18a)
xj = 1.6 √(DS t) for D ~ C (γ = 1)
2
xj = 1.1 √(DS t) for D ~ C (γ = 2)
...(6.18b)
xj = 0.87 √(DS t) for D ~ C3 (γ = 3)
...(6.18c)
Thus it is seen that the abruptness of the doping profile gives a junction depth independent of the
background doping concentration.
6.7 FIELD-AIDED DIFFUSION
The presence of a drift field can result in motion of charged impurities in the direction of the electric
field. Assuming that the random scattering of impurities by the lattice gives a resultant drift velocity v,
the equation of motion due to an electric field E is given by
F = q Z E = m* dv/dt + α v
...(6.19)
*
where F = force on impurity ion, qZ = charge of impurity ion, m = effective mass and α = proportionality factor. The direction of the force obviously depends on the sign of the charge on the impurity ion.
In the steady state when a steady drift velocity vd is attained
vd = q Z E/α = μ E
...(6.20)
where μ = q Z/α = mobility of impurity ion. If the motion of impurity ions due to drift and diffusion
are considered to be independent then the flux density in presence of drift can be written as
j = − D ( ∂N ∂x ) + μNE
...(6.21)
DIFFUSION, OXIDATION
AND ION IMPLANTATION
369
1.0
0.8
0.6
D = Constant
0.4
C/CS
0.2
(a)
D~C
0.1
0.08
0.06
(b)
0.04
D~C
(c)
D~C
2
3
0.02
0.01
0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
X/ Dst
Fig. 6.7 Normalised diffusion profiles for concentration-dependent extrinsic diffusion [1]
In the case of diffusion of a n-type (donor) impurity, the ionised donor produces electrons which
can diffuse much faster than the donors thus giving rise to an electric field as shown in Fig. 6.8 which
further aids the motion of positively charged donors. Thus the motion of donors is aided by the space
charge created by the diffusing electrons giving an enhanced diffusion coefficient.
e
F
e
e
-
F
Donors
Electrons
Fig. 6.8 Electric field-aided diffusion
The diffusion coefficient is related to the mobility by
D = (kT/q) μ
...(6.22)
370 SEMICONDUCTOR MATERIALS & DEVICES
Further in equilibrium the flow of electrons due to drift is balanced by the flow due to diffusion.
Thus
μnE = − D ( ∂n ∂x ) = ( kT q ) μ ( ∂n ∂x )
Simplifying
a
fa fa
E = − kT q 1 n dn dx
f
...(6.23)
...(6.24)
Substituting in eqn. (6.21)
j = −D (1 + dn/dN) ( ∂n ∂x )
...(6.25)
Thus the impurities move with an effective diffusion coefficient Deff
Deff = D (1 + dn/dN)
...(6.26)
n/ni = N/2 ni + [(N/2ni)2 + 1]1/2
...(6.27)
For an n-type impurity
so that
dn/dN =
1
{1 + [1 + (2ni /N)2]−1/2}
2
...(6.28)
Thus there can be a substantial increase in the effective diffusion coefficient with doping concentration, by even a factor of 2. This has been observed experimentally for substitutional diffusers.
Example: Formation of n-p-n transistors by diffusion
It is required to form a p-n junction at a depth of 2 μm below the surface of an n-type Si wafer with
n = 1016/cm3. (Given B source concentration N0 = 5 × 1018/cm3). Find the required diffusion time and
temperature.
For Constant Source diffusion the profile is given by N (x, t) = N0 erfc [x/2 (Dt)1/2] (6.10)
In this problem N (x = 2 μm, t) = 1016 = 5 × 1018 . erfc [x/2 (Dt)1/2]
erfc [ x/2 (Dt)1/2] = erfc y = 1016/(5 × 1018) = 2 × 10−4
∴
From erfc tables y = 2.25 = x/2 (Dt)1/2 = (2 × 10−4)/2 (Dt)1/2
Thus
(Dt)1/2 = 4.4 × 10−5
Let time t = 2 hrs = 7200 s. Then D = 2.5 × 10−13 cm2/s.
From the B diffusion graphs T = 1080° C.
Thus the required diffusion condition is t = 2 hrs diffusion at T = 1080° C.
Note: This is not an unique answer. If t = 1 hr = 3600 s, T = 1150° C.
Thus, a small change in temperature results in a large change in D due the exponential dependence.
Hence the diffusion furnace must be designed to provide ±1° C control in time and along its length.
The npn bipolar transistor can be fabricated by an Instantaneous Source p-type base diffusion
followed by a Constant Source n-type emitter diffusion as shown in Fig. 6.9. The base diffusion is
chosen so as to lower the surface concentration for subsequent emitter diffusion.
DIFFUSION, OXIDATION
AND ION IMPLANTATION
371
N
5 × 10
20
n - type erfc
p - type gaussian
19
10
3 × 10
n - type background
16
0
x
N
N
+
P
xAB
0
N
xBC
x
Emitter
Base
0
1.4
1.7
Collector
x(mm)
Fig. 6.9 Doping profiles of a n-p-n bipolar transition formed by Instantaneous Source Diffusion (Gaussian
profile) for base followed by Constant Source Diffusion (erfc profile) for emitter [1]
6.8 DIFFUSION SYSTEMS
The choice of dopants in Si and GaAs has been discussed. There are broadly 2 types of diffusion
systems employed (i) open tube and (ii) closed tube. There are some general requirements for diffusion
systems. These are:
(a) the surface concentration should be capable of being controlled over a wide range up to the
solid solubility limit
(b) the diffusion process should not result in any damage to the surface
(c) the dopant remaining after diffusion should be capable of easily removed and
(d) the system should be reproducible and capable of handling a large number of wafers
simultaneously.
1
(e) the temperature control should provide a central flat zone with ± °C variation in temperature.
2
372 SEMICONDUCTOR MATERIALS & DEVICES
A diffusion furnace is a carefully designed apparatus capable of maintaining uniform temperature
between 600 – 1200° C with a feedback controller. The diffusion tube made of high purity fused silica
must be handled with great care, one tube and slice carrier being used for each type of dopant to prevent
contamination. The length of the tubes vary from 10 cm – 150 cm or more for industrial furnaces. For
large tubes the insertion of the carrier is done mechanically from one end, the other end being used for
flow of gases and dopants. The temperature of the furnace is gradually ramped up from 600° C after
insertion of the wafers with a programmed temperature controller ramping up the temperature at a
linear rate of 3 – 10° C/min. This is to prevent thermal shock to the wafers as well as to the tube and
components. In practice the diffusion tube is always kept above 600° C and never allowed to cool to
room temperature to avoid devitrification. A gas source diffusion system is shown in Fig. 6.10(a).
