A New Method to Analyze Closely Spaced Deep Defect Levels Caused by Multiexponential Transients

Assem. Bakry Physics Department

Ha’il University Ha’il, KSA

a.elsedfy@uoh.edu.sa

Abstract— A new method is presented to analyze non-exponential capacitance transients, caused by closely-spaced deep defect levels active at the same temperature range, into the appropriate components. It is capable to resolve deep-level transient spectroscopy (DLTS) signals having one or more shoulders, generated by two or more trap levels. Closely-spaced traps are accompanied by the observation of multiple emission rates making the differentiation between them almost impossible using conventional analysis techniques. The proposed method utilizes a hybrid between the conventional DLTS technique, based on Lang’s method [1], and the non-linear double exponential fitting routine previously published by the author. This technique was successfully tested on Se-doped n-type AlxGa1-xAs sample, having what is known as DX centers, and was capable of resolving up to seven deep levels with activation energies ranging from 270 – 486 meV.

Keywords— Deep levels, Multiexponential transients, DLTS, AlxGa1-xAs

I. INTRODUCTION The properties of deep level impurities in semiconductors

are of importance for both the performance and reliability of devices. Proper characterization of such levels is also nec-essary for a better understanding of basic physics and material properties. DLTS is one of the existing tools among the most powerful for characterizing semiconductors [1]. This method relies on an assumed simple exponential-like capacitance decay. However, in most cases, non-exponential capacitance transients exist. The main cause of such non-exponential behavior might be multiple closely spaced deep levels with comparable emission rates. One of the limitations of the conventional DLTS is its inability to distinguish defects having energy levels closely located in the energy gap.

Several attempts have been made to overcome such limitation using different approaches [2-16]. Most of these attempts relied on a relatively complicated mathematical treatment.

A previous attempt has been published by the author and others [17] to analyze multi-exponential transients using a nonlinear double exponential fitting routine. This technique was successfully applied to a two-trap model yielding the

thermal activation energies and capture cross sections of the two closely spaced traps.

In this paper, a simple and straightforward method is introduced to detect a third, or more, trap closely spaced causing the existence of a shoulder on either, or both, sides of DLTS spectrum. This could be considered as an extension for the previously published work dealing with multi-exponential transients. The new method was tested on a Se-doped AlxGa1-xAs grown by metal-organic chemical vapor deposition.

II. EXPERIMENTAL This method uses a hybrid between the conventional DLTS

system and that used for the double exponential fitting method. The conventional DLTS scan was performed using a SULA Technologies spectrometer, SULA TECHNOLOGIES Palo Alto California USA. The DLTS setup consists of a bias pulse generator, a fast capacitance meter, a cryostat permitting continuous temperature change, a correlator and is interfaced with a computer for data acquisition and analysis. The capacitance meter operates at 1 MHz, as in most commercial capacitance meters, which proved to be adequate. An additional advantage of the lower measuring frequency is that shallow levels can respond to the signal at lower temperature. The experimental setup used for digitally recording the capacitance transients for the double exponential fitting method was previously explained [17].

III. METHODS OF CALCULATION In a DLTS measurement, if a p+n diode is pulsed from a

reverse bias to zero volts, part of the depletion region will be converted to neutral n-type material. Any deep level impurity present in this region will thus be filled with electrons. When the reverse bias is restored, levels in the upper half of the bandgap in the depletion region are no longer in thermal equilibrium with the conduction band and emit electrons with a characteristic time constant, given by;

1 exp( )ng E kTτ = ∝ −Δ (1)

where gn is the emission rate, ΔE the thermal activation energy of the level k Boltzmann constant and T the absolute

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temperature. The emission changes the space charge density in the

depletion region resulting in a capacitance transient which can be detected. DLTS setup measures the capacitance at two different times (windows) t1 and t2 after the bias pulse is removed and outputs the capacitance difference S =ΔC(t2)-ΔC(t1).

According to Lang [1], S has a maximum when the emission time constant τ matches the rate window tR defined by

( )2 1

2 1lnRt t

tt t−

= (2)

Thus if S is recorded as a function of temperature, a spectrum is obtained where each impurity manifests itself as a peak at a temperature Tmax, which depends on the rate window tR. A plot of log tR versus 1/Tmax according to equation (1) gives a straight line, the slope of which is proportional to ΔE.

