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Without exaggeration almost all of the basic MOSFET parameters
are affected by the distribution of dopants in the device.
Doping refers to the process of introducing impurity atoms into a
semiconductor region in a controllable manner in order to define the
electrical properties of this region. The doping with donors and
acceptors allows to modify the electron and hole concentration in silicon
in a very large range from 10cm up to 10cm.
The carrier concentration can also be varied spatially quite accurately
which is used to produce pn-junctions and built-in electric fields.
All electronic and optical semiconductor devices incorporate dopants as
a crucial ingredient of their device structure.
2. Semiconductor Doping Technology
Ion implantation is the primary technology to introduce doping atoms into
a semiconductor wafer to form devices and integrated
This low-temperature process uses ionized dopants which are accelerated
by electric fields to high energies and are shot into the wafer.
The main reason in applying this technique is the precision with which
the amount and position of the doping can be controlled.
Dopant ions can be masked by any material which is thick enough to stop
the implant as well as by existing device structures, which is referred
to as self-aligned implants. After the implantation process the crystal
structure of the semiconductor is damaged by the implanted particles and
the dopants are electrically inactive, because in the majority of cases,
they are not part of the crystal lattice. A subsequent thermal annealing
process is required to activate the dopants and to eliminate the produced
Continuous growth and dominance of CMOS technology has directly resulted in
the growth of ion implantation applications . Leading edge
CMOS processes which are used to fabricate a modern microprocessor require
up to twenty ion implants per wafer. The doping requirements span several
orders of magnitudes in both, energy and dose, for a wide range of dopant masses.
An important implantation application for CMOS processing is, for instance, to
form the source/drain regions in the substrate. Downscaling of MOS transistor
dimensions requires the reduction of the source/drain junction depth to
compensate the influence of the shorter channel length on the threshold
voltage . The subsequent application of an enhanced annealing
process step like the flash-assist RTA (rapid thermal annealing) technique
leads to a very limited diffusion which barely changes the as-implanted doping
profiles and junction depth . The distribution of dopants in the
final device is therefore mainly determined by the ion implantation step,
whereby channeling of implanted ions, which results from the regular
arrangement of atoms in the silicon crystal structure, plays a major role.
The starting material used for the fabrication of semiconductor devices is
monocrystalline silicon. Silicon wafers are produced either by the Czochralski
crystal pull method or by the floating-zone crystal growth
technique . Dopants are added to the silicon during the growth
process in order to set the resistivity of the wafer in the range from
1mcm - 30cm . Defects in the silicon
crystal become much more severe for smaller device dimensions. Today, silicon
wafers with a surface plane are commonly used in semiconductor
manufacturing , because the lowest defect density at the
Si/SiO interface can be achieved by thermal oxidation of silicon.
In this work we consider crystalline substrates of silicon, silicon-germanium,
and germanium. At zero temperature the conductivity in a pure semiconductor
crystal is zero, because the vacant conduction band is separated by an energy
gap from the filled valence band. As the temperature is increased,
electrons are thermally excited from the valence band to the conduction band.
Both the electrons in the conduction band and the vacant orbitals or holes
left behind in the valence band contribute to the electrical conductivity.
Fermi-Dirac distribution function for various temperatures.
An intrinsic semiconductor is one that contains a negligibly small amount of
impurities compared with thermally generated electrons and holes.
