A.1.2 The Concrete MOSFET (I): Long-Channel Transistors

A modified version of the rather hypothetical device in Fig. A.1 is shown in Fig. A.2. A legend of materials is shown Fig. A.19). It consists of a metal-oxide-semiconductor (MOS) structure, where the metal (or doped polysilicon) forms the gate, the oxide acts as gate insulator, and the semiconductor makes up the area of the channel and below. The four terminals S, G, D, and B are referred to as source, gate, drain, and bulk, respectively. The n+ doped regions contact the channel which forms below the semiconductor-oxide interface.

The basic operation principle is the same as for the device in Section A.1.1: the electric field at the oxide-semiconductor interface controls the electron density in the semiconductor. The p doped region below the channel is depleted to a certain depth

$$\ensuremath{X_{\mathit{d}}}\xspace = \sqrt{{\displaystyle\fr... ...{\ensuremath{q}\xspace \ensuremath{N_{\mathit{A}}}\xspace }}} ,$$ (A.6)

with $\ensuremath{\psi _{\mathit{s}}}\xspace = 2\vert\ensuremath{\Phi _{\mathit{B}}}\xspace \vert \approx \rm 1V$, so that the negative acceptor charges, together with the gate oxide thickness and the work function differences of the gate and contact materials determine the threshold voltage (for a detailed derivation see [2,81]):

$$\ensuremath{V_{\mathit{T,inv}}}\xspace = -\ensuremath{\Phi _... ...athit{BS}}}\xspace -2\ensuremath{\Phi _{\mathit{B}}}\xspace } .$$ (A.7)

For n-type polysilicon as gate material the workfunction difference evaluates to

$$\ensuremath{\Phi _{\mathit{MS}}}\xspace = -0.56{\rm V} -\ensuremath{\Phi _{\mathit{B}}}\xspace$$ (A.8)

with the built-in potential defined as

$$\ensuremath{\Phi _{\mathit{B}}}\xspace = -\ensuremath{U_{\ma... ...it{A}}}\xspace }{\ensuremath{n_{\mathit{i}}}\xspace } \right) ,$$ (A.9)

and the body factor

$$\gamma = \frac{\sqrt{2\ensuremath{\epsilon _{\mathit{s}}}\xs... ...{\mathit{A}}}\xspace }}{\ensuremath{C_{\mathit{ox}}}\xspace } ,$$ (A.10)

where $\ensuremath{C_{\mathit{ox}}}\xspace = \ensuremath{\epsilon _{\mathit{i}}}\xspace /\ensuremath{t_{\mathit{ox}}}\xspace$ is the gate capacitance per area and is the acceptor concentration. In the presence of fixed charges at the interface the threshold voltage shifts by $-\ensuremath{Q_{\mathit{ss}}}\xspace \ensuremath{C_{\mathit{ox}}}\xspace$.

Figure A.2: Principle structure of a MOSFET