OLED and TFT controller chips generate all their own voltages internally. The module manufacturer would have mounted any external capacitors specified by the chip maker.
You generally do not need to worry about these details. Just provide a stable power supply and use a respected library. As others have suggested, add 10uF and 100nF to the board. Possibly a series inductor / choke as well.
There will always be some electrical noise. Good layout, short wires, adequate decoupling capacitors should keep it manageable.
All great points. I didn't realize the charge pump was in the OLED itself. Neat!
I'm using the SSD1306ASCII library from https://github.com/greiman/SSD1306Ascii. I'm pretty sure this is a legit library.
A bit more information regarding the power.
* I'm using a 1SPOT PRO CS12 isolated power supply (120VAC to 9VDC). I don't think I can get much cleaner.
* The 9V goes thru a 1N5817 to the Arduino, which uses its internal 5V vreg. I power the OLED from this vreg.
* The 9V also goes to a DC-DC buck converter to step down to 5VDC. I use this to power the relays and most of the other stuff. I don't know if matters for my design, but the IN- and OUT- of the DC-DC buck converter are connected to the same GND.
* I have tried a LM7805 instead of the DC-DC buck converter. No change. (However, I do realize that this does not power the OLED).
I'm definitely not a true PCB guy. I do it as a hobby for guitar effects. However, showing my layout to other EEs, they saw nothing immediately wrong. I tried to keep the SDA/SCL traces short, and tried to keep a ground pour between them.
Every other IC on my board has a 100n decoupling cap.
I could probably shorten the wires I'm using to test my OLED.
For the 10uF and 100nF caps that we're talking about: you mean just from VCC to GND, right, in parallel?