User:Sistemx/Draft:Mosfets

A MOSFET is composed of two parts: a MOS Capacitor and a channel, a MOS stands for Metal Oxide Semiconductor, and FET stands for Field Effect transistor. It has 3 pins, a gate, drain and source, there are N-Mosfets, and P-Mosfets. A MOSFET is symmetric, that means Drain and Source are physically identically, the only way that it is determined which is which, is by it's potential, when the Potential in one end is bigger than the potential in the other, the end with a bigger potential is for the n-MOSFET the Drain, and the other end would be the Source, for a p-MOSFET, it's the inverse.

A CMOS is an eletrical elemental that has both a n-MOSFET and a p-MOSFET. Usually they're manufactured together on the same block, the main block also called Bulk is usually p-doped, for the p-MOSFET you need a n-doped region, so you create a n-well, the contacts of the mosfet are more highly doped, because there is a Metal-Semiconductor junction, that can create a large enough voltage difference, which is unwanted because there would be no good way of setting the potential of the bulk, or of the MOSFET.

Modes of Operation
In this document we talk about 3 modes of operation of a MOSFET, saturation mode, triode mode, and simply off.

There is also the effect of the source-bulk voltage  $$U_S$$ where


 * $$U_{th,n}=U_{th,0}+\gamma \lfloor \sqrt{2 \Phi_s+U_{SB}-\sqrt{2 \Phi_s}}\rfloor$$
 * Where:
 * $$U_{th,n}$$ is the Threshhold Voltage.
 * $$U_{SB}$$ is the Source-Bulk potential
 * $$\gamma$$ is the substrat-effect-coefficient.
 * $$\Phi_s$$ Is the surface potential for strong inversion typically approx 300mV.

since $$\gamma$$ is typically small, this effect is usually negligible.

More importantly, is the drain current flowing through the Transistor. depends on the modes. The effective gate source voltage is the gate source voltage minus the threshold voltage. $$U_{GS_{eff}}=U_{GS}-U_{th,n}$$ When $$U_{GS_{eff}}<0\implies U_{GS}<U_{th,n} $$ the n-MOSFET is off or not on.
 * $$I_D\approx 0$$

When $$0<U_{GS_{eff}}<U_{DS} $$ the n-MOSFET is in saturation mode.
 * $$I_D=\frac{1}{2} \frac{W}{L} K_{N,p} U_{GS_{eff}}^2 (1+\lambda \frac{L_{min}}{L}(U_{DS}-U_{GS_{eff}}))$$
 * Where:
 * $$K_{N,n}=\mu_n C_{ox}$$ is the Technological constant, the mobility of the electron times the oxide capacitance.
 * $$\gamma$$ is the substrat-effect-coefficient.

When $$0<U_{DS}<U_{GS_{eff}} $$ the n-MOSFET is in Triode mode.
 * $$I_D= \frac{W}{L} K_{N,n} (U_{GS_{eff}}-\frac{1}{2}U_{DS})U_{DS}$$

for a p-MOSFET the formulas are the same but inverted, however we can make them look similar to the n-MOSFET by changing the notation a little bit $$U_{SG_{eff}}=U_{SG}-|U_{th,p}|$$ When $$U_{SG_{eff}}<0\implies U_{SG}<|U_{th,p}|$$ the p-MOSFET is off or not on.
 * $$I_S\approx 0$$

When $$0<U_{SG_{eff}}<U_{SD} $$ the p-MOSFET is in saturation mode.
 * $$I_S=\frac{1}{2} \frac{W}{L} K_{N,p} U_{SG_{eff}}^2 (1+\lambda \frac{L_{min}}{L}(U_{SD}-U_{SG_{eff}}))$$
 * Where:
 * $$K_{N,p}=\mu_p C_{ox}$$ is the Technological constant, the mobility of the electron times the oxide capacitance.
 * $$\gamma$$ is the substrat-effect-coefficient.

When $$0<U_{SD}<U_{SG_{eff}} $$ the p-MOSFET is in Triode mode.
 * $$I_S= \frac{W}{L} K_{N,p} (U_{SG_{eff}}-\frac{1}{2}U_{SD})U_{SD}$$

MOSFET circuits
Base cicruits.

A MOSFET has 3 pins, gate, source, drain, a circuit is called x-circuit configuration, where x stands for the pin that is shared between the input voltage and the output voltage. Each configuration has an input and output characteristic line.

When the gate is connected to another end, this is called the Diode configuration because it's characteristic lines, look like a typical PN-Junction diode. On this configuration, the MOSFET is always in saturation mode if it's on.

When talking about nesting MOSFETS, we use the terms cascading and cascoding, cascading means connecting transistor in parallel, while cascoding means connecting them in series.

A current mirror

Mosfet small Signal model
It's possible to make a small signal model of a mosfet by performing 4 steps.

1. Replace all Source voltages with short circuits, that usually means that you place $$U_{DD}$$ on Ground too. 2. Replace all Source currents with open circuits. 3. A transistor will be replaced as a current source and a resistor, this resistor is usually given in Siemens.


 * $$g_m=\frac{\partial I}{\partial U_{gs}}$$
 * $$g_{ds}=\frac{\partial I}{\partial U_{ds}}$$

In saturation mode:
 * $$g_m\approx\frac{W}{L} k U_{g_{eff}}$$
 * $$g_{ds}\approx \frac{1}{2} \frac{W}{L} k \frac{L_{min}}{L} \lambda U_{g_{eff}}$$