Download Current mechanisms – Exam January 27, 2012

Current mechanisms – Exam January 27, 2012
There are four mechanisms that typically cause currents to flow: thermionic emission, diffusion,
drift, and tunneling.
Explain briefly which kind of current mechanisms are important in the following devices. (For some
devices more than one type of current flows.)
(a) pn diode
(b) Schottky diode
(c) MOSFET
(d) bipolar transistor
(e) JFET
(f) MESFET
1. General explanation of current mechanisms
1.1. Drift
Drift is the movement of charge carriers induced by an electric field.
Without an electric field the electrons move randomly due to thermal excitation. Their movement
can be described by:
and
with: …mean free path,
…time between scattering events
The electrons scatter but the net movement 〈 〉 is zero, so no current flows.
With an electric field the charge carriers move ballistically ( ⃑
⃑
random scattering events. There is a net movement so current flows.
⃑⃑
) between
⃑⃑
With this the drift velocity can be deduced: ⃑
⃑⃑
Since electrons and holes have a different effective mass they also have different drift velocities:
⃑⃑
⃑
⃑⃑
⃑
with:
… mobility of electrons / holes
This then gives the drift current density:
⃑
⃑
⃑
(
) ⃑⃑
⃑⃑
with:
with: σ…conductivity
The scattering can be from defects (extra atoms, missing atoms…) or from internal motion of the
crystal (phonons).
Electrons move in the opposite direction of the electric field, the current by the electrons flows in the
direction of the field.
Holes move in the direction of the electric field, the current by the holes flows in the direction of the
field.
1.2. Diffusion
Diffusion is the current that occurs when there is a gradient in the charge carrier concentration. The
charge carriers diffuse in order to establish equilibrium. Diffusion is driven by thermal movement.
The current density can be calculated with the changes in electron density:
(
with
)
(
)
… diffusion coefficient
And for holes:
A electron gradient as pictured above makes the electrons move to the left, the current flows in the
opposite direction (to the right).
A hole gradient (with the same scheme) makes the holes also move to the left, the current flows in
the same direction (to the left).
Einstein relation
is the relation between mobility and diffusion coefficient:
1.3. Tunneling
Tunneling describes the quantum mechanical effect of electrons tunneling through a thin barrier. The
number of electrons that tunnel through a barrier depends on the thickness of the barrier. The
tunneling current drops exponentially when the barrier thickness grows. Nevertheless a barrier of
constant width acts as a linear resistor.
Among others it is used for tunneling diodes or to make good contacts in semiconductors.
1.4. Thermionic emission
Thermionic emission is the heat-induced flow of charge carriers over a barrier. The thermal energy of
the charge carrier can overcome the energy barrier.
The Richardson’s law describes the current density of the thermionic emission:
(
)
In this class the thermionic emission of a metal semiconductor contact was discussed. When a metal
and a semiconductor are brought into contact the Fermi energies adjust. This causes electrons to
flow from the material with the lower workfunction (higher Fermi energy) to the material with the
higher workfunction (lower Fermi energy). These moved charges in turn cause bending in the
semiconductor bands. If the Fermi energy is in the middle of the bands at the interface (see picture
below) the contact is a Schottky contact (with thermionic emission when barrier is low enough). If
the Fermi energy cuts one of the bands at the interface the contact is an ohmic contact (with
ohmic/linear resistance).
Nevertheless the type of contact is actually mainly determined by the interface states and not by the
workfunctions of the materials. This is because there are defects at the interface (different crystals,
different lattice constants). These defects can act like dopants and their number is very high. They
can pin down the Fermi energy.
When the barrier is low enough electrons can “hop” over it:
2. Current mechanisms in devices
(a) pn-diode
Without bias the electrons from the n-region diffuse into the p-region and the holes vice-versa. The
electrons and holes are pushed back by the built in electric field.
In forward bias minority electrons are injected into the p-region and minority holes are injected into
the n-region. The depletion width gets narrower and the diffusion current rises which makes it able
for a drift current (which dominates) to flow.
In reverse bias the charge carriers are driven away from the junction. The depletion region gets
wider. The wider depletion region means that the carrier gradient is smaller, therefore the diffusion
current is lower, no drift current is possible.
(b) Schottky diode
As the saturation current in a Shottky diode depends on thermionic emission this kind of current
mechanism dominates over diffusion current.
For very small depletion widths tunneling can occur.
(c) MOSFET
Types of contacts:
p+ & p:
ohmic contact
n+ & metal:
tunnel contact
p+ & metal:
tunnel contact
p & n+:
pn-jct. (diffusion when in reverse bias, drift when in forward bias)
Weak inversion mode:
The transistor is turned off. No current should be flowing from source to drain. Nevertheless a bit of
leakage always occurs where higher energetic electrons can pass (drift) from the source to the drain.
Linear regime:
A channel has been created and current can flow. The MOSFET is acting like a linear resistor with drift
current as main current mechanism.
Saturation (pinch-off) regime:
The channel has been pinched off near the drain. The current does not flow through a thin channel
anymore but is now further away from the interface and deeper in the substrate. The current
between source and drain does not depend on the drain voltage anymore but on the gate voltage.
(d) bipolar transistor
Forward active mode (Emitter-Base: forward, Base-Collector: reverse):
In the Emitter: drift current. From the Emitter electrons are injected into the Base. The electrons
diffuse through the base (~99% diffuse, ~1% recombines with holes). At the interface between
Collector and Base the electrons “feel” the electric field and are pushed (collected) into the Collector
Reverse active mode (Emitter-Base: reverse, Base-Collector: forward):
The transistor is used in opposite direction. Works like forward active mode but less good since the
gain depends on the high doping of the injecting semiconductor.
Saturation mode (Emitter-Base: forward, Base-Collector: forward):
High current flows from Emitter to Collector. The transistor corresponds to a logical on.
Cutoff mode (Emitter-Base: forward, Base-Collector: forward):
Very little current flows. The transistor corresponds to a logical off
(e) JFET
Types of contacts:
n+ & source/drain:
n+ & n:
p+ & gate:
p+ & n:
tunnel contact
ohmic contact (resistor)
tunnel contact
one sided pn-junction (depletion width is almost only in the n-region)
The current between source and drain is mainly carried by drift.
The reverse biased pn-junction uses the diffusion mechanism
(f) MESFET
MESFETs are similar to JFETs but they do not have the p+ region.
As in the JFET the current between source and drain is carried by the drift mechanism. The n-gate
interface is a Shottky-diode in reverse bias – since it is in reverse bias diffusion dominates this region.