The energy distribution of electrons in solids is given by the Fermi-Dirac
statistics . The probability that an electronic state at energy
is occupied by an electron in thermal equilibrium is given by the Fermi-Dirac
In Fig. 2.1 the Fermi-Dirac distribution function versus energy
is presented for different temperatures. The Fermi energy
is the energy at which the probability of occupation by an electron is exactly
one-half. The probability of not finding an electron at energy , ,
is the probability of finding a hole there. At absolute zero temperature,
= 0K, all the states below the Fermi level are filled,
, and all the states above the Fermi level are empty
for . At finite temperatures, continuous thermal
agitation exists, which results in excitation of electrons from the valence
band to the conduction band and an equal number of holes are left in the
valence band. This process is balanced by recombination of the electrons in the
conduction band with holes in the valence band. The width of the transition
from one to zero of the probability distribution increases with the
thermal energy . Note that is symmetrical around the Fermi level
. For energies that are above or below the Fermi energy, the
exponential term in (2.1) becomes larger than 20 or smaller then 0.05,
respectively. The Fermi-Dirac distribution can thus be approximated by simpler
expressions according to
The electron and hole concentrations in an intrinsic semiconcuctor under thermal
equilibrium condition depend on the density of states , that is, the
number of allowed energy states per unit energy per unit volume and is given
The electron concentration in the conduction band is given by integrating
the product of the density of states and the probability of occupying an
energy level according to
where is the energy at the bottom of the conduction band.
Substituting (2.2) and (2.4) into (2.5) and
solving the integral results in
where is the effective density of states in the conduction band .
In a similar way the hole concentration in the valence band can be obtained
where is the energy at the top of the valence band. Substituting
(2.3) and (2.4) into (2.7) and solving the integral
where is the effective density of states in the valence band .
For an intrinsic semiconductor the number of electrons in the conduction band
is equal to the number of holes in the valence band, that is,
where is the intrinsic carrier concentration. In Fig. 2.2 the
intrinsic electron and hole concentrations are obtained graphically from the
product of and .
The Fermi level for an intrinsic semiconductor is obtained by equating
(2.6) and (2.8) which yields
Density of states, probability distribution, and
resulting electron and hole concentration in an intrinsic semiconductor .
The intrinsic Fermi level lies very close to the middle of the bandgap
, because the second term in (2.9) is much smaller than
the bandgap at room temperature.
The intrinsic carrier concentration can be calculated from equations
(2.6), (2.8), and (2.9) according to
Bandgap and intrinsic carrier concentration at 300K
for three common semiconductors .
The intrinsic carrier concentration is largely controlled by , the
ratio of the band gap and the temperature. When this ratio is large, the
conductivity will be low. Table 2.1 summarizes these key values for
germanium, silicon, and gallium arsenide at room temperature and Fig. 2.3
shows the temperature dependence of for these semiconductors.
Intrinsic carrier densities of Ge, Si, and GaAs as
a function of reciprocal temperature .
Schematic bond representation for n-type silicon
doped with arsenic and p-type silicon doped with boron.
In processing of modern semiconductor devices, doping refers to the process
of introducing impurity atoms into a semiconductor wafer by ion implantation.
The purpose of semiconductor doping is to define the number and the type of
free charges in a crystal region that can be moved by applying an external
voltage. The electrical properties of a doped semiconductor can either be
described by using the ``bond'' model or the ``band'' model. When a
semiconductor is doped with impurities, the semiconductor becomes extrinsic
and impurity energy levels are introduced. In Fig. 2.4 the bond model is
used to show that a tetravalent silicon atom (group IV element) can be replaced
either by a pentavalent arsenic atom (group V) or a trivalent boron atom
(group III). When arsenic is added to silicon, an arsenic atom with its five
valence electrons forms covalent bonds with its four neighboring silicon
atoms. The fifth valence electron has a relatively small binding energy to its
arsenic host atom and can become a conduction electron at moderate temperature.
The arsenic atom is called a donor and a donor-doped material is referred to
as an n-type semiconductor. Such a semiconductor has a defined surplus of
electrons in the conduction band which are the majority carriers, while the
holes in the valence band, being few in number, are the minority carriers.
In a similar way, Fig. 2.4 demonstrates the behavior, if a boron atom with
its three valence electrons replaces a silicon atom, an additional electron
is ``accepted'' to form four covalent bonds around the boron, and a hole
carrier is thus created in the valence band. Boron is referred to as an
acceptor impurity and doping with boron forms a p-type semiconductor.
