**4. Parameters characterizing deep levels by DLTS technique**

Below are described some of the ways in which the DLTS technique can be used to study defect centers in semiconductors and to obtain their different characteristic parameters.

### **4.1. Deep level concentration**

As mentioned in the previous section the DLTS signal S is proportional to the magnitude of the capacitance transient ∆C. Equation (12) can be rewritten as

$$\frac{\Delta C}{C\_0} = \frac{N\_T}{2N\_D}$$

where it is assumed that all the traps have been filled.

### *4.1.1. Transition Distance, λ*

The DLTS peak height gives a direct measure of the deep level concentration. Here it must be remarked that in obtaining Eq. (12) the edge region contribution has been neglected. Figure 3 illustrates the edge region in a p-n junction under zero and reverse bias. The distance between the edge of the depletion layer and the point where the Fermi level crosses the trap level is referred to as the transition distance, λ, given by.

Deep Level Transient Spectroscopy: A Powerful Experimental Technique for Understanding the Physics… http://dx.doi.org/10.5772/59419 207

$$\mathcal{A} = \sqrt{\frac{2\mathcal{L}\,\,\varepsilon\_0 (E\_F - E\_T)}{q^2 N\_D}}\tag{17}$$

where ε0 and ε are the permittivity of vacuum and of the material, Ef is the Fermi level, ET is the trap energy level above the valence band, q is the electronic charge and the carrier concentration p is essentially equal to the acceptor concentration, Na.

In the absence of deep levels and when the doping is uniform, plots of 1/C2 vs V are straight lines. However, if the criterion NT << Na is not met then the additional capacitance of the charge trapped by deep levels within the distance λ contributes to the measured depletion capaci‐ tance. This produces a shoulder in the 1/C2 vs V plot at low reverse bias. Also the apparent carrier concentration, *N*measured, as a function of distance, x, deduced from the derivative dC \dV from the same C-V data becomes approximately (for a *uniform* distribution of a single compensating trap level) [13].

$$N\_{measured}(\mathbf{x}) = N\_a(\mathbf{x}) - \frac{\lambda}{w} N\_T(\mathbf{x}) \tag{18}$$

DLTS monitors the capacitance transient associated with the gradual emission of charge from trap centers when the depletion layer is abruptly widened by increasing the applied reverse bias (e. g. switching from V=0 as in Figure. 3a) to V=-V as in Figure 3b)). The calculation of the trap concentration must take into account the fact that the volume within which the charge state of the traps is changed upon the increase of reverse bias and which therefore contributes to the DLTS signal (corresponding to the interval x2-x1 in Figure 3) is different to the volume by which the depletion layer is increased (w2-w1 in Figure 3).

For exponential transients, this leads to the approximate expression for the trap concentration,

$$N\_T = 2\frac{\Delta \mathcal{C}}{\mathcal{C}} N\_s \left(\frac{w\_2^2}{\mathbf{x}\_2^2 - \mathbf{x}\_1^2}\right) \tag{19}$$

where

We can get τ max by differentiating S with respect to t and setting the derivative equal to zero.

( ln( / )

Thus it is seen that the peak height is independent of the absolute value of t1 and t2, rather it depends upon their ratio. Moreover, it is seen that Smax is proportional to ∆C<sup>o</sup> and therefore to the defect centre concentration NT. Therefore, the DLTS peak height can directly give the defect

Below are described some of the ways in which the DLTS technique can be used to study defect

As mentioned in the previous section the DLTS signal S is proportional to the magnitude of

<sup>0</sup> 2

The DLTS peak height gives a direct measure of the deep level concentration. Here it must be remarked that in obtaining Eq. (12) the edge region contribution has been neglected. Figure 3 illustrates the edge region in a p-n junction under zero and reverse bias. The distance between the edge of the depletion layer and the point where the Fermi level crosses the trap level is

*C N C N* <sup>D</sup> <sup>=</sup>

*T D*

max 0 *S C xx xxx* =D - - - - - é ù exp( ln( ) / ( 1)) exp( ln( ) / ( 1) ë û (16)

(15)

*t t tt*

max 1 2 1 2 1

( 1) ln( )

**4. Parameters characterizing deep levels by DLTS technique**

the capacitance transient ∆C. Equation (12) can be rewritten as

where it is assumed that all the traps have been filled.

referred to as the transition distance, λ, given by.

centers in semiconductors and to obtain their different characteristic parameters.

= t

Substituting this value in the expression for S gives Smax as:

*xt x* = -

This gives:

206 Solar Cells - New Approaches and Reviews

where *x* =*t*<sup>2</sup> / *t*<sup>1</sup>

centre concentration.

**4.1. Deep level concentration**

*4.1.1. Transition Distance, λ*

$$
\infty\_1 = \varpi\_1 - \mathcal{X} \tag{20}
$$

and

$$
\infty\_2 = \varpi\_2 - \mathcal{A} \tag{21}
$$

**Figure 3.** Band diagram of p-type material close to an n+\p junction indicating a deep level at energy ET above the valence band a) with zero applied bias and b) with applied reverse bias of -V.

The activation energy for emission and the capture cross section of the trap are deduced from an Arrhenius plot of the DLTS maxima as a function of temperature.

As an example of the importance of the inclusion of the transition distance in the calculations, in the case of a sample irradiated with 3 x 1016e /cm2 , p=4 x 1014 /cm3 , Ef =0.09 eV at 125K and thus for the di-vacancy with ET=EV+0.18 eV, Ef - ET =0.011 eV. Application of Eq. (17) gives 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 the value obtained if the transition distance is ignored.

### *4.1.2. Non exponential transients*

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 analyses of this situation exist [1,14] and we have considered the method of Stievenard et al. [13] to calculate a non-exponential transient analysis. In this case, if the transition region is negligibly small then the capacitance transient can be written as

$$\frac{\Delta C}{C} = 1 - \sqrt{1 - \frac{z}{1+z} \exp(-et)}\tag{22}$$

where z=NT/Na
