Chapter 1
Overview of Processes
1.1    Evaporation
1.1.1     Kinetická teorie plynů
Maxwell-Boltzmannovo rozdělení rychlostí
m   \3/2        /   mV
™=»(^r«>(-w)-              (ll)
Předpokládáme, že u = 0 nebo se pozorovatel pohybuje střední rychlostí plynu => v = V:
*, x a          /   m   \3/2        /   mv2\  ,o
nv)*' = n(*är)   exp{-m)llv-                    (L2)
Protože M.-B. rozdělení je izotropní, můžeme definovat rozdělení velikosti rychlosti v = |v|. Přejdeme do sférických souřadnic
d3v = v2 sin 6(16(1(1).                                                     (1.3)
Rozdělovači funkce rychlostí F (v)
F(v)dv=  í í f (v)v2 sin 6(16d^dv                                         (1.4)
Je J<j>
a tedy
t-,/ s      ,      /   m   \3/2         of   mv2\                                     ,_,   .
f{v) = aH-^ť)    ^v 2{-lä)                    (L5)
Střední hodnota velikosti rychlosti
1   ľ                1   f°°
< v >= - / fv(rv = - /     F(v)vdv                                      (1.6)
n J v               n Jo
a po výpočtu
< v >= (8/7r)1/2(fcT/m)1/2.                                              (1.7)
Tok částic
Tn = n <vn>=  / /v • ňd3v                                             (1.8)
J v
je pro náhodný pohyb částic roven nule. Jaký je tok na jednu stranu myšlené plochy?
í kT \ l/2      1
T = n------        =-n<v>                                            (1.9)
\27rmJ          4
1
1.1.   EVAPORATION
CHAPTER 1.   OVERVIEW OF PROCESSES
Stavová rovnice
^ = NkB^^=nkB                                   (1.10)
Z této rovnice dosadíme za n v (1.9) a dostáváme
T = p(2irkBTm)-l/2                                                  (1.11)
1.1.2     General Considerations
Thermal evaporation or vacuum evaporation (purely physical process) is composed of following sequential basic steps:
1.   Generation of Vapor by sublimation or evaporation of solid or liquid material, respectively => heating to sufficiently high temperatures.
2.   Transportation of vapor from the source to a substrate.
3.   Condensation of vapor as a solid film on a cooler substrate surface.
Thin films of carbon deposited by evaporation inside an electric bulb were probably first observed by Edison. Historically, however, the deposition of a metal film from a wire exploded by a high current density is attributed to Faraday, and by vacuum evaporation to Nahrwold, Pohl and Pringsheim.
Because of collisions with ambient gas atoms, a fraction of the vapor atoms will be scattered and hence randomized in direction in a distance d during their transfer through the gas. The flux of particles at the distance d that did not undergo any collision is given as
r(d) =T0exp(-d/A).                                                 (1.12)
Here A is the mean free path of gas atoms which for air molecules at 25 °C and pressures 10~2 and 10~4 Pa is about 60 and 6000 cm. Thus, pressures lower than 10~3 Pa are necessary to ensure a straight-line path for most of emitted vapor atoms, for substrate-to-source distances of «10 to 60 cm in a vacuum evaporator.
The rate of free evaporation of vapor atoms from clean surface of unit area in dimensions m_2.s~l is given by the Langmuir expression:
revap = Pev(^kBTevmev)~1/2                                           (1.13)
where pev and Tev are equilibrium vapor pressure and temperature of evaporated material, respectively, mev is mass of vapor molecules and kB is Boltzmann constant. It is the same equation as for the flux of particles (1.11) because of particle conservation law.
The rate of evaporation can be alternatively expressed in dimensions kg.m_2.s~l
Deposition rate from clean, uniform emitting point source onto a plane receiver varies as cos6/r2 (Knudsen cosine law), where r is the radial distance of the receiver from the source and 9 is the angle between the radial vector and the normal to the receiver direction. If to and t are the thicknesses of deposits at the receiver vertically below the source at a distance h, and a at a horizontal distance x from the vertical line, respectively, then the deposit distribution (assuming the same condensation coefficient) is given by
t _            1
h = [i + (^A)2]3/2'                                               (1'15)
2
CHAPTER 1.   OVERVIEW OF PROCESSES
1.2.   CHEMICAL REACTIONS
For evaporation from a small area onto a parallel plane receiver, the deposition rate is proportional to cos2 6/r2 and the thickness distribution is given by
íl                                                             ,
(1.16)
ío      [l + (x/W
In both cases, the thickness decreases by about 10% for x = h/4.
A parameter of interest in understanding the influence of ambient gases on the properties of films is the impingement rate of gas atoms or molecules. This is given by the kinetic theory of gases under equilibrium conditions (1.11)
rg=pg(27rfcBTgmg)-1/2.                                              (1.17)
The Table ?? lists the mean free paths, impingement rate and other related quantities for air molecules at different pressures. Note that at constant gas and evaporation temperatures, the ratio Tg/Tevap ~ Pg/Pevap- From Table ?? implies that under commonly employed experimental conditions of vacuum (~ 10~3) and deposition rate (~ lA/s), the impingement rate of gas atoms is relatively quite large, so that if the sticking coefficient of gas atoms is not negligible small, a considerable amount of gas sorption could occur.
1.2    Chemical Reactions
Chemical reactions can involve gas, liquid or solid phases. The reaction is called homogeneous if the reactants are in the same phase, while heterogeneous reactions have reactants in two or more phases. Reactions that take place on the surface of a catalyst of a different phase are also heterogeneous. A reaction between two gases, two liquids or two solids is homogeneous. A reaction between a gas and a liquid, a gas and a solid or a liquid and a solid is heterogeneous.
1.2.1     Reaction Rate
We consider an isolated volume in the reactor. This volume contains one single fluid (gas or liquid) phase only. It is uniform in composition and temperature. If the reactor is spatially uniform, the representative volume is the total volume; if not, the representative volume is limited to a differential element.
The rate of a homogeneous reaction is determined by the composition of the reaction mixture, the temperature, and the pressure. The pressure can be determined from an equation of state together with the temperature and composition. Thus, we focus on the influence of latter factors.
Consider the reaction
aA + bB...—>qQ + sS...                                            (1.18)
It can be stated that A and B react at rate
dNA      ,          dNB
rA = -^r rs = -^r                      (L19)
and Q and S are formed at rates
dNs      ,          dNQ
dt      Tq ~      dt
>'S = -^    >*« = -^                                                   (L»)
where Nj represents the molar amount of one of the chemical species in the reaction (from here in kmol), and t is time.
The following equalities exist between the different rates
_1 dNA = _1 dNe = 1 dNQ = 1 dNs_ a   dt           b   dt        q   dt        s   dt
3
1.2.   CHEMICAL REACTIONS
CHAPTER 1.   OVERVIEW OF PROCESSES
Each term of these equalities may be considered as the rate of the reaction.
This can be generalized to the case of N chemical species participating in M independent chemical reactions,
diiAx + ai2A2 + ... + aiNAN = 0                                       (1.22)
nebo
N
0 = J2aiJA3    i = 1,2,... M                                           (1.23)
i=i
with the convention that the stoichiometric coefficients a%j are taken positive for products and negative for react ants.
The rate of reaction is generally expressed on an intensive basis, say reaction volume, so that when V represents the volume occupied by the reaction mixture,
1   1   SdNj\                                                     .     „
V aij \ dt )i
For the simpler case,
-ldNA      -1 d                 -1 Í.JCa          dV\
r = ^v^f = ^yJt{CAV) = äv [v-ďT + Ca^J                (1-25)
where C a represents the molar concentration of A (kmol/m3). When the reaction volume does not vary
-ldCA                                                         n o^
r =-------;—.                                                        (1-26)
a    dt                                                           v       '
In this case it suffices to measure the change in concentration to obtain the rate of reaction.
