Most of your questions can be answered "yes", but be careful with Schottky vs. (ultra) fast diodes:
"Can I just buy the higher voltage and current rated Schottky diode and sub them for the lower rated ones?"
Should Work.
"Is the main reason for getting the exact match the cost and ability to fit?"
Some issues like the diode's capacitance have an influence on switching speed and, as a consequence, switching losses, i.e. heat generated in the diode. Try to find at least a similar device. Also, pay attention to peak values for current spikes and the like. Average current is one thing, peak current and power handling capabilities are another.
"Do I only need to match package/voltage/current?"
This is what designers do when looking for second source parts. In most cases, you will be good to go.
"Are Schottky and fast recovery the same?"
Usually, fast recovery is a label for p-intrinsic-n diodes, i.e. Si diodes, that are trimmed towards blocking fast upon being reverse biased. Schottky diodes are, really, always as fast as can be and should not be replaced with slower Si diodes, even when they're labeled "fast". The general rule is: Don't replace Schottky with Si diodes.
"Can I sub an ultra-fast for a fast recovery?"
Using an ultra-fast Si diode in place of a fast Si diode should work as far as switching losses go, but the faster switching action might cause worse electro-magnetic emissions.
"And... at the moment I need a Schottky that is in the TO220 package. Can I use two axial leads and just wire the cathodes together?"
Diodes in three-pin TO220 packages are really just two diodes. They are, however, very similar. When connected in parallel, they will share the load really well. Different packages are also often a hint towards different peak current/power handling capabilities. And, of course, thermal properties will be different. A TO220 has its own little heat sink even when mounted in free air; axial diodes don't have this nice feature.
There's a few things that you can do:
- Find a SPICE model for your particular LED. SPICE uses the Shockley diode model, so you can just pull Is and N from the model card.
- Find a datasheet for the LED in question (with a graph indicating a voltage-current relationship) and model only Is and N, which is actually not very difficult. See my answer on "How to model a LED" for most of what you need to get started. Only solving for Is and N will work well until you start trying to use the equation for peak currents (high current, low duty cycle).
- Take the forward threshold voltage of the diode, and solve the diode equation for Is. Guess about 1.8-2.0 for N and just be satisfied with the result. It won't track reality very well, but it will behave like a diode.
Take the values for this red LED and hope that they mostly work for your LED.
IS=1a RS=3.3 N=1.8
Keep in mind that different color LEDs have different forward voltage drops, and that even diodes with the same color can have different voltages. Also, the diode equation neglects series resistance, which can have a significant effect at high currents. It is up to you to understand your accuracy requirements, and to know the limitations of your calculations.
Best Answer
Walter H Schottky was a physicist, wikipedia He did much work around emission of electrons from surfaces, which led to the metal-semiconductor junction being named after him.
William Schockley was an engineer, mainly at Bell Labs. wikipedia. His work on the junction diode included the Schockley equation, which relates current to an exponential of voltage. $$ I=I_S(e^\frac{V_D}{nV_T}-1)$$
Many people confuse the two. I can't think why.