EE66: olid tate evices Lecture 22 MOcap Frequency Response MOFET I- haracteristics erhard Klimeck gekco@purdue.edu. Background 2. mall signal capacitances 3. Large signal capacitance 4. Intermediate ummary 5. ub-threshold (depletion) current 6. uper-threshold, inversion current 7. onclusion Outline Ref: ec. 6.4 of F 2
Topic Map Equilibrium mall signal Large ignal ircuits iode chottky BJT/HBT MOAP 3 mall ignal Equivalent ircuit ate p semiconductor is small (only tunelling current) J J / o Low khz frequency High frequency For insulated devices, consider only majority carrier junction capacitance J 4
mall ignal Equivalent ircuit ate p semiconductor is small (only tunelling current) J J / o Low khz frequency High frequency For insulated devices, consider only majority carrier junction capacitance J 5 rey: gate Red: oxide Blue: inversion reen: depletion Junction apacitance + ~ - + υ sinωt dq d p-i Q = ψ = d ( Q ) d O d dψ d Q d Q ( ) ( ) = + O = + O 6
Junction apacitance O = + O which we already understand! d ( Q ) dψ ( ) Q ψ s is not fixed Remember the Qs vs phi_s figure we mentioned in the previous lecture 7 efinition of m for later use ( ) m = + O body effect coefficient ( ) m = + κ x κ W O T W T depends on the voltage in practice:. m.4 ψ ψ O O O = + m 8
Outline. Background 2. mall signal capacitances 3. Large signal capacitance 4. Intermediate ummary 5. ub-threshold (depletion) current 6. uper-threshold, inversion current 7. onclusion Ref: ec. 6.4 of F 9 J u n c t i o n a p a c i t a n c e in accumulation κ ε ox j, acc x κ sε = W o s, acc j, acc s, acc o + s, acc acc + Q -Q + Q W acc / o Low frequency Arrows is the charge induced by small signal Two blue arrow Two red arrow s These two capacitors are in series
Junction apacitance in depletion j, dep = = + + = s o s + s κ ε x κ ε W s = o + δ + Q -Q 2 qn AW qn AW = x + κoε 2κ sε First term is the drops on oxide econd term is band bending / o Low frequency κo W = + κ x s δ Junction capacitance in inversion + Q > T Exposed Acceptor s -Q Electron s κ ε s j, inv x j, inv κ ε = W o inv s inv o + inv inv / o Time to generate inversion charge. ms to µs Low frequency 2
Equivalent Oxide Thickness Q i = ( ) T = = < o inv j, inv o inv + o / ox Low frequency o κoε o = x κ ε i nv κ sε o W inv κ ε = + Winv > x ox O = ox O EOTelec xo EOT e le c κ sεo Equivalent oxide thickness - electrical O 3 High frequency curve at inversion κ ε s j, inv x High Frequency W T T / o Low frequency High frequency - TH The red region contribute to the, as if it is still in depletion What about high frequency part of the curve? 4
Response Time > T ielectric Relaxation σ τ = κ ε s RH Recombination-eneration 2 np ni ni R = τ ( p + p ) + τ ( n + n ) τ + τ n p n p Ref. Lecture no. 5 5 High frequency response in MO- Low Frequency High Frequency W T W T - / o Low frequency - High frequency 6
Ideal vs. Real - haracteristics Blue dot: Flat band voltage / o / o Red dot: Threshold voltage 7 Outline. Background 2. mall signal capacitances 3. Large signal capacitance 4. Intermediate ummary 5. ub-threshold (depletion) current 6. uper-threshold, inversion current 7. onclusion Ref: ec. 6.4 of F 8
Topic Map Equilibrium mall signal Large ignal ircuits iode chottky BJT/HBT MO 9 Large ignal eep epletion W dm ρ(x) W dm j, dep s = = + κ s ox W + κ s x o = + δ (even beyond threshold) / o - For large signal, the green do not have time to response; continue to deplete. mall signal Klimeck there EE66 is Fall green 22 notes because adopted from of Alam the bias builds it. N A x - Low frequency High frequency 2 N A
Relaxation from eep epletion / ox Low frequency epending on the measurement frequency, it will either merge with low-freq. or high-freq. curve. High frequency eep depletion low frequency ρ(x) High frequency ρ(x) ρ(x) W dm W dm W dm N A x - - x - N A 2 Ideal vs. Real - haracteristics Flat band voltage / o / o Real case ideal Threshold voltage If the signal rise slower, it will be closer to ideal case 22
Low or High frequency? n + -i n + -i typically observe hifrequency p-i = n i 2τ p-i typically observe low-frequency No deep-depletion as well What happens if I shine light on a MO capacitor? 23 Intermediate ummary ) ince current flow through the oxide is small, we are primarily interested in the junction capacitance of the MO-capacitor. 2) High frequency of MO- is very different than lowfrequency -. 3) In MOFET, we only see low frequency response. 4) eep depletion is an important consideration for MO-capacitor that does not happen in MOFETs. 24