If the temperature is ramped down at a rate T = T0 – Ct where T0 = initial temperature and
C = constant, it can be shown that this is equivalent to the wafers being subject to an additional time
kT02/CE0 at the initial diffusion temperature where E0 = activation energy for diffusion.
B Diffusion
The most common p-type impurity is Boron because of its high solid solubility which is 6 × 1020/cm3
as given in Table 6.1. However due to the large misfit factor of B of 0.254 which introduces straininduced defects, the actual upper limit is 5 × 1019/cm3. Diffusion systems for Boron in Si are summarised in Table 6.5.
Table 6.5 Diffusion Systems for Boron in Si
Impurity
source
R.T state
Temp
range (°C)
Impurity
conc. range
Advantages
Disadvantages
BN
Solid
Pre-oxidise at
750 –1100
High & low
High surface conc.
B skin formation;
Sticking to Si
BCl3
Gas
R.T
High & low
Accurate control
Halogen pitting
B2H6
Gas
R.T
High & low
Accurate control
Highly toxic and
explosive
Solid, liquid and gaseous sources are available for B diffusion. One of the most common is Boric
oxide B2O3. A preliminary reaction with B2O3 gives:
2 B2O3 + 3 Si → 4 B + 3 SiO2
...(6.29)
The Si and B2O3 are kept at the same temperature and pre-deposition is carried out in N2 ambient
with 2–3 % O2. The temperature of the B2O3 controls the surface concentration of B as shown in
(Fig. 6.10(c)). Excessive amounts of B2O3 leads to the formation of a B skin which is difficult to
remove. Slices are thus exposed to B2O3 source for a short time to form a glassy layer on the Si surface.
The source is then removed and drive-in diffusion carried out in an oxidizing ambient. This protects the
surface against impurities. This process gives a 2 step-diffusion profile.
BN slices slightly larger than the Si wafers can be used which can be sandwiched between Si slices
with a spacing of 2 – 3 mm. These must be pre-oxidised at 750 – 1100° C to form a thin skin of B2O3
on the surface which forms the diffusion source:
4 BN + 7 O2 → 2 B2O3 + 4 NO2
...(6.30)
DIFFUSION, OXIDATION
AND ION IMPLANTATION
Slices on carrier
To vent
Quartz diffusion tube
Valves and flow meters
To vent
Dopant gas
Chemical trap
Carrier
gases
(a)
Slices on
carrier
To vent
Quartz
diffusion tube
Valves and
flow meters
Liquid source
Carrier
gases
Temperaturecontrolled bath
(b)
Platinum
source boat
Slices on
carrier
To vent
Quartz
diffusion tube
Valves and
flow meters
Carrier gases
(c)
Fig. 6.10 (a) Gas source (b) Liquid-source and (c) Solid-source diffusion systems
373
374 SEMICONDUCTOR MATERIALS & DEVICES
No carrier gas is required but a flow of 1 l/min of dry N2 prevents back diffusion of contaminants.
This process is extremely reproducible with excellent uniformity across the wafers. To avoid sticking,
BN in a silica matrix is often used which also reduces B skin formation.
In thick film technology often used for the fabrication of solar cells, mixtures of B2O3 and SiO2 in
a polyvinyl alcohol solvent are used as spin-on sources. Mixtures of carborane and alkylsiloxane which
have better viscosity control have also been used. An initial bake out is required before diffusion to
convert the components into B2O3 and SiO2.
Gaseous sources Fig. 6.10(a) which are used are diborane (B2H6) and BCl3 which give the following reactions:
300° C
B2H6 + 3 O2 ⎯⎯⎯
→ B2O3 + 3 H2O
...(6.31)
4 BCl3 + 3 O2 → 2 B2O3 + 6 Cl2
...(6.32)
P Diffusion
The activation energy is the same as for B but the misfit factor is small compared with B. High doping
up to 5 × 1020/cm3 makes this an attractive system. The sources available are:
Liquid sources: POCl3, PCl3 and PBr3
4 POCl3 + 3 O2 → 2 P2O5 + 6 Cl2
...(6.33)
Table 6.6 Diffusion Systems for Phosphorus in Si
Impurity
source
R.T. state
Temp.
range (°C)
Impurity
conc. range
Advantages
POCl3
Liquid
0 – 40
High & low
Clean system;
good control over
wide range of
impurity conc.
PCl3
Liquid
170
High & low
Can be used in
non-oxidising
diffusion
PH3
Gas
R.T.
High & low
Accurate control by
gas flow control
Disadvantages
System geometry
important
Highly toxic &
explosive
Of these the most popular is POCl3. An oxidising gas mixture is used in the pre-deposition stage.
The presence of O2 reduces halogen pitting which becomes appreciable only for doping conc. >
1021/cm3. Adjustment of bubbler temperature gives good control over surface concentration (Fig. 6.10b).
Gas Source
PH3 with 99.9 % N2. The reaction is:
PH3 + 4 O2 → P2O5 + 3 H2O
...(6.34)
Sb Diffusion
This is used in special cases when the dopant impurity should be immobile under further processing
because Sb has a relatively high diffusion activation energy of 3.95 eV The sources available are:
DIFFUSION, OXIDATION
AND ION IMPLANTATION
375
Solid sources: Sb2O3 and Sb2O4 at 900° C
Liquid sources: Sb3Cl5 in a bubbler
In the last case Sb is transported as an oxide. Diffusion occurs through a glassy layer following
surface reaction with Si.
As Diffusion
As has misfit factor = 0 with Si and hence does not give rise to strain on heavy doping. It is thus used
for the fabrication of low resistivity epitaxial layers. It is highly toxic and hence the diffusion systems
must be handled with extreme care. The sources used are:
Solid sources:
2 As2O3 + 3 Si → 3 SiO2 + 4 As
...(6.35)
2 AsH3 + 3 O2 → As2O3 + 3 H2O
Gas sources:
...(6.36)
Au Diffusion
Au is a very rapid diffuser in Si, almost 105 faster than B or P. It is used as a deep level recombination
centre to reduce the minority carrier life-time and hence switching time in diodes and transistors. Prior
to diffusion it is vacuum deposited on Si as a ~ 10 nm thick layer on the back surface of the wafer.