1.2.2     Conversion and Extent of Reaction
Conversions, rather than concentrations, are often used in the rate expressions, as follows:
x'a = Nao-Na    x'b = NB0-Nb                                       (1.27)
or for constant volume
x"a = CAq-Ca    x"b = Cbo-Cb.                                       (1.28)
Most frequently, fractional conversion are used
Nao - NA              Nm - NB
XA = ^aV~    XB = ^r-                    (L29)
which show immediately how far the reaction has progressed.
One must be very careful when using the literature because it is not always clearly defined which kind of conversion is meant. The following relations may be derived easily from Eqs. (1.27)-(1.29):
(1.30)
(1.31)
nr       ~~                                                            (1-32)
	Xj     -	=     NiOXj
xA	xB	_XQ
a	b T.TD	Q b Nao ----------------------T. A
4
CHAPTER 1.   OVERVIEW OF PROCESSES
1.2.   CHEMICAL REACTIONS
An alternate but related concept to the conversion is the extent or degree of advancement (stupeň rozvoje reakce) of the general reaction Eq. (f .23), which is defined as
,      Ni - Ni0
e = ——-                                                       (1-33)
ay a quantity that is the same for any species. Also,
Nj = NjQ + aj£                                                     (1.34)
where Njo is the initial amount of Aj present in the reaction mixture. For multiple reactions,
M
W; = iVj-o + 5>y&.                                                 (1-35)
i=\
Eqs. (1.29) and (1.34) can be combined to give
Nj = Njo + ctj—XA.                                                (1-36)
If species A is the limiting reactant (present in least amount), the maximum extent of reaction is found from
0 = iV^o + a^max                                                   (1-37)
and the fractional conversion defined by Eq.(1.29) becomes
XA = t^-.                                                         (1-38)
S max
Either conversion or extent of reaction can be used to characterize the amount of reaction that has occured. For industrial applications, the conversion of a feed is usually of interest, while for other scientific applications, the extent is often more useful.
In terms of the extent of reaction, the reaction rate Eq. (1.24) can be written
l~ val3 \dt )r v df                            [    j
With this rate, the change in moles of any species is, for a single reaction,
dNj = a3Vr                                                       (1.40)
and for multiple reactions
dt
rlN        M
-± = Y^al3Vrl = VRr                                             (1.41)
i=\
1.2.3    Order of Reaction
Based on experimental observation and later explained by the collision theory, it is found that the rate of reaction in Eq. (1.18) can be expressed as
r = kcCACbB.                                                       (1.42)
The proportionality factor kc is called the rate coefficient, or rate constant. By definition, this rate coefficient is independent of the quantities of the reacting species, but is dependent on the
5
1.3.   INTERACTION OF IONS WITH SOLID CHAPTER 1.   OVERVIEW OF PROCESSES
other variables that influence the rate. When r is expressed in kmol m 3 hr 1, then kc has dimensions
(kmol/m3)1-(a+6+-)hr-1                                              (1.43)
The dimensions of the rate coefficient used with the conversions are the same as those given for use with the concentrations. Partial pressures may also be used as a measure of the quantities of the reacting species,
r = kppaApbB.                                                                  (1.44)
In this case the dimensions of the rate coefficient kp are
(kmol/m3)hr-1Pa-(a+6+-)                                             (1.45)
According to the ideal gas law
so that
a = £                                          (1.46)
kc = kp(RT)a+b+-.                                                   (1.47)
The powers a, b, ... are called "partial orders" of the reaction with respect to A, B... The sum a + b + ... may be called the "global order", or generally just "order" of the reaction. In reality, the orders in the above equations should be replaced by the quantities a', b', ... that do not necessarily coincide (only for elementary processes) with the stoichiometric coefficients a, b, ... but has to be determined experimentally. Only for elementary reactions does the order have to be 1, 2, or 3. When the stoichiometric equation (1.18) is only an "overall" equation for a processes consisting of several mechanistic steps, the order cannot be predicted on the basis of this stoichiometric equation.
For an irreversible first-order constant volume reaction, we have
r a = ~ = kCA.                                    (1.48)
When the rate coefficient k (hr-1) is known, Eq. (1.48) permits the calculation of the rate r a for any concentration of the reacting component. Conversely, when the change in concentration is known as a function of time, Eq. (1.48) permits the calculation of the rate coefficient. This method for obtaining k is known as the "differential" method. Integration of Eq. (1.48) leads to
kt = In (^-\                                       (1.49)
and a semilog plot of Cao/Ca versus t gives k.
1.3    Interaction of Ions with Solid
6
Chapter 2
Interaction of ions with solids
Interaction of ions or atoms with solids is a part of many material processing techniques because it can result in structural changes of the material, implantation of incident particles or sputtering of the material. Additionally, several physical methods of material and surface characterization are based on detection of reflected or released particles resulting from ion/atom bombardment. The emitted particles include atoms or ions of the material, electrons, photons and products of nuclear reactions. All the processes initiated by an impact of ion or atom projectile are schematically shown in Fig. ??.
The processes caused by impact of an ion or an atom on a surface depend on several parameters such as the energy of incident projectile (-£4,0), angle of incidence with respect to the surface normal, incident flux (7;), mass and atomic number of the projectile (M; and Z;, respectively), mass and atomic number of the target atom (Mt and Zt, respectively), and the charges of the projectile and target atom. At the conditions relevant to the material processing, the interaction of the projectile with the solid can be divided in two different mechanisms
•  nuclear collisions, i.e., elastic collisions with atoms
•  electronic collisions, in which electrons are excited or ejected from the material. At high energies ...nuclear reaction have to be taken into account.
2.1    Ion stopping
As mentioned above the projectile penetrating a solid is slowed down by interactions with the electrons and atoms of the material. The energy lost per unit path length dx
* = -f
is called stopping power or, less frequently, specific energy loss.  The stopping cross section is
defined as
IdE                                                           ,     .
S = ——                                                            2.2
n ax
or
I dE                                                           ,     .
S = ——                                                            2.3
q ax
where n is the volume density in atoms/cm3 and q is the mass density in kg/cm3. The quantity S is called sometimes also the stopping power.
Generally, the total energy loss experienced by the projectile moving through the material is obtained as a sum of nuclear and electronic contributions:
S = Sn + Se.                                                         (2.4)
7
2.1.   ION STOPPING
CHAPTER 2.   INTERACTION OF IONS WITH SOLIDS
At projectile velocities vi;o significantly lower than the Bohr velocity of the atomic electrons (vq), the projectile carries its electrons and, in case of ion, it tends to become neutralized by electron capture. At these velocities elastic collisions with the target nuclei, i.e., the nuclear energy losses, dominate. As the velocity is increased the interaction with the material electrons leading to inelastic collisions (electronic stopping) becomes more important. The term inelastic is used to signify that the collisions may result both in excitations of bound electrons of the medium, and in excitations of the electron cloud of the ion.
