As shown in panel (b) of Fig. 16.1, in the range 1–8 kV/cm, the mean energy
slowly rises to ~0.1 eV. Higher values of driving fields produce a rapid increase of
the electron energy up to a saturation regime at about 0.4 eV. This outcome was
twice surprising for learners who first expected that the mean energy trend follows
that of the electron velocity and accordingly mean energy decreases as the mean
velocity does, and then they did not expect a saturation of the energy levels, but at
most a growth for higher values of the driving fields. The instructors encouraged a
debate on how this phenomenon could be physically justified.
From the theory the students learned that charge carriers traveling within a
semiconductor, depending on their energy, may reside in different valleys, in
which are characterized by different effective masses. The application of an electric
voltage causes the electrons are not more in equilibrium with the crystal lattice and
increase their energy; this happens until they have the opportunity to migrate from
the Γ valley to the higher energy valleys (L- and X-valleys), where the effective mass
is greater (heavy electrons). This carrier transfer was corroborated by the numerical
investigation of the electron occupancy in each valley as a function of the electric
field, reported in panel (c) of Fig. 16.1. The students observed that electrons begin to
occupy the higher energy valleys when the amplitude of the electric field achieves
values greater than %10 kV/cm, the same intensity characterizing the maximum in
the velocity-field curve. This evidence pointed up the significance of considering the
effective mass of charge carriers and the important role played by scattering events,
accountable for intervalley transitions.
16.2.5 Stage 2: Investigation of the Role Played by
the Effective Mass
A cogent query drove the students through an extensive examination of the importance of the part played by the effective mass of drifting electrons. The students
conducted various simulations and made a comparison between the numerical outcomes achieved by employing a three-valley model and those coming from the
one-valley (Γ) model, in which the electron shifts to higher energy valleys are
interdicted. Furthermore, they explored the effects of considering all electrons
having a same mass equal to the mean value among the effective masses of the
different valleys (Persano-Adorno et al. 2016b).
16.2.6 Stage 3: Study of the Effects Due to a Change
of the Doping Density
With the aim to point out the consequence of the interactions among free electrons
and ionized impurities, randomly disseminated inside the InP bulk, the instructors
16 Inquiry-Based Approach and Numerical Simulations: A Powerful Integration in. . .
207
slowly rises to ~0.1 eV. Higher values of driving fields produce a rapid increase of
the electron energy up to a saturation regime at about 0.4 eV. This outcome was
twice surprising for learners who first expected that the mean energy trend follows
that of the electron velocity and accordingly mean energy decreases as the mean
velocity does, and then they did not expect a saturation of the energy levels, but at
most a growth for higher values of the driving fields. The instructors encouraged a
debate on how this phenomenon could be physically justified.
From the theory the students learned that charge carriers traveling within a
semiconductor, depending on their energy, may reside in different valleys, in
which are characterized by different effective masses. The application of an electric
voltage causes the electrons are not more in equilibrium with the crystal lattice and
increase their energy; this happens until they have the opportunity to migrate from
the Γ valley to the higher energy valleys (L- and X-valleys), where the effective mass
is greater (heavy electrons). This carrier transfer was corroborated by the numerical
investigation of the electron occupancy in each valley as a function of the electric
field, reported in panel (c) of Fig. 16.1. The students observed that electrons begin to
occupy the higher energy valleys when the amplitude of the electric field achieves
values greater than %10 kV/cm, the same intensity characterizing the maximum in
the velocity-field curve. This evidence pointed up the significance of considering the
effective mass of charge carriers and the important role played by scattering events,
accountable for intervalley transitions.
16.2.5 Stage 2: Investigation of the Role Played by
the Effective Mass
A cogent query drove the students through an extensive examination of the importance of the part played by the effective mass of drifting electrons. The students
conducted various simulations and made a comparison between the numerical outcomes achieved by employing a three-valley model and those coming from the
one-valley (Γ) model, in which the electron shifts to higher energy valleys are
interdicted. Furthermore, they explored the effects of considering all electrons
having a same mass equal to the mean value among the effective masses of the
different valleys (Persano-Adorno et al. 2016b).
16.2.6 Stage 3: Study of the Effects Due to a Change
of the Doping Density
With the aim to point out the consequence of the interactions among free electrons
and ionized impurities, randomly disseminated inside the InP bulk, the instructors
16 Inquiry-Based Approach and Numerical Simulations: A Powerful Integration in. . .
207