Topic Map Equilibrium mall signal Large ignal ircuits iode chottky BJT/HBT MOAP MOFET 25 Outline. Background 2. mall signal capacitances 3. Large signal capacitance 4. Intermediate ummary 5. ub-threshold (depletion) current 6. uper-threshold, inversion current 7. onclusion Ref: ec. 6.4 of F 26
ubthreshold Region ( < th ) E E n+ n+ p n y No voltages What happens with a gate bias? Remember this is a 2 device! Back-gate grounded => fixed potential Looks like 2 pn junctions In 2 not MOcap as discussed before with surface psi_s 27 ubthreshold Region ( < th ) n W inv Q Q 2 W I = q log I n qww Q Q L 2 inv ch n = q W Win v Lch N n L N ch 2 i A 2 i A qψ sβ ( e ) q / ( β m e ) High injection E E y ubthreshold lope =>6m/dec Ψ s or /m m = body coefficient typically.~.4 28
ubthreshold Region ( < th ) n Q Q 2 E E 29 Recall the definition of body coefficient (m) ( ) m = + O Body Effect oefficient ( ) m = + κ x κ W O T ψ O in practice:. m.4 m O ψ = O + 3
Outline. Background 2. mall signal capacitances 3. Large signal capacitance 4. Intermediate ummary 5. ub-threshold (depletion) current 6. uper-threshold, inversion current 7. onclusion Ref: ec. 6.4 of F 3 Post-Threshold MO urrent ( > th ) I W = eff L µ ch Q i ( ) d Formula overview derivation to follow ) quare Law 2) Bulk harge 3) implified Bulk harge [ ] Q ( ) = ) i T 4) Exact (Pao-ah or Pierret-hields) i T ( φ + ) 2qε 2 in A B Q ( ) 2 i = FB ψ B O Q ( ) = ) [ m ] 32
Effect of ate Bias W W M n+ n+ P B y BI > T 2ψ B No source-drain bias ated doped or p-mo with adjacent n + region a) gate biased at flat-band b) gate biased in inversion A. rove, Physics of emiconductor evices, 967. 33 The Effect of rain Bias 2 band diagram for an n-mofet a) device b) equilibrium (flat band) c) equilibrium (ψ > ) d) non-equilibrium with and > applied epletion very different in source and drain side Alam ate voltage EE-66 must ensure 9channel formation=> LARE 34 M. ze, Physics of emiconductor evices, 98 and Pao and ah. F N
Effect of a Reverse Bias at rain W W M R R R > T ( R ) BI + R ψ = 2ψ B + R ated doped or p-mo with adjacent, reverse-biased n + region a) gate biased at flat-band b) gate biased in depletion c) gate biased in inversion A. rove, Physics of emiconductor evices, 967. 35 Inversion harge in the hannel Q = ( ) n+ n+ P B i ox th + qn ( W ( ) W ( = ) ) A T T = = = > B > > B 36
Inversion harge at one point in hannel B th qn AWT ( = ) = 2φF ox * th qn AWT ( ) = ( 2φF + ) ox ( W ) W = ) * qn A T ( T ( ) th = th + ox Q * i = ox( th ) 37 Approximations for Inversion harge ( ) Q = ( ) + qn W ( ) W ( = ) i O th A T T ( 2φ + ) κ ε ( φ ) = ( ) O th + 2qκ ε on A 2q on 2 B A B Approximations: Q ( ) i ox th Q ( m ) i ox th quare law approximation implified bulk charge approximation 38
The MOFET = > n+ n+ P F n = F p = E F B F n = F p q F n increasingly negative from source to drain (reverse bias increases from source to drain) 39 Elements of quare-law Theory > y A : E y << E x [ ] Q ( y) = m ( y) i ox th 4
Another view of hannel Potential ource rain N+ N+ P-doped x F P F P F N F N F P F N E E F E x 4 d J = Q µ E = Q µ dy d J2 = Q2 µ E2 = Q2 µ dy d J3 = Q3 µ E3 = Q3 µ dy d J4 = Q4 µ E4 = Q4 µ dy Jidy = µ i =, N i =, N J µ dy = ( m ) d i =, N Q d i ox th 2 ox = ( th ) Lch 2 2 3 4 µ J m Q quare Law Theory > Q Q 2 Q 3 Q 4 42
quare Law or implified Bulk harge Theory 2 µ ox I = W ( th ) m Lch 2 di * = = ( th ) m, sat = ( th ) m d I AT = ( T )/ m W µ o I = 2mL ( ) 2 T ch 2 µ ox J = ( th ) m Lch 2 W I = µ ( ) L o T 43 Why does the curve roll over? I W µ o I = 2mL ( ) 2 T ch AT = ( T )/ m Q ( m ) i ox th > Q loss of inversion Expression Klimeck is EE66 only Fall 22 valid notes for adopted voltages from Alam up to pinch-off 44
Linear Region (Low ) I W I = µ ( ) o T Lch = R H lope gives mobility small Actual Mobility degradation at high ubthreshold onduction T Intercept gives T an get T also from - 45 ummary ) MOFET differs from MOAP in that the field from the / contacts now causes a current to flow. 2) Two regimes, diffusion-dominated ubthreshold and drift-dominated super-threshold characteristics, define the I - - characteristics of a MOFET. 3) The simple bulk charge theory allows calculation of drain currents and provide many insights, but there are important limitations of the theory as well. 46