2.1.1     Nuclear Stopping
Kinematics of Binary Elastic Collision
In nuclear collisions the mass of the incident particle is comparable with the mass of target atom. Therefore, the elastic nuclear collision can involve significant discrete losses of projectile energy, a significant angular deflection of projectile trajectory and a creation of energetic recoil atoms. It implies from the energy and momentum conservation laws that the energies of the projectile and the recoil atom after the collision, En and Et, respectively, are given by
Eiyi    =   KEifi Et    =    (l-K)Ei>Q
(2.5) (2.6)
where K is the kinematic factor determined by the relative mass Mi/Mt and the laboratory angle 6\ of scattered projectile. If the mass of incident particle exceeds the mass of the target atom, Mi/Mt > 1, the kinematic factor is given by:
K =
If Mi/'Mt < 1 the expression is reduced to
cos 0\ ±
f2 - «m2 Oi
1/2-
Mt +1 Mi ^ x
(2.7)
K =
cos#i+(f|2-sin2^1/2
-i 2
Mt  +1 Mi ^ x
(2.8)
The energy transfered to the target atom can be expressed by simplification of Eq. (??) as
4MM           2 9C
Et = (mTmF     2" Ei'°
(2.9)
where 6C is the center-of-mass scattering angle.
Dynamics of Binary Elastic Collisions and Scattering Cross Section
Irradiation of material by ions or atoms is the interaction of many particles. Therefore, it is conveniently described by a statistical approach that introduces a measure of scattering probability. We consider the particles incident at a distance b off-center from the target particle. The situation of the scattering event is depicted in Fig. ??. The quantity b is the impact parameter and particle flux will be denoted as T. The conservation of particle flux requires that the particles incoming through the differential area bdbdcfti leave, after the scattering, through the differential solid angle proportional to dQ defined by the scattering angle 9i and the orientation of the scattering plane (/>; as
dQ. = únOidOidcpi.                                                        (2.10)
8
CHAPTER 2.   INTERACTION OF IONS WITH SOLIDS
2.1.   ION STOPPING
The proportionality constant is the differential scattering cross section a(9i,<fii):
Tbdbd<t> = o(6h<t>-l)Tdi1.
(2.11)
Since both sides of Eq. (2.11) are equal to the number of particles scattered per unit time, dN/dt, the differential scattering cross section is the number of particles scattered per unit time and unit incident flux into the solid angle dQ:
'(*.« = 5^0                               (2J2)
The differetial scattering cross section is obtained from Eqs. (2.10) and (2.11) as
a(9i,fr) =
sin#i
db
dOi
(2.13)
The quantity db/d9 is determined from the scattering force. The absolute value is used since 9 normally decreases with increasing b whereas a(9i,(f)i) is inherently a positive quantity.
We can calculate the total scattering cross section at by integrating a over the solid angle
at =      a(9i,^i)dÜ = /      /   <r(0i,0i)d0#.                                   (2.14)
Jn                          Jo    Jo
Both a(9i,(pi) and at depend on the magnitude of relative particle velocity. In the case of central force, the interaction potential depends only on the particle separation r. Such potential is isotropic and the differential scattering cross section is independent of <fi:
at = 2vr /    a{9-l)d9. lo
(2.15)
Namely, this is the case of Coulomb force.
Consider static target particles having density nt- For infrequent collisions within dx, the number of incident particles per unit volume at x that undergo an interaction within a differential distance dx, removing them from the incident beam is according to Eq. (2.12)
dn = —atotnritdx.
(2.16)
When studying the nuclear stopping it is useful to know the probability that a projectile with energy ü^o will transfer an amount of energy between Et and Et + dEt to a target atom. Such probability function defines the differential energy-transfer cross section aE(Et) that is related to a(9i,(pi) by
aE(Et)dEt = a{9h (f)i)d9id(f)i.                                                (2.17)
In order to determine differential cross section from Eq. (??) it is necessary to establish a relation between the impact parameter b and the scattering angle 9\. We can derive a general formula without knowledge of an exact expression of the interaction force for the force acting along a straight line joining the two particles. Such central force F(r) = F(r)r is related to the potential energy U(r) by
dU(r)„
F(r) = -VU{r)
Then, the scattering angle 9\ is expressed by
f°°   b 0i(M)=7T-2 /      -,   1
dr
-r.
(2.18)
hl
where v is relative velocity of interacting particles and rn given by
2f/(rmin)
2U{r)
ßV*
-1/2
= b
1
[IV c
dr                              (2.19)
is the distance of the closest approach
-1/2
(2.20)
9
2.1.   ION STOPPING
CHAPTER 2.   INTERACTION OF IONS WITH SOLIDS
Interatomic Potentials
The interaction of two atom nuclei is described by Coulomb potential energy
Uc(r) = J-***.                                                 (2.21)
Ak£q     r
However, the interaction of two atoms involves also influence of atomic electrons in dependence on the interatomic distance. There are two useful reference points that scale the problem, the Bohr radius of the hydrogen atom, ao,
a0 =-----V>                                                         2-22
and the spacing between neighboring atoms in the crystal, tq. The Bohr radius, ao = 0.053 nm, indicates the extent of the atomic electron shells. The spacing between atoms, typically ro = 0.25 nm, is the distance between two bonded atoms related to the minimum potential energy of the crystal. The nuclear charges are well screened by atomic electrons at the distances r ľ> ro. As the atoms come closer to each other the valence shells begin to overlap and there may be attractive interaction of the type forming the bonds. At the extreme case of r <C ao, the nuclei become the closest pair of charged particles in the system and since their Coulomb interaction dominates, the potential energy of interaction is well defined by Eq. (2.21). At the intermediate distances ao < r < ro, a positive interaction energy, resulting in repulsive force, has two components (i) the electrostatic repulsion between the positively charge nuclei and (ii) the increase in energy caused by Paulli exclusion principle.
Although the description of the interatomic interaction involves complicated effect of atomic electrons we can see from the above discussion that a reasonable choice is the Coulomb interaction given by Eq. (2.21) moderated by a proper function. Thus, the atomic interaction is generally described by the screened Coulomb potential energy
"<*•>=^¥-m                                     (2-23)
where % is the screening function. Under ideal circumstances, %(r) should tend to zero or unity for large or very small distances, respectively.
Basically, there are two approaches to express the screening function, (i) the simple statistical and (i) the quantum-mechanical Hartree-Fock atomic models. The statistical, Thomas-Fermi (TF), description assumes that the electrons behave as an ideal gas of particles of energy E obeying Fermi-Dirac statistics and fill the potential well around the positively charged core. Clearly, this model does not take into account the different electron shells.
Accurate solutions of the TF model of the screening function are typically obtained through numerical approaches as discussed by Torrens [?]. However, for many applications it would be desirable to have available an analytical expression that approximately satisfies the TF equation. The earliest and best known of these analytical expressions is the Sommerfeld asymptotic form:
X(P)
i + tf
(2.24)
where the constant a, A and c were chosen as a = 122'3 and c\ = 3. The normalized interatomic distance x = r/axF is scaled by the TF screening radius for collision between the atoms
1 /3-7r\ '     ao                                                  ,
°™ = -Át)   I?                                (2-25)
eft
10
CHAPTER 2.   INTERACTION OF IONS WITH SOLIDS
2.1.   ION STOPPING
where Ze^ is the effective charge number in the interaction of two unlike atoms
Zeff = (Zi1/2 + Zt1/2)2.                                                 (2.26)
Sommerfeld found that at large x the appropriate values for A and c are A = 0.772 and c = 3.886. Another often used approximation to the TF screening function was given by Moliere in the form of three exponentials:
X(x) = 7pex\>{—qx) + llpexp(—Aqx) + 2pex\>(20qx)                         (2.27)
where p = 0.05 and q = 0.3. Mathematically simple analytical expression of the screening function can be constructed using inverse powers of x = r/axF with exponent differening in different ranges of r/axF:
X(D = "j (T)'"'                                P-»)
with s = 3/2, 2,3... and a constant ks.
