ECE 875: Electronic Devices Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University

VM Ayres, ECE875, S14 Lecture 40, 18 Apr 14 Chp 06: MOSFETs Aspects of realistic MOSFET operation (n-channel p-substrate) Subthreshold swing: definition 01 example definition 02 example Chp 14: Sensors Chemical ion sensors Temperature sensors Mechanical sensors

How do you turn the MOSFET OFF: (n-channel) Reduce V G below threshold. No inversion layer. Want: I D = 0. But leakage current is still a problem: why: diffusion and EHP formation can’t be stopped. Subthreshold swing S is a metric for turning a MOSFET device OFF Test conditions: use a small V DS to get a current I D running. Then see how that current responds to changes in V G Motivation: It is hard to turn a device OFF. I D when the MOSFET is supposed to be OFF is called leakage current. VM Ayres, ECE875, S14

If the bottom distortion is examined carefully, it is small but it doesn’t = exactly 0. Small currents matter. Definition 01 for Subthreshold swing S: S =  V G /decade I D = 1/slope, not slope VM Ayres, ECE875, S14

S = 100 mV/decade I D  V G = V = 0.1 V Decade I D : starts where:(I D, V G ) I D = A, when V G = V T = 0.5 V Actual I D : finishes where:(I D, V G ) Find finish I D = ?? A, when V G = 0 V Goal I D : finishes where:(I D, V G ) I D = A, when V G = 0 V Find start V G = V T +  V T = ?? VM Ayres, ECE875, S14 bias

Example: try changing device to a MOSFET with: N A = 5 x cm -3 d = 10 nm = 100 Angstroms Effective insulator charge = 4 x q C cm -2 Keep: S = 100 mV/decade I D  V G = V = 0.1 V Set up answer to same questions: I D = A, when V G = 0 V Find start V G = V T +  V T = ?? Find finish I D = ?? A, when V G = 0 V Find first: what else?? VM Ayres, ECE875, S14 bias

S = 100 mV/decade I D  V G = V = 0.1 V Decade I D : Find: starts where:(I D, V G ) I D = A, when V G = V T = ?? V Actual I D : finishes where:(I D, V G ) Find finish I D = ?? A, when V G = 0 V Goal I D : finishes where:(I D, V G ) I D = A, when V G = 0 V Find start V G = V T +  V T = ?? VM Ayres, ECE875, S14 bias New MOSFETNew V T Answer:

Find V T : n-channel: -++- signs: VM Ayres, ECE875, S14

Find V T : V

VM Ayres, ECE875, S14 Streetman and Banerjee, Chp. 06, p. 286:

S = 100 mV/decade I D  V G = V = 0.1 V Decade I D : Find: starts where:(I D, V G ) I D = A, when V G = V T = V Actual I D : finishes where:(I D, V G ) Find finish I D = ?? A, when V G = 0 V Goal I D : finishes where:(I D, V G ) I D = A, when V G = 0 V Find start V G = V T +  V T = ?? VM Ayres, ECE875, S14 bias New MOSFETNew V T

V T = V

S = 100 mV/decade I D  V G = V = 0.1 V Decade I D : Find: starts where:(I D, V G ) I D = A, when V G = V T = V Actual I D : finishes where:(I D, V G ) Find finish start: I D = A, when V G =0V Find finish I D = A, when V G = - ## V Goal I D : finishes where:(I D, V G ) I D = A, when V G = 0 V Find start V G = V T +  V T = ?? VM Ayres, ECE875, S14 bias New MOSFETNew V T

V T = V V T-new = V +  V T

VM Ayres, ECE875, S14 Lecture 40, 18 Apr 14 Chp 06: MOSFETs Aspects of realistic MOSFET operation (n-channel p-substrate) Subthreshold swing: definition 01 example definition 02 example Chp 14: Sensors Chemical ion sensors Temperature sensors Mechanical sensors

Definition 01 for Subthreshold swing S: S =  V G /decade I D Definition 02 for Subthreshold swing S: VM Ayres, ECE875, S14

Definition 02 incorporates analysis of an important problem in turning a MOSFET OFF: stopping diffusion current Lots of e- few e- Lots of e- VM Ayres, ECE875, S14

Two points: Lots of e- 1. few e-: in depletion region, not charge sheet: x-dependence Lots of e- VM Ayres, ECE875, S14 2. V DS = extra depletion region in real OFF

These are the source and drain ends of the channel, not the n+ regions VM Ayres, ECE875, S14 Investigate the diffusion current issue:

VM Ayres, ECE875, S14

Investigate the diffusion current issue: Diffusion current:

IDID Surface potential is related to V G : Examine change in I D per change in V G starting with change in  s per change in V G VM Ayres, ECE875, S14 Diffusion current I D = f(  s )  V G :

VM Ayres, ECE875, S14

Influence of interface traps:

VM Ayres, ECE875, S14

Consistent? S = 100 mV/decade I D  V G = V = 0.1 V Decade I D : Find: where:(I D, V G ) I D = A, when V G = V T = V Actual I D : finishes where:(I D, V G ) Find start: I D = A, when V G =0V Find finish I D = A, when V G = - ## V Goal I D : finishes where:(I D, V G ) Find finish I D = A, when V G = 0 V Find start V G = V T +  V T = + ## V VM Ayres, ECE875, S14 bias New MOSFETNew V T

VM Ayres, ECE875, S14 Did C ox and/or C D change?

VM Ayres, ECE875, S14 Did C ox and/or C D change? Yes. Example: Find S for this device. Assume room temperature operation at 300 K.

VM Ayres, ECE875, S14 Answer: 3.45 x F cm x F cm -2

S 3.45 x F cm x F cm x F cm -2 Answer: eV e

Definition 01 for Subthreshold swing S: S =  V G /decade I D Definition 02 for Subthreshold swing S: VM Ayres, ECE875, S14 S Units:

VM Ayres, ECE875, S14 Lecture 40, 18 Apr 14 Chp 06: MOSFETs Aspects of realistic MOSFET operation (n-channel p-substrate) Subthreshold swing: definition 01 example definition 02 example Chp 14: Sensors Chemical ion sensors Temperature sensors Mechanical sensors

VM Ayres, ECE875, S14 What has changed from a conventional MOSFET? Choices: Gate Insulator Channel Substrate

VM Ayres, ECE875, S14 What has changed from a conventional MOSFET: Gate Insulator Channel Substrate