Thermal properties in mesoscopics: physics and ... - ResearchGate

oration from a source material per unit area per unit
time can be expressed by the Hertz-Knudsen relation
Ne = a[P ∗ V (T ) − P ][2πMkBT ] −1/2 , where a is the evaporation
coefficient (a = 1 for a clean evaporant surface), P
is the ambient hydrostatic pressure acting on the evaporant
in the condensed phase, P ∗ V (T ) is the equilibrium
vapor pressure of the evaporant, and M its molecular
weight. This expression shows that the evaporation rate
strongly depends on the evaporant vapor pressure. Most
common metals typically deposited by thermal evaporation
(such as Al, Au, Ga, and In) usually have vapor
pressures in the range between 10−2 to 1 Torr in the temperature
window of 600◦ ...2000◦ C; conversely refractory
metals (such as Nb, Mo, Ta, W and Pt) or ceramics (such
as BN, and Al2O3) reach such vapor pressures at much
higher temperatures, thus making more difficult the exploitation
of this technique for the deposition.
Usually evaporation is performed in high or ultrahigh
vacuum (in the range 10−5 ...10−10 Torr), where the mean
free path ℓ for the evaporant species is much larger than
the substrate-source distance. This translates in an almost
line of sight evaporation which prevents covering of
edges perpendicular to the source, the latter also referred
to as the lack of step coverage (Madou, 1997) (note that
this property is at the basis of lift-off processes (Moreau,
1988) as well as of angle (shadow) evaporation technique
using suspended masks (Dolan, 1977; Dolan and Dunsmuir,
1988)). Furthermore, vacuum evaporation is a
low-energy process (implying a negligible damage to the
substrate surface), where the typical energy of the evaporant
material impinging on the substrate is of the order
of 0.1 eV. Nevertheless, radiative heating can be high.
Resistive heating and electron-beam deposition are the
two most common methods of evaporation. The former
relies on direct thermal heating to evaporate the
source material. This method is fairly simple, robust and
economic but suffers from a limited maximum achievable
temperature (of the order of 1800◦ C), which prevents
the evaporation of refractory metals and several
oxides. On the other side, electron-beam evaporation
represents a crucial improvement over resistive heating.
This method exploits a high-energy electron beam that is
focused through a magnetic field on a localized region of
the source material. A wide range of materials (including
refractory metals and a wide choice of oxides) can
be deposited owing to the generation of high temperatures
(in excess of 3000◦ C) over a restricted area. Its
main drawback relies on the generation of X-rays from
the high-voltage electron beam which may damage sensitive
substrates (such as semiconductors) (Moreau, 1988;
Sze, 1985). Achievable deposition rates are up to several
hundreds ˚A/sec (e.g., 0.5 µm/min for Al) (Madou, 1997).
2. Sputter deposition
The sputtering process has been known and used for
over 150 years (Chapman and Mangano, 1988; Chapman,
47
1980; Rossnagel, 1998; Wasa and Hayakawa, 1992). It
is a PVD method widely used nowadays for many applications,
both in the electronic and mechanic industry
fields as well as in the pure research environment. This
process is based on the removal of material from a solid
target through its bombardment caused by incident positive
ions emitted from a (rare) gas glow discharge. The
transferred momentum of the ions leads to the expulsion
of atoms from the target material, thereby enabling
the deposition (condensation) of a film on the substrate
surface. Sputter deposition is generally performed at energies
in the range of 0.4 to 3 keV. Furthermore, the
average energy of emitted ions from the target source
is in the range 10...100 eV. At these energies bombarding
ions can penetrate up to two atomic layers in the
substrate thus leading to a great improvement of the adhesion
of the sputtered film (Maissel and Glang, 1970;
Wasa and Hayakawa, 1992). Normally, relatively high
pressures (from 10 −4 to 10 −1 Torr) are maintained in
the growth chamber during deposition. At these pressures
the mean free path is short (of the order of 1 mm
at 10 −1 Torr) so that the material atoms reach the substrate
surface with random incident angles. As a consequence,
a very good step coverage can be achieved. Being
essentially mechanical in nature, sputtering successfully
allows the deposition of refractory metals (superconductors)
like Nb, NbN, Ta, Mo and W at temperatures well
below their melting points.
D. Thin film insulators
The roles of thin film insulators in solid state electronics
are various. In particular, deposited films are often
used as interlevel dielectrics for metals, to realize lithographic
masking for diffusion and implantation processes,
as well as for passivation and protective layers (Ghandhi,
1983; Nicollian and Brews, 1983; Sze, 1985). In addition
they can be exploited as thin amorphous membranes
on which micro- and nanostructured devices are realized
(Clark et al., 2005; Fisher et al., 1999; Irwin et al.,
1996; Lanting et al., 2005; Luukanen et al., 2000; Nahum
and Martinis, 1995) in light of their specific electric and
thermal properties (Leivo and Pekola, 1998; Leoni et al.,
2003; Manninen et al., 1997). In the following we discuss
those insulators which are considered particularly
relevant for microelectronic fabrication processing, i.e.,
silicon dioxide and silicon nitride.
Silicon dioxide (SiO2) is one of the most exploited insulators
in micro- and nanoelectronics based on Si, mainly
due to the high quality of the SiO2/Si interface. SiO2
films can be grown on Si substrates by thermal oxidation
using oxygen or steam. Thermal oxidation of Si is generally
carried out in reactors at temperatures between 900 ◦
C and 1200 ◦ C. The resulting SiO2 film is amorphous and
characterized by good uniformity, lack of porosity and
very good adhesion to the substrate. Some typical parameters
of thermally grown silicon dioxide at 1000 ◦ C are