Au-Si alloy forms resulting in damage to the Si surface. The diffusion time is typically 10 – 15 min at
800 – 1050 °C and results in Au diffusion throughout the wafer. Au diffusion must be followed by rapid
withdrawal and cooling to room temperature to prevent out-diffusion effects. Since gold doping is
difficult to control it is being replaced by alternative techniques such as radiation-induced centers which
can be area-selective with the dose and energy being easier to control.
Diffusivity of B, P and As in Si
Table 6.1 gives the average diffusion coefficients of substitutional impurities in Si. The actual diffusion
process is much more complex, as discussed above, involving interaction with charged vacancies. Let
us examine the detailed diffusion mechanisms for B, P and As.
B: The diffusion of B in Si involves interaction with donor-type vacancy V+ and D varies approximately with doping concentration. D is given by
a
f
D = D0¢ exp - Ea¢ kT p pi
...(6.37)
where D0¢ = 1.52 cm2/s and Ea¢ = 3.46 eV. The measured profile for B shown in Fig. 6.11 is slightly less
abrupt than the As profile but much steeper than the erfc profile. The experimental data for B can be
fitted to the expression
...(6.38)
N = NS (1 – Y 2/3)
Y = [x2/6 Ds t]3/2
where
...(6.39)
The junction depth is given by
xj = 1.6 (DS t)1/2 where DS is given by eqn. (6.37) and p = NS
Thus
xj = 1.6 [ D0′ exp (− Ea′ /kT) { NS/pi} t]1/2
...(6.40)
As: The diffusion of As in Si is associated with the acceptor-type vacancy V − and the diffusion coefficient
for n > ni is given by eqn. (6.37) with p being replaced by n, which is the dopant concentration with
D0′ = 45.8 cm2/s and Ea′ = 4.05 eV. Eqn. (6.40) is equivalent to eqn. (6.18a) with γ = 1 and hence
376 SEMICONDUCTOR MATERIALS & DEVICES
2
(a) 1- 0.87 - 0.45 Y (As)
1.0
x x
x
(b) 1 - Y
x
x
2/3
(B)
x
x
x
0.1
x
C/Cs
(c) erfc
x
0.01
Arsenic
Boron
1050°C, ½ hr.
1200°C, 2/3 hr.
1050°C, 1hr.
x 870°C, 16 hr.
0.001
0
0.2
0.4
0.6
0.8
1.0
Y/Yj
Fig. 6.11 Normalised diffusion profiles for B and As in Si
D ~ N. The junction depth xj is again given by Eqn. (6.40). A closed form solution of the diffusion
equation with D given by eqn. (6.37) may be written as a polynomial
N = NS (1 – 0.87 Y – 0.45 Y 2)
...(6.41)
t)1/2
...(6.42)
where
Y = x/(4 DS
The measured diffusion profile of As is shown in Fig. 6.11. It is seen that the As profile is more
abrupt than that of B. Because of this As is used to form shallow source and drain junctions in n-channel
MOS devices.
P: The diffusion of P in Si is associated with a doubly charged acceptor vacancy V 2− and D at high
concentrations varies as N2 as shown in Fig. 6.12. This should correspond to the case of γ = 2 (Fig. 6.7).
However, the profile exhibits an anomalous behaviour due to a dissociation reaction as discussed
below.
At low concentrations the profile follows an erfc curve as shown in Fig. 6.13. As the concentration
increases the profile begins to deviate and at reasonably high concentrations it is similar to the curve
for of γ = 2 in Fig. 6.7. At still higher concentrations at n = ne a kink appears followed by rapid diffusion
in the tail region. At this concentration the Fermi level lies 0.11 eV below the conduction band which
DIFFUSION, OXIDATION
AND ION IMPLANTATION
377
T = 1000 °C
2
D(cm /s)
10
10
DµN
-12
2
Phosphorus
-13
D µN
10
-14
Arsenic
10
-15
10
18
10
19
10
20
10
21
-3
N (cm )
Fig. 6.12 Extrinsic diffusivities of As and P in Si as a function of dopant concentration
corresponds to the V 2− level. Thus the P + − V 2− pair dissociates
P + − V 2− → P + + V − + e−
...(6.43)
−
This produces a large number of singly-charged acceptor vacancies V which enhances the diffusion of P in the tail region. The diffusivity in this region is > 10−12 cm2/V.s which is 2 orders of
magnitude larger than the intrinsic diffusivity at 1000° C. This high diffusivity makes P well-suited to
form deep junctions such as n-tubs in a CMOS.
6.9 DIFFUSION IN POLYCRYSTALLINE SILICON
Polycrystalline Si is used as a gate electrode in VLSI technology and also when doped, as a conductor.
Doping can be done by implantation or diffusion. Diffusion in polycrystalline semiconductors is quite
different from diffusion in single crystals and is often dominated by grain boundaries. Since these
boundaries can be considered to act as an array of dislocations, diffusion is enhanced compared with
diffusion in single crystals. Impurities tend to diffuse much faster along grain boundaries and also
segregate along these boundaries.
Accordingly grain growth is affected, which in turn affects impurity diffusion. Since the microstructure of polysilicon depends on growth temperature and other parameters and subsequent annealing,
it is difficult to obtain universally accepted diffusion data. However, the impurity diffusion profiles are
found to follow Gaussian or erfc curves from which the diffusion coefficients and activation energies
can be extracted.
378 SEMICONDUCTOR MATERIALS & DEVICES
10
-3
Phosphorus concentration (cm )
10
10
21
Kink
20
19
Tail region
10
10
10
18
17
(d)
16
(a)
(c)
(b)
1000 °C
1 hr
10
15
0
1.0
2.0
Depth ( mm)
Fig. 6.13 P diffusion profiles in Si for various surface concentrations diffused
for 1 hr at 1000° C
There are 3 regimes of diffusion in polycrystalline materials [3] depending on the relative values
of the grain boundary and lattice diffusion coefficients as shown in Fig. 6.14:
(i) when the diffusion coefficients are of the same order there is hardly any difference between the
penetration in the bulk and along grain boundaries (Fig. 6.14(a))
(ii) when grain boundary diffusion is much faster than bulk diffusion, the impurity penetrates
mainly along the grain boundaries (Fig. 6.14(b))
(iii) when the lattice diffusion is negligible, penetration occurs only along the grain boundaries.
