Page 141 - Rashid, Power Electronics Handbook

9 Static Induction Devices 129

W 0 -2 -4 -6
I -8 -10
DS
F [mA] -12 -14
2F
F 500 -16

L 400
V =-18
G
300
FIGURE 9.4 Potential distribution in the vicinity of the barrier
approximated by parabolic shapes. 200

100
Integrating Eq. (9.5) ®rst along the channel and then across V DS
the channel yields a very simple formula for drain currents in [V]
20 40 60 80 100 120
n-channel SIT transistors
FIGURE 9.5 Characteristics of the static induction transistor drawn in
linear scale.

W F
I ¼ qD N Z exp ð9:8Þ
D
p
S
L V T
11
where L is the channel length and n 10 mm=s is the
where F is the potential barrier height in reference to the sat
carrier saturation velocity. In practical devices the current-
source potential, N S is the electron concentration at the voltage relationship is described by an exponential relationship
source, the W=L ratio describes the shape of the potential
Eq. (9.9) for small currents, a quadratic relationship eq. (9.11),
saddle in the vicinity of the barrier, and Z is the length of the
and, ®nally, for large voltages by an almost linear relation-
source strip.
ship Eq. (9.12). The SIT characteristics drawn in linear and
As barrier height F can be a linear function of gate and
logarithmic scales are shown in Fig. 9.5 and Fig. 9.6,
drain voltages,
respectively.

W aðV GS þ bV DS þ F Þ
0
I ¼ qD N Z exp ð9:9Þ
S
D
p
L V T
I DS 0 -1 -2
Equation (9.9) describes the characteristics of a static [A] -3 -4 -5 -6
induction transistor for small current range. For large current -7
-9
levels the device current is controlled by the space charge of 10 -1
-11
moving carriers. In the one-dimensional (1D) case the poten-
tial distribution is described by the Poisson equation: 10 -2 -13
V =-15
G
2
d j rðxÞ I DS -3
¼ÿ ¼ ð9:10Þ 10
dx 2 e e AnðxÞ
Si 0
10 -4
Where A is the effective device cross section and nðxÞ is
carrier velocity. For a small electrical ®eld nðxÞ¼ mEðxÞ and
10 -5
the solution of Eq. (9.10) is
9 2 A 10 -6
I DS ¼ V me e ð9:11Þ
Si 0
DS
8 L 3
10 -7
and for a large electrical ®eld nðxÞ¼ const and Eq. (9.10)
results in:
20 40 60 80 100 120 140 V [V]
DS
A FIGURE 9.6 Characteristics of the static induction transistor drawn in
I DS ¼ 2V n e e ð9:12Þ
DS sat Si 0
L 2 logarithmic scale.