Quantitative Icts Measurement of Interface States at Grain Boundaries in ZnO Varistors
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intensive method to characterize deep electronic states in semiconductors[2], it has been applied to characterize electronic interface states at grain boundaries in ceramic semiconductors such as zinc oxide varistors[3, 4]. However, these works have been limited to qualitative analysis of ICTS intensity. Since ICTS intensity corresponds to the density of interface states, quantitative relation between the density of interface t states and I-V characteristics can be understood by + quantitative analysis of ICTS intensity. Present work + will discuss the characteristics of electronic interface states of DSB and establish quantitative analysis of ICTS intensity and discuss the relation between I-V nonlinearity and electronic interface states. Moreover direct characterization of single grain boundary using microelectrodes will be reported.
THEORY ICTS measurement is one of capacitance transient methods by which electronic states in the forbidden band of semiconductors are characterized
Fig. 1 Double Schottky barrier at grain boundary
213 Mat. Res. Soc. Symp. Proc. Vol. 500 © 1998 Materials Research Society
like DLTS measurement. When we apply this method to ceramic semiconductors, we can estimate the characteristics of electronic interface states at grain boundaries. When a certain voltage is applied across a grain boundary, capacitance will decrease because electrons are injected to the interface states as shown in Fig. 2(a). Then if the applied voltage is eliminated, capacitance will increase up to the initial value because captured electrons are emitted from the interface states as shown in Fig. 2(b). ICTS method measures this transient recovery of capacitance and obtains the emission rate and other parameters of the interface states by mathematical processing described bellow. ICTS signal S(t) is defined as following equation[2], S(t) = t df(t) dt
(1)
where f(t) is given by[4]
f(t) =ct)
0c0)
(2)
where C(t) is the capacitance of the varistor at time t after the elimination of the applied voltage, Coo) is capacitance at the steady state without the applied voltage. Since capacitance transient occurs by emission of electrons at the interface states, f(t) is described as following relation.
(3)
f (t)oo exp(-e,,t)
where e, is thermal emission rate of electrons from the interface states which are given by e, = Nc rlv,hg-' exp(-Els / kT)
Emission
Injection
Increase in
(4)
Decrease in depletion layer
-
depletion layer
(a) During the pulse
(b) Transient state
V=V
V=O
Fig.2 Change of DSB in ICTS measurement 214
where Nc is the effective density of states in the conduction band, oa, is the capture cross section, vt. is the thermal velosity, g is the degeneracy, Els is level of the interface states
below the conduction band edge, k is the Boltzmann constant, and T is absolute temperature, respectively. From eq. (1) and (3), one can find that SQ) has a peak value Sm. at e,.t = 1.
Sm= =
NIs
(5)
e,NDAe
where N1 s is the density of interface states, e. is dielectric constant of semiconductor grain
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