A screening function based on quantum mechanically derived charge distribution gives rise to what is commonly referred to as the universal interatomic potential. The extensive work of Ziegler, Biersack and Littmark (ZBL) [?] and Wilson et al. [?] produced the ZBL universal screening function
Xu = 0.1818 exp(-3.2a;) + 0.5099 exp(-0.9423a;) +0.2802 exp(-0.4028a;)+ 0.02817exp(-0.2016)
(2.29) where the reduced distance x is given by
x = —                                                            (2.30)
av
and a\j, the universal screening length, is defined by
0.8854a0 Z;0-23 + Z°-
au —   ^0.23   ,    -70.23 •                                                                     (2-31)
The application of the power law screening function, Eq. (2.28), to the scattering process results in a power law differential cross section [?]

o-e(E0 = —^                                                  (2.32)
where m = 1/s in Eq. (2.28) and the constant Cm is given by
2   ,2m)^'(2.33)
where Am is given by [?]
Winterbon et al.
vr        2    ( Z,Zte2 V
Cm"2W      2K0OTF/
Ai/3 = 1.309    Ai/2 = 0.327    A0.5 = 0.5.                                   (2.34)
11
2.1.   ION STOPPING
CHAPTER 2.   INTERACTION OF IONS WITH SOLIDS
Nuclear Stopping Cross Section
The average energy loss by the moving particle in the distance dx is obtained with the help of differential energy-transfer cross section <te defined by Eq. (2.17) as
AT?                  ľ Et, max
<—) = n I           EtaEdEt                                               (2.35)
m                                                                      ^       ■
-a.min
dx ■           .iE,
where £t,min and £t,max are minimum and maximum energies transferred to the target atom, respectively.
Applying the power law differential cross section given by Eq. (??), the power law nuclear stopping cross section is [?]
Sn(E) =
CmEl~2m \    4MiMt    ll_m
I — m
(Mi + Mt)2
(2.36)
where Cm is defined by Eq. (??).
The nuclear stopping cross section increases in the range of low energies reaching the maximum at some keV or hundreds of keV for light or heavy ions, respectively. It may be calculated at the ion energy E (in keV) from Ziegler et al.  [?] as
8.462ZjZt5n(£;r                   2      15
6n=(M1 + Mt) + (^3 + ^3)eVcm/10   at0mS                         (2-37)
where Er is the reduced energy defined by
32.53Mt£ ZiZt(Mi + Mt)Z°-23 + Z°-
E*   ~     ry   ry   1^*      ,      » í  WO.23     ,      ^0.23\                                                      (2.38)
and Sn(EY) is the reduced nuclear stopping given as
SJEY = -------------ln^ "Vo'ilof3^----------7^        for        £r<30keV          (2.39)
v           2(Eľ + 0.0I32I£;r0-21226 + O.I9593£r0-5)                                                       y       J
or
Sn(Eľ=1-^-        for        £r>30keV.                                   (2.40)
2Er
Above 200 keV/amu the nuclear stopping contribution is small, typically below I % of the electronic stopping.
2.1.2    Electronic Stopping
Since the number of collisions an ion experiences with electrons is large, and since the charge state of the ion while traversing the medium may change frequently, it is very difficult to describe all possible interactions for all possible ion charge states. Instead, the electronic stopping power is often given as an average taken over all energy loss processes for different charge states. It can be theoretically determined to an accuracy of a few percent in the energy range above several hundred keV per nucleon from theoretical treatments, the best known being the Bethe formula:
S =
4-7T   nz2 (  e2   V
mec2 ß2   \4ireoJ
,2 «2
2mec2ß           2
(2.41)
where v is the velocity of particle, c is the speed of light, ß = v /c, ze is particle charge, me is the rest mass of electron, n = N^Zp/A is electron density of the target and / is the excitation potential of the target. For lower energies
12
CHAPTER 2.   INTERACTION OF IONS WITH SOLIDS
2.2.   SPUTTERING
At energies lower than about 100 keV per nucleon, it becomes more difficult to determine the electronic stopping theoretically [?].
2/3
In the velocity range from w O.lfo to Z-J vq the electronic energy loss is approximately proportional to E1/2 as derived by Lindhard et al. [?,?]. At higher velocities v-lto » vq the charge state of the projectile increases and finally it becomes fully stripped of its electrons. At a given velocity the energy loss is proportional to the square of ion charge.
2.2     Sputtering
The yield, Y, describes how many atoms are ejected during the sputtering event. The total yield is defined as the average number of atoms ejected per incident ion.
The collective response of the atoms in the target to the strike of energetic atom or ion can be divided into five distinct groups according to E\, Z\ and M;, Z% and Mt. These 3D regions are demonstrated by two plane cross-sections with E\ = 50 keV and Zt = 50 in Figure ??a and ??b, respectively [?]. The response that can be described by a linear cascade theory [?,?,?,?], is depicted by an unshaded area. In this theory the incident particle shares its kinetic energy with target atoms initially at rest in a series of binary collisions and produces fast recoils. These, in turn, set other target atoms in motion and a continuously increasing number of progressively slower atoms participate in created isotropic cascade. About 1-5x 1013 s after impact, the recoil energies at the edges of the cascade have become less than the threshold energy to displace an atom, which is of the order of some 10 eV. The cascade is damped by energy dissipation through, e.g., , phonon-assisted processes. Using this approach, the sputter yield can be described by an analytical formula [?, ?]
Y{Eh 00 = ^ S^Eí/Ek) f (60                                         (2.42)
where Uq is the surface binding energy (in eV), Klt and E-lt are scaling constants dependent on the initial target and projectile species, Sn(E\/Eit) is the reduced nuclear stopping cross section (e = Ei/Eit is reduced energy) and f(9\) is the angle-of-incidence function.
It primarily occurs at intermediate energies (5 to 100 keV). A cascade of recoil atoms is produced along the path of the incident ion. The number of atoms produced at any point depends linearly on the amount of energy lost by the incident ion at that point. The energy loss is due to electron drag from the free electrons in the solid and screened Coulomb interactions with the nuclei, i.e.,   analytical expressions for sputter yield
2.3     Plasma processes
2.4     Processes in glow discharge plasmas
The electrons couple to the applied electric field which powers the discharge, thus gaining energy. Any ions present are relatively unaffected because of their much heavier mass. The accelerated free electrons lose little energy in elastic collisions with atoms or molecules because of the large difference in mass. Furthermore, they initially lose little energy in inelastic collisions (e.g., excitation and ionization) until their energies reach the corresponding threshold energies (e.g., 11.56 eV excitation and 15.8 eV ionization for argon). Consequently, these free electrons gain relatively high energy quickly from the field. This energy is transfered to the gas by electron-gas collisions that produce excited and ionized species. The latter generating additional electrons which are in turn accelerated by the field. For a plasma to be sustained, the electron must be produced by the ionization and emission from positive ion bombardment on the electrodes and walls at a rate equal to that of electron and ion losses by plasma-phase and surface recombination.
13
2.4.   PROCESSES IN GLOW DISOM/B(3EBI2kSMIX!ERACTI0N OF IONS WITH SOLIDS
Since plasma-phase recombination is a three-body reaction which is slow at the low pressures used in glow discharges, the majority of recombination occurs at the surfaces.
