9.9. DESIGN PROBLEMS 485
P-type Si
OXIDE: 20 nm
n+ n+
Gate
1016
cm-3
p-type doped 10^17 cm-3
Figure (c)
p-type doped 10^17 cm-3
Figure (b)
50 nm
Figure 9.33: Figure for problem 9.21.
Problem 9.22Consider that a MOS system on p-type silicon is biased to deep depletion
by the sudden deposition of a total chargeQGon the gate at timet=0. Carrier generation
in the space charge region at the silicon surface results in a charging current for the
channel chargeQnaccording to the net generation rate equation
JG=qn 2 τi 0 xi
whereτ 0 is the maximum recombination rate, andxiis the width of the space charge
region. This allows us to write dQn
dt =−
qni(xd−xdf)
2 τ 0
wherexdis the (time dependent) depletion region width at the surface. The quantityxdfis
the space charge region width at thermal equilibrium; that is, whenxd=xdf, channel
charging by generation is zero.
(a) Show that the time evolution ofQnis governed by the differential equation
Qn+(^2 τ^0 nNiA)(dQdtn)=−(QG−qNAxdf)
(b) Solve this equation subject to the BC thatQn(t=0)=0, and thus show that the
characteristic time to form the surface inversion layer is of the order
T∼^2 NnAiτ^0
9.9 DESIGN PROBLEMS ...............................
Problem 9.1Consider ann-MOSFET made from Si-dopedp-type atNa=10^16 cm−^3 at
300 K. The source and drain contacts are ohmic (negligible resistance) and are made from
