tesi R. Miscioscia.pdf - EleA@UniSA

18 Working Principles
In eq. 14, an approximated estimation of the contribution to the IDS
due to charge injection is related to the second term. Such term can be
rewritten as in eq. 15:
eq. 15
X
∫
0
=
t
ch
X
∫
0
ε
t
ch
ch
ε
dE
ch
x
dx
X
( x)
dV ( x)
dEx
( x)
dx = t ε ( −E
( x)
)
⋅ dE
with E ≡E
( ) − ( 0)
Δ .
x x X Ex
x
dx
( x)
( −E
( x)
)
x
∫
0
ch
t
= −
ch
ch
ε
ch
dx
( ΔE
)
2
x
2
x
dx =
Therefore, it’s possible to relate the injected current contribution
(Injection-FET – IFET [1]) to the electric field magnitudes near the
electrodes by eq. 15 then, by extending the integration results to the
[0, L] interval by putting X=L, a drain current approximation can be
derived as follows:
eq. 16
eq. 17
Or simply:
X = L
− ∫
n
0
I DS dx = −C
μ W
n
I DS L = C
μ W
ins
⎛
⎜
⎜V
⎝
G
V
ins
DS
⎛
⎜
⎜V
⎝
G
V
DS
2
V ⎞ DS tchε
− +
2 ⎟
⎠
2
V ⎞ DS tchε
− −
2 ⎟
⎠
ch
( ΔE
)
2
x
ch
2
( ΔE
)
2
+ C
( ΔE
)
x
ins
2
− C
V V
2
2
W⎡
⎛ V ⎞ DS tchε
ch x
I ⎢ ⎜ −
⎟
DS μ n Cins
VGVDS
+
+ CinsV0V
L⎢⎣
⎝ 2 ⎠ 2
0
DS
ins
V V
= DS
2
W⎛
V ⎞ 1 W
I DS = μ
nC
ins VG
V0
VDS
+ n cht
ch ΔE
L⎜
+ −
2 ⎟
μ ε
⎝ ⎠ 2 L
eq. 18 ( ) ( ) 2
DS ⎜ ⎟
0
x
DS
⎤
⎥
⎥⎦