Professor Membrane, arguably the most famous person on the version of Earth which Invader ZIM takes place in, is best known for his numerous devices he has created to benefit mankind. This article contains a complete list of the professor's inventions.
Inventions from the TV series
First seen under development in "The Nightmare Begins", Supertoast appears to be ordinary toast. However, it appears to have been the result of heavy genetic modification, and has an instantaneous, steroid-like effect on anyone who ingests it.
Perpetual Energy Generator
The Perpetual Energy Generator, abbreviated to "PEG", was an infinite power-generating machine built by Membrane that would have supplied free power to all of Earth, or - if the machine failed - would have sent out a shockwave of destruction that would destroy all life on the planet. At the unveiling ceremony, "Da Cone" threw an ice cream cone, followed by the Dib robot's eye, onto the stage. This angered the Professor, who decided that the Earth wasn't ready for unlimited free power. Therefore, he never turned PEG on, much to the dismay of the crowd.
PEG seems to be a cross between the real-life National Ignition Facility (NIF) and the Large Hadron Collider (LHC), due to its ability to create infinite amounts of energy (NIF), and to possibly destroy Earth (LHC). However, the LHC's supposed ability to destroy the world was later proven false. The generator also somewhat resembles the core of Wardenclyffe Tower. What's interesting is that the Professor referred to the machine as 'her' when describing it.
Giant Anti-Santa Robot
Membrane has a deep hatred of Santa Claus, borne of an unpleasant childhood experience when Santa gave him an endless mountain of socks for Christmas, instead of what Membrane dreamed of: A Uranium-238 (238U). Deeply disappointed and angered, Membrane devoted a portion of his life to destroying Santa by making an Anti-Santa arsenal; this included the giant Anti-Santa robot. Dib later used the robot to combat Zim when the Invader attempted to gain control over the human race by impersonating Santa.
Temporal Object Displacement Device
Professor Membrane revealed his Temporal Object Displacement Device on his TV show, Probing the Membrane of Science. The device replaces one object with another in the past (for example, turning Breakfast Chunks to Breakfast Squids), but it is impossible to predict the outcome of the replacement. Professor Membrane said that anyone who dare use the device would be a "complete moron" for messing with the flow of time and changing history.
In the episode "Bad, Bad Rubber Piggy", Zim built one to try to kill Dib. The name is possibly a reference to Vasquez's earlier work Squee!, as the acronym for the Temporal Object Displacement Device is "TODD" for short (which is Squee's real name).
The Hoverhelmet makes its only appearance in "Bad, Bad Rubber Piggy", when Dib used it to float into the sky and spy on a family of Nosferatus down the street. In an alternate timeline, while Dib was airborne, Zim turned the Hoverhelmet into a rubber piggy, using the Temporal Object Displacement Device, and Dib plummeted to the ground. The damage this impact had on Dib forced him to wear an oxygen tank, with tubes attached to his neck, in order to breathe.
The MegaBoy 3000 is a fusion-powered titanium exoskeleton created by Professor Membrane in the episode "Bad, Bad Rubber Piggy". He created it for his son Dib, whose skeleton was crushed by a paramedic in a freak piggy accident. Of course, the piggy accident was caused by Zim, who had been replacing random objects in Dib's childhood with rubber piggies. The exoskeleton gave Dib the strength of ten thousand little boys, and allowed him to easily infiltrate Zim's base in the present time. Zim attempted to weaken Dib further by throwing more rubber piggies into the Temporal Object Displacement Device, but instead of weakening Dib it made him grow stronger. This time each piggy added an upgrade to the MegaBoy 3000, such as lasers or missile launchers.
Finally, Zim used his last piggy to send a warning back to himself not to use the Device, resetting reality and removing the MegaBoy from existence.
The Nanoship is an unmanned microscopic ship that Dib used to combat Zim's micro-sub when the Invader shrank down to microscopic size and invaded Dib's body. The ship has the ability to transform into a two-legged mech, much like Zim's. Its weapons include a grapple hook and lasers.
The Nanoship's controls are similar to that of the design for the Game Slave (not only are the typical D-pad and A and B buttons available, there is also an extra joystick), as Gaz, an avid video gamer, was able to effortlessly defeat Zim in Dib's body, while Dib was unable to.
The Nanoship's design is based on the microsub from the film Innerspace.
Foodio is a robot that Membrane invented to solve world hunger. It makes its sole appearance in the unfinished episode "Ten Minutes to Doom", where immediately after its activation it goes off to fulfill its programming. It is not seen again after this, though a PAK-controlled Dib does take a copy of the robot that Membrane had lying around and reprogram it for destruction, renaming it Destructio.
A presumably upgraded version of Foodio called Foodio 3000 appears a few times in the comic series. It seems that Membrane keeps this version of the robot around to serve as his family's personal chef. And it would seem to be quite good at its job, given that in Issue 5, Membrane states that its poached eggs are worth choosing it over Dib when Lord Voxelrot comes to abduct him.
Inventions from the Comic Series
Parallel Universe Device
Issue 5 of the comic series has Membrane aid Gaz in finding a parallel universe ruled by gamers, though how is not shown.
Issue 9 features a Flesh Printer, which can create limbs and alter appearances. Dib uses it to disguise himself as an alien and infiltrate Zim's base, while Gaz gives herself extra limbs so that she can play multiplayer games by herself.
In Issue 14, Dib had accidentally ingested a vile of the professor's experimental nanosploder bots. It was actually Gaz who had given the vial to him when she was mad at him for hogging the TV, and because of this Gaz had to be nice to Dib for the whole day. If Dib became sad, the nanosploder bots would react badly with brain chemicals released during depressive states, causing him to explode. The nanobots run out of power after about eleven hours.
In Issue 16, Membrane provides Dib with a Fear Siphon, which sucks up all the fear input in his brain, rendering him fearless. The input is stored in the siphon as a slurry, which Membrane apparently believes can one day be used as fuel to reach the Moon (seemingly unaware that humans have already been there).
Jhonen stated in a DVD commentary that, in a later episode, it would be revealed that Dib himself (and possibly Gaz too) had actually been an experiment made by Membrane for an unknown purpose. How this would be revealed is unknown, as the series was cancelled before anything could be scripted out.