Please interrupt me as I speak, maybe I can make this last 20 min.
Just don't ask anything difficult. - Neither during nor after the presentation.
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Metal on semi
-There are two kinds of possible contacts between metals and semiconductors.
-Which is formed depends on the difference in work functions.
-I usually dislike when the speaker has to push a button to get up each single line in his
presentation, but since everyone does it, I want to do the same.
-So here goes:
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-The two different contacts are
-Schottky contacts - where the charge carriers can be more easily moved from the
semiconductor to the metal than vice versa,
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-and ohmic contacts, which are not really ohmic in the real world, but are much less
rectifying compared to the Schottky contact
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Schottky contacts
-So, what happens when we bring a metal and a semiconductor together?
-We here look at metal and an n-type semiconductor, with the metal work funktion
larger than that of the semiconductor. That is, the Fermi level of the metal, E_F,m, is
lower than that of the semiconductor, E_F,s, compared to the vacuum level.
-phi_n is a label we assign to the potential difference between the conduction band and
the Fermi level.
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-When the metal and semiconductor are brought together, electrons will flow from the
semiconductor to the metal and cause a positively charged depletion region and
lowering of the Fermi level in the semiconductor.
-The result is this band structure where a barrier phi_b is created for electrons
intending to cross from the metal to the semiconductor.
-Without an applied bias, electrons experience a barrier V_0 in the opposite direction.
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Forward bias
-Applying a positive potential to the metal, causes a reduction of the barrier over to
the metal and electrons are excited thermally over it.
-The current due to this flow is given by the diode equation.
-For a forward bias, the term -1 becomes neglishible...
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-...and can be omitted.
-Thus, the current has an exponential dependency on the applied forward bias.
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Reverse bias
-Then, doing the opposite, applying a positive potential to the semiconductor, we get an
increase in barrier height for electrons wanting to cross from the semiconductor to the
metal, but the electrons flowing in the other direction still experience phi_b which is
practically unchanged
-Looking at the diode equation again, we see that the exponential term becomes very
small for reverse biases...
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-... and we are left only with -I_0.
[I_0=RT^2A exp(-phi_ms_or_b/kT]
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IV of Schottky contacts
-Thus, a Schottky contact gives IV characteristics with properties similar to that of a
pn junction, with a constant reverse current and a forward current with an exponential
bias dependency.
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Real-life problems
-This is the ideal voltage dependency of the current.
-Little in our world can be said to be ideal, and this is no exception.
-The most important causes for this is believed to be:
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-Schottky effect.
-If I understand correctly, this incorporates image-force lowering and something
called E-field lowering.
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-Series and parallel resistance
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-Presence of other mechanisms, such as
tunnelling current,
recombination in the depletion region at low voltages
and alteration of the charge distribution near the interface due to surface charges.
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-Inhomogeneous barrier height.
This is different barrier height at different positions at the junction
-If you object to any of this I suggest you take that with these guys.
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-These effects cause deviation from the ideal diode equation.
-Linear increase of the barrier height with forward bias and series resistance can be
accounted for by inserting an...
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...ideality factor, like this.
-But there are still plenty of effects left to make the behaviour different from this
equation.
-I will now look quickly at...
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-...image-force-induced barrier lowering, and...
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-...surface states
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Image force
-A charge close to a metal, induces an attractive mirror charge in the metal.
-The potential due to this effect is shown here. This adds with the ideal potential of the
Schottky contact...
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-...and causes a reduction of the barrier height both from the metal side and the
semiconductor side.
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Surface states
-If there are surface states present, like illustrated here, electrons will jump from the
conduction band to occupy the states with lower energy.
-This reduces the Fermi level and causes band bending.
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Ohmic contacts
-Semiconductor devices usually need to be connected to the rest of the world.
-Ohmic contacts are preferred, because then the voltage is, ideally, proportional to the
current and nonlinear elements are not introduced into the circuit.
-There are two general types of ohmic contacts that are possible:
-Non-rectifying barriers
-Tunneling barriers
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Ideal non-rectifying barriers
-If the work function of the metal is smaller than that of the semiconductor, electrons
will flow into the semiconductor and cause the Fermi level to rise, thus causing a
bending of the band...
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-...like this.
-The electrons flowing from the semiconductor will not experience a barrier, and the
electrons flowing from the metal will only have to overcome the barrier phi_n, which
can be quite small for moderate to high doping.
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Tunneling barriers
-If metal is put in contact with a very highly doped semiconductor, with a Fermi level
that may be even above the conduction band, the Schottky barrier will be very narrow.
-This enables the charges to easily tunnel through the barrier.
-Here it is also impossible to avoid the same barrier that we saw for the non-rectifying
case, because the highly doped part is connected to the lower doped part, further out.
-And with the necessary band bending to attain equilibrium, the same barrier will result.
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-The tunneling current is proportional to this expression, where E_infty is
proportional to the square root of the doping concentration.
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Specific contact resistance
-I will tell about the personal problems I have had with specific contact resistance.
-I think I finally got some understanding for what this R_c now.
-It is defined like this...
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-This is not something I can easily relate to, and I need to look at it in a more banal
way.
-Hence!...
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-...specific contact resistance according to Jan.
-And like so many times before, the result is just dead wrong.
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-My problem is that R_c is occasionally referred to as resistance per unit area.
-I therefore thought it would be quite natural to divide the contact resistance by the
area.
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-But this doesn't make sense, because the dimension is wrong, Ohm divided by m^2, not
Ohm times m^2, and the larger the area, the smaller the specific contact resistance.
-That seems undesirable.
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R_c cont.
-A better idea is to use this logic with the contact conductance:
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-My self-defined specific contact conductance equals contact conductance divided by
area.
-A new&improved version of Jan's specific contact resistance can now be worked
out.
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-The resistance is the inverse of the conductance.
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-My specific contact conductance is given here.
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-We now replace the contact conductance with the inverse of the contact resistance and
get...
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-...the contact resistance multiplied by the area.
-Now the dimension and area dependence are much more sensible.
-Although I expect the formula to be wrong, it makes me better understand why it
makes sense to talk about specific contact resistance.
-And I understand why the dimension is as it is.