Ch1-2, ASF: XALS AND QM
1. The arrangement of atoms on a 3D periodic lattice are
described by three vectors (each with three components),
called ___________. The description of a plane or a direction
in the crystal is given by one vector with three components
called ___________.
2. The energy levels of a quantum mechanical system are
constant provided its ___________ does not vary with time.
3. When an electron hits a potential barrier with energy greater
than the barrier height, its transmission shows __________ at
specific energy values. These values correspond to a barrier
width that is a multiple of its ___________.
4. When an electron hits a potential barrier with energy lower
than the barrier height, its transmission shows __________ at
specific energy values.
5. It is impossible to specify the position and ___________ of
an electron at the same time. This is called the
_________________ Principle. One can, however, compute
its average values. These follow Newtonian mechanics.
Ch 3, ASF: SOLIDS AND BANDS
1. In presence of a crystal potential, the electronic energy
eigenvalues coalesce into _________ separated by forbidden
_________. The corresponding eigenvectors look like
__________ on an atomic scale, modulated by a longer
ranged ___________.
2. Each energy eigenstate is thus labeled by two numbers, the
________ taken from the plane wave part, and the
_________ taken from the _________ part.
3. Listing the energy values against ________ gives us an
_____ diagram, with the number of k-points given by the
number of _________ in the entire solid that we model.
Furthermore, the number of eigenvalues at each k-point
depends on the number of ___________.
4. While the _________ diagram does not directly capture the
electron dynamics in real space, they are related through a
__________ transform. In fact, the slope of the ______
diagram gives us the real space ________ of the electrons,
while the curvature near the band bottom gives us the
_________ of the electrons. This _________ is not the true
______ of the electron, but lumps in the effect of the
interactions of the electron with its background ___________
potentials. This number can thus be positive, negative, zero
or infinity.
5. A downward directed, inverse parabolic band has a negative
________ for electrons, and is easier to understand in terms
of ________ with a positive _________.
6. The reason solids have band-gaps is because the electrons
form standing waves that ____________ each other.
7. The band-gaps open at specific values of k, called the
_____________ zone.
8. In the Kronig-Penny model, the size of the band-gap
_________ with increasing energy.
9. An electron in a periodic solid behaves like a free particle.
However, its ________ hides information about the atomic
interactions.
10.
Silicon has __________ constant energy ellipsoids at
________ of the Brillouin Zone along the [_____] direction.
Germanium has _________ ellipsoids at __________ of the
Brillouin Zone along the [_______] direction.
Ch 4, ASF: STATE COUNTING AND STATE FILLING
1. Once we can list the states in the form of a systematic
_______ diagram for a solid, we can count the number of states
in a given energy range. This is called __________. Each state
corresponds to a unique ________, with the number of and
separation between ______ points determined by the ________
of the entire solid.
2. The ________ thus depends on the dispersion of the
___________ diagram, and the __________ of the space they
live in. e.g. diamond is _______, graphite is ________, carbon
nanotubes are _______ and buckyballs (C60) are ________.
3. We still need to know what fraction of the states is filled at a
given temperature. This is given by the ____________
distribution, which also depends on the _______ energy that
separates filled from empty states.
4. The product of the _______ and the ________ distribution
gives us the electron density (and with slight modifications, the
hole density). If the ________ energy is a few kT away from the
band-edges, the bands only sample the Boltzmann like
exponential tails of the _________ distribution, whereupon the
integrals simplify. A simple equation that emerges thereof at
equilibrium is np = ni^2, where ni is the _________ density that
represents a solid with equal _____ and _____ numbers. ni
depends on the geometric mean of the lumped densities of states
(ie, _________) of the two bands, and exponentially on the
______.
5. The _______ can be moved by doping a solid that introduces
a _______ in the bandgap that pins the ______ to values near it.
However, the effectiveness of the dopants depends on the
________ to make sure they are not __________ but are in fact,
fully ionized.
6. Constant energy ellipsoids show surfaces in k-space that have
the same _________. Si has ______ ellipsoids along the ______
directions, while Ge has _________ ellipsoids along the ______
directions.
Ch 5, ASF: RECOMBINATION-GENERATION
1. RG processes drive a system towards ________. Thus, they
are always proportional to np-_____.
2. For indirect band-gap materials, the most efficient RG
mechanism is through Shockley-Reed-Hall, which involves
charge capture and emission by deep level _______.
3. The recombination rate is given in units of _________. It
involves the minority carrier lifetime, which is inversely
proportional to (i) the trap _________, (ii) the trap _________,
and (iii) the thermal ________ of the electrons.
4. For low-level injection, the RG simplifies. For p-type
materials, it only depends on the deviation in the _____ density
from equilibrium, and the ____________ of the _________
5. For surface recombination, the minority carrier times are
replaced by carrier _________, while the trap energies need to be
generalized to include a __________ of trap energies.