The dopant impurities used in controlling the conductivity type of a
semiconductor usually have very small ionization energies, and hence, these
impurities are often referred to as shallow impurities. The energy required
to remove an electron from a shallow donor impurity such as arsenic,
phosphorus, and antimony can be estimated based on the Bohr model of the
hydrogen atom [30,31]. The ionization energy of hydrogen
is given by
where is the free electron mass, is the elementary charge,
is the dielectric constant, and is the Planck constant. The evaluation
of (2.12) results in
for the ionization energy
of the free hydrogen atom. The hydrogen atom model may be modified to take into
account the dielectric constant of the semiconductor and the effective mass of
an electron in the periodic potential of the crystal. Thus, the donor ionization
energy is obtained by replacing with
and by the
effective mass according to
The Bohr radius of the donor can also be derived from the hydrogen atom model
The applicability to silicon and germanium is complicated due to the anisotropic
effective mass of the conduction electrons. To obtain a first order
approximation of the impurity levels we use
electrons in silicon and
in germanium. Then the
ionization energy for donors , measured from the conduction band edge,
can be calculated from (2.13), and is
for silicon and
for germanium. Calculations using the correct anisotropic
mass tensor predict
for silicon and
for germanium. According to (2.14), the Bohr
radius for donors is
in silicon and
in germanium, which is much larger than the
Bohr radius of
for the hydrogen atom.
Therefore, the average distance between the electron and the positive
charged donor ion is also much larger than the inter-atomic spacing of the
semiconductor crystal. These large radii of the donor orbits overlap at
relatively low donor concentrations in the crystal and an ``impurity band''
is formed from the donor states, which enables electron hopping from donor
Shallow acceptor impurities in silicon and germanium are boron, aluminium,
gallium, and indium. An acceptor is ionized by thermal energy and a mobile
hole is generated. On the energy band diagram, an electron rises when it
gains energy, whereas a hole sinks in gaining energy. The calculation of
the ionization energy for acceptors is similar to that for donors, it can
be thought that a hole is located in the central force field of a negative
charged acceptor. The calculated ionization energy for acceptors, measured
from the valence band edge, is
in silicon and
in germanium. The used approach for the calculation
of the ionization energy is based on a hydrogen-like model and the effective
mass theory. This approach does not consider all influences on the
ionization energy, in particular it cannot predict the ionization energy
for deep impurities. However, the calculated values do predict the correct
order of magnitude of the true ionization energies for shallow impurities.
The ionization energy for shallow impurities can also be calculated by
means of the density functional theory (DFT). In  both
approaches are compared to experimental data. The results obtained by the
DFT calculation are only for some impurities slightly more accurate than
the simple approach. Table 2.2 presents the measured ionization
energies for various donor and acceptor impurities in silicon and germanium.
Ionization energies of shallow impurities in
silicon and germanium, in meV.
For shallow donors, it can be assumed that all donor impurities are ionized
at room temperature. A donor atom which has released an electron becomes
a positive fixed charge. The electron concentration under complete ionization
is given by
where is the donor concentration. From (2.6) and (2.15),
we obtain the distance of the Fermi level from the conduction band edge
Under complete ionization, the hole concentration is equal to the acceptor
In a similar way we obtain the distance of the Fermi level from the top of
the valence band,
Equation (2.16) states that the higher the donor concentration, the
smaller the energy difference
, which means that the Fermi
level will move up closer to the conduction band edge. On the other hand side,
for a higher acceptor concentration, the Fermi level will move closer to the
top of the valence band according to (2.18). According to the implanted
impurity type, either n- or p-type carriers will dominate, but the product of
and is equal to . Note that this result is equal to the
intrinsic case, Equation (2.10), which is called the mass action law.
Fig. 2.5 shows the graphic procedure for obtaining the carrier
concentrations in an n-type semiconductor under thermal equilibrium.
Density of states, probability distribution, and
carrier concentration in an n-type semiconductor.
