**4.4. Activation energy**

The activation energy for emission and the capture cross section of the trap are deduced from

**Figure 3.** Band diagram of p-type material close to an n+\p junction indicating a deep level at energy ET above the

As an example of the importance of the inclusion of the transition distance in the calculations,

λ=0.48 μm. The Fermi function is of the order of 10-3 and to a close approximation the trap is filled with holes. During a fill pulse from -2V to 0V, the depletion region is collapsed from a width of 3 μm at a quiescent bias of -2V to 1.6 μm at zero bias. Thus application of Eqs. (18) to (21) results in an increase of a factor 1.9 in the calculated trap concentration in comparison with

When the condition NT << Na is not fulfilled, there is a significant probability that emitted charge will be recaptured before it can be swept out of the depletion region, leading to a nonexponential capacitance transient. In this case, Eq. (19) is no longer appropriate. Several

, p=4 x 1014 /cm3

**b) V=-V**

**Ec** 

**ET EF Ev**

**a) V=0**

**Ec** 

**ET EF Ev**

, Ef


=0.09 eV at 125K and

an Arrhenius plot of the DLTS maxima as a function of temperature.

valence band a) with zero applied bias and b) with applied reverse bias of -V.

**x=0 x2 w2**

l

**x=0 x1 w1**

**qV**

l

in the case of a sample irradiated with 3 x 1016e /cm2

the value obtained if the transition distance is ignored.

thus for the di-vacancy with ET=EV+0.18 eV, Ef

*4.1.2. Non exponential transients*

208 Solar Cells - New Approaches and Reviews

Under thermodynamic equilibrium, the emission rates and the capture coefficients of a deep level are related according to the following equations:

electron emission,

$$e\_n = \sigma\_n \left< v\_n \right>\_{\hbar} N\_\odot \exp\left(-\frac{E\_\odot - E\_T}{kT}\right) \tag{23}$$

where σn is the capture cross-section and <νn>th the average thermal velocity of the electron, and Nc is the effective density of states in the conduction band.

hole emission,

$$e\_p = \sigma\_p \left\langle v\_p \right\rangle\_{th} N\_V \exp\left(-\frac{E\_T - E\_V}{kT}\right) \tag{24}$$

where σ<sup>p</sup> is the capture cross-section and <νp>th the average thermal velocity of the hole, and NV is the effective density of states in the valence band.

Thus the emission rate variation with temperature is given by

$$e\_{u,p} \propto \exp(-1/T) \tag{25}$$

Hence a plot of log(e) versus 1/Tpk, where Tpk is the temperature position of the peak in the corresponding time window, gives a straight line with the slope -EA/kT, where EA is the activation energy of the level. Such a plot is known as an Arrhenius Plot. From the intersection of the plotted line with 1/T = 0, the capture cross-section σ n,p at T = ∞ can be calculated.

One may often encounter plots of log(e/T2 ) versus 1/T instead of log(e) versus 1/T. The factor T2 comes in because of the temperature dependence of <vth > and effective density of states NC,V. The activation energy thus obtained may still not be the true activation energy because in some cases, the capture cross-section is found to be temperature dependent. Thus the true thermal activation energy in such cases would be obtainable if the temperature dependence of capture cross-section is first determined independently and then the relevant correction is applied to the apparent activation energy.
