Page 149 - Organic Electronics in Sensors and Biotechnology

126 Cha pte r F o u r

100
90
V 1
Layer voltage/bias voltage (%) 50 tot
80
V
C 1 C 2 C 3 70 V V 2 3
60
R c
R 1 R 2 R 3 40
30
20
10
0
1.E–06 1.E–04 1.E–02 1.E+00 1.E+02
Time (s)
FIGURE 4.6 Evolution of layer voltages of a three-layer structure (V is voltage at
1
layer 1, V is voltage at layer 2, V is voltage at layer 3, V is total voltage at all
3
2
tot
three layers; parameters: R = 10 kΩ, C = 100 nF, R = 10 MΩ, C = 50 nF, R =
C 1 1 2 2
1 GΩ; C = 2 nF, R = 100 kΩ; hence τ = 19 μs, τ = 3.5 ms, τ = 1.5 s, V /V =
3 3 s m l 1,s,0
1.9%, V = 3.8%, V /V = 94.3%, V /V = 32.4%, V = 67.5%,
2,s,0 3,s,0 1,m,0 2,m,0
V /V = 0.1%, V /V = 0.99%, V /V = 99%, V /V = 0.01%).
3,m,0 1,l,0 2,l,0 3,l,0
The solutions were simplified assuming that the contact resistance
is much smaller than the layer resistances (R << R , R , R ). As in the
c 1 2 3
double-layer structure, the layers first charge with a time constant τ =
s
C R to a voltage determined by the layer capacitance (see Table 4.2).
tot c
Moreover, the final layer voltage is determined by the respective layer
resistances (see Fig. 4.6).
Short time
regime Intermediate regime Long time regime
⎛ B ⎞ ⎛ B ⎞
Time τ = CR τ = A ⎜ 1 − 1 − ⎟ τ = A ⎜ 1 + 1 − ⎟
2
2
constant s tot c m R ⎝ A ⎠ l R ⎝ A ⎠
tot tot
C R
,
(,
Layer 1 V 1, s = tot V V 1, m = V f 12 3) V = 1 V
l
l
1,
1,
C R
1 tot
C R
,
(,
Layer 2 V 2, s = tot V V 2, m = V f 23 1) V 2, l = 2 V
2,
l
C R
2 tot
C R
,
(,
Layer 3 V = tot V V = V f 31 2) V = 3 V
3, s 3, m 3, l 3, l
C R
3 tot
TABLE 4.2 Time Constants and Layer Voltages of a Three-Layer Structure