If donor and acceptor impurities are introduced together, the impurity
present in a higher concentration determines the type of conductivity in
the semiconductor. The Fermi level must adjust itself to preserve charge
neutrality. Overall charge neutrality requires that the negative charges
(electrons and ionized acceptors) must be equal to the total positive charges
(holes and ionized donors):
Combining (2.10) and (2.19) results in the equilibrium electron
and hole concentrations in an n-type semiconductor:
The index refers to the n-type semiconductor. In a similar way the holes
and electrons can be calculated in a p-type semiconductor:
The index indicates the majority carrier type being holes.
Electron density as a function of temperature for a
Si sample with a donor concentration of cm.
Generally, the magnitude of the net impurity concentration
is larger than the intrinsic carrier concentration and the relationships
for and can be simplified to
Fig. 2.6 shows the electron concentration in doped silicon with
as a function of the
At low temperatures the thermal energy in the crystal is not sufficient to
ionize all available impurities. Some electrons are ``frozen'' at the donor
level and the electron concentration is less than the donor concentration.
As the temperature is increased, the condition of complete ionization is
As the temperature is further increased, the electron concentration remains
essentially the same over a wide temperature range. This region is called
extrinsic. As the temperature is increased further, we reach a point where
the intrinsic carrier concentration becomes comparable to the donor
concentration. Beyond this point the semiconductor becomes intrinsic.
The temperature at which the semiconductor becomes intrinsic depends on the
impurity concentration and the bandgap value. It can be obtained from
Fig. 2.3 by setting the impurity concentration equal to .
Ion implantation is a process whereby a focused beam of ions is directed towards
a target wafer. Ionized particles are used in this process, because they can be
accelerated by electric fields and separated by magnetic fields in an easy way
in order to obtain an ion beam of high purity and well-defined energy. The
ions have enough kinetic energy that they can penetrate into the wafer upon impact.
The basic features of an ion implanter for doping semiconductors and the need to
anneal the implant were patented by Shockley in 1957 .
The accelerators developed for nuclear physics research and isotope separation
provided the technology from which ion implanters have been developed and the
specific requirements of the semiconductor industry defined the evolution of the
architecture of these small accelerators . The next section describes
some key elements of a modern ion implanter like the ion source and the beam
transport system as well as a technique to achieve uniform doping over large
wafers. The wafers are processed one at a time or in batches and are moved in
and out of the vacuum by automated handling systems. The productivity of an ion
implanter is of economic importance and there is continuing need to increase
the usable beam current especially at low energies.
Commercial ion implanters are linear accelerators (linacs) that accelerate ions
up to an energy of several MeV. Early machines of the 1970s typically used cold
cathode ion sources, which were able to produce ion currents of up to A.
In 1978, the first true high current ion implanter was introduced, which used a
Freeman ion source and produced 10mA of ion current at energies up to
80keV . The rapid change in manufacturing process has led to new
and improved implanters being developed almost on a yearly basis. The wafer size
is now 300mm and has increased seven times since 50mm wafers in 1970. Each size
change obsoleted the previous generation of implanters. The changes needed were
not only related to wafer handling, but the increase in area of 36 times meant
that to maintain equivalent wafer throughput, the beam current needed to be
increased correspondingly and as a result effects such as wafer heating, wafer
charging, space charge and contamination became quite significant problems .
Cross-sectional schematic of a Bernas ion source with
indirectly heated cathode and vaporizer (left) and corresponding photo (right) .
The ion source in an implanter must be capable of producing stable beams of the
common dopants such as boron, phosphorus, arsenic, antimony, and indium. A beam
current of up to 30mA and a lifetime of more than 100h before failure are required
for cost effective productivity . Among several different sources that
have been developed the Bernas source with an indirectly heated cathode has become
the source of choice for almost all implanters built today, and each
manufacturer has developed a specialized design for their equipment .