As discussed in Chapter 7 polysilicon is usually deposited by pyrolysis of silane (SiH4) at temperatures between 600 – 650° C. If the deposition temperature is below 575° C fine grain material results
while below ~ 450° C the film is amorphous. Polysilicon deposited above 625° C has columnar structure with grain size between 30 – 300 nm. After high temperature annealing there is significant grain
growth and/or recrystallisation. An impurity such as As which is used as a dopant diffuses both along
the grain boundary (T ~ 800° C) Fig. 6.14 (b) and also into the grains, if these are undoped, above
900° C. The latter is similar to diffusion into single crystal Si. The activation energies as seen from
Table 6.7 are found to be (0.1 – 1.0 eV) less than for crystalline Si.
DIFFUSION, OXIDATION
(a)
AND ION IMPLANTATION
Source
(b)
(c)
Grain boundaries
(a)
Diffusion in Solids
-12
polycrystal
2
log (D cm /s)
single crystal
-14
-16
-18
0.8
1.0
1.2
1.4
(b)
Fig. 6.14 (a), (b) Regimes of diffusion in a polycrystalline material
1.6
379
380 SEMICONDUCTOR MATERIALS & DEVICES
Table 6.7 Diffusion Data for Polycrystalline Silicon [3]
Element
D0 (cm2/s)
Ea (eV)
D (cm2/s)
T (°C)
As
8.6 × 104
3.9
2.4 × 10−14
800
0.63
3.2
3.2 × 10−14
950
B
P
(1.5 – 6) ×
10−3
2.4 - 2.5
–
10−14
900
4 × 10−14
925
9×
–
6.9 ×
10−13
1000
7 × 10−13
1000
6.10 ELECTROMIGRATION
This is the phenomenon of transport of matter due to the flow of an electric current. It is thus different
from field-aided diffusion which is the enhancement of diffusion in the direction of an applied electric
field. It was found to be responsible as an important failure mechanism in semiconductor devices and
ICs operating at high current densities > 104 A/cm2.
When a metal conductor is placed in an electric field E, there are 2 forces acting on metal ions:
(i) force F1 due to the electric field E on the metal ions whose magnitude depends on the field and the
charge on the metal ion and is directed in the direction of E towards the negative terminal (ii) force F2
due to transfer of momentum from the electron flow to the metal ions and is directed in the opposite
direction towards the positive terminal (Fig. 6.15).
It is the second force that is found to dominate and cause failures. Ideally the simultaneous motion
of metal ions cannot cause void formation, but small variations in mobility of the ions along the length
of the conductor will cause metal ions to move at slightly different rates resulting in the eventual
formation of voids.
E
+V
-V
F1
F2
+
Conductor
Electron
+ Metal ion
Fig. 6.15 Electromigration phenomenon
According to the Nernst-Einstein diffusion relation the flux of material is given by
J = NDF/kT
...(6.44a)
where N = density of mobile species, D = their mobility and F = driving force. For the case of
electromigration
F = eE Z *
...(6.44b)
where E = electric field across conductor and Z * = effective charge on the metal atoms/ions.
DIFFUSION, OXIDATION
AND ION IMPLANTATION
381
Hence
J = N D eE Z */ kT
...(6.45a)
It was observed in thin conducting films of Al, Au etc that on prolonged passage of current there
was physical transport of material from one end to the other, with accretion occurring at one end and
depletion at the other end, often leading to open-circuit failure. The direction of transport was found to
be opposite to the direction of flow of current but in the direction of electron flow. Thus the driving
force of electromigration is the ‘electron wind’ which results in momentum transfer between the electrons and the metal atoms. Electromigration was found to be enhanced through grain boundaries and
hence is related to grain-boundary diffusion. The electromigration flux was found to be given by
Jem = Nb Dgb δ Zb* e E / d kT
...(6.45b)
where Nb = density of moving ions in the grain boundary, Dgb = grain diameter, δ = effective charge of
mobile ions in the grain boundary Zb* which may not be the same as in the lattice, d = width of grain
boundary. Values of many of these quantities are difficult to obtain experimentally.
Thus empirically it was found that the rate of metal transport is given by
R ∝ J 2 exp (− Ed / kT)
...(6.46)
where Ed is the activation energy for grain boundary diffusion in the material. Thus the mean time-tofailure (MTF) is found to be given by
MTF ~ (1/J 2) exp [Ed / kT]
...(6.47)
For Al, Ea ~ 0.4 for small grain and ~ 0.5 eV for large grain evaporated films. This is much lower than
the value of 1.4 eV found for self-diffusion in bulk single crystal Al. It was found that the MTF can be
increased by several techniques, the most common being alloying with 1.5 at% Si + 4 at% Cu which
has been found to increase MTF by a factor of ~10. Other possible alloying additives in Al are Ni and
Mg while for Au films Ta increases Ed considerably. Other techniques include encapsulating the conductor in a dielectric or increasing the grain size by heat treatment thereby reducing the density of
grain boundaries. The best solution at present is to restrict the current density J < 105 A/cm2.
6.11 OXIDE MASKING
Since semiconductor devices and ICs require selective area doping, masks are required to prevent
diffusion in certain areas. The properties of SiO2 are ideal for acting as a mask since the diffusion
coefficients of most impurities such as B, P and As are orders of magnitude smaller in SiO2 than in Si.
However SiO2 cannot act as a mask for Ga and Al, the latter attacking SiO2 reducing it to Si. SiO2 can
be grown easily on Si by thermal oxidation and windows etched in it by photolithography such that the
remaining areas act as masks. The windows permit impurity diffusion to form p-n junctions as required.
The minimum thickness of the SiO2 layers to act as a mask for a particular diffusion process must be
determined.
The diffusion process in SiO2 can be considered to consist of 2 steps: in the first the dopant
impurities react with the SiO2 to form a glass. As the process continues the glass thickness increases
until it penetrates the entire thickness of the oxide. At this point the second step commences – the
impurity after diffusing through the glass reaches the glass – Si interface and starts diffusing into the
Si. The first step is when the SiO2 is effective as a mask against a given impurity. The required oxide
thickness depends on the diffusivity of the impurity in SiO2. Typical diffusivities at 900° C, 1100° C and
1200° C are given in Table 6.8.
