**4.5. Measurement of capture cross-section**

The third important parameter for identifying a defect centre is the capture cross-section σn,p. One can extrapolate the Arrhenius plot to 1/T = 0 and obtain the capture cross-section at T = ∞ from the intercept. But this usually leads to a far from true value of the capture cross-section because of the following two reasons: a) σn,p may be temperature dependent and hence the extrapolation is not valid; b) a slight error in extrapolation may lead to several orders of magnitude difference in values of capture cross-section. Hence, the capture cross-section must be directly measured whenever possible and over as long a range of temperatures as possible.

Measurement of majority carrier capture cross-section is relatively simple as compared to minority carrier capture cross-section measurements. A fixed emission rate is chosen and DLTS scans carried out while the filling pulse-width is varied from scan to scan. As the pulse width increases from a small value so does the peak height until for a certain value of pulse width, it reaches a maximum i.e. at this value all defect centers are completely filled during a single saturation pulse. The peak height is related to the filling pulse width tp via the following equation:

$$\mathbf{1} - \mathbf{S}/\mathbf{S}\_{\circ} = \exp(-t\_p/\tau) \tag{26}$$

where S is the peak height for any pulse width tp and S∞ the saturated peak height.

The slope of ln(1-S/S∞) versus tp gives 1/τ.

now

where σn is the capture cross-section and <νn>th the average thermal velocity of the electron,

exp *T V*

*kT*

(24)

, exp( 1 / ) *n p e T* µ - (25)

) versus 1/T instead of log(e) versus 1/T. The factor

è ø

and Nc is the effective density of states in the conduction band.

*p pp V th*

s

NV is the effective density of states in the valence band.

One may often encounter plots of log(e/T2

applied to the apparent activation energy.

**4.5. Measurement of capture cross-section**

Thus the emission rate variation with temperature is given by

*E E e vN*

æ ö - <sup>=</sup> ç ÷ -

where σ<sup>p</sup> is the capture cross-section and <νp>th the average thermal velocity of the hole, and

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.

 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

The third important parameter for identifying a defect centre is the capture cross-section σn,p. One can extrapolate the Arrhenius plot to 1/T = 0 and obtain the capture cross-section at T = ∞ from the intercept. But this usually leads to a far from true value of the capture cross-section because of the following two reasons: a) σn,p may be temperature dependent and hence the extrapolation is not valid; b) a slight error in extrapolation may lead to several orders of magnitude difference in values of capture cross-section. Hence, the capture cross-section must be directly measured whenever possible and over as long a range of temperatures as possible.

Measurement of majority carrier capture cross-section is relatively simple as compared to minority carrier capture cross-section measurements. A fixed emission rate is chosen and DLTS scans carried out while the filling pulse-width is varied from scan to scan. As the pulse width increases from a small value so does the peak height until for a certain value of pulse width, it reaches a maximum i.e. at this value all defect centers are completely filled during a single

hole emission,

210 Solar Cells - New Approaches and Reviews

T2

$$
\sigma\_u = \mathbf{1} \{ \langle \tau n(V\_{\text{th}}) \rangle \} \tag{27}
$$

Thus capture cross-section is known if n and <vth > are known.

The calculation of capture cross-sections for minority carriers is complicated due to the difficulty in determining the concentration of electrons/holes, which is a function of the current during the injection pulse.
