MOSFET: Subthreshold Operation

1. MOSFET: Subthreshold Operation Professor Paul Hasler

2. MOSFET Channel Picture

3. MOS Capacitor Picture

4. MOSFET Channel Picture

5. MOSFET Channel Picture

6. Calculation of Drain Current

7. 2 d n No recombination = Dn = Ax + B Dn 0 0 0 2 0 dx D 2 dn d n = + - D G R n 2 dt dx 0 l y varies as kVG (qDn / l) (e-(Y - Vs)/UT - e-(Y - Vd)/UT) - n n dn = = = source drain J qD qD n n dx l ( ) ( ) ( ) k - k - V V / u V V / u = - I I e e g S T g d T 0

8. ( ) ( ) ( ) k - k - V V / u V V / u = - I I e e g S T g d T 0 MOSFET Current-Voltage Curves ( ) - - = - / / KV u V u / V u I I e e e G T S T D T 0 DS ( ) ( ) ( ) k - V V / u - - = - V V / u I e 1 e g S T d S T 0 ( ) - - = - ( ) / / KV V u V u I e 1 e G S T dS T 0 - = ( ) / KV V u I e G S T 0

9. Channel Current Dependence on Gate Voltage In linear scale, we have a quadratic dependence In log-scale, we have an exponential dependence

10. -6 10 -7 10 -8 10 Drain current (A) -9 10 k = 0.58680 Io = 1.2104fA -10 10 -11 10 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 Gate voltage (V) Channel Current Dependence on Gate Voltage In linear scale, we have a quadratic dependence In log-scale, we have an exponential dependence

11. -6 10 -7 10 -8 10 Drain current (A) -9 10 k = 0.58680 Io = 1.2104fA -10 10 nFET pFET S D -11 10 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 Gate voltage (V) G G B D S Subthreshold MOSFETs In linear scale, we have a quadratic dependence In log-scale, we have an exponential dependence

12. 1.1 1 0.9 0.8 0.7 Drain current / subthreshold fit 0.6 0.5 VT = 0.86 0.4 0.3 0.2 0.1 0.4 0.5 0.6 0.7 0.8 0.9 1 Gate voltage (V) Determination of Threshold Voltage

13. -7 10 -8 10 -9 10 UT = 25.84mV Drain current (A) -10 10 -11 10 k = 0.545 -12 10 0.6 0.65 0.7 0.75 0.8 0.85 0.9 Gate voltage (V) Drain Current --- Source Voltage