Parasitic Resistance L R W. Polysilicon gate. Drain. contact L D. V GS,eff R S R D. Drain

Transcription

1 Parasitic Resistace G Polysilico gate rai cotact V GS,eff S R S R S, R S, R + R C rai

2 Short Chael Effects

3 Chael-egth Modulatio Equatio k ( V V ) GS T suggests that the trasistor i the saturatio mode acts as a perfect curret source. This is ot etirely correct. The effective legth of the coductive chael is modulated by the applied V : icreasig V causes the depletio regio at the drai to grow, reducig the legth of the effective chael. k ( V V ) ( + λv ) GS T λ is the chael-legth modulatio / short chaels, the drai-juctio depletio regio presets a larger fractio of the chael, ad the chael-modulatio effect is more proouced. That s why log chael trasistors are used whe high-impedace curret sources are desiged.

4 Velocity Saturatio i short chael devices The behavior of trasistors with very short chael legths deviates cosiderably from the resistive ad saturatio models just preseted, maily due to the velocity saturatio effect. Equatio υ µ dv dx states that the carrier velocity is proportioal to the electrical field, where the carrier mobility is costat. However, at high (horizotal) field stregths, the carriers fail to follow this liear model. he the electrical field alog the chael reaches a critical value ξ C, the velocity of the carriers ted to saturate due to scatterig effects (collisios suffered by the carriers). For a ξ C.5V/µm,.5V is required for velocity saturatio i a.5µm device. This coditio s very easily met i cotemporary short-chael evices (t is easier to go ito saturatio i cotemporary devices). υ (m /s) This pheomeo has a profoud impact o the operatio of the device. This is illustrated with a first-order derivatio of the device characteristics Uder velocity saturatio. The velocity ca be roughly approximated by: υ µ ξ + ξ / ξ C for ξ ξ C υ sat 5 Costat velocity Costat mobility (slope µ) ν sat for ξ ξ C ξ c.5 ξ (V/µm)

5 Velocity Saturatio The cotiuity requiremet betwee the regios dictates that ζ / C ν sat µ the resistive regio, the drai curret ca be expressed as: µ Cox + ( V / ζ k c ( ) ( V ) ( V V ) V Κ ( V ) GS T GS V T ) V V V The Κ(V) factor measures the degree of velocity saturatio ad is defied as Κ( V ) + ( V ) K(V) for log chaels or small V values. For short chaels, K is less tha, which meas that the delivered curret is less tha what would ormally be expected. he icreasig V, the electrical field i the chael ultimately reaches the critical value, ad the carriers at the drai become velocity saturated. The saturatio drai voltage V AT ca be calculated by equatig the curret at the drai uder saturatio coditios to the resistive curret for V V AT. / ξ C e get Κ( V ) µ C AT AT ν sat AT C ox ox V GS V AT ( VGS VT ) VAT V T V AT

6 Velocity Saturatio creasig the drai-source voltage does ot yield more curret, ad the trasistor curret saturates at AT. This leads to two observatios: ) For a short-chael device ad for large eough values of V GS -V T, V AT < V GS -V T. The device eters saturatio before V reaches V GS -V T. Short-chael devices therefore experiece a exteded saturatio regio, ad ted to operate more ofte i saturatio coditios that log-chaels. ) The saturatio curret AT displays a liear depedece with respect to V GS, which is i cotrast with the squared depedece i the log-chael device. This reduces the amout of curret a trasistor ca deliver for a give cotrol voltage V GS V V AT og-chael device Short-chael device V - V V GS T

7 Curret-Voltage Relatios The eep-submicro Era.5 x -4 Early Saturatio VGS.5 V.5 VGS. V (A) VGS.5 V iear Relatioship.5 VGS. V V (V)

8 versus V Same techology, ad idetical / ratio (A) 6 x VGS.5 V Resistive Saturatio VGS. V V V GS - V T VGS.5 V (A).5 x.5-4 Velocity saturatio VGS.5 V VGS. V VGS.5 V VGS. V.5 VGS. V V (V) og Chael (quadratic depedecy bet. ad V GS ) V (V) Short Chael (liear depedecy bet. ad V GS, ad small V AT )

9 versus V GS 6 x -4.5 x -4 (A) quadratic (A).5 liear V GS (V) og Chael.5 quadratic V GS (V) Short Chael Saturated devices (V.5V): Same techology, ad idetical / ratio