**3. Basic methodology of DLTS**

Thus the emission rates and trap concentrations can be determined from the changes in the capacitance of a p-n junction due to bias pulses. These changes are in the form of capacitance

DEEP LEVEL TRANSIENT SPECTROSCOPY(DLTS)

BASIC IDEA OF DLTS METHOD

or current) signals from deep levels

A novel spectroscopy technique to process transient (capacitance)

TEMPERATURE

C(t1)-C(t2)

emax= *ln*(t1/t2) t1-t2

1000/T

LOG(e/T )2

PEAK POSITION SHIFTS WITH RATE WINDOW(emax)

DLTS can be used to determine following deep level characteristics

**Figure 2. Diagram illustrating the basic principles of DLTS (a) the rate window concept (after Lange [1]), (b) application of the rate window concept using a time filter such as dual-gate box car shown here (after Lange [1]), (c) showing the shift of the peak positions in temperature with the rate window and the Arrhenius plot** 

**Figure 2.** Diagram illustrating the basic principles of DLTS (a) the rate window concept (after Lange [1]), (b) applica‐ tion of the rate window concept using a time filter such as dual-gate box car shown here (after Lange [1]), (c) showing the shift of the peak positions in temperature with the rate window and the Arrhenius plot obtained from the peak

SYSTEM RESPONCE PEAKS WHEN TRAP EMISSION RATE IS WITHIN RATE WINDOW ADJUSTABLE RATE WINDOW

transients.

204 Solar Cells - New Approaches and Reviews

CAPACITANCE TRANSIENTS

**(b)** 

DLTS SIGNALS

**obtained from the peak positions ( [31].** 

**(c)** 

positions ([31].

SYSTEM RESPONSE

**(a)** 

LOG(THERMAL

EMISSION RATE)

AT VARIOUS TEMPERATURES

0 t1 t2

T

a. Activation engergy and emmison rates b. Nature of majority carrier / minority carrier trap c. Concentration and concentration profile

d. Cature cross-sections

Emission rate at Peak Temperature

RALIZATION OF THE IDEA

The capacitance transients of Eq. 13 can be obtained by holding the sample at constant bias and temperature and applying a single filling pulse. The resultant isothermal transient can then be analyzed to obtain the emission rate of the carriers at that particular temperature. For obtaining a wide range of emission rates, this is a time consuming technique. Also if a lot of deep levels are present, the experiment and its analysis become difficult. This is where DLTS has a major edge over the conventional techniques.

The essential feature of DLTS [1] is its ability to set up a *rate window* so that the measuring apparatus gives an output only when a transient occurs with a rate within the window. This concept is illustrated in Figure 2 (adopted with permission from IEEE Proc. of WCPEC-4, 2006, p. 1763).Thus if the sample temperature is varied at a constant rate, causing the emission rate of carriers from defect center(s) present in it to vary, the measuring instrument will give a response peak whenever the defect center emission rate is within the window. Instead of talking about rate window, we can say that the DLTS technique uses a time filter, which gives an output signal only when the transient has a time constant coinciding with the center of the time window of the filter. A very important property of such a filter (time or rate) is that the output is proportional to the amplitude of the transient. Thus we can excite the diode repeat‐ edly while the temperature is varied and by scanning over a large temperature interval we can directly get information as to which levels are present, what are their concentrations and by using different time/rate windows we can obtain the thermal activation energies of the levels.

There are many ways of constructing a time filter. One of the widely used methods is one in which a variation of the dual-gate boxcar integrator is employed. It precisely determines the emission rate window and provides signal-averaging capabilities to enhance the signal-tonoise ratio, making it possible to defect center having very low concentrations. The use of a double boxcar for rate window selection is illustrated in Figure 2b. The capacitance transients are observed on a fast-response capacitance bridge. A series of transients for a typical defect center are shown on the left-hand side of Fig. 2.8b. These transients are fed into the double boxcar with gates set at t1 and t2. The boxcar measures the capacitance at the two times t1 and t2. The difference C(t1) - C(t2) = ∆C is calculated. It is clear from the figure that this ∆C goes through a maximum. This ∆C after going through some filtering is converted into the DLTS output S(T) given by (assuming an exponential transient):

$$S(T) = \Delta C\_0 \left[ \exp(-t\_1/\tau) - \exp(-t\_2/\tau) \right] \tag{14}$$

where ∆Co is the capacitance change due to the pulse at time t = 0.

It can easily be seen that S(T) really has a maximum for a certain time constant τmax. First consider a transient that is very rapid. Then it has already finished before the first gate opens and hence C(t1) = C(t2), and S(T) =0. Similarly when the transient is too slow, it will not change much between the two gates and so again S(T) =0. Thus there will be an output with some maximum value Smax only for transients having time constants in between these two.

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

$$\begin{aligned} \tau\_{\text{max}} &= (t\_1 - t\_2 / \ln(t\_1 / t\_2)) \\ &= (\infty - 1)t\_1 / \ln(\infty) \end{aligned} \tag{15}$$

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

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

$$S\_{\text{max}} = \Lambda \mathcal{C}\_0 \left[ \exp(-\ln(\text{x})/(\text{x}-1)) - \exp(-\text{x}\ln(\text{x})/(\text{x}-1)) \right] \tag{16}$$

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 centre concentration.
