Lecture 8 MOS (Metal Oie Semiconuctor) Structure In thi lecture you will learn: The funamental et of equation governing the behavior of MOS capacitor Accumulation, Flatban, Depletion, an Inverion Regime Small ignal moel of the MOS capacitor MOS (Metal Oie Semiconuctor Fiel Effect Tranitor (FET) MOS FET Source Drain AlGaA InGaA (Quantum Well) GaA (Subtrate) High Electron Mobility FET 1 nm A 173 nm gate length MOS tranitor (INTEL) nm gate length MOS tranitor (INTEL) 1
A -MOS (or MOS) apacitor + Si or Metal metal contact SiO + _ Subtrate (or Bulk) Doping: N Metal contact A MOS apacitor + Si or Metal SiO o Doping: N Aumption: t o 1) The potential in the metal gate i M If the gate i + Si then M p ) The potential eep in the p-si ubtrate i p 3) The oie (SiO ) i inulating (near zero conuctivity; no free electron an hole) an i completely free of any charge 4) There cannot be any volume charge enity inie the metal gate (it i very conuctive). But there can be a urface charge enity on the urface of the metal gate 5) Dielectric contant: 3. 9 o o 11. 7 o
A MOS apacitor in Equilibrium + - SiO Doping: N t o otential lot: B M n Aume: B otential? n B t o M We nee to fin the potential in equilibrium everywhere A MOS apacitor in Equilibrium: Depletion Region Step 1: harge Flow + - SiO Doping: N Tunnel t o Step : Depletion region i create in the ubtrate an a urface or heet charge enity on the metal gate + - SiO + Doping: N t o o Negative urface charge enity (/cm ) oitive epletion charge enity (/cm 3 ) QG o 3
A MOS apacitor in Equilibrium: harge Denitie + - SiO + t o o harge enity plot: Q G o t o o Depletion region charge enity (/cm 3 ) Total charge per unit area in the emiconuctor (/cm ) QB o A MOS apacitor in Equilibrium: Electric Fiel + - SiO + t o Electric fiel in the emiconuctor: E E E o o o Linearly varying t o E o E o 4
Some Electrotatic onier an interface between meia of ifferent ielectric contant: 1 E 1 E Suppoe you know E 1, can you fin E??? Ue the principle: The prouct of the ielectric contant an the normal component of the electric fiel on both ie of an interface are relate a follow: E 1 1 E Q I Interface heet charge enity Note that E 1 i the electric fiel JUST to the left of the interface an E i the electric fiel JUST to right of the interface A MOS apacitor in Equilibrium: Electric Fiel + - SiO + t o Electric fiel in the oie: E o E contant E o o t o E o o o E E E E o o Eo o 5
A MOS apacitor in Equilibrium: otential + - SiO + otential in the emiconuctor: E o o n o t o o n t o o n Start integrating the fiel beginning from the ubtrate (bulk) to fin the potential A MOS apacitor in Equilibrium: otential + - SiO + otential in the oie: E n o o t o o o o o n o n t o o 6
A MOS apacitor in Equilibrium: otential + - SiO + t o o n B t o o M Mut have: Therefore: t o o o n to M o o o o B B M Oie capacitance (per unit area) o o t o n A MOS apacitor in Equilibrium: otential + - SiO + t o o n B M B o S B t o E o o o otential rop in the oie t o o S o otential rop in the emiconuctor E o B M o n o Oie capacitance (per unit area) o o to 7
A Biae MOS apacitor: > + - SiO o + t o o All of the applie bia fall acro the epletion region an the oie B t o o n B B o otential rop in the oie otential rop in the emiconuctor A Biae MOS apacitor: > + - SiO o + t o o All of the applie bia fall acro the epletion region an the oie B t o o n The epletion region hrink an the oie fiel alo ecreae for > o o B E o a o 8
A Biae MOS apacitor: Flatban onition + - SiO o t o When i ufficiently poitive, the epletion region thickne hrink to zero Thi value of i calle the flatban voltage otential in flatban conition: n t o Flatban voltage: B o o B M n A Biae MOS apacitor: Accumulation ( > ) + - SiO o otential: t o harge accumulation (ue to electron) on the emiconuctor urface B n t o harge Denity: Q G o The entire potential rop for > fall acro the oie t o Total charge per unit area in the electron accumulation layer QN o 9
A Biae MOS apacitor: Depletion ( < ) + - SiO o + t o B t o n B o o S The epletion region wien an the oie fiel alo increae for < otential rop in the oie otential rop in the emiconuctor A Biae MOS apacitor: Depletion ( < ) + - SiO o + t o B t o n S n o n o n 1
