Why is electron mobility so important for microwave circuits?

[fonograph]

Why its so important when making super fast transistors? I read that semiconductor resistivity depends on charge mobility and carrier concentration.From that it seems to me that it should not matter if you have many slow electrons or lesser amount of fast electrons yet the super fast circuits all use the fast electron,not many,type of semiconductor like InP and GaAs.

Is this just coincidence or is carrier,especially electron mobily somehow more special that it would seem from resistivity calculations?

[Kleinstein]

In a crude approximation the input current to a FET or BJT provides a limited number of carriers. So for a given input current / power the carrier mobility is what determines the possible higher frequency gain. 

Using more carriers is not a real option as it takes more input current.

[fonograph]

Yeah but when there is more carriers,wouldnt it take less voltage to get that current than in high mobility low carrier concentration material? If you have more current but less voltage,power stays same.

[jpb]

I used to work in modelling microwave GaAs FETs and HEMTs. The electrons at operating potentials generally are moving at their saturated velocity so mobility doesn't affect this.
These devices are complicated in real operation.
Even with HEMTs where the 2D electron gas is supposed to moving away from the donor ions, in real devices they get heated and scattered . A lot of the high gain comes from high doping. I was part of a research project that looked at comparing HEMTs and FETs and found that a suitably doped FET could be as low noise as a HEMT (at room temperature - a cooled HEMT at low current might be a different case).

For microwave circuits, a big advantage of GaAs over Si is that it has a semi-insulating state which makes for low loss transmission lines (for monolithic microwave integrated circuits).

[fonograph]

jpb Your claiming electron moblity doesnt matter much becose they are moving at saturation velocity?  Tell me about that GaAs semi insulating state,never heard about that before... 

Also,how is carrier saturation velocity different from carrier mobility? When some material have high carrier mobility,it must automatically mean it also have high saturation velocity... or is that wrong? Are carrier moblity and saturation velocity unrelated? Can there exist a high mobility low saturation velocity material?

[jpb]

jpb Your claiming electron moblity doesnt matter much becose they are moving at saturation velocity?  Tell me about that GaAs semi insulating state,never heard about that before... 

Also,how is carrier saturation velocity different from carrier mobility? When some material have high carrier mobility,it must automatically mean it also have high saturation velocity... or is that wrong? Are carrier moblity and saturation velocity unrelated? Can there exist a high mobility low saturation velocity material?

The mobility of an electron is how much it accelerates under the application of an electric field, but at a high enough field the velocity saturates. The electrons change energy valleys and in theory (and under some circumstances) the electrons exhibit negative conductivity (their velocity decreases with increased field) but in real devices this tends to be smeared out. If the opening under the depletion layer under the gate was constant then the I(V) curve would be flat in the saturated region but because of two dimensional field effects the depletion layer extends and rises so the curves continue to rise.

It is complicated to model (I'm talking about GaAs FETs here with schottky gates).

There is a brief paragraph on semi-insulating GaAs in the Wikipedia article:
https://en.wikipedia.org/wiki/Gallium_arsenide

I used to work on modelling and design of Monolithic Microwave Integrated Circuits where the semi-insulating state allowed relatively low loss transmission lines as well as active devices:
https://en.wikipedia.org/wiki/Monolithic_microwave_integrated_circuit

One popular circuit was the distributed amplifier where the capacitance of the FETs combine with the inductance of the connecting transmission lines to produce an artificial transmission line which allows amplifiers with bandwidths from dc to 10s of GHz. What I found interesting was the circuit idea for distributed amplifiers was invented at Thorn EMI (I think) in the 1940s for use with Valves and then was re-used when peopled started working on MMICs.

[fonograph]

GaAs with shottky gates... you mean mesfet? Also you say carrier mobility is acceleration under voltage,isnt it speed rather than acceleration?

Carrier mobility = average speed for given voltage
Saturation velocity = maximum speed limit

[jpb]

GaAs with shottky gates... you mean mesfet? Also you say carrier mobility is acceleration under voltage,isnt it speed rather than acceleration?

Carrier mobility = average speed for given voltage
Saturation velocity = maximum speed limit

Yes, mobility is the slope of the v/E curve (line in the linear region). I was rather loosely using the term acceleration to indicate that increasing field increases the velocity.

[T3sl4co1l]

Also something about thermal equilibrium and carrier diffusion, being in the drift velocity regime.

I think that means mobility is effectively lower once you hit saturation velocity?

(Which is also kind of a quirk of GaAs, the electric field required to reach saturation is below that required for impact ionization (avalanche), whereas it's the other way around in silicon for example.)

Eh, it's been forever since I worked with these equations... 

Tim