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

Lecture 34, 04 Apr 14 Chp 06: MOSFETs Channel Current IDS (n-channel p-substrate) Finish theory Examples Goal: IDS in charge sheet constant mobility model, good for both linear and saturation I-V regimes VM Ayres, ECE875, S14

Goal: IDS in charge sheet constant mobility model, good for both linear and saturation I-V regimes VM Ayres, ECE875, S14

Why this is the Charge sheet model: Note that Qn = Qn(y) ≠ Qn(x,y). That means neglecting “thickness of Qn near the Source L z Width = Z y: S to D SiO2 x VM Ayres, ECE875, S14

Why this is the Charge sheet model: Charge Qn(y) does vary in y-direction: Lots of e-s near source end of channel Few e-s in pinch near drain end of channel when VDS in ON L z Width = Z y: S to D SiO2 x VM Ayres, ECE875, S14

Write Qn(y) in terms of VDS: Why do it this way: because VDS is something you actually know: Means: when y = L Means: when y = L VM Ayres, ECE875, S14

Approximate the change that happens along y when VDS is ON as rise over run: d D yi(y) / dy. The D yi(y) part = the rise. See how it changes along y: nergy (y) VM Ayres, ECE875, S14

Also: D yi(y) is a potential in volts Also: D yi(y) is a potential in volts. Potentials can be related to E –fields E –fields can be related to that charges Q that cause them VM Ayres, ECE875, S14

E –fields are related to charge Qn(y) as shown in (14) The E –fields in the oxide (constant value) and semiconductor are: Substitute (17) and (18) into (14) to get the expression for Qn(y): VM Ayres, ECE875, S14

Now get IDS: recall Lec 32, our Units-based guess: Z ✔ cm C cm = C = Amps cm2 s s Need vel. vel = average drift velocity <vel>. This is related to the mobility and the E –field along transport direction: VM Ayres, ECE875, S14

Constant mobility model: Mobility is average particle drift velocity per unit electric field Assume that E = E (y) but that m is constant. Then: VM Ayres, ECE875, S14

Therefore: Channel current IDS is: Blue is 0 < dy < L Red is VS - VS =0 volts < Dyi(y) < VD – VS = VDS volts Need to put one in terms of the other to finish the integral VM Ayres, ECE875, S14

It really is an easy integral. Start: Finish. It really is an easy integral. VM Ayres, ECE875, S14

Goal: IDS in charge sheet constant mobility model, good for both linear and saturation I-V regimes Achieved goal: IDS in (23) is good for any combination of VG and VDS VM Ayres, ECE875, S14

Behavior regimes Saturation: VD ≈ VG - VT Linear: VD < VG - VT VM Ayres, ECE875, S14

Lecture 34, 04 Apr 14 Chp 06: MOSFETs Channel Current IDS (n-channel p-substrate) Finish theory Examples Goal: IDS in charge sheet constant mobility model, good for both linear and saturation I-V regimes VM Ayres, ECE875, S14

Example: What regime?

Answer: VD ? What relation to? VG - VT 0.1 V < 1V – 0.5V = 0.5V Linear Use linear regime approximate equation for ID Conductance g = dID/dVD

Example: What regime?

Answer: Only VG is given, little about VD and nothing about VT But Saturation regime is stated

ox ox ox

Easy to solve for VT Note that you are reading two VG curves at some VD in saturation VG = 3 V 200 mA VG = 1 V 50 mA

Example: What regime?

Answer: Not clear but not needed. VT is a requirement that is fixed by the materials properties of the semiconductor and the insulator (oxide)