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^{1}, Pankaj Kumar

^{2}, S. C. Jain

^{2,a)}, Vikram Kumar

^{2,b)}, R. Kaur

^{3}and R. M. Mehra

^{4}

### Abstract

There is no signature of the trap filled limit voltage in the characteristics of a sample containing exponentially distributed traps. We show that and the voltage at which dependence sets in can be determined accurately. These voltages are independent of the energy distributions of the traps and depend strongly on the trap density . Contrary to the literature results, it turns out that is significantly smaller than the . In a specific case with and for a 5% accuracy in the current the value of is about whereas is . Universal curves in reduced units are derived and plotted. The reduced value of is 0.5. These curves are valid for all organics and inorganic semiconductors and for all energy distributions of traps. It is shown mathematically that all curves approached Mott’s law asymptotically as increases to infinity. To validate the theory, the experimental curves in polycrystalline undoped and Al dopedZnO thin films are made. The experimental results show good agreement with the theory. In the undoped ZnOfilms the traps are exponentially distributed and the trap concentration is calculated to be . The trap distribution in Al dopedZnOfilms is found to be discrete at a single level with trap concentration of .

### Key Topics

- II-VI semiconductors
- 12.0
- Zinc oxide films
- 11.0
- Thin films
- 9.0
- Doping
- 8.0
- Charge carriers
- 6.0

## Figures

Calculated SCL curves in a semiconductor using different models. Solid line 1 is the plot of Eq. (1). The numerically calculated curve is shown by curve 2 (single level trap) and dashed curve 4 (for exponential traps). The short straight line 3 is the plot of Eq. (2). The plot of curve calculated using the present model is shown by the dashed curve 5. Note that curves 2, 4, and 5 merge into one curve above . Inset: Curves 1 and 5 of the main figure are plotted in reduced units. These curves are universal applicable to all semiconductors and for all energy distributions.

Calculated SCL curves in a semiconductor using different models. Solid line 1 is the plot of Eq. (1). The numerically calculated curve is shown by curve 2 (single level trap) and dashed curve 4 (for exponential traps). The short straight line 3 is the plot of Eq. (2). The plot of curve calculated using the present model is shown by the dashed curve 5. Note that curves 2, 4, and 5 merge into one curve above . Inset: Curves 1 and 5 of the main figure are plotted in reduced units. These curves are universal applicable to all semiconductors and for all energy distributions.

The experimental curve for undoped ZnO thin films is compared with theory. Symbols are the experimental data. Solid line is Mott’s law, dotted line is the numerically calculated curve for exponentially trap, and the dashed curve shows the curve after TFL. Note again that dotted and dashed curves merge together above TFL. The values of the parameters used in these calculations are , , , , , , and .

The experimental curve for undoped ZnO thin films is compared with theory. Symbols are the experimental data. Solid line is Mott’s law, dotted line is the numerically calculated curve for exponentially trap, and the dashed curve shows the curve after TFL. Note again that dotted and dashed curves merge together above TFL. The values of the parameters used in these calculations are , , , , , , and .

The experimental curve of Al doped ZnO thin films is shown by “+” symbols. The theoretical curve of single level traps at is shown by dotted curve. The concentration of traps is . Mott law is shown by solid line and the curve after all the traps are filled is reached shown by dash dot curve. The values of the parameters used in these calculations are , , , , , and .

The experimental curve of Al doped ZnO thin films is shown by “+” symbols. The theoretical curve of single level traps at is shown by dotted curve. The concentration of traps is . Mott law is shown by solid line and the curve after all the traps are filled is reached shown by dash dot curve. The values of the parameters used in these calculations are , , , , , and .

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