382 SEMICONDUCTOR MATERIALS & DEVICES
Table 6.8 Diffusivities of Dopants in SiO2
D at 900° C (cm2/s)
Element
3 × 10−19
B
Ga
P
1×
10−18
Sb
D at 1100° C (cm2/s)
D at 1100° C (cm2/s)
3 × 10−17 – 2 × 10−14
2 × 10−16 - 5 × 10−14
5 × 10−11
5 × 10−8
2.9 ×
10−16
9.9 ×
10−17
−2×
10−13
2 × 10−15 – 7.6 × 10−13
1.5 × 10−14
Figure 6.16 shows the minimum thickness of dry-oxygen grown SiO2 required as a mask against
B and P as a function of temperature and time. It is noted that P requires thicker masks for the same
diffusing conditions since it has a higher diffusivity in SiO2. For a given temperature the thickness d
varies as t1/2 since the diffusion length varies as (Dt)1/2. An oxide mask thickness of 0.5 – 0.6 μm is
adequate for most conventional diffusion steps.
t (hr)
1
10
10
T = 1200 °C
1
1100
P
Oxide mask thickness d(mm)
1000
900
10
-1
1200 °C
B
10
1100
1000
-2
900
10
-3
10
10
2
10
3
t (min)
Fig. 6.16 Minimum thickness of SiO2 required to mask against B and P diffusion [1]
DIFFUSION, OXIDATION
AND ION IMPLANTATION
383
6.12 IMPURITY REDISTRIBUTION DURING OXIDE GROWTH
During thermal oxidation dopant impurities are redistributed between the oxide and Si. This is because
when 2 solid surfaces are in contact an impurity will redistribute between the two until it reaches
equilibrium. This depends on several factors including the segregation coefficient k which is defined as
in the case of zone melting in Chapter 4, as
k = equilibrium concentration of impurity in Si/equilibrium concentration of impurity in SiO2.
Another factor is the rapid diffusion of the impurity through the oxide and escape into the ambient.
This will depend on the diffusivity of the impurity in the oxide. A third factor is the growth of the oxide
into the Si and the consequent motion of the Si-oxide interface. Thus the redistribution will depend on
the rate of movement of the oxide in comparison with the rate of diffusion of the impurity through the
oxide. Since the oxide layer is about twice as thick as the Si it replaces the same impurity will be
redistributed in a larger volume thus resulting in depletion of the impurity from Si even if k = 1.
SiO2
SiO2
Si
k<1
Slow diffusant
in SiO 2
(e.g., B)
1.0
C/CB
0
Si
1.0
k<1
Fast diffusant
in SiO 2
(e.g., B in H 2
ambient)
0
1.0
1.0
x(m m)
x(m m)
(a)
(b)
SiO2
SiO2
Si
Si
1.0
1.0
k>1
Fast Diffusant
in SiO 2
(e.g., Ga)
k>1
Slow diffusant
in SiO2
(e.g., P)
C/CB
0
1.0
x(m m)
(c)
1.0
0
x(m m)
(d)
Fig. 6.17 Redistribution of impurity between thermal oxide and Si (a) and (b) k < 1;
(c) and (d) k > 1 [1]
Four distinct cases may arise:
(i) k < 1 : the oxide takes up the impurity which diffuses slowly through the oxide. e.g. B with
k = 0.3. Consequently there is build-up of impurity in the oxide (Fig. 6.17(a))
(ii) k < 1 : the oxide takes up the impurity which diffuses rapidly out through the oxide. e.g. B
heated in H ambient, as H in SiO2 enhances the diffusivity of B (Fig. 6.17(b))
384 SEMICONDUCTOR MATERIALS & DEVICES
(iii) k > 1 : the oxide rejects the impurity and the diffusivity of the impurity in SiO2 is slow resulting
in build-up at the Si interface e.g. k = 10 for P, Sb and As (Fig. 6.17(c))
(iv) k > 1 : the oxide rejects the impurity and the diffusivity of the impurity in SiO2 is rapid so that
the impurity escapes from the solid into the gaseous ambient that there is overall a depletion
of the impurity e.g. Ga with k = 20 and a fast diffuser in SiO2 (Fig. 6.17(d))
In practice redistribution effects are important for B with the surface concentration being reduced
to 50% of its value in the absence of redistribution. For P the overall effect is negligible since the
redistribution and diffusion effects cancel each other out. The impurities in the oxide are hardly electrically active but they affect processing and device properties. The oxidation rate is affected by high
dopant concentrations in Si. Non-uniform distribution of impurities in the oxide affect the interfacestate properties.
6.13 LATERAL DIFFUSION
Diffusion of impurities into a semiconductor slice being treated as a 1-dimensional problem is valid
since the horizontal dimensions are much larger than the vertical diffusion depth. This is true except at
the edge of the oxide diffusion mask where the impurities can diffuse laterally below the oxide mask.
It is found that the ratio of lateral to vertical diffusion is between 65 –70 %. This obviously limits the
proximity between adjacent windows in the mask and poses one limit to device miniaturization.
A 2-dimensional diffusion equation is required to solve this problem. Numerical solutions of the
problem for different initial and boundary conditions are shown in Fig. 6.18. Contours of constant
doping concentration for a constant-surface-concentration diffusion C/CS are shown assuming that the
diffusion coefficient is independent of concentration. The contours give the location of junctions formed
by diffusion into a wafer with various doping concentrations. The x and y axes are normalized with
respect to (Dt)1/2. Taking a value of C/CS = 10−4 the appropriate constant-concentration curve shows
that the vertical penetration is 2.8 units compared with a horizontal penetration of 2.3 units.
Diffusion Mask
0 2.3
C/C s = 0.5
0.5
x/2 Dt
0.3
1.0
rj
0.1
1.5
0.03
0.01
2.0
0.003
0.001
0.0003
0.0001
2.5
3.0
-2.0
-1.0
0
y/2 Dt
1.0
2.8
2.0
Fig. 6.18 Lateral diffusion effects at the edge of an oxide mask window [1]
DIFFUSION, OXIDATION
AND ION IMPLANTATION
385
Lateral diffusion causes p-n junctions to have cylindrical edges with a radius of curvature rj. If the
mask has sharp corners the shape of the junctions near the corners will be roughly spherical. Cylindrical
and spherical junction regions have higher curvature and hence higher avalanche breakdown voltages
than for planar junctions with the same background doping concentrations.