Fig. 2.7 shows a typical example of this ion source. The ionizing electrons
oscillate between the indirectly heated cathode and an anticathode and are confined
by the magnetic field of a small electromagnet. The plasma density and the shape
of the exit aperture of the ion source in combination with the extraction
electrodes are important elements in the beam line since the quality and density
of the ion beam entering the analyzing magnet system are determined in this region.
A detailed discussion of extraction geometries can be found in a review by
Hollinger , and of the beam transport system by Rose and
When ion implantation was first adopted for doping semiconductors it was not
realized what a large range of capabilities would ultimately be needed. Today,
different machine types are used to cover the entire range of both energies and
beam currents required for semiconductor fabrication. The machines can be grouped
in medium current, high current, high energy implanters, and specialized implanters,
for example, the oxygen implanter for SIMOX (separation by implantation of oxygen)
Schematics of the medium-current implanter EXCEED3000AH .
Almost all the medium-current implanters which deliver beam currents in the range
of a few mA incorporate the concept of hybrid scanning by combining a beam scan
and a one-axis mechanical wafer scan. Fig. 2.8 shows an example of a
modern medium-current implanter from Nissin Corp. for 300mm wafers which can be
employed for the 45nm technology and beyond . The ion beam is
generated in the ion source, mass analyzed at the analyzing magnet, accelerated
or decelerated at the acceleration column, energy filtered at the final energy
magnet, swept by the beam sweep magnet, and then collimated through the collimator
magnet. This implanter uses a one-dimensional hybrid scan, where the ion beam is
scanned and collimated by magnetic fields in horizontal direction and the wafer
is then mechanically scanned in vertical direction. The typical energy range
covered is between about 3keV and 250keV for singly charged ions. Using double or
triple charged ions extends the energy range to approximately 750keV.
Several manufacturers produce machines of this type and they are widely employed,
because they satisfy many of the lower doping requirements for devices, they
have a wide energy range and wafer throughputs as high as 450 wafers/h can be
When source/drain implants requiring doses of 10 ions/cm became
important, high-current implanters capable of beam currents larger than 10mA were
developed to allow fast processing of wafers. The decreasing junction depth
is creating a challenge for high-current implanters because below a few keV it
is difficult to obtain reasonably high beam currents .
2.2.2 Crystallographic Considerations
Channeling of implanted ions results from the regular arrangement of silicon
atoms in rows and planes in crystalline silicon. The silicon crystal has a
diamond structure, where each silicon atom is covalently bonded to four other
silicon atoms in a tetrahedral arrangement. This configuration belongs to the
face-centered cubic (FCC) crystal system with silicon atoms in all corners of
a cube, in the center of each cube face, and at four interstitial positions
within the cube, as shown in Fig. 2.9. The unit cell of the silicon
crystal with its lattice constant of 5.4307
C defines the channels in silicon, where complex channeling behavior
can arise from this relatively simple arrangement of atoms.
The Miller indices are commonly used to define planes of atoms and directions in the
The Miller indices of a particular plane are a set of three integers which are
derived arithmetically from the intercepts , , of that plane with the
coordinate axes , , . The length of the intercepts is a related quantity which
is specified in multiples of the lattice constant . The Miller indices are
Illustration of the silicon crystal structure and Miller index notation.
where the factor is the lowest common multiple (LCM) of the three intercepts
, , . This is illustrated in Fig. 2.9, which shows the Miller
indices for three of the major planes in the silicon lattice. If a plane has a
negative intercept value, this is indicated with a bar over the corresponding
Miller index. For example, a plane with the intercepts 1, -1, 2 is designated as
There are some additonal important points concerning the Miller index notation.
In the FCC crystal structure, a direction that has the same , , values
in its Miller indices as a plane is perpendicular to that plane. Thus, ,
, and directions are perpendicular to , , and
planes, as demonstrated in Fig. 2.9. There are directions and
planes that are identical with respect to physical properties like channeling.
For example, the directions , , ,
are all equivalent and referred to as
the corresponding group of equivalent planes is designated as planes.