A broad range of chemical and physical reactions occur in a plasma. Listed below are some of the more significant electron-gas and gas-gas reactions:
Excitation	A2 + er ■	-^A*2 + er
Dissociation	A2 + er ■	-^2A + e~
Electron Attachment	A2 + er ■	-^
Dissociative Attachment	A2 + er ■	->■ A- + A
Ionization	A2 + er ■	-»■ A\ + 2e
Photoemission	A*2^A2	+ fe/
Abstraction	A + B2-	-* AB + B
where A^ is excited molecule A2.
The rate at which free radicals, ions, or other excited states are formed by electron impact in a plasma can be quantified in terms of a chemical reaction rate expression,
d[nj]/dt = kij[er][ni]                                                  (2.43)
where d[rij]/dt is the rate of formation of species rij from precursor m, [e~] is the concentration
of electrons, and [rii] is the concentration of the neutral precursor species. The rate coefficient kij
can be calculated from the collision cross section (Tíj(E) specific to the reaction. The cross section
is proportional to the probability that a given jth process will occur upon collision between m
and an electron with an energy E. If the electron has an energy lower than that required for jth
process, the cross section equals zero.  The collision cross section is a function of the electron
energy E, and thus kij is:
00
ľ   P2E kij = / \ —<Tij(E)f(E)dE                                            (2.44)
J     V   Wie
0
where f(E) is the electron distribution function which describes the fraction of free electrons with a given energy, and me is the electron mass. The Maxwell-Boltzmann distribution is usually used to approximate the energy distribution, i. e., a large fraction of the electrons have an energy at or below the average electron energy, but the fraction of electrons at higher electron energies decays exponentially with increasing electron energy. In the glow discharge, the electrons attain high average energies, typically 1-10 eV, with the fastest electrons having energies as high as 10-30 eV [?].
The energy of the electrons is primarily dissipated through inelastic collisions with gas molecules give rise to reactive species, such as excited neutrals and free radicals. In this manner the energy of the electrons, which is acquired from the applied electric field, is used to create highly reactive species without significantly raising the gas temperature. PECVD uses these highly reactive species to deposit thin films at lower temperatures than are possible with thermally driven CVD. Furthermore, the ion bombardment of the any surface in the touch with the plasma that is result of different potentials, as discussed in section ??, can induce several specific processes during the film deposition:
•  The ion may be reflected, probably being neutralized in the process.
•  The impact of the ion may cause the target to eject an secondary electron.
•  The ion may become buried in the target. This is the phenomenon of ion implantation.
14
CHAPTER 2.   INTERACTION OF I0MS mtDEEgmwm GLOW DISCHARGE PLASMAS
•  The ion impact may also be responsible for some structural rearrangements in the growing material. Rearrangement may vary from simple vacancies (missing atoms) and interstitials (atoms out of position) to more gross lattice changes like recrystallisation.
•  The ion impact may set up series of collisions between atoms of the surface, possibly leading to the ejection of one of these atoms. This ejection process is know as sputtering.
15
2.4.   PROCESSES IN GLOW DISOM/B(3EBI2kSMIX!ERACTI0N OF IONS WITH SOLIDS
16
Chapter 3
Overview of Material Processing Methods
There are basically three different activities applied within material processing
•  removal of material,
•  deposition of thin films,
•  modification or forming of material.
The removal of thin layers of material, as for example in lithography, can be achieved by (i) sputter etching using inert ions, i.e., purely physical processes, (ii) by chemical etching, i.e., purely chemical processes, or (iii) by the combination of both, i.e., by reactive ion etching (RIE). The advantage of RIE is the significant enhancement of removal rate as compared to the pure chemical or physical processes. The processes requiring interaction of ions with solids can be achieved either by using ion beam or plasma techniques. Thus, the first and the last method of material removal fall either into ion beam or plasma processing technology and can be further divided according to the ion or plasma source used. Similar sources can be also applied to the film deposition.
The general clasification of the technologies for the deposition of films, a few nanometers to about ten micrometers thick, is similar to that of material removal. Thin film deposition techniques are (i) purely physical, such as vacuum evaporation and ion beam or plasma sputter deposition, (ii) purely chemical, such as gas- and liquid- phase chemical processes and (iii) a considerable number of methods combine both, physical processes and chemical reactions. The physical-chemical approaches include the ion beam method combined with the chemical processes and various modifications of the chemical vapor deposition (CVD) in which a certain physical process helps to initiate the chemical reactions. A wide range of CVD methods are based on electrical discharges and they create their own extensive group called plasma enhanced chemical vapor deposition (PECVD). A brief survey of all the deposition methods classified according to the general processes is given in Tables 3.1 and 3.2.
Methods for the modification or forming of materials cover many different phenomena. They include thermal or plasma forming processes such as oxidation or nitridation. They are applied in the processing of polymers such as polymer cross-linking, surface modifications for variation of surface free energy or grafting of new functional groups. They cover ion beam processes like ion implantation or ion beam modifications.
As mentioned above, plasma processing technologies can be used in sputter etching, reactive ion etching, sputter deposition, PECVD and plasma surface modifications. They have already established a key role in many industrial products such as microelectronic devices, solar cells,
17
CHAPTER 3.   OVERVIEW OF MATERIAL PROCESSING METHODS
Table 3.1: First part of the survey of technologies for thin film deposition classified according to general processes applied: evaporative, MBE, liquid-phase chemical, gas-phase chemical and gas-phase physical-chemical techniques (except ion beam and plasma processes).
evaporative techniques:
method/processes                             specification
thermal (vacuum) evaporation         resistive heating
flash evaporation arc evaporation exploding-wire technique laser evaporation rf heating electron-beam evaporation
molecular beam epitaxy (MBE)
liquid-phase chemical techniques:		
method/processes		specification
electro processes		electroplating electrolytic anod iz at ion
mechanical techniques		spray pyrolysis
liquid phase epitaxy		
gas-	-phase	chemical techniques:
method/processes		specification
chemical vapor deposition (CVD)    CVD epitaxy
metalorganic CVD (MOCVD) low-pressure CVD (LPCVD) atmospheric-pressure CVD (APCVD) atomic layer deposition (ALD)
gas-	■phase physical-chemical techniques:
	(except plasma and ion beam)
method/processes	specification
modifications of CVI	)                        hot filament CVD (HFCVD)
	laser-induced CVD (PCVD)
	photo-enhanced CVD (PHCVD)
	electron enhanced CVD
protective or anticorrosion coatings on machining tools or automobile parts. In many other cases, it is still an emerging technology with a large potential for further grow. However, there is always a need for better understanding of plasmachemical processes and testing different deposition conditions as well as new mixtures and multi-step procedures [?].
One of the most important plasma processing techniques is PECVD. It is very complex method combining physical and chemical processes in the plasma phase as well as at plasma-solid interface. It is based on the molecule dissociation in the gas phase by impact of energetic electrons and atoms in metastable states followed by chemical reactions of gas radicals. As compared with classical chemical methods PECVD has several advantages: low substrate temperature (necessary condition in many applications), possibility to produce materials of new properties and to vary the film properties simply by changing some deposition parameters, film production without toxic by-products, ozone and the like.
