EE 30357: Semiconductors II: Devices Lecture Note

1
EE 30357 Semiconductors II DevicesLecture Note
15 (02/13/09)Fundamentals of Field Effect
Transistors (FETs) Grace Xing

• Outline
• Last class basics of MOSFET current equations
• Ideal current-voltage family curves of MOSFETs
  (quick review)
• Deviation from the ideal long channel constant
  mobility I-Vs (MOSFET)
• Channel length modulation
• Mobility reduction due to transverse e-field
• Mobility reduction due to velocity saturation
  (due to longitudinal e-field )
• Parasitic resistance

2
Long-channel MOSFET model with constant mobility
(Lgt 5mm) Step 1 calculate the channel charge
velocity
3
Long-channel MOSFET model with constant mobility
(Lgt 5mm) Step 2 calculate the channel charge
density (cm-2, underneath gate of unit
area) Qch 0, VGS VT, ? ID 0 Qch ?, VGS
gt VT. Recall C-V of a MOSFET
Can you locate threshold condition (VT) from the
C-V below?
Above VT, Qch is determined by the gate oxide
capacitor
VT
4
Long channel FET model with constant
mobility Step3 solve for current by solving 1st
order differential equation
5
The ID-VDS characteristics of the NFET of Example
7.2 results from the simple model. For this
device W/L 5, tox 4 nm, Cox 8.63 10-3
F/m2, and mn 500 cm2/Vs. Figure 7.19
Non even spacing or even spacing? Square law or
linear law model Long channel or short?
6

• Illustration for current saturation.
• The conduction band edge along the channel bends
  more at the drain end than at the source end for
  large rain voltage VDS.
• Since the longitudinal field is proportional to
  the slope of EC, the field changes rapidly at the
  drain end for increasing values of VDS but not at
  the source end.
• (c) The field at the source end is constant as
  VDS increases beyond a certain point thus the
  current is constant as well.
• Figure 7.20

VGS-VT 2V
7
The ID-VDS characteristics of a typical MOSFET.
The threshold voltage for this MOSFET is 0.5 V.
Figure 7.14
Feature 1 threshold voltage lt 0.5 V
Feature 2 the current saturates (J
qnv)? Since n is determined by VGS, it must be
due to v.
Reason 1 saturation velocity of carriers (short
channel)
Reason 2 electric field at the source end
saturates (long channel)
Concept-Graph
8
Deviations from ideal I-Vs Channel length
modulation ? finite output conductance (ideally
zero)
Experimental ID-VDS characteristics for an
n-channel MOSFET for three values of gate
voltage. The current actually increases with
increasing VD in the current saturation region
because of channel-length modulation. For this
device, tox 4.7 nm, L 0.27 mm, W 8.6 mm,
and VT 0.3 V. Figure 7.21
Concept
9
Qualitative explanation for channel-length
modulation. Parts (a) to (c) repeat the
explanation of the simple long-channel model. In
(d), as the drain voltage continues to increase,
the point at which the channel charge approaches
0 (shaded region), or the point at which Vch
VGS - VT, moves along the channel toward
the source. The channel becomes effectively
shorter. (e) The corresponding points on the
ID-VDS characteristics. From point (c) on, the
simple model predicts constant current (dashed
line). Figure 7.22
10
Finding the channel-length modulation parameter
requires finding the slope of the ID-VDS
characteristic in the saturation region
(Example 7.4.). This is the same device as in
Figure 7.21. Figure 7.23
Equation
11
Deviations from ideal I-Vs Transverse e-field ?
reduced carrier mobility
The effect of the transverse electric field on
the mobility. (a) The electrons in the channel
collide with the walls of the channel. (b) The
energy band diagram shows that the walls are
potential barriers at the oxide interface and the
barrier of the depletion region in the
semiconductor is sloped. Figure 7.24
Concept
12
Geometry for Example 7.5. We consider only the
transverse component of the electrons motion.
Figure 7.25
13
-
-
With increased band bending, the transverse field
eT increases. This in turn reduces l, t, and
mlf. Figure 7.26
The transverse field depends on doping, bias and
depth in the channel.
14
Variation of the low-field mobility as a function
of VGS - VT - Vch for an n-channel MOSFET. The
low-field mobility can be expressed as mlf m01
- q(VGS - VT - Vch). Figure 7.27
Equation
15
Comparison of ID-VDS characteristics computed by
using the constant mobility model (q 0, dashed
lines) and taking into account the effect of the
transverse field (solid line) for q 0.13 V-1.
The transverse field tends to reduce the
currents. Figure 7.28
16
Deviations from ideal I-Vs Lateral e-field ?
reduced carrier mobility
Channel electron mobility and velocity (v me)
as a function of lateral field for VGS 1.42
V. Figure 7.29
Concept-Graph-Equation
17
The calculated I-VDS characteristics for the
simple model and for NMOS and PMOS with carrier
velocity saturation accounted for. The case of
VGS - VT 2.6 V and L 0.5 mm is considered.
The W/L ratios of the NFET and PFET have been
scaled to produce the same I-VDS curve as
predicted from the simple model. The differing
mobilities cause the scaled devices to be
different. Figure 7.30
18
The saturation voltage as a function of channel
length for (VGS - VT) 2.6 V. Figure 7.31
19
Saturation current IDsat as a function of L for
n- and p-channel silicon MOSFETs. Here (VGS -
VT) 2.6 V, the width-to-length ratio is W/L
10, and Wp 2.5 Wn. Figure 7.32
20
Deviations from ideal I-Vs Parasitic resistance
? reduced voltage drop across the intrinsic device
Schematic of an NMOS indicating the channel
resistance Rch, the source resistance RS, and the
drain resistance RD. Figure 7.33
21
Comparison of the simple long-channel model, the
model including velocity saturation, the model
including both velocity saturation and the
series resistances RS and RD, and the actual
measured data. For this NFET device, L 0.25 mm,
W 9.9 mm, and VT 0.3 V. The gate-source
voltage is 1.8 V. Figure 7.34