ELEC 3908, Physical Electronics, Lecture 27 MOSFET Scaling and Velocity Saturation
Lecture Outline Industry push is always to pack more devices on a chip to increase functionality, which requires making MOSFET devices smaller generally increases process cost Shrinking the size of MOSFET devices, termed scaling, results in important performance effects which may have to be addressed through structure and bias changes Lecture 25 already introduced one effect of making devices smaller, the dependence of V T on channel length One effect which will become important in smaller devices is velocity saturation, first discussed in lecture 21 when drift conduction was introduced Velocity saturation will be incorporated into the square law model Page 27-2
Geometrical Scaling Constant effort to reduce MOSFET size in order to pack more devices, and hence functionality, onto the same chip area Size can be reduced by geometrical scaling, the reduction of all dimensions by a factor ξ This reduces the size of the device, but adversely affects the performance Page 27-3
Consequences of Geometrical Scaling In normal operation, the transverse field E x is much larger than the lateral field E y - this was one of the fundamental assumptions of the square law model (1D charge balance) If pure geometrical scaling is applied, L is reduced by a factor ξ, so if the drain-source potential remains unchanged the lateral field increases approximately by ξ (E V DS /L, at least in triode operation) Page 27-4
Reduction of Drain-Source Potential The problem of increased lateral field can be solved by reducing V DS, but circuit design will be made much more difficult if all devices are required to have lower V DS without changes in other circuit potentials Therefore, the only viable solution is to lower all potentials in the circuit via a reduction in the power supply (can t actually do this by ξ) But... Page 27-5
Constant Field Scaling Reducing all potentials recreates the original field problem! The solution to the E field imbalance caused by the L scaling is therefore to reduce all potentials by the factor ξ as well as reducing the oxide thickness by the same factor This re-establishes (approximately) the original magnitudes of E fields, since both potentials and both separations have been scaled by the same factor, hence the term constant field scaling Page 27-6
Further Scaling Requirements With no other changes, the scaled structure has another problem - the source and drain depletion regions have been moved closer together The device is now more susceptible to punchthrough breakdown -the connection of the two source/drain controlled depletion regions To avoid this problem, the substrate doping is increased to reduce the depletion widths Junction depths are also reduced to mitigate short channel V T effect Page 27-7
Summary of Constant Field Scaling The final requirements for constant field scaling are therefore Reduce all dimensions including L by the scaling factor ξ to decrease the size of the device Lower all potentials by the scaling factor ξ to offset the lateral field increase caused by geometrical scaling Lower t ox by ξ to reestablish the relationship between lateral and transverse fields Raise N A by ξ in order to reduce the depletion widths to prevent punchthrough breakdown Lower the junction depths to lessen short channel V T effects Page 27-8
Consequences of Constant Field Scaling If constant field scaling is applied to the MOSFET, several consequences ensue Since both W and L have been reduced by the scaling factor ξ, the W/L ratio is unchanged Reduction of t ox by ξ results in an increase in C ox of a factor ξ The drain current therefore scales as ˆ W 2 1 ξ 1 1 ID μncox V 1 ξ 2 L 1 ξ ξ ξ The static power dissipation scales as the current and voltage factors 1 1 1 P = IV 2 ξ ξ ξ Page 27-9
Scaling Effect on Speed and Power In addition to increasing device density, scaling has more important benefits in speed performance Intrinsic capacitances are reduced. For example C GS 2 = WLC$ 1 1 1 ox 3 ξ ξ ξ ξ Both V and I are scaled by 1/ξ, so the ratio is unchanged The delay time is therefore approximately scaled by 1/ξ The power-delay product therefore decreases as approx. 1/ξ 3 In practice, these performance increase factors are generally optimistic Potentials do not usually scale by ξ, resulting in an increase in E Other physical effects such as velocity saturation then become important Page 27-10
Review of Velocity Saturation True constant field scaling cannot usually be achieved in practice 1980 s process was 3 μm channel length, 5V supply Modern production process 0.05 μm, 0.08V power supply? Circuit design very difficult As a result, fields generally increase as processes are scaled, and velocity saturation becomes more important (v is no longer proportional to E) Page 27-11
Square Law Velocity Assumption Recall that one of the assumptions on which the square law model was based was non-saturated velocity, the assumption that velocity is proportional to electric field This was the basis for writing the initial current density expression J n( x, y) = qn( x, y) μ n( x, y) E y( x, y) 1 442443 velocity Page 27-12