Gas Immersion Laser Doping (GILD)
A variety of new techniques are being developed for the very shallow junctions (~ 0.05 μm) required
for the source and drain regions of state-of-the art MOS devices. Among these are very low energy
implantation, Plasma Immersion Doping and Gas Immersion Laser Doping (GILD). Since implantation
must be followed by anealing at temperatures ~ 1000 °C, this results in impurity redistribution which
increases junction depth. Plasma immersion doping uses ions from a glow discharge in BF2 for example
and gives high fluence at low energies. However this suffers from the presence of different types of ions
in a plasma and selectivity is a problem. In the GILD technique a Si wafer is immersed in a precursor
gas such as BCl3 which is adsorbed on the surface. High energy uv laser pulses are then incident on the
surface which results in surface melting and impurity diffusion. This technique has been used to achieve
B doping upto 4.2 × 1021/cm3 (8.4 at %), much above the solid solubility limit of 6 × 1020/cm3.
Superconductivity at ambient pressures has been observed for the first time by Bustarret et al. [4] in
such heavily doped Si:B. The transition temperature is however very low 0.35 K with a critical field of
0.4 T. The importance lies in the verification of earlier theoretical predictions of superconductivity in
diamond-structured materials.
6.14 EVALUATION OF DIFFUSED LAYERS
Three parameters which are important for the evaluation of diffused layers are:
(i) junction depth (ii) sheet resistance and (iii) the doping profile.
xj
n
+
0
NB
Log N(x)
xj
b
a
p
x
(a)
(b)
Fig. 6.19 Measurement of junction depth by beveling and staining
(i) The junction depth is the position below the surface xj where the dopant concentration equals
the background concentration. It can be found by forming a groove on the semiconductor
surface with a tool of radius R0. If the surface is then etched with a solution of HF + HNO3 (few
drops in 100 ml) the p-type region is stained darker than the n-type region. The junction depth
is then given by
xj = (R02 – a2)1/2 - (R02 – b2)1/2
...(6.48)
386 SEMICONDUCTOR MATERIALS & DEVICES
where a and b are as indicated in Fig. 6.19. If R0 >> a, b, then
xj (a2 – b2)/2 R0
...(6.49)
The above technique is subject to errors of geometric measurement and is often superceded
by an optical interference technique. This is similar to that described in Chapter 7 for thin film
thickness measurement. The sample surface is lapped at an angle of 12°. An optical flat is
placed on the upper surface of the wafer which is illuminated by collimated monochromatic
radiation from a Na vapour lamp at 589.593 and 588.996 nm. The resulting interference fringe
pattern gives directly the junction depth in terms of the fringe spacing which is ~ 0.29 μm.
Another technique not employed in industry but useful in R & D laboratories where a SEM
is available is Electron Beam-Induced Current (EBIC) outlined in Chapter 5. After angle lapping as above an electron beam is used to scan the edge of the sample and the beam-induced
current measured. The current goes to zero and changes sign as the beam crosses the junction,
the beam diameter being an important factor in the accuracy of the measurement.
(ii) If the junction depth xj and the background doping concentration NB are known the surface
concentration NS and the impurity distribution can be calculated provide the doping profile
follows the Constant-Source or Instantaneous Source profiles given by eqns. (6.10) & (6.12).
Other techniques of determining the impurity profile are by C-V measurements of a reversebiased junction which determines the majority carrier or ionized impurity profile (if the impurity
atoms are fully ionized). This is discussed in Chapter 8.
A direct technique is using Secondary Ion Mass Spectroscopy (SIMS) discussed in Chapter
7. In this atoms are sputtered off by energetic ions and detected in a mass spectrometer. Thus
a small crater is formed whose depth can be measure by a stylus. The mass spectrometer
detects the different species and plots the counts vs. time of sputtering. This technique has high
sensitivity for B and P and plots the doping profile and finds the junction depth as well. It is
ideally suited for very shallow junctions and high doping concentrations and has depth resolution
~ 10 nm. One difference is that SIMS detects total number of ions present while the
C-V and such techniques finds the concentration of ionized impurities. For B & P in Si all
impurities are ionized at 300 K but in the case of impurities with deeper levels this will not be
the case and hence SIMS will give a higher value than that obtained by the C-V technique.
(iii) The sheet resistance RS of a diffused layer can be measured using the 4 point probe
technique described in Chapter 1. This is related to the junction depth xj and the carrier mobility
μ (which is a function of the total impurity concentration) and the impurity distribution N(x) by
RS
F
=1 / Gq
GH
z
xj
0
I
a f JJ
K
m N x dx
...(6.50)
For a given diffusion profile the average resistivity ρ = RS xj is uniquely related to the surface
concentration NS and the background concentration NB for an assumed doping profile. Design curves
are available relating the measured ρ with NS for erfc and Gaussian doping profiles. Diagrams plot NS
vs. RS . xj with Np as a parameter for the above 2 profiles for n and p-type dopants. Thus measuring RS
and xj and knowing NB , the surface concentration NS can be found. This method is accurate for low
concentrations and deep diffusions provided the profiles follow the assumed types. For high concentrations
and heavy doping the diffusion profiles cannot be represented by the simple functions as discussed
earlier.
DIFFUSION, OXIDATION
AND ION IMPLANTATION
387
6.15 THERMAL OXIDATION
The Si-SiO2 system together comprise an unique combination which is at the heart of modern IC
technology and which keeps it ahead of other semiconductor materials with inherently superior properties. In comparison, the thermally grown oxide on GaAs is non-stoichiometric consisting of both
gallium and arsenic oxides and does not have the desirable properties of SiO2. Amorphous SiO2 can be
grown or deposited by a number of techniques but it is the thermally grown oxide which has been found
to have the most desirable superior properties. Recently due to its relatively low dielectric constant
there have been attempts to replace SiO2 by other oxides for nanoscale devices with some recent
success. These attempts are discussed in Chapter 10. SiO2 has the following important functions in
modern IC technology:
(i) it serves as the gate dielectric i.e. ‘gate oxide’ in MOS devices giving very low interface state
density and high breakdown field
(ii) it gives surface protection after device fabrication with edges of p-n junctions buried under an
oxide layer. It also acts as a ‘field oxide’ in an IC and serves to isolate devices from each other.
(iii) it acts as a diffusion barrier permitting the diffusion of dopants only through windows etched
in it
(iv) it is an excellent dielectric which serves as a substrate on which metal interconnects between
devices are made and also as an interlayer insulator.
