172
Compact Models for Integrated Circuit Design
4.2 For a device with p-type substrate concentration, N a = 2.5 × 10 16 cm −3 ;
gate oxide thickness, T ox = 100 A; and V fb = −0.97 V, calculate and plot
ln(Q i ) versus V gb in weak inversion.
4.3 Brews charge-sheet model:
a. Carry out the integration to derive the simplified surface potential based MOSFET drain current (Brews) model Equations 4.48
and 4.51.
b. Derive an expression for f s0 in terms of the source-to-body bias
V sb to calculate I–V characteristics of the drift and diffusion
components of I ds for the above model. Clearly define all parameters and explain.
c. Derive an expression for f sL in terms of drain-to-body bias V db
to calculate I–V characteristics of the drift and diffusion components of I ds for the above model.
Clearly define all parameters and explain.
4.4 Consider an nMOSFET device with N a = 5 × 10 17 cm −3 , T ox = 6 nm,
V fb = −1 V, μ = 600 cm 2 V −1 sec −1 , W = L = 2 µm, biased with V sb = 1 V
and V db = 3 V, while V gb is varied from 0 to 3 V. Use (Brews model) to
calculate the following I ds as a function of V gb :
a. Drift component of I ds , I ds,drift
b. Diffusion component of I ds , I ds,diff
c. Total current I ds
d. Plot I ds –V gb from part (a)–(c) using the same log drain current I ds
axis
e. Plot surface potentials (f s0 and f sL ) as a function of (V gb − V fb )
4.5 Consider Basic MOS models. Explain physically why I–V characteristics of MOSFETs are more sensitive to temperature in the
subthreshold region than they are in the strong inversion.
4.6 Show that in the subthreshold region of MOSFETs, the surface
potential is given by:
φ
γ
γ
ss
gb
fb
V V
= − +
+
−
2
4
2
2
4.7 In weak inversion, the drain current I ds is exponentially proportional
to an inverse of (60 mV dec I −1 )(1 + C d /C ox ) at room temperature. Once
strong inversion is reached, most of the gate charge resulting from
higher V gs value is balanced by channel charge Q i not depletion charge.
Write a simple expression, analogous to the slope expression above,
which approximately models the MOSFET devices in strong inversion.
State any assumptions you make and explain your results.
Compact Models for Integrated Circuit Design
4.2 For a device with p-type substrate concentration, N a = 2.5 × 10 16 cm −3 ;
gate oxide thickness, T ox = 100 A; and V fb = −0.97 V, calculate and plot
ln(Q i ) versus V gb in weak inversion.
4.3 Brews charge-sheet model:
a. Carry out the integration to derive the simplified surface potential based MOSFET drain current (Brews) model Equations 4.48
and 4.51.
b. Derive an expression for f s0 in terms of the source-to-body bias
V sb to calculate I–V characteristics of the drift and diffusion
components of I ds for the above model. Clearly define all parameters and explain.
c. Derive an expression for f sL in terms of drain-to-body bias V db
to calculate I–V characteristics of the drift and diffusion components of I ds for the above model.
Clearly define all parameters and explain.
4.4 Consider an nMOSFET device with N a = 5 × 10 17 cm −3 , T ox = 6 nm,
V fb = −1 V, μ = 600 cm 2 V −1 sec −1 , W = L = 2 µm, biased with V sb = 1 V
and V db = 3 V, while V gb is varied from 0 to 3 V. Use (Brews model) to
calculate the following I ds as a function of V gb :
a. Drift component of I ds , I ds,drift
b. Diffusion component of I ds , I ds,diff
c. Total current I ds
d. Plot I ds –V gb from part (a)–(c) using the same log drain current I ds
axis
e. Plot surface potentials (f s0 and f sL ) as a function of (V gb − V fb )
4.5 Consider Basic MOS models. Explain physically why I–V characteristics of MOSFETs are more sensitive to temperature in the
subthreshold region than they are in the strong inversion.
4.6 Show that in the subthreshold region of MOSFETs, the surface
potential is given by:
φ
γ
γ
ss
gb
fb
V V
= − +
+
−
2
4
2
2
4.7 In weak inversion, the drain current I ds is exponentially proportional
to an inverse of (60 mV dec I −1 )(1 + C d /C ox ) at room temperature. Once
strong inversion is reached, most of the gate charge resulting from
higher V gs value is balanced by channel charge Q i not depletion charge.
Write a simple expression, analogous to the slope expression above,
which approximately models the MOSFET devices in strong inversion.
State any assumptions you make and explain your results.