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## Trap Parameter (level energy and capture cross-section) Evaluation

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The exchange of carriers between the deep level in the semiconductor and the band is described by SHR (Shockley-Read-Hall) Statistics 2,3)
From the detailed balance principle on the elementary process between the level and the band, the thermal emission rate: eΤ(inverse number of τe mentioned above) of electrons from the electron trap level to the conduction band is expressed by the following formula. NC：effective density of states in a conduction band, σ C C: capture cross-section, νth：thermal velocity, g: level degeneracy MC :shape factor, mmr: effective mass of electrons, mm0: rest mass of electrons, h: Plank's constant From the formulas (A-7) to (A-9) By taking the logarithm of both sides, the basic formula (A-11) of the Arrhenius plot for calculating the activation energy is obtained. By measuring τe at various temperatures, taking the temperature dependence into consideration, τeΤ2 multiplied by Τ2 is subjected to a semi logarithm plot (Arrhenius plot) for 1 / T, then the energy of the level: ΕT is obtained from the slope of the straight line, and capture cross-section (is obtained) from the intercept.
(Strictly speaking, the capture cross-section obtained here is the effective capture cross section: σn, eff = gσc, and it contains the degeneracy factor of the level.As a method for independently obtaining the capture cross-section, there is a "pulse- filling method".)

In the DLTS spectrum measurement in the previous section (Figure A-4), for a certain deep level, the temperature at which its thermal emission time constant reaches a certain value (τe) was determined.
In the DLTS method, such a measurement is performed by a combination of differing t1 and t2 , so that the temperature corresponding to another τe: (Tmax) is obtained.
Thus, for example, by repeating such measurements five times, five data points can be plotted on the Arrhenius plot.

#### ● References

2) W. Shockley and W.T. Read, Phys. Rev. 87, 835 (1952).

3) R. N. Hall, Phys. Rev. 87, 387 (1952).

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