HO #3: ELEN Review MOS TransistorsPage 1S. Saha Long Channel MOS Transistors The theory developed for MOS capacitor (HO #2) can be directly extended to Metal-Oxide-Semiconductor Field-Effect transistors (MOSFET) by considering the following structure: The gate bias, V G provides the control of surface carrier densities. –For V G < V th ( threshold voltage ), the structure consists of two back to back diodes and only leakage currents flow (  I o of PN junctions), i.e., I D  0 –For V G > V th, inversion layer exists, a conducting channel exists from D  S and current I D will flow. Where V th is determined by the properties of the structure. n+ SD G P

HO #3: ELEN Review MOS TransistorsPage 2S. Saha Long Channel MOS Transistors V th is given by Eq we derived for MOS capacitors. That is, (1)

HO #3: ELEN Review MOS TransistorsPage 3S. Saha 1. NMOSFETs: Band Diagram

HO #3: ELEN Review MOS TransistorsPage 4S. Saha NMOSFETs: Band Diagram

HO #3: ELEN Review MOS TransistorsPage 5S. Saha 2. NMOSFETs: I - V Characteristics

HO #3: ELEN Review MOS TransistorsPage 6S. Saha NMOSFETs: I - V Characteristics

HO #3: ELEN Review MOS TransistorsPage 7S. Saha I  V Characteristics: Basic Equations Note: The depletion region is wider around the drain because of the applied drain voltage V D. The potential along the channel varies from V y = L to y = 0 between the drain and source. The channel charge Q I and the bulk charge Q B will in general be f(y) because of the influence of V D, i.e. potential varies along the channel length. +V D +V G P IDID Q I (y) Q B (y) n+ Inversion layer Depletion region

HO #3: ELEN Review MOS TransistorsPage 8S. Saha I  V Characteristics: Basic Equations where W = width of the device V(y) = voltage drop along the channel due to V D Solving the above three Eq we get I D - V D characteristics.

HO #3: ELEN Review MOS TransistorsPage 9S. Saha I  V Characteristics: Basic Equations VDVD IDID VG6VG5VG4VG3VG2VG1VG6VG5VG4VG3VG2VG1 Linear Region Saturation Region V D = V DSAT  I D ((amps) 1/2 ) 

HO #3: ELEN Review MOS TransistorsPage 10S. Saha 3. MOS Device Scaling 3.improve current drive (transconductance, g m ) Benefits of scaling MOSFETs: 1.increase device packing density 2.improve frequency response (transit time)  1/L n+ P L t ox xjxj n+ lolo

HO #3: ELEN Review MOS TransistorsPage 11S. Saha MOS Device Scaling Note that g m and therefore, the current drive of MOSFETs can be increased by: –decreasing the channel length, L –decreasing the gate oxide thickness, t ox Therefore, much of the scaling is driven by decrease in L and t ox.

HO #3: ELEN Review MOS TransistorsPage 12S. Saha MOS Device Scaling Though, MOSFET scaling is driven by scaling down L and t ox, many problems such as increased electric fields are encountered if scaled only these two parameters. In 1974, Dennard et al. proposed a scaling methodology which maintains the electric field in the device constants. (R.H. Dennard, et al., IEEE JSSC, vol. 9, p , 1974). Device/circuit parameters Constant field scaling factor Dimension: t ox, L, W, x j, l o 1/K Substrate doping: N a K Supply voltage:V1/K Supply current: I1/K Parasitic capacitance: WL / t ox 1/K Gate delay: CV / I1/K Power dissipation: CV 2 / delay1/K 2

HO #3: ELEN Review MOS TransistorsPage 13S. Saha MOS Device Scaling In practice, constant field scaling has not been strictly observed. Since I D  gate overdrive, (V G – V th ), thus, the demands for high performance have dictated the use of higher supply voltage. However, high supply voltage implies increased power dissipation (CV 2 f). In the recent past, low power applications have become important and have required a scaling scenario with lower supply voltage. Parameters Channel length (  m) Gate oxide (nm) Junction depth (  m) > Supply voltage

HO #3: ELEN Review MOS TransistorsPage 14S. Saha MOS Device Scaling Device/circuit parametersQuasi Constant voltage scaling (K > B > 1) Dimension: t ox, L, W, x j, l o 1/K Substrate doping: N a K Supply voltage:V1/B Ref: B. Davari, et al., Proc. IEEE, April 1995

HO #3: ELEN Review MOS TransistorsPage 15S. Saha 4. Limitations of Scaled MOSFETs A number of factors have been neglected in the simple MOS theory which became increasingly important in scaled devices.  bi,  F, and  ms of S/D junctions were neglected –V th dependence on W, L, and V D is not predicted by simple theory –I  0 for V G < V th. Rather I is exponentially dependent on V G. –Current flow D  S can be initiated by V D rather than V G. This can be modeled by a V th which depends on V D and V G. –Since  fields cannot be held constant because of  bi etc. (and because V D has not been scaled in the industry), higher   higher carrier velocity. Material limits like v sat become important.