18
CHAPTER 3.   OVERVIEW OF MATERIAL PROCESSING METHODS
Table 3.2: Second part of the survey of technologies for thin film deposition classified according to general applied processes: ion beam and plasma techniques.
method/processes
plasma techniques: specification
sputter deposition
PECVD in low temperature discharges
plasma processing in high temperature discharges
dc sputtering
rf diode sputtering
magnetron sputtering
dc discharge
rf capacitively coupled plasma (CCP)
rf inductively coupled plasma (ICP)
microwave ECR deposition
microwave resonantor reactor
atmospheric pressure dielectric barrier discharge (DBD)
atmospheric pressure glow discharge (APGD)
atmospheric pressure surface barrier discharge
etc.
vacuum arc dc torch microwave torch etc.
method/processes
ion beam techniques: specification
sputter deposition ion deposition dual processes
ion beam sputtering reactive ion beam sputtering
ion beam deposition ionized cluster beam deposition (ICB) ion beam assisted deposition (IBAD) dual ion beam sputtering
19
CHAPTER 3.   OVERVIEW OF MATERIAL PROCESSING METHODS
20
Chapter 4
Evaporative Technologies
4.1    Thermal Evaporation
Thermal evaporation or vacuum evaporation (purely physical method) is one of the oldest techniques used for depositing thin films. It is still widely used in the laboratory and in industry for depositing metals and metal alloys. There are several evaporation methods:
• Resistive Heating. This method consists of heating the material with a resistively heated filament or boat, generally made of refractory metals such as W, Mo, Ta and Nb, with or without ceramic coatings.
—  Direct heating is obtained when evaporant
*   hangs for example on the wire spiral in the form of U-shaped staples (the evaporant has to be able to wet the wire so to be able to cling to the wire after melting),
*   is inserted into a basket shaped wire (it need not wet the wire because it will coalesce into a blob that will not flow out through the spacing)
*   is placed in dimpled boat. The dimple is about 0.3 cm deep, and the overall dimensions of the boat are about 10 cm long and 1 or 2 cm wide. Power requirements for these sources are appreciably higher than for wire sources but thicker coatings can be deposited.
*  or is inside a closed source design (furnace) developed to prevent evaporant specks from being ejected and striking the substrates. The furnace chamber is filled with evaporant vapours that streams out of the holes.
—  Crucibles of quartz, graphite, alumina, beryllia and zirconia are used with indirect heating.
=> Sublimation. If a material has a sufficiently high vapour pressure before melting occurs, it will sublime, and the condensed vapours form a film (low deposition rates).
=> Multiple-component Evaporation. When multicomponent alloys or compounds are thermally evaporated, the component may evaporate at different rates because of their different vapour pressures, their different tendencies to react with the support material, and possible thermal decomposition of the parent material. Due to vapour pressure difference alone, the ratio of the evaporation rates of components A and B of an alloy may be obtained from Langmuir's expression (1.13) by assuming that the vapour pressure of each component is
21
4.1.   THERMAL EVAPORATION            CHAPTER 4.   EVAPORATIVE TECHNOLOGIES
depressed by an amount proportional to the relative concentrations Ca, Cb'-
Ja = Capa  ßgg                                        ^ ^
j b     Cb'Pb V mA
A point of technical interest is that the higher the evaporation temperature of an alloy of widely different vapour-pressure components is, the closer is the composition of the film to the bulk alloy.
•  Flash Evaporation. A rapid evaporation of a multicomponent alloy or compound, which tends to distill fractionally, may be obtained by continuously dropping fine particles of the material onto a hot surface so that numerous discrete evaporations occur.
•  Arc Evaporation. By striking an arc between two electrodes of a conducting material, sufficiently high temperatures can be generated to evaporate refractory metals such as Nb and Ta. This method is also widely used for evaporation of carbon for electron-microscope specimens.
•  Exploding-Wire Technique. This technique consists of exploding wire by a sudden resistive heating of the wire with a transient high current density approaching 106 A/cm2. This is achieved by discharging a bank of condensers (w 10 to 100 /xF), charged to a voltage w 1 to 10 kV, through a metallic wire.
•  Laser Evaporation. The enormous intensity of a laser may be used to heat and vaporize materials by keeping the laser source outside the vacuum system and focusing the beam onto the surface of the evaporant.
•  RF Heating. The rf induction heating may be supplied to the evaporant directly or indirectly from the crucible material
•  Electron-Beam Evaporation. The simple resistive heating of an evaporation source suffers from the disadvantages of possible contamination from the support material and the limitations of the input power, which make difficult to evaporate high-melting-point materials. => Overcome with electron bombardment of the material.
The simplest arrangement consists of a heated W filament to supply electrons which are accelerated by applying a positive potential to the material for evaporation. The electrons lose their energy in the material => molten drops, evaporation.
22
CHAPTER 4.   EVAPORATIVE TECHNOLOGIES     4.2.   MOLECULAR BEAM EPITAXY
4.2    Molecular Beam Epitaxy
MBE is a sophisticated, finely controlled method for growing single-crystal epitaxial films in a high vacuum (10~9 Pa). The films are formed on single-crystal substrates by slowly evaporating the elemental or molecular constituents of the film onto substrates held at an appropriate temperature. MBE deposition equipment consists of:
•  Vacuum system construction closely follows this of surface analysis equipment - standard UHV practises are employed. A typical current MBE system is composed of four separate vacuum chambers: a load-lock for substrate entry and exit, a growth chamber, an auxiliary chamber for analysis or metallization and an intermediate or "buffer" chamber for pregrowth processing.
•   Sources are key elements of any MBE system. They must be designed to supply the needed uniformity and material purity.
-  Knudsen Cells are standard thermal evaporation sources. They are deep crucibles in furnaces with cooled shrouds, equipped with a thermocouple. Construction materials are usually refractory metals such as Ta and Mo and insulators like alumina.
-  Solid Source Cracking Cells. Some materials, As and P, evaporate in more than one molecular form. Often the larger molecule will have a higher vapour pressure and a lower sticking coefficient for a given substrate temperature than the smaller molecules. => the efficiency can be improved by cracking the larger molecule at the source. Source construction follows standard K-cell with the addition of a secondary heat zone at the source exit for cracking.
-   Continuous Sources. Sources which can be maintained in a liquid state (e.g., mercury) .
-  Electron Beam Heated Sources are used for materials with very high melting temperatures (W, Co, Ni, Si, Ge).
-  Implantation Sources. The gas is ionised, optionally mass separated and the ions are accelerated towards the substrate.
-  Source Shutters. One of the main virtues of MBE originates from the fact that fast acting shutters coupled with a slow growth rate allow for monolayer film growth control. Shutter actuation times below 0.1 s are nominal.
•   Sample Manipulation. MBE samples are mounted to Mo holders using In solder. At film growth temperatures, In is liquid and provides adequate attractive force and good thermal conductivity. Sample temperature can be set and maintained by either thermocouple or pyrometer feedback. Standard practise with large substrates (> 5 cm) is to rotate the wafer during the deposition.
23
4.2.   MOLECULAR BEAM EPITAXY     CHAPTER 4.   EVAPORATIVE TECHNOLOGIES
24
Chapter 5
Gas-Phase Chemical Processes
Methods of film formation by purely chemical processes using the gas or vapour phase reactants on the one hand side and the solid phase reactants on the other hand side. It includes chemical vapour deposition and thermal forming processes.
5.1     Chemical Vapour Deposition (CVD)
Chemical vapour deposition (CVD) is a materials synthesis processes whereby constituents of the vapour phase react chemically near or on a substrate surface to form a solid product. Most CVD processes are chosen to be heterogenous reactions. Undesirable homogeneous reactions in the gas phase nucleate particles that may form powdery deposits and lead to particle contamination. Both chemical composition and physical structure can be tailored by control of the reaction chemistry and deposition conditions. Fundamental principles of CVD encompass an interdisciplinary range of gas-phase reaction chemistry, thermodynamics, kinetics, transport mechanisms, film growth phenomena and reactor engineering.