Ch 6, ASF: DRIFT-DIFFUSION
1. Electrons and holes drift under the action of an external
_______. The proportionality between velocity and field is
called ________, while that between current density and field
is called __________.
2. Increasing doping density _______ the mobility through
scattering processes. Increasing temperature reduces impurity
scattering but increases __________ scattering.
3. At high speeds, the mobility saturates through velocity
saturation. For GaAs, the velocity overshoots and then drops as
electrons move from the _______ valley with _______ mass to
the ______ valley with ______ mass.
4. A constant drift corresponds to the _______ of an electron
increasing linearly with time. The proportionality constant is
called _______. A constant diffusion corresponds to the
_______ of an electron increasing linearly with time. The
proportionality constant is called _________. The relation
between these two proportionality constants is called
_________ relation.
5. The drift-diffusion with RG gives the overall ______, which
satisfies charge conservation represented by the equation of
________. This, coupled with _________ equation forms a
complete set of equations to solve.
6. Simplifying the equations by (i) ignoring ________, (ii)
ignoring ________ and (iii) invoking the low-level injection
approximation, the 1D equations for non-degenerate
semiconductors form the _______ equations.
SDF: PN junctions
1. PN junctions are characterized by a ______ potential and a
_____ width at their interface. At forward bias, the P end is
connected to the _______ terminal of the battery, which _______
both these quantities and gives us a large current. This gives us an
asymmetry I-V, captured by the ________ equation.
2. The built-in potential varies _______ with doping for a 1sided PN junction. The depletion width varies _________ with
doping and also depends on the built-in potential.
3. The ideal diode equation is obtained by (1) solving
_________ equations in the ____________ regions with the
__________ boundary condition near the junction with the
______ region, and (2) adding the separate minority currents
from the P and N sides by ignoring _______ processes in the
________ region.
4. Real diodes show deviations on the reverse bias side due to
(1) ________, (2) _________ at large negative voltages, and (3)
_______ at small negative voltages. For forward bias, the
deviations are due to (1)___________ at low bias, (2)
__________ at higher bias, and (3) __________ at very high
positive bias.
5. Diodes are slow in switching because delays are caused by
the need to get rid of ___________ which depends on the
_________ time.
However, __________ diodes are faster as
they are based on __________ carrier motion, which is limited by
the _________ time, determined by the dielectric constant and the
conductivity.
6. Reverse bias diodes act like static __________. Forward bias
diodes have an additional frequency dependent _________ and a
frequency dependent ___________, which varies when the
operating frequency is faster than the _____________.
SDF: BJTs
1. BJTs amplify an incoming ________ current into an
outgoing _______ current. This requires grounding the third
terminal, which implies a common _________ configuration.
2. BJTs can show digital switching between the ________
mode where both emitter-base and collector-base are ________
biased, and the _________ mode where both are ________
biased. They show analogue amplification in the _________
mode where the emitter-base is ______ biased and the _______ is
______ biased.
3. The gain is maximized by ensuring that for every _____ that
escapes from the emitter into the base in a P+NP BJT, the number
of _________ entering the emitter is kept to a minimum. This is
guaranteed by keeping the emitter _______ much larger than the
base ________.
4. To collect the amplified current at the collector terminal with
no losses, the base is made very _______ compared to the
________, while the collector bias is ______ biased at a very
large voltage.
5. The base-collector bias leads to ____________ of the base
width, which prevents the ______ current from saturating, an
effect known as _______ effect. This can be controlled by
increasing the base doping, but that reduces the ________.
Another way to control this is to create an offset between the base
and emitter ________, which leads to an ___________.
6. The _______ model describes the circuit level operation of a
BJT, which together with _______ laws helps us understand the
input and output characteristics of the BJT. The model treats the
BTJ as two __________ diodes and two __________ related by a
________ coefficient.
SDF: FETs
1. The MOSFET operates by controlling the source to drain
current with a _________ voltage. At sufficiently large positive
______ voltage, a P-type substrate gets _________, meaning that
the concentration of ___________ at the surface exceeds the
concentration of _____________. This creates a pool of highly
mobile _________ that shorts the N+ source and drain contacts
and turns the transistor ON.
2. The surface charge density varies _______ with voltage in
the accumulation and inversion regions, and ________ with
voltage in the _________ region.
3. The threshold voltage for ________ the channel requires us
to obtain the voltage division between the ________ and the
_______ region. In the depletion region, the largest drop is across
the ________, while in the inversion region, the largest drop is
across the ________.
4. The C-V of a MOS capacitor shows a minimum at
__________ voltage as long as the voltage varies slower than the
__________.
5. A shift in the C-V curve indicates the presence of fixed and
mobile _______ .
6. The current in a MOSFET saturates due to ________, which
starts at the ______ end where inversion is removed as the
_______ and the ________ voltages oppose each other.