# CALTECH EE 40 - Threshold Voltage for an MOS Junction (8 pages)

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**View the full content.**# Threshold Voltage for an MOS Junction

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## Threshold Voltage for an MOS Junction

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- Pages:
- 8
- School:
- California Institute of Technology
- Course:
- Ee 40 - Introduction to Semiconductors Devices

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Threshold Voltage for an MOS Junction At threshold the concentration of electrons at the surface equal to the concentration of holes in the bulk n surface p p 0 EV q B q S 2 q B q B EI EF EV At threshold s 2 B It is assumed that all the charge in the semiconductor is due to the depletion region VTH Vox T 2 B dEox T 2 B d S Es T 2 B ox QD 2 B Cox Boundary s Es ox Eox By Gauss s Law s Es QD ox With Cox d Oxide Capacitance per unit Area Q VTH D 2 B Cox For a real MOSFET VTH VTH VFB Q Q VTH ms ss 2 D for p type for n type Cox Cox where Qss is the charge trapped at the oxide semiconductor interface MOSFET Metal Oxide Semiconductor Field Effect Transistor If Vds VT or in subthreshold diffusion current dominates n 0 n p 0 e q s x kT Vgs G S n Vds D d W n p 0 Cox L Cd Semiconductor Gate s Vox Vgs s x Cox Vgs V x Cox Vgs x Cox C D Cox C D n L n p 0 Exp q s 0 Vds kT n 0 J ds drift nq n E V ds J ds diffusion qD n 0 n L VT n L qVgs Cox CD q 0 J ds J ds diffusion Exp s Exp where Cox kT kT Ohmic Mode Triode Source and Drain have ohmic like contacts to the channel d n Vgs Vds n p 0 L dx x Qn x Cox Vgs VTH V x With C ox ox d V 0 0 and V L Vds Resistance of a length dx dx dx dR A n qn x A qn x A Charge per unit length in x direction WQn x dx nQn x W dV I D dR dR Vds WC n 0 ox L Vgs VTH V x dV I d dx 0 2 Vds W I d n C ox V gs VTH Vds L 2 Onset of Saturation Pinch Off S d n Vds Vgs G D n p 0 dx x L L qn x C ox V gs VTH V x qn L C ox V gs VTH Vds Vds sat n L 0 the channel is pinched off near For Vds Vgs VTH the drain Ideally further increase of Vds doesn t increase the source drain current Vds sat 0 Id L W nCox Vgs VTH V x dV I d dx 0 W W nCox Vgs VTH 2 nCoxVds sat 2 I d sat 2L 2L Vds Id 2 Ohmic Mode V gs 4 V gs 3 V gs 2 V gs1 V gs1 VTH Saturation Mode V gs Vds Beyond Pinch off Channel Length Modulation S d n Vds Vgs G D n p 0 L dx x L L After Saturation i

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