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Modeling of transient electrical characteristics for granular semiconductors
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10.1063/1.3457854
/content/aip/journal/jap/108/3/10.1063/1.3457854
http://aip.metastore.ingenta.com/content/aip/journal/jap/108/3/10.1063/1.3457854

Figures

Image of FIG. 1.
FIG. 1.

1D geometrical model structure of a granular semiconductor with identical GBs. Electric current flows in the direction of the axis.

Image of FIG. 2.
FIG. 2.

Electronic energy bands in the GB region of a -type semiconductor (a) in the thermodynamical equilibrium and (b) when a voltage is applied across the GB region. Trapping of a conduction electron in acceptor-type interface states (energy level ) at GB is illustrated in (a). is the bottom of the conduction band, the top of the valence band, and the Fermi level. and are lengths of the depletion regions in the GB region. Regions I and II are indicated.

Image of FIG. 3.
FIG. 3.

dc electric current density and dc voltage across GB region (inset) plotted as a function of the dc voltage applied across the sample, calculated at 300 K using ATLAS and the present semianalytical model with the parameter values listed in Table I.

Image of FIG. 4.
FIG. 4.

Figure Steady-state trap occupancy and electron density at GB (inset) plotted as a function of the dc voltage applied across the sample, calculated at 300 K using ATLAS and the present semianalytical model with the parameter values listed in Table I.

Image of FIG. 5.
FIG. 5.

Evolution of (a) the total current density and (b) the trap occupancy in the GB region after linearly ramping up temperature between 0 and 0.1 ms from 300 K to various values (350–500 K). The data was calculated using the present semianalytical model and ATLAS with the applied voltage and the parameter values listed in Table I and .

Image of FIG. 6.
FIG. 6.

Evolution of (a) the total current density and (b) the trap occupancy in the GB region after ramping down temperature from various values (350–500 K) to 300 K in 0.1 ms. The data was calculated using the present semianalytical model and ATLAS with the applied voltage and the parameter values listed in Table I and .

Image of FIG. 7.
FIG. 7.

Dynamic behavior of (a) total electric current density in the GB region and (b) trap occupancy after applying a 0.2 V voltage up-ramp between 0 and 1 ns (on-transient) calculated at 300 K using ATLAS and the present semianalytical model with the parameter values listed in Table I and various values of in the range .

Image of FIG. 8.
FIG. 8.

Dynamic behavior of total electric current density in the GB region after applying various voltage upramps between 0 and 1 ns (on-transient) calculated at 300 K using ATLAS and the present semianalytical model with the parameter values listed in Table I. For the capture cross-sections the following values were used: (ATLAS), and (model).

Image of FIG. 9.
FIG. 9.

Dynamic behavior of trap occupancy after applying various voltage upramps between 0 and 1 ns (on-transient) calculated at 300 K using ATLAS and the present semianalytical model with the parameter values listed in Table I. For the capture cross-sections the following values were used: (ATLAS), and (model).

Image of FIG. 10.
FIG. 10.

Electron density in the GB region calculated using ATLAS during the 1.6 V on-transient shown in Figs. 8 and 9. The GB is at .

Image of FIG. 11.
FIG. 11.

Dynamic behavior of total electric current density in the GB region after ramping down the voltage from various initial values to 0.1 V in (off-transient) calculated (a) in the ramping phase (logarithmic time scale) and (b) in the rest of the transient (linear time scale) at 300 K using ATLAS and the present semianalytical model with the parameter values listed in Table I. For the capture cross-sections the following values were used: (ATLAS) and (model).

Image of FIG. 12.
FIG. 12.

Dynamic behavior of trap occupancy after ramping down the voltage from various initial values to 0.1 V in (off-transient) calculated at 300 K using ATLAS and the present semianalytical model with the parameter values listed in Table I. For the capture cross-sections the following values were used: (ATLAS), and (model).

Image of FIG. 13.
FIG. 13.

Dynamic behavior of the trap occupancy after applying various voltage steps in the range 20–80 mV calculated at 300 K using the present semianalytical model and the analytical formulas [Eqs. (37)–(39)] with the parameter values listed in Table I and .

Image of FIG. 14.
FIG. 14.

Time constant of the trap-occupancy transient plotted as a function of temperature with various values of the trap occupancy calculated at 0 V using Eq. (39) with and the parameter values listed in Table I and . The squares indicate the temperature which corresponds to the steady-state value of . The arrows describe the evolution of during transients with increasing (, ) and decreasing temperature (, ), respectively.

Image of FIG. 15.
FIG. 15.

Time constant of the trap-occupancy transient plotted as a function of the voltage applied across the GB region with various values of the trap occupancy calculated at 300 K using Eq. (39) with and the parameter values listed in Table I and . The squares indicate the value of which corresponds to the steady-state value of . The arrows describe the evolution of during an on (, ) and off-transients (, ).

Image of FIG. 16.
FIG. 16.

(a) Steady-state trap occupancy and (b) time constant of the trap-occupancy transient plotted as a function of the dc voltage applied across the GB region at various temperatures calculated using (a) the present semianalytical model and (b) Eq. (39) with , , and the parameter values listed in Table I and . The curves (b) were calculated using the values of in (a).

Image of FIG. 17.
FIG. 17.

(a) Measured (Ref. 15) and calculated dc electric current density and (b) the trap occupancy plotted as a function of the dc voltage applied across the GB region. The data was calculated using the present semianalytical model with , , , , and .

Image of FIG. 18.
FIG. 18.

(a) Measured (Ref. 15) and calculated total electric current density , (b) the voltage applied across the GB region, and (c) the trap occupancy plotted as a function of time. The density of the calculated capacitive current is shown by the dotted curve. The data was calculated using the present semianalytical model with , , , , , , and .

Tables

Generic image for table
Table I.

Parameters used in the calculations.

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/content/aip/journal/jap/108/3/10.1063/1.3457854
2010-08-06
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Modeling of transient electrical characteristics for granular semiconductors
http://aip.metastore.ingenta.com/content/aip/journal/jap/108/3/10.1063/1.3457854
10.1063/1.3457854
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