Properties
The properties of crystalline SiO2 have been discussed in Ch 2. Here we are concerned with amorphous
or fused silica with a softening point of 1710° C, which is grown on single crystal wafers by controlled
Oxygen
0
2.27Å
1.60 Å
Silicon
Si
0
0
0
(b)
(a)
(c)
Fig. 6.20 (a) Si–O tetrahedra (b) structure of crystalline and (c) amorphous SiO2
388 SEMICONDUCTOR MATERIALS & DEVICES
heating in dry or wet environments. Structurally it consists of a 3-dimensional random network of Si
and O, having coordination numbers of 4 and 2 respectively, forming polyhedra (tetrahedral and triangles) with Si4+ at the centre and O2− at the corners (Fig. 6.20). The distance between Si - O ions is 1.62
Å while that between O - O is 2.27 Å. These polyhedra are randomly stacked and joined by bridging
and non-bridging oxygen. Crystalline SiO2 contains only bridging oxygen and has a density of 2.65
compared with 2.15 – 2.25 for amorphous SiO2. The atomic packing fraction (APF) is only 0.43.
The principal defects in fused silica are O ion vacancies which represent positively charged defects.
Fused silica has an open structure which permits interstitial diffusion of impurities. The diffusion of O2.
H2O, H2 and Na are represented by Arrhenius plots. The activation energies for O2 and H2O are 1.18
eV and 0.79 eV respectively while H and Na have very high diffusivities with low activation energies.
Na is important as a contaminant in the thermal oxide. Oxidation involves the transport of a charged
species O2− or O22− through silica to the SiO2 – Si interface where the oxidation takes place.
6.16 OXIDATION SYSTEM
A reactor used for thermal oxidation of Si is shown in Fig. 6.21. It consists of a horizontal resistanceheated furnace with a cylindrical fused silica tube containing the Si wafers mounted vertically in a
slotted quartz boat. The furnace is designed to have a long flat zone in which the temperature can be
controlled from 900 °C to 1200 °C within ± 1 °C. One end of the furnace has provisions for the flow
of pure dry oxygen or water vapour while the other end opens into a vertical flow clean air bench where
the wafers can be loaded into the reactor. The hood is designed to keep out particulate matter and
minimize contamination during wafer loading. Gas flow, insertion and withdrawal of wafers as well as
the furnace temperature are micro-processor controlled. The furnace temperature is ramped up and
down to prevent thermal shock to the wafers. Utmost cleanliness is essential in wafer handling as well
as in maintenance of the diffusion tube which must be cleaned at intervals. In special cases the slotted
quartz boat can be replaced by one made of polysilicon.
Resistance
heater
Filtered
air
Ceramic
comb
support
Silicon wafers
O2 or
H2 O +
Carrier
gas
To vent
End cap (Quartz)
Fused quartz boat
Fused quartz
furnace tube
Exhaust
Fig. 6.21 Schematic diagram of reactor for thermal oxidation of Si
Wet oxidation gives a relatively porous oxide which can be used for diffusion masks and for surface
coverage. Steam causes etching and pitting, hence a carrier gas (oxygen, nitrogen or argon) is passed
through a bubbler containing water at 95 °C corresponding to a vapour pressure of 640 torr (0.84 atmos)
DIFFUSION, OXIDATION
AND ION IMPLANTATION
389
Kinetics of Oxidation
Thermal oxidation of Si by dry oxygen or water vapour consists of the following reactions:
Si (s) + O2 (g) → SiO2 (s)
...(6.51)
...(6.52)
Si (s) + 2 H2O (g) → SiO2 (s) + 2H2 (g)
The Si – SiO2 interface moves into the Si during oxidation with a fresh interface available for
oxidation. Since the densities of Si and SiO2 are 2.33 and 2.21 gm /cm3 respectively and the molecular
weights are 28.09 and 60.08 respectively it can be shown that an oxide thickness tox consumes a layer
of Si of thickness 0.44 tox. Thus the oxide consumes Si as well as expands by 0.56 tox beyond the
original surface as shown in Fig. 6.22.
SiO2 surface
Original Si Interface
SiO2
Silicon substrate
(a)
Oxidant
Oxide
Semiconductor
C
d
CO
CS
F2
F1
x
0
d
(b)
Fig. 6.22 (a) Growth of SiO2 on Si by thermal oxidation (b) Model for
thermal oxidation of Si
390 SEMICONDUCTOR MATERIALS & DEVICES
The oxidation process consists of
(a) diffusion of O species through the silica
(b) reaction of O with Si at the Si – Si O2 interface and
(c) rapid out-diffusion of H2 through the silica film.
The growth kinetics can be examined using the model shown in Fig. 6.22(b). Here the oxidant
species with surface concentration N0 molecules/cm3 is brought into contact with the a-SiO2 surface.
The magnitude of N0 is essentially the solid solubility of the species at the oxidation temperature
which is:
At 1000° C and 1 atmos. pressure: Dry oxygen – 5.2 × 1016 molecules/cm3
Water vapour – 3.0 × 1019 molecules/cm3
Suppose the concentration of the oxidizing species at the Si-SiO2 interface is N1. Transport of the
species occurs by both drift and diffusion. Drift is ignored in this analysis. If the diffusion coefficient
is D, the flux density arriving at the interface is given by Fick’s first law:
J1 = D (∂N/∂x) = D (N0 − N1)/x
...(6.53)
where x = thickness of the grown oxide at a given time.
The species then reacts with the Si surface the flux being assumed to be proportional to the
concentration N1 of the species at the surface. Thus
J2 = kN1
...(6.54)
where k = interfacial reaction rate constant. Under steady-state diffusion conditions these fluxes must
be equal. Thus combining eqns. (6.53) and (6.54)
...(6.55)
J = D N0 /(x + D/k)
Let n = no. of molecules of the oxidizing species that are incorporated into unit volume of the
oxide. There are 2.2 × 1022 SiO2 molecules/cm3 in the oxide and for oxidation one molecule of O2 is
required (eqn. 6.51) compared with 2 molecules of H2O (eqn. 6.52). Thus for oxidation in dry O2
n = 2.2 × 1022 molecules/cm3 and for wet oxidation n = 4.4 × 1022 molecules/cm3 Thus the rate of
change of the oxide layer thickness is given by
dx/dt = j/n = D N0 /n (x + D/k)
...(6.56)
Solving this equation with the boundary condition x = 0 at t = 0 gives
x2 + (2 D/k) x = (2 D N0 /n) t
...(6.57)
Thus
x = (D/k) [(1 + 2 N0 k2 t/D n)1/2 − 1]
This is a general expression for the oxide thickness as a function of time t.
For very small t this reduces to
x = (N0 k/n) t
...(6.58)
...(6.59)
and for large values of t
...(6.60)
x = (2 D N0 /n)1/2 t1/2
Thus initially the growth is linear with time and limited by the rate constant k while for longer times
the growth is parabolic with the diffusion constant D being the limiting factor.