•  chemical reactions in CVD: pyrolysis (thermal decomposition), oxidation, reduction, hydrolysis, nitride and carbide formation, synthesis reactions, chemical transport. A sequence of several reaction types may be involved.
•  deposition variables: temperature, pressure (from low pressures, i.e., 10-1000 Pa - LPCVD, up to atmospheric pressures - APCVD), input concentration, gas flow rates, reactor geometry, operating principles. Kinetics of the reactions may depend on such factors like substrate material, structure and orientation.
•  starting materials: inorganic, organometallic and organic reactants. Gases are preferred because they can be easily handled and distributed to the reactor. Liquid and solid reactants must be vaporized without decomposition at suitable temperatures and transported with a carrier gas through heated tubes to the reaction chamber.
•  thin film materials: broad range of elements and compounds. Materials deposited at low temperatures (bellow 600 °C for silicon) are generally amorphous. Higher temperatures tend to lead to polycrystalline phases. Very high temperatures (typically 900-1100 °C in the case of silicon) are necessary for growing single-crystal films.
•  applications:
- fabrication of solid-state devices - dielectrics (oxides, silicates, nitrides), elemental and compound semiconductors (Si, GaAs, etc.), conductors (W, Mo, Al, refractory metal silicides),
25
5.1.   CHEMICAL VAPOUR DEPOSIVIDAPpmfí}.   GAS-PHASE CHEMICAL PROCESSES
-  tool technology - hard and wear resistant coatings such as boron, polycrystalline diamond, borides, carbides and nitrides,
-  metallurgical applications - corrosion resistant coatings for protection of metals, especially oxides and nitrides
Chemical reactors must provide several basic functions:
•  transport of the reactant and diluent gases to the reaction site,
•  provide activation energy to the reactants (heat, radiation, plasma),
•  maintain a specific system pressure and temperature,
•  allow the chemical processes for thin film deposition to proceed optimally,
•  remove the by-product gases and vapours.
Reactor geometry affects the gas flow characteristics which, in turn affect the properties of the deposited layer. Two basic flow type reactors:
•  Displacement or plug flow reactor in which the entering gas displaces the gas already present with no intermixing of successive fluid elements. Plug flow is a simplified and idealized picture of the motion of a fluid, whereby all the fluid elements move with a uniform velocity along parallel streamlines. Mass balance for reactant A involved in a single reaction is very simple: Fa — (Fa + <IFa) = taAV.
•  Perfectly mixed flow reactor is the opposite extreme from the plug flow reactor. To approach the ideal mixing pattern, the feed has to be intimately mixed with the contents of the reactor in a time interval that is very small compared to the mean residence time of the fluid flowing through the vessel. The essential feature is the assumption of complete uniformity of concentration and temperature throughout the reactor.
There are different types of CVD techniques:
•   CVD epitaxy and metal-organic CVD
CVD epitaxy or vapour-phase epitaxy (VPE) and metal-organic chemical vapour deposition (MOCVD) are used for growing epitaxial films of e.g. silicon or compound semiconductors. Layers of accurately controlled thickness and dopant profile are required to produce structures of optimal design for device fabrication.
•  low pressure and atmospheric pressure CVD
These two methods are used for deposition of polycrystalline or amorphous materials like polysilicon, silicon nitride and Low Temperature Oxide (LTO). The deposition of thin films for semiconductor device manufacture by CVD at atmoshperic pressure (APCVD) was a widely accpeted process in f976 when equipment for low-pressure CVD (LPCVD) was introduced into the marketplace. At that time, the 3-inch wafer was the predominantly wafer size used in production with some residual presence of smaller wafers and the 4-inch wafer just being introduced into advanced lines. In the next few years, the LPCVD process became the preferred method for chemical vapour deposition of thin films. The transformation to a new technology that required massive capital expenditure for new equipment took place at a rapid rate throughout the industry. The reason for this rapid change were: (I) a superior film quality, (2) a greatly reduced processing cost, and (3) greatly increased thtoughput per unit of capital investment. Improved film quality also means increased yields and decreased unit costs in an industry that was becoming increasingly competitive.
26
CHAPTER 5.   GAS-PHASE CHEMICAL P.ROC^mSCAL VAPOUR DEPOSITION (CVD)
5.1.1     Epitaxy by Chemical Vapour Deposition
The world epitaxy is derived from the Greek "epi" - upon and "taxis" - to arrange. Thus, epitaxial deposition requires the ability to add and arrange atoms upon a single crystal surface. Epitaxy is a regularly oriented growth of one crystalline substance upon another. Specific applicat ions require controlling the crystalline perfection and the dopant concentration in the added layer. Two different kinds of epitaxy are recognized:
•  Homo-epitaxy is growth in which the epitaxial layer is of the same material as the substrate.
•  Hetero-epitaxy is growth in which the layer is a different material than the substrate.
Epitaxial layers can be prepared by a wide range of techniques including evaporation, sputtering and molecular beams. Epitaxial deposition by CVD uses a gaseous transport and chemical reactions. Important application of CVD epitaxy is a production of crystalline silicon (c-Si). With the silicon epitaxy radical changes in material properties can be created over small distances within the same crystal. This capability permits the growth of lightly-doped single c-Si on the top of heavily-doped c-Si, n-type Si over p-type Si and vice versa, Si layer with controlled dopant profiles etc. Successful silicon epitaxy depends upon having:
•  high surface mobility for arriving atoms,
•  numerous, equivalent growth sites,
•  commercially significant growth rates.
For deposition of epitaxial c-Si films, chlorosilanes (SiCU, SÍHCI3, SÍH2CI2) and SÍH4 are used in H2 atmosphere. The heterogenous reaction involves the following steps:
•  Arrival
-  bulk transport of reactants into the process volume
-  gaseous diffusion of reactants to the surface
-  adsorption of reactants onto the surface
•   Surface reaction
-  surface reaction (reaction can also take place in the gas volume immediately above the surface)
-  surface diffusion
-  crystal lattice incorporation
•  Removal of reactant by-products
-  reaction by-product desorption
-  gaseous transport of by-products
-  bulk transport of by-products out of process volume
The rate of CVD is primarily controlled by one of the following major groups of process steps:
•  rate of arrival of reactants,
•  surface reaction rate,
•  rate of removal of by-products.
27
5.1.   CHEMICAL VAPOUR DEPOSIVIDAPpmfí}.   GAS-PHASE CHEMICAL PROCESSES
For typical epitaxy process (the best crystal quality), the reaction conditions are established so that the rate of arrival of the reactants controls the growth rate. The crystal quality of the epitaxial layer is controlled primarily by
•  nature of the surface prior to the epitaxial growth: If the surface has a contamination, such as oxides or if the crystal is defective => crystal defects. Surface is prepared by chemical/mechanical polishing and native oxide etching. H2 bake at 1150 °C for 10 min remove a native oxide. The heating-up and etching with gaseous HCI/H2 (0.1% HCI/H2 mixture at 1150 °C => 0.1-0.3 /xm/min) can etch the silicon. However, if the etching rate is too high for given temperature the surface will be pitted instead of being polished.
•  arrival rate relative to the surface diffusion rate: If the rate of arrival reactants greatly exceeds the surface diffusion rate, then diffusing atoms cannot move to the positions of the lowest energy => deflects.
•  nature of the lattice incorporation: the rate of lattice incorporation is a function of crystal orientation because the density of atomic sites is a function of crystallographic faces. The low growth rate for (111) planes encourages a defect called faceting or orange peel. To prevent faceting, (111) surfaces are cut a few degrees off the (111).
