60
T. B. Asafa et al.
The resistivity of a thin film is independent of the interprobe spacing s, so the
sheet resistance R s is given by the following equation:
R s =
ρ
t
= k
V
I
(17)
where the geometric factor k =
π
ln2
, which is 4.53 for a semi-infinite thin sheet
which may differ for non-ideal samples. The resistivity of poly-SiGe film measured
with four-point probe, showing in Fig. 32c, decreases asymptotically with the film
thickness and fairly stabilizes at a thickness of 40 nm. The trend observed can also
be used to describe the stages of resistivity evolution which are: initial stage (regime
I), transient stage (regime II), and stagnation stage (regime III). Details of the results
are available elsewhere (Asafa et al. 2014).
3.2.2 Carrier Concentration and Hall Mobility
Hall mobility and carrier concentration are parameters that are obtained based on
the Hall effect principle which explains the behavior of charge carriers when they
are exposed to electricity and magnetic fields. Carrier concentration refers to the
number of charge carriers per unit volume while Hall mobility is a measure of how
fast electrons or holes can travel in a metal or in a semiconductor. Hall mobility is a
critical factor in electronic and semiconductor devices/materials as it helps to determine switching frequency in transistors, photoconductive gain in photodetectors, and
transport properties in solar cells and emitting devices (Ponce et al. 2020). The hall
mobility can be estimated by Eq. 18:
μ n or μ p = σ n R H
(18)
where μ n is hall mobility for electrons, μ p is hall mobility for holes, σ is conductivity
of the material in the conductor, n is number of charge carriers per unit volume, and
R H is the hall coefficient.
In theory, the Hall effect is generated when a magnetic field of magnitude B
is applied perpendicular to a moving carrier (van der Pauw 1958). Because of the
magnetic field, the moving carrier is deflected perpendicularly to both the magnetic
field and the plane the carrier was traveling in (Fig. 33a). The Lorenz force, F =
−qv × B where q is the carrier charge (1.602 × 10
−19 C), introduces a potential
difference or Hall voltage, V H , across the sample resulting in an electric field (Lin
et al. 1981). Measurement of the Hall voltage is done following the van der Pauw
technique (Fig. 33b) where a constant current is forced through contacts positioned
opposite to each other while the Hall voltage is measured across the other two. The
magnitude of the Hall voltage, V H , is related to the current I traveling through the
sample, the applied field B, and the sheet density of carriers N s by the following
equation.
T. B. Asafa et al.
The resistivity of a thin film is independent of the interprobe spacing s, so the
sheet resistance R s is given by the following equation:
R s =
ρ
t
= k
V
I
(17)
where the geometric factor k =
π
ln2
, which is 4.53 for a semi-infinite thin sheet
which may differ for non-ideal samples. The resistivity of poly-SiGe film measured
with four-point probe, showing in Fig. 32c, decreases asymptotically with the film
thickness and fairly stabilizes at a thickness of 40 nm. The trend observed can also
be used to describe the stages of resistivity evolution which are: initial stage (regime
I), transient stage (regime II), and stagnation stage (regime III). Details of the results
are available elsewhere (Asafa et al. 2014).
3.2.2 Carrier Concentration and Hall Mobility
Hall mobility and carrier concentration are parameters that are obtained based on
the Hall effect principle which explains the behavior of charge carriers when they
are exposed to electricity and magnetic fields. Carrier concentration refers to the
number of charge carriers per unit volume while Hall mobility is a measure of how
fast electrons or holes can travel in a metal or in a semiconductor. Hall mobility is a
critical factor in electronic and semiconductor devices/materials as it helps to determine switching frequency in transistors, photoconductive gain in photodetectors, and
transport properties in solar cells and emitting devices (Ponce et al. 2020). The hall
mobility can be estimated by Eq. 18:
μ n or μ p = σ n R H
(18)
where μ n is hall mobility for electrons, μ p is hall mobility for holes, σ is conductivity
of the material in the conductor, n is number of charge carriers per unit volume, and
R H is the hall coefficient.
In theory, the Hall effect is generated when a magnetic field of magnitude B
is applied perpendicular to a moving carrier (van der Pauw 1958). Because of the
magnetic field, the moving carrier is deflected perpendicularly to both the magnetic
field and the plane the carrier was traveling in (Fig. 33a). The Lorenz force, F =
−qv × B where q is the carrier charge (1.602 × 10
−19 C), introduces a potential
difference or Hall voltage, V H , across the sample resulting in an electric field (Lin
et al. 1981). Measurement of the Hall voltage is done following the van der Pauw
technique (Fig. 33b) where a constant current is forced through contacts positioned
opposite to each other while the Hall voltage is measured across the other two. The
magnitude of the Hall voltage, V H , is related to the current I traveling through the
sample, the applied field B, and the sheet density of carriers N s by the following
equation.