I've recently talked with a friend about LaTeX compilation. LaTeX can use only one core to compile. So for the speed of LaTeX compiliation, the clock speed of the CPU is most important (see Tips for choosing hardware for best LaTeX compile performance)

Out of curiosity, I've looked for CPUs with the highest clock speeds. I think it was Intel Xeon X5698 with 4.4 GHz (source) which had the highest clock speed.

But this question is not about CPUs that get sold. I would like to know how fast it can get if you don't care about the price.

So one question is: Is there a physical limit to CPU speed? How high is it?

And the other question is: What is the highest CPU speed reached so far?

I've always thought that CPU speed was limited because cooling (so heat) gets so difficult. But my friend doubts that this is the reason (when you don't have to use traditional / cheap cooling systems, e.g. in a scientific experiment).

In [2] I've read that transmission delays cause another limitation in CPU speed. However, they don't mention how fast it can get.

What I've found


[1] Scientists Find Fundamental Maximum Limit for Processor Speeds: Seems to be only about quantuum computers, but this question is about "traditional" CPUs.
[2] Why are there limits on CPU speed?


About me

I am a computer science student. I know something about the CPU, but not too much. And even less about the physics that might be important for this question. So please keep that in mind for your answers, if it's possible.

Practically, what limits CPU speed is both the heat generated and the gate delays, but usually, the heat becomes a far greater issue before the latter kicks in.
Recent processors are manufactured using CMOS technology. Every time there is a clock cycle, power is dissipated. Therefore, higher processor speeds means more heat dissipation.
http://en.wikipedia.org/wiki/CMOS
Here are some figures:
Core i7-860   (45 nm)        2.8 GHz     95 W
Core i7-965   (45 nm)        3.2 GHz    130 W
Core i7-3970X (32 nm)        3.5 GHz    150 W


You can really see how the CPU transition power increases (exponentially!).
Also, there are some quantum effects which kick in as the size of transistors shrink. At nanometer levels, transistor gates actually become "leaky".
http://computer.howstuffworks.com/small-cpu2.htm
I won't get into how this technology works here, but I'm sure you can use Google to look up these topics.
Okay, now, for the transmission delays.
Each "wire" inside the CPU acts as a small capacitor. Also, the base of the transistor or the gate of the MOSFET act as small capacitors. In order to change the voltage on a connection, you must either charge the wire or remove the charge. As transistors shrink, it becomes more difficult to do that. This is why SRAM needs amplification transistors, because the actually memory array transistors are so small and weak.

In typical IC designs, where density is very important, the bit-cells have very small transistors. Additionally, they are typically built into large arrays, which have very large bit-line capacitances. This results in a very slow (relatively) discharge of the bit-line by the bit-cell.

From: How to implement SRAM sense amplifier?
Basically, the point is that it is harder for small transistors to drive the interconnects.
Also, there are gate delays. Modern CPUs have more than ten pipeline stages, perhaps up to twenty.
Performance Issues in Pipelining
There are also inductive effects. At microwave frequencies, they become quite significant. You can look up crosstalk and that kind of stuff.
Now, even if you do manage to get a 3265810 THz processor working, another practical limit is how fast the rest of the system can support it. You either must have RAM, storage, glue logic, and other interconnects that perform just as fast, or you need an immense cache.
