lecture_04_MOS_modeling_I

# lecture_04_MOS_modeling_I - Handout#4 EE 214 Winter 2009...

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Handout #4 EE 214 Winter 2009 MOS Transistor Modeling for Analog Design Part I B. A. Wooley and B. Murmann Stanford University Basic MOSFET Operation (NMOS) How to calculate drain current (I D ) current as a function of V GS , V DS ? B. A. Wooley, B. Murmann EE214 Winter 2008-09 2

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Simplifying Assumptions 1) Current is controlled by the mobile charge in the channel. This is a very good approximation. 2) "Gradual Channel Assumption" - The vertical field sets channel charge, so we can approximate the available mobile charge through the voltage difference between the gate and the channel 3) The last and worst assumption (we will fix it later) is that the carrier velocity is proportional to lateral field ( ν = μ E). This is equivalent to Ohm's law: velocity (current) is proportional to E-field (voltage) B. A. Wooley, B. Murmann EE214 Winter 2008-09 3 law: velocity (current) is proportional to E field (voltage) Derivation of First Order IV Characteristics (1) [ ] =− no x G S t Q (y) C V V(y) V =⋅ Dn IQ v W = μ ⋅ vE [ ] μ Do x G S t IC V V ( y ) V E W B. A. Wooley, B. Murmann EE214 Winter 2008-09 4
Derivation of First Order IV Characteristics (2) = dV(y ) E dy [ ] = −− μ Do x G S t IC V V ( y ) V E W [ ] x G S t Idy W C V V (y) V dV DS V L [ ] ∫∫ 00 x G S t Id yWC V V ( y )Vd V ⎡⎤ V W ( ) ⎢⎥ ⎣⎦ 2 DS x G S t D S V V V L ± For V DS << V GS -V t device behaves like a resistor: I=1/R × V ± For V DS > V GS -V t , pinch-off occurs B. A. Wooley, B. Murmann EE214 Winter 2008-09 5 Pinch-Off V + G S + + V D S N N y Q ( y ) , V ( y ) n Voltage at the end of channel is fixed at V -V ± Effective voltage across channel is V GS -V t y = 0 y = L GS V t – At the point where channel charge goes to zero, there is a high lateral field that sweeps the carriers to the drain • Recall that electrons are minority carriers in the P-region of a PN junction; they are being swept toward the N-region – The extra drain voltage drops across depletion region ± To first order, the current becomes independent of V DS B. A. Wooley, B. Murmann EE214 Winter 2008-09 6

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Plot of Output Characteristic Saturation Triode Region Region I D V DS V GS -V t ⎡⎤ DS V W ( ) ⎢⎥ ⎣⎦ 2 Do x G S t D S IC V V V L Triode Region: Saturation Region GS t (V V ) W V V ( V V ) Saturation Region: ( ) −− 2 2 1 2 x G S t G S t ox GS t L W C( V V ) L B. A. Wooley, B. Murmann EE214 Winter 2008-09 7 Plot of Transfer Characteristic (in Saturation) V GS V t V OV () == μ = μ D mo x G S t o x O V GS dI W W gC V V C V dV L L = 2 2 D x OV I W LV B. A. Wooley, B. Murmann EE214 Winter 2008-09 8
Channel Length Modulation (1) V G S + + V D S N N Q ( y ) , V ( y ) n y y = 0 y = L Δ L(V DS ) ± Increasing V DS causes the depletion region around the drain to widen ± This pushes the pinch-off point further away from the drain, resulting in This pushes the pinch off point further away from the drain, resulting in an effective shortening of the channel – Modeled as Δ L(V DS ) B. A. Wooley, B. Murmann EE214 Winter 2008-09 9

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lecture_04_MOS_modeling_I - Handout#4 EE 214 Winter 2009...

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