Velocity Saturation Model To incorporate velocity saturation into the square law derivation requires an analytic model for velocity A useful model is v μoe = + 1 EE crit μ o is the low field mobility and E crit is the critical field (not the same E crit as for avalanche) Typical numbers for silicon are μ o = 710 cm 2 /Vsec and E crit = 1.7x10 4 V/cm Page 27-13
Square Law Model with Velocity Saturation In the derivation of the original square law model without velocity saturation (lecture 23), the following intermediate result was obtained I D = W μ ne y ( y ) q n( x, y) dx 142 43 velocity The original derivation did not allow for velocity saturation - the μe product can increase without bound as E increases x C 0 Page 27-14
Square Law Model with Velocity Saturation The new model for velocity incorporating velocity saturation can be substituted for the original velocity in this equation to yield c E( y) E( y) I (, ) ˆ D = W μn q n x y dx = μnw Qm( y) 1 + E( y) E crit 1 + E( y) E 0 crit 1442443 saturation limited velocity Rearranging and integrating over y gives L L E ( y ) IDdy + ID dy = μ n W E ( y ) Q $ m( y ) dy E 0 0 crit 0 x L Page 27-15
Square Law Model with Velocity Saturation (con t) Solving the integrals on the left hand side gives I D L + V E DS crit = μ W E( y) Q $ ( y) dy n L 0 m This expression can be rearranged to I D = μ n W E( yq ) $ m( ydy ) L + V L ( E ) ( ) DS crit 1 0 L This equation is very similar to the corresponding intermediate result in the square law derivation, with an extra factor multiplying the channel length Page 27-16
Square Law Model with Velocity Saturation (con t) The square law model expressions can therefore be modified to include velocity saturation by modifying the L term to include the new factor 2 ˆ W VDS ID =μncox ( GS T) DS ( 1 DS) triode ( 1 V V V +λv L + VDS ( LEcrit )) 2 ( V V ) 2 ˆ W GS T =μ ncox ( 1+λVDS) saturation L ( 1 + VDS ( LEcrit )) 2 Page 27-17
Physical Interpretation of Model Result 2 ˆ W VDS ID =μncox ( VGS VT) VDS ( 1+λVDS) triode L ( 1 + VDS ( LE crit )) 2 1442443 length scaling factor length scaling factor ( V V ) 2 ˆ W GS T =μ ncox ( 1+λVDS) saturation L ( 1 + VDS ( LEcrit )) 2 1442443 The equations suggest that velocity saturation is modelled as an effective increase in the channel length As V DS increases the length factor becomes larger than 1, since the lateral field will increase and velocity saturation is more important As E crit increases the length scaling factor reduces to 1, since velocity saturation occurs at higher fields For long channels the length scaling factor reduces to 1 Page 27-18
Example 27.1: Effective Length Increase Calculate the increase in effective length for the device of the previous examples if the critical field for velocity saturation is 1.7x10 4 V/cm. Recall that the lateral diffusion is 0.1 μm on each side. Page 27-19
Example 27.1: Solution From the structure and potentials, VDS = 4 1= 3 V L = 2 10 2 01. 10 = 18. 10 4 4 4 cm The length increase term is therefore VDS 3 1+ = 1+ LE 18. 10 17. 10 crit 4 4 = 198. This result indicates that velocity saturation has the same effect as nearly doubling the channel length, indicating that velocity saturation is important in this device Page 27-20
I D -V DS with Velocity Saturation The plot to the right shows I D vs. V DS for the square law model with and without velocity saturation taken into account For this device, velocity saturation is a significant effect Page 27-21
Velocity Saturation and I D (L) Experimentally, it is observed that for very short channel devices, the drain current is no longer a strong function of the channel length (!) This can be explained using the velocity saturation model length scaling factor ( V V ) 2 ˆ W GS T ID =μ ncox ( 1+λVDS) saturation L( 1+ VDS ( LEcrit )) 2 1442443 For small values of L, the V DS /LE crit term dominates 1, so L cancels in the correction term product (triode or saturation) Physically, this corresponds to channel lengths which are short enough that the velocity is saturated and therefore no longer a function of the lateral field E y With no dependence on E y, I D is therefore not a function of L Page 27-22
Lecture Summary The effects of scaling on MOSFET performance as well as the required structural and bias changes were discussed Constant field scaling by a factor ξ requires reduction of dimensions (including t ox and junction depths) and potentials by ξ, increase in substrate doping by ξ Benefit is reduction in delay time and power-delay product Smaller devices become more susceptible to velocity saturation effects, which reduces current for the same bias condition and reduces the sensitivity of current to L Velocity saturation can be incorporated fairly easily into the square law model, and the resulting expression gives physical insight into the reduced dependence of I D on L Page 27-23