HO #3: ELEN Review MOS TransistorsPage 16S. Saha 4(a). Effect of Scaling Down L: V th degradation In long channel MOSFETs, the gate is completely responsible for depleting the semiconductor (Q B ). In very short devices, part of the depletion is accomplished by the drain and source biases. Since less V G is required to deplete Q B, V th  as L . Similarly, as V D , more Q B is depleted by V D and hence V th . This effect dominates in lightly doped substrates.

HO #3: ELEN Review MOS TransistorsPage 17S. Saha Effect of Scaling Down L: Punchthrough If the channel length, L becomes too short, the depletion region from the drain can reach source side reducing e- injection barrier. This phenomenon is known as punchthrough.

HO #3: ELEN Review MOS TransistorsPage 18S. Saha Effect of Scaling Down L: DIBL In very short channel devices: –less V G is required to deplete Q B  the barrier to electron injection from source to drain decreases. –I D  at a given V G. This effect is known as the drain induced barrier lowering (DIBL).

HO #3: ELEN Review MOS TransistorsPage 19S. Saha Effect of Scaling L: Effect of DIBL on I D DIBL results in an increase in I D at a given V G.  V th  as L . Similarly, as V D , more Q B is depleted by V D and hence V th .

HO #3: ELEN Review MOS TransistorsPage 20S. Saha 4(b). Carrier Mobility: Velocity Saturation The mobility of the carriers reduces at higher e-fields in small channel length devices due to velocity saturation (v sat ). As L , while V D  constant: -lateral e-field  -carrier velocity  v E c  10 4 V/cm for e-.  for nMOSFETs with L < 1  m, v sat causes current to saturate for V D < (V G  V th ).

HO #3: ELEN Review MOS TransistorsPage 21S. Saha Effect of V sat on MOSFET I - V Characteristics MOSFETs with: L = 2.7 um t ox = 500 A (a)(b)(c) (a) Experimental data; (b) simulated data including velocity saturation; (c) simulated data ignoring velocity saturation.

HO #3: ELEN Review MOS TransistorsPage 22S. Saha 4(c). Sub-threshold Conduction For VG < Vth, the surface is in weak inversion and a conducting channel starts to form. As a result, a low level of current flows between the source and drain. In MOS subthreshold slope, S is limited to kT/q (60 mv/dec I)  I D leakage  ; Static power  ; and circuit instability .

HO #3: ELEN Review MOS TransistorsPage 23S. Saha 4(d). Hot Carrier Effects Gate IgIg n+ Drainn+ Source I sub m hole hot e  l llllll V D > V DSAT The maximum e-field at the drain-substrate junction is: As L , in the channel near the drain E max  more rapidly than long L devices. The free carriers passing through the high e-field gain sufficient energy to cause hot-carrier effects.

HO #3: ELEN Review MOS TransistorsPage 24S. Saha Hot Carrier Effects

HO #3: ELEN Review MOS TransistorsPage 25S. Saha I sub flowing into the substrate causes an IR drop in the substrate resulting in Body bias – Substrate Current induced Body Effect (SCBE). –SCBE results in V th drop and manifold increase in  I sub  I DS. Hot Carrier Effects

HO #3: ELEN Review MOS TransistorsPage 26S. Saha 4(e). Band-to-Band Tunneling For small V G ~ 0 and high V D a significant drain leakage can be observed, especially for short channel devices. For V G = 0, and V D high, the e-field can be very high in the drain region causing band-to-band tunneling (BTBT): –BTBT happens only when e-field is sufficiently high to cause a large band bending.

HO #3: ELEN Review MOS TransistorsPage 27S. Saha 4(f). Effect of Scaled Channel Width The depletion region extends sideways in the areas outside the gate controlled region increasing the apparent channel width. As a result V th  opposite to short channel devices.