Channels exhibit a lower stopping power for the incoming ions since the atomic and
electronic densities in the channels are considerably lower than elsewhere in the
crystal. This means that ions which are moving along a channel have longer ranges
than ions which are traveling in non-channeling directions. Channeling arises not
only by the lower stopping power in the center of the channel but also by a
focusing effect due to the atoms at the edges of the channel .
Lever and Brannon have performed comprehensive investigations of boron channeling
in silicon in the region - tilt from the
axis in order to identify the major axial and planar channels .
The strongest channeling occurs due to the
axial channel which
produces the two peaks at tilt, twist and at tilt,
twist in Fig. 2.10. Other major channels appear in the
direction (planar channel), and in
direction (axial channel). It can also be observed that the effect of tilt angle
is much stronger than that of the twist angle. For instance, a tilt of
and a twist of can be used to minimize the channeling of ions.
Simulated average path lengths of boron ions which are
implanted with an energy of 100keV (Lever and Brannon ).
Channeling is a significant phenomenon for implantation energies from 1keV up to
several MeV. In the lower energy regime a larger deflection of an ion occurs even
when the ion is traveling near the center of the channel .
This behavior is a direct consequence of the fact that the effective radius of
silicon atoms along the channel increases as the ion energy is reduced. At a low
enough energy the efective radii of the silicon atoms defining the channel
become large enough to block that channel. Channeling can be reduced by a
screening layer or by pre-amorphization. An amorphous layer, preferable silicon
dioxide, can be deposited on the crystalline substrate to scatter the implanted
ions. The pre-amorphization implant is performed before the desired implant in
order to destroy the crystal structure of the substrate. Preferred ion species
are silicon, germanium, or xenon. Both methods were investigated by simulation
studies in .
2.2.3 Process Parameters for Ion Implantation
The ion implantation process is mainly determined by the following five process
- dopant species,
- ion beam energy,
- implantation dose,
- and tilt and twist angles.
The simplest semiconductor device is the pn-junction diode which can be easily
formed by ion implantation. Fig. 2.11 illustrates a typical n/p-doping
profile which is formed by a p-well implant followed by the n-implant with
its maximum concentration near the surface.
Typical implant doping profiles for pn-junction formation.
Physical properties of common impurities in silicon.
||Small diffusion coefficient
||Strong channeling effect
Ion implantation is a random process, because each ion follows an individual trajectory
which is determined by the interactions with the atoms and electrons of the target material.
The final position of an implanted ion is reached where it has lost its kinetic energy.
The average depth of the dopant distribution is referred to as the mean projected
range . The junction depth is the point where the donor and acceptor
concentrations are equal, as shown in Fig. 2.11.
Simulated distribution of dopant ions implanted in crystalline silicon
with an energy of 100keV and a dose of cm.
Several dopant species are used for ion implantation applications. Table 2.3
summarizes some properties of the most important dopants for CMOS technology.
Arsenic, phosphorus, and sometimes antimony are used for n-type doping, while the
common p-type dopant is boron. The distribution of these dopants are compared in
Fig. 2.12, using equal implantation dose and energy. The profiles were
simulated with the ion implantation simulator .
If different ions are implanted with the same energy, heavy ions like antimony stop
at a shallower depth than the light ions. The very light boron atom has the largest
projected range and the broadest distribution, since a deeper penetration
gives rise for more random collision events. Sometimes electrically inactive
species like silicon or germanium are implanted before the boron implant to form
an amorphous layer beneath the surface which suppresses the channeling effect
for boron. Amorphizing pre-implants by germanium facilitate the forming of
ultra-shallow junctions for the p-MOSFET, not only by controlling channeling,
since germanium also reduces significantly the boron diffusion during the
subsequent RTA annealing step. Shallower boron profiles can also be obtained by
implanting molecular ion species like BF or BH.
The disadvantage of the molecular ion implantation is that additional impurities
Projected range for dopant atoms in amorphous
silicon versus energy.
