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.
2) W. Shockley and W.T. Read, Phys. Rev. 87, 835 (1952).
3) R. N. Hall, Phys. Rev. 87, 387 (1952).