Eqn. (6.57) can be simplified to be written as
x2 + Ax = B t
...(6.61)
DIFFUSION, OXIDATION
AND ION IMPLANTATION
391
Eqns (6.59) and (6.60) can then be written
for the linear region as
x = (B/A) . t
...(6.62)
and for the parabolic region as
x = B1/2 t1/2
...(6.63)
B/A = No k/n.
...(6.64)
where the linear rate constant
and the parabolic rate constant
B = 2 D No/n
...(6.65)
A = 2 D/k
An initial oxide layer of thickness d0 may be present. This is easily taken care of in the analysis,
eqn. (6.57) being modified to
...(6.66)
x2 + (2 D/k) x = (2 D N0 /n)(t + τ)
τ = (d02 + 2D d0/k) N1/2 D N0
where
...(6.67)
T(°C)
1200
10
10
1100
1000
900
800
700
1
H2O (760 torr)
0
Ea = 2.05 eV
Linear rate constant B/A (mm/hr)
(111) Si
(100) Si
-1
10
10
-2
Dry O 2
Ed = 2.0 eV
(111) Si
(100) Si
10
10
-3
-4
0.6
0.7
0.8
0.9
1.0
-1
1000/T(K )
Fig. 6.23 Linear rate constant vs temperature
1.1
392 SEMICONDUCTOR MATERIALS & DEVICES
which represents the time for the growth of the initial oxide layer. Eqns. (6.59) and (6.60) are then
modified to
x = (N0 k/n). (t + τ) or x = (B/A) (t + τ)
...(6.68)
x = (2 D N0 /n)1/2 (t + τ)1/2 or x2 = B (t + τ)
and
...(6.69)
For wet oxidation d0 ≡ 0 but for dry oxidation the extrapolated value of d0 ≡ 20 nm at t = 0.
Experimentally determined values of the linear rate constants B/A as a function of temperature are
given in Fig. 6.23 for dry and wet oxidation. The linear rate constant B/A varies as exp (−Ea / kT) for
both dry and wet oxidation with Ea = ~ 2 eV for both cases. This agrees reasonably well with the energy
of 1.83 eV/molecule required to break the Si-Si bond. The growth rate for wet oxidation is larger
because of a higher value of the rate constant k.The oxidation rate is orientation dependent since the
density of Si atoms on (111) plane is higher than that on the (100) plane thus providing more sites for
incorporation into the SiO2 network.
The parabolic rate constant B is plotted in Fig. 6.24 as a function of temperature. The activation
energies for wet and dry oxidation are different as expected since in this region the growth is diffusion1200
10
1100 1000
900
800
700
600
550
0
H2O (760 torr)
-1
Ea = 0.71 eV
2
Parabolic rate constant B ( mm /hr)
10
10
-2
O2 (760 torr)
10
-3
Ea = 1.24 eV
10
-4
0.7
0.8
0.9
1.0
1.1
Fig. 6.24 Parabolic rate constant vs temperature
1.2
DIFFUSION, OXIDATION
AND ION IMPLANTATION
393
limited. Ea for dry oxidation is 1.24 eV, comparable to the activation energy for diffusion of oxygen in
fused silica. For wet oxidation Ea = 0.71 eV comparable to the activation energy of water in fused silica.
The parabolic rate constant B is independent of orientation because diffusion takes place through a
random network in amorphous silica.
While dry oxidation provides the highest quality oxide for gate dielectrics with high density and
low concentration of traps and interface states, the growth rate is much slower and hence longer time
is required for a thick oxide. Hence, thin gate oxides < 100 nm are grown by dry oxidation while thick
field oxides ~ 500 nm are grown by wet oxidation or a combination of dry-wet-dry steps to provide
better interfacial layers.
Ultra-thin Oxides
In VLSI and ULSI technology with reduced device dimensions the oxide thickness is required to be
< 20 nm. It has been seen that an initial oxide layer of this order of thickness exists and hence the above
theory is not valid for very thin oxide layers. In the early stages of oxide growth large compressive
stress exists in the oxide which reduces the diffusion coefficient of O in the oxide. Thus for thin oxides
the term Ax in eqn. (6.61) can be neglected i.e. D/k is considered very small. Thus this eqn. becomes
x 2 − d02 = Bt
b
g
where from eqn. (6.66) d 0 = 2 DN 0 τ N1
...(6.70)
12
is the initial oxide thickness extrapolated to t = 0. The initial growth in a dry oxide thus follows a
parabolic law. Figure 6.25 shows the oxide thickness vs oxidation time for the growth of dry oxide at
400
1030 °C, 0.5 ATM
980 °C, 0.1 ATM
(a)
Oxide thickness (Å)
300
1030 °C, 0.1 ATM
930 °C, 0.1 ATM
200
1030 °C, 0.02 ATM
1030 °C, 0.01 ATM
100
(b)
0
20
40
60
Oxidation time (min)
Fig. 6.25 Oxide thickness vs. time for thin dry oxides
80
394 SEMICONDUCTOR MATERIALS & DEVICES
different temperatures and oxygen partial pressures. The solid lines are for the parabolic oxidation
equation. It is observed that the initial oxide thickness at t = 0 is d0 = 2.7 nm.
Since B = 2DN0 /n and N0 is proportional to the partial pressure P of the oxidizing species in the gas
phase, the rate of oxidation depends strongly on the partial pressure as seen from Fig. 6.25.
High Pressure Oxidation
The dependence of the oxidation rate on the partial pressure of oxygen thus provides the possibility of
increased rate of oxidation at high pressures. Thus oxidation in high pressure steam can substantially
reduce the time for the growth of thick field oxides and grow these at comparatively low temperatures
at high pressure. This is advantageous in that it minimizes the movement of previously diffused or
implanted impurities. Figure 6.26 gives the oxide thickness as a function of steam pressure at 2 temperatures for 1 hour oxidation. Analysis using a linear-parabolic model as before shows that both the
linear rate constant B/A and the parabolic rate constant B have a linear dependence on pressure. This
is because B itself is proportional to partial pressure. Such oxidation is carried out in high pressure
stainless steel autoclaves.
4.0
(111)
(100)
t = 1 hr
920 °C
Oxide thickness ( mm)
1.0
750 °C
0.1
0.01
0.6
1
10
Steam pressure (atm)
40
Fig. 6.26 Oxide thickness for high pressure oxidation in steam