Relationship of clock, die temperature and Vcore
As far as Vcore, clock and die temperatue relationship, a chip (CPU) can be modeled as
a capacitor C and a resistor R in parallel driven by Vcore. C models the useful active power to substain the computation by charging and discharging 100 millions of internal capacitors (from coupling between transistors, wires and silicon subtrate). R models the wasted leakage power through the internal current paths through the dozens millions of transistors.
If the die temp is kept low enough, in theory, todays XP and P4 can be clocked as high as 3 GHz, 4 GHz. The power (the C component) going into the chip to run the clock at a frequency f and Vcore V is given by
P_active = C V^2 f
And this can go on to 3-4 GHz if the die is kept below certain temp. Most of the power are used to power the clock faster as Vcore is increased.
But in reality, for any cooling used, air, water, vapor, liquid nitrogen, ..., the die temperature will eventually increase as Vcore increases due to leakage current which heats up the chip. Though at a different rate depends on what cooling is used. The leakage current is small at low temp, and increases with temp increases and also at a faster rate as temp increases. The power that heats up the chip (the R component) is given by
P_leak = V^2 / R
From my experiment with the TB B 1700+ DLT3C, when die temp reaches around 40C, the
chip leakage current begins to increase at a faster pace, and heats up the chip more. Once this starts, any Vcore increase will split between powering faster clock, but also in heating up the chip. The exact Vcore when this occurs varies from chip to chip (100-200 mV difference), it depends on the "gene" how a particular CPU was born.
P = P_active + P_leak = CV^2 f + V^2 / R
After passing that temp threshold, the portion P_leak going into heating the chip (the R component) will become larger and larger, as Vcore is increased. In other word, the useful P_active to power the chip faster (the C component) will eventually become very very small. And the chip is just being heat up and cannot be clocked faster any more.
If better cooling than air such as vapor, liquid nitrogen are used, the chip may reach that temperature threshold (40C) at a much higher Vcore. That is, more power can be used to power the P_active portion to a much higher clock frequency before the CPU reaches that temperature threshold of high "run away" leakage. But still, the leakage current will still increase, but at a much slower pace due to lower die temperature, until which the die temp reaches, say 40C again, but at a much higher Vcore for a much higher clock frequency (hopefully 3-4 GHz). And at that point, overclocking will still begin to hit a wall like air cooling then.