The sheet resistance was measured by Cypress Semiconductor
for RTA annealed wafers using the Prometrix four-point probe.
The ion energy controls mainly the penetration depth of ions, and the amount of
implanted ions is given by the dose, expressed in ions/cm. In modern
semiconductor technology, the energy ranges from 100eV to 3MeV, and the dose
from to ions/cm. Energies below a few keV at a high
dose are used for the formation of ultra-shallow junctions. Energies in the
medium range are applied for poly doping or for channel engineering like
threshold voltage adjust or halo implant. Higher energies are required for some
low dose applications like retrograde wells. Within the energy range for each
doping application, lower mass species are typical implanted at lower energies
than heavier species. The dose of the application depends on device design
requirements and is independent of the dopant species. The process parameters
energy and dose can be controlled very accurately by electrical measurements.
A modern implanter guarantees a deviation in energy below 1%. The beam current
is a measure of the flow of charged particles, whereby
current corresponds to
ions/s. The ion beam is turned off
by the dose integrator when it has counted the desired number of ions.
Fig. 2.13 shows the experimentally determined mean projected range
of the most important dopant species as a function of the implantation
The values are extracted from profiles measured by secondary ion mass
spectrometry (SIMS). Note that the data are averaged since SIMS data
exhibit a wide variation in results and only amorphous target materials are
commonly used to identify the versus energy dependence.
In Fig. 2.13 it can be observed that the projected range of an ion is
larger for lower mass species. Therefore, boron has the largest projected range
of all investigated dopants, while antimony has the shortest projected range.
An exception of this rule can be observed for arsenic and antimony at lower
energies. This effect arises because the stopping power is dominated by nuclear
stopping in the low energy regime, while it is dominated by electronic stopping
in the high energy regime (as described in Section 3.1.3). Antimony has the maximum
position of the nuclear stopping power at a slightly higher energy than arsenic
which results in a lower stopping power below 5keV (inverse region) and a larger
The total dose can be calculated by numerical integration of the dopant
concentration profile from the wafer surface to at least the junction
Fig. 2.14 shows the sheet resistance versus dose
. The concept of sheet resistance is often used to characterize
doped layers. The resistance of a rectangular block of uniformly doped
material with resistivity , length , width , and thickness
can be written as
However, to avoid confusion between and , the sheet resistance is
specified in the unit of ``Ohm per square''
. The L/W ratio, defined
by the unmasked implantation area, can be thought of as the number of unit
squares of material in the ion implanted resistor.
The maximum resonable dose around cm for the formation of highly
conductive regions is determined by the solid solubility of the dopant species in
the semiconductor material. At dopant concentrations higher than the solid
solubility a part of the dopants cannot be activated, because they precipitate and
form immobile clusters during the subsequent RTA annealing process.
Definition of tilt and twist angle for the ion beam .
The direction of incidence of the ion beam with respect to the wafer crystal
orientation is defined by the tilt and twist angle, as shown in Fig. 2.15.
The tilt is the angle between the ion beam and the normal to the wafer surface.
Wafer rotation or twist is defined as the angle between the plane containing the
beam and the wafer normal, and the plane perpendicular to the primary flat of
the wafer containing the wafer normal. The primary flat defines the orientation
of the silicon crystal, which is aligned to a direction in a
oriented wafer. The Miller index notation for describing directions and planes
in the crystal lattice system is explained in Section 2.2.2.
An appropriate tilt and twist can be used to minimize the channeling effect.
Large tilt angles are required in some implantation applications, for instance,
in halo implants.
There are two silicon crystal orientations that are used in IC manufacturing,
and silicon , which means that the crystal
terminates at the wafer surface on or planes, respectively.
Primarily because of the superior electrical properties of the Si/SiO
interface, wafers are dominant in manufacturing today.
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Up: Dissertation Robert Wittmann
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R. Wittmann: Miniaturization Problems in CMOS Technology: Investigation of Doping Profiles and Reliability