A Biae MOS apacitor: Hole Denity B t o n S n A i ecreae, S alo ecreae The hole enity in the emiconuctor epen on the potential a: p o q qn q n q n n KT KT KT KT ie nie e Ne Hole enity i the larget right at the urface of the emiconuctor where the potential i the lowet q n p N KT e n A Biae MOS apacitor: Threhol onition t o n B S n q n p N KT e N When i ecreae an the urface potential S reache - n the poitive hole charge enity at the urface become comparable to the poitive charge enity in the epletion region an cannot be ignore The gate voltage at which S equal - n i calle the threhol voltage T : n T n o 11
A Biae MOS apacitor: Inverion ( < T ) + - T SiO o + t o Inverion layer charge (ue to hole) on the emiconuctor urface When the gate voltage i ecreae below T the hole enity right at the urface increae (eponentially with the ecreae in the urface potential S ) Thi urface hole enity i calle the inverion layer (aume to be of zero thickne in thi coure) Q Inverion layer charge enity (/cm ) t o QG Q A Biae MOS apacitor: Inverion ( < T ) t o ma n B T S n B When the gate voltage i ecreae below T the inverion layer charge increae o rapily that the etra applie potential rop entirely acro the oie, an the urface potential S remain cloe to - n onequently, the epletion region thickne (an the epletion region charge) oe not increae when the gate voltage i ecreae below T n T n o S n ma n T ma ma o 1
A Biae NMOS apacitor: Inverion ( < T ) + - T SiO o + Q How to calculate the inverion layer charge Q when < T? Start from: By Gau law: Therefore: Q Q o o o Q E E o t o o T o t o o Q T S o ma a ma ma ma S ma A Biae MOS apacitor: Summary of Different Regime Flatban ( = ): No epletion region in the emiconuctor an no accumulation charge Accumulation ( > ): No epletion region in the emiconuctor but majority carrier accumulation charge on the urface of the emiconuctor Depletion ( T < < ): Depletion region in the emiconuctor but no majority carrier accumulation charge or minority carrier inverion charge on the urface of the emiconuctor Inverion ( < T ): Depletion region in the emiconuctor an minority carrier inverion charge on the urface of the emiconuctor 13
A Biae MOS apacitor: harge Depletion Region harge (/cm ) T Q B Q B QB ma n Q B o o Inverion Layer harge (/cm ) Q T Q o T Q N Q N A Biae MOS apacitor: harge Accumulation Layer harge (/cm ) T Q N QN Q N QN o harge (/cm ) Q G T QG Q QN QB 14
The Small Signal apacitance of a MOS apacitor The mall ignal capacitance (per unit area) of the MOS capacitor i efine a: QG where Q G i the charge enity (unit: /cm ) on the gate (1) Accumulation ( > ): Q G o o v gb o The Small Signal apacitance of a MOS apacitor () Depletion ( T < < ): QG QG Differentiate the equation (erive earlier): o To get: 1 o Define: b v gb o Finally: 1 1 1 o b b 15
The Small Signal apacitance of a MOS apacitor (3) Inverion ( < T ): Q G ma Q Q o T Q o G Q ma oe not change with in inverion v gb o The Small Signal apacitance of a MOS apacitor harge (/cm ) Q G T Q G o Inverion o Accumulation Depletion T 16
A MOS apacitor with a hannel ontact SiO metal contact + + -Si -Si _ B _ Inverion layer Subtrate (or Bulk) Metal contact In the preence of an inverion layer, the aitional contact allow one to irectly change the potential of the inverion layer channel w.r.t. to the bulk (ubtrate) A Biae MOS apacitor: Inverion with B ma ma( ) t o B n S n B S n B We ha ai that the urface potential S remain fie at n when i ecreae below T But with a non-zero B, the urface potential S in inverion can be change to ( n + B ) The new value of the epletion region with i: n n Quetion: How o we now fin the inverion layer charge Q when B i not zero? B ma 17
A Biae NMOS apacitor: Inverion with B + - T SiO o + Q + - B t o ma How to calculate the inverion layer charge Q? Same way a before.. Start from: o S E ot ma a o S ma By Gau law: Therefore: o E Q o o Q Q o o ma ma ma o ma ma A Biae NMOS apacitor: Inverion with B + - T SiO o + Q + - B Q o t o a ma o ma a ma Q o T ma o n B T ma n B o Same a before but now T epen on B 18
MOS apacitor: Effect of B ( < T ) gate + ource rain + - B - + - ource gate rain B < Inverion charge ecreae Depletion region epan gate + ource rain + - B - B > Inverion charge increae Depletion region hrink 19