The conditions for acceptable commercial silicon epitaxy:
variable	horizontal	cylinder	bell jar
tilt angle	major	major, fixed	not applicable
gas inlet	minor	major	varies
wafer/carrier	recessed	recessed	recessed
wafer/wall	major	major	minor
exhaust pressure	minor	major	minor
In the horizontal reactor it is useful to break the thickness profile in the direction of gas flow into the front and back half. Each half can then be described as thick or thin in front, or thick or thin in back. The adjustments for thickness uniformity are divided in the same manner.
In the cylinder reactor
•  Thickness is increased in the front (top of carrier) by increasing temperature and/or concentration of react ant
•  and in the back by increasing the total flow rate, directing the gas jets in a more downward direction, reducing the process pressure (slower heating of gas) and bringing the back pressure toward a more positive value.
•  Thickness uniformity is improved within a wafer from left to right by balancing the two jet flows, by lowering the temperature (controlled by surface reactions) and by increasing the distance between the wafer and the walls.
•  Thickness variation at any distance along the carrier is averaged by rotation.
In the bell jar reactor the uniformity at any radius is averaged by rotation of the susceptor. The
radial variation is a function of total flow rate:
low flow rate —> thin outside, high flow rate —> thick outside => optimum value
Adjustment parameters for the tapered cavity reactor follow those for the horizontal reactor. Rotation of the circular cluster of tapered cavities averages the initial velocities and concentrations from multiple gas inlets.
28
CHAPTER 5.   GAS-PHASE CHEMICAL P.ROC^mSCAL VAPOUR DEPOSITION (CVD)
Control of operator variables
•   Leak testing includes bubble testing with sensitive detergent solutions, He mass spectrometers, high sensitive combustile gas detectors and pressure decay techniques
A»   V
leak rate {seem} = —---------                                         (5.1)
1        J      AtPatm                                         v     ;
•   Gas flow control is possible by four different methods
—  fixed or variable orifices
—  ball-in-tube flowmeters. The calibration is a function of pressure in the gauge tube
actual flowrate           /   actual pressure
(5.2)
calibrated flowrate      y calibrated pressure
—  mass flow controllers are based on the principle of measuring mass flow using gas heat capacity. There is the possibility of a back-loop control.
—  source controllers for liquids (bubblers). In this case a gas (e.g. H2) is bubbled through a liquid (e.g. SiCU)
«(SICU) = Qm P(SiCU) |eff-'                                  (5.3)
Ptotal
Bubblers require a constant temperature and pressure. Bubbler efficiency is fixed primarily by the size of the bubbles and the path lenght the bubbles travel through the liquid.
•  Higher temperature is achieved by the heating systems:
—  Induction heating, using frequencies 3-400 kHz, with coils located internally or externally to the process chamber.
—  Radiative heating, using high intensity infrared heating lamps, located externally.
—  Resistance heating, using heaters located internally.
—  Combination of the above.
and controlled by the measurements. For Si epitaxy it has to be controlled with a precision of a few °C in the range 900-1300 °C and the only convenient method is radiation pyrometry (thermocouples are not stable in H2 environment)
—  Disappearing filament pyrometers: brightness within a narrow wavelength range (650 nm) of a heated filament of known temperature is matched with the brightness of the target.
—  Electronic pyrometers: intensity of light within a narrow range of wavelenght is directly measured by a photovoltaic cell (Si photocells - 0.8 /xm, PbS photocell - 2.2 /im) or a thermopile (assemplies of thermocouples on which the radiation is focused - broad band detectors).
•   Pressure from the range 5-760 Torr implies viscous gas flow and for the constant mass flow rate, there is a little effect on the rate of arrival of reactants => the effect of gas flow on the uniformity is the same. The number of volume changes per unit time is inverse proportional to the pressure => strong effect on the material properties (dopant incorporation, crystal perfection).
29
5.2.   THERMAL FORMING PROCEBSBSPTER 5.   GAS-PHASE CHEMICAL PROCESSES
Defects in epitaxy layers
•   Haze, as revelaed by reflected light, is a fine pitting or slightly texture surface caused by oxidizer in the process sapce or by subsurface crystal damage in the substrate
•   Pits are localized etching of substrate defects or local inhibition of epitaxy growth, often caused by contamination left on the surface prior to heat-up.
•   Orange peel is a roughened surface appearance caused by having the growth rate too high for the deposition temperature. Subsurface crystal damage can also cause orange peel.
•   Faceted growth is irregular, stepped growth over the surface caused by growing on (111) faces.Si should be cut 3-5° off the (111) plane towards the nearest (110) plane.
•   Edge growth occurs when the growth rate at the edge of the wafer greatly exceeds that over the rest of the wafer surface.
•   Etch pit are created by decorative etch technique and reveal crystal dislocations produced by slip, as well as other defects.
•   Crystallographic slip is dislocation motion in response to thermall stress during epitaxy.
•   Stacking faults are geometric defects nucleated at crystallographically disturbed sites on or near the growth surface. A uniform size of stacking faults indicates that the disturbance was all at the original surface prior to epitaxy.
•   Spikes and hillocks are severe defects also caused by crystallographically disturbed sites. The larger defects are usually the result of particle contamination.
•   Shallow pits or haze are revealed by decorative etching alone or etching followed by an oxidation cycle and indicate the presence of heavy metal precipitates.
Stavová rovnice:
vV                N
ľ—=nR = —R = Nk                                                (5.4)
T                NA                                                              v     '
kde k = 1.38xl0"23 J.K"1, NA = 6.022xl023 mol"1
5.2    Thermal Forming Processes
In the gas phase, thermal oxidation and nitridation is a chemical thin-film forming process in which the substrate itself provides the source for the metal or semiconductor constituent of the oxide and nitride, respectively. This technique is obviously much more limited than CVD.
5.2.1     Thermal Oxidation
The thermal oxidation has extremely important applications in silicon device technology where very high purity oxide films with high quality SÍ/SÍO2 interface are required. Thermal oxidation of silicon surfaces produces glassy films of SÍO2 for protecting highly sensitive p-n junctions and for creating dielectric layers for MOS devices. The temperature for this process lie in the range of about 700 °C to 1200 oC with either dry oxygen or water vapour (steam) as the oxidant. Steam oxidation proceeds at a much faster rate than dry oxidation. The oxidation rate is a function of the oxidant partial pressure and is controlled essentially by the rate of oxidant diffusion through the growing SÍO2 layer interface, resulting in a decrease of the growth rate with increased oxide thickness. The process is frequently conducted in the presence of hydrochloric acid vapours or vapours of chlorine-containing organic compounds. The HCl vapour formed acts as an effective impurity getter, improving the SÍ/SÍO2 interface properties and stability.
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CHAPTER 5.   GAS-PHASE CHEMICAL PROCESSESTHERMAL FORMING PROCESSES
Silicon oxidation under elevated pressure is of technological interest where the temperature must be minimized, such as for VLSI devices. Since the oxidation rate of silicon is approximately proportional to pressure, higher product throughput and/or decreased temperatures can be attained. The oxidant in commercial systems is H2O, which is generated pyrogenically from H2 and O2. Pressures up to 10 atm are usually used at temperatures ranging from 750 °C to 950 oC.
Gas-phase oxidation of other materials is of limited technical importance. Examples include metallic tantalum films converted by thermal oxidation to tantalum pentoxide for use as antireflection coating in photovoltaic devices and as capacitor elements in microcircuits. Other metal oxides grown thermally have been also used as capacitor dielectrics in thin-film devices, to improve the bonding with glass in glass-to metal seals and to improved corrosion resistance.
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