Abstract
The letter presents a two-dimensional analytical model of the space charge limited (SCL) current injection in a solid with exponentially distributed trap energy state. By considering that the electrons are injected from an infinitely long emission strip of width
W
, the one-dimensional SCL current density is enhanced by a factor of
1
+
F
(
4
∕
π
)
∕
(
W
∕
L
)
, where
F
=
1
∕
(
l
+
2
)
measures the mean position of the injected electrons in the solid of length
L
, and
l
is the ratio of the distribution of the traps to the free carriers. The analytical formula is verified by using a two-dimensional device simulator.