As for the nonlinear double exponential fitting technique for a two trap model [17], considering the equation

32 21 4

0 1

c tc t T

T

NC c e e cC N

−−⎛ ⎞Δ = + +⎜ ⎟⎝ ⎠

(3)

where ΔC is the capacitance caused by applied pulse (pF), C0 is the equilibrium capacitance(pF), c1 is the ratio NT1/2Nd , NT is the density of defect states(cm-3), Nd is the donor density(cm-3), c2 and c3 are the appropriate emission rates and c4 is an additional constant to adjust for small baseline variations.

This equation was used to analyse the data by determining the ci's with a nonlinear fitting routine. In order to find the best ratio for NT2/NT1, the fitting procedures had to be run iteratively keeping this ratio constant until the best two Arrhenius plots were obtained.

The proposed new addition starts by considering the equation derived from the theory of detailed balance [1]

exp( )e e e c n Bg v N E k Tσ= − Δ (4)

where σe is the electron capture cross section (cm2), ev is the thermal velocity for electrons (cm/s), Nc is the effective density of states in the conduction band (cm-3). The capture cross section can be temperature dependent so can be the effective density of states. Considering that ev T∝ and

32

cN T∝ , equation (4) could be rewritten as

( )2ln ( ) ( / )e Bg T F T E k T= − Δ (5)

Plotting ( )2ln eg T vs 1/T results in a straight line where the slope of the Arrhenius plot yields the thermal activation energy and F(T) is the intercept with the y-axis (yi). Equation (5) could be rewritten as

2 iE kTyieig T e e−Δ= (6)

As previously mentioned, the DLTS setup measures the

capacitance difference at two different windows t1 and t2. The equation describing this output for a majority carrier trap could be written as

2 1( ) ( )C C t C t−Δ = Δ − Δ (7)

From equations (3) and(7)

1 2 2 2 1 1 2 12 2

1 1

e e e eg t g t g t g tT T

T T

N NC x e e e eN N

− − − −⎡ ⎤⎛ ⎞ ⎛ ⎞−Δ = + + +⎢ ⎥⎜ ⎟ ⎜ ⎟

⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦(8)

where 10 2

T

D

Nx CN

=

We assume that we have three closely spaced traps causing the DLTS spectrum to have a main peak, caused by two of the three traps, and a shoulder, caused by the third trap. The calculation using the new proposed method is carried out according to the following procedure. First, the conventional DLTS is used from which the maximum value for ΔC and Tmax are determined. Then applying the nonlinear double exponential fitting technique to the main spectrum, two Arrhenius plots are determined giving values for the y-intercept and the activation energy for each individual trap. These values along with that of Tmax are plugged in equation (6) giving values for ge1 for the first trap and ge2 for the second. Then using equation (8), and substituting with the constant ratio NT2/NT1 determined from the nonlinear fitting, a value for x is calculated. Finally, using equations (6) and (8), a complete spectrum could be reproduced for the two traps for all the temperature range. Subtracting this spectrum from that produced using the conventional DLTS technique, the spectra for the shoulders could be separated.

IV. RESULTS AND DISCUSSION This method was tested on a Se-doped AlxGa1-xAs sample

grown by metal organic chemical vapour deposition (MOCVD) with x value of 0.29. For the DLTS measurement, Schottky barrier diodes with gold contacts were prepared. In AlxGa1-xAs, donors such as S, Te, Se, Si Ge and Sn form not only a shallow level, but also a deep level known as DX center. The DX center is a complex consisting of a donor atom and an anion vacancy in n-type AlxGa1-xAs. The electrons trapped at the DX center are strongly localized. This is accompanied by the observation of multiple emission rates. Thus electron capture by these centers is non-exponential and strongly temperature dependent.

Fig. 1 shows the output of the conventional DLTS setup for a window of 12.5 and 32.5 msec. The Schottky diode was reverse biased to -3 Volts. A pulse width of 60 msec and a period of 200 msec were used for all the traps to have enough time for capturing and re-emitting of charge carriers. The figure shows two main peaks besides three shoulders appearing at different temperature ranges, from 110 to 134°K, from 170 to 190°K and from 224 to 240°K. The two main

DLTS peaks are located at 148°K with a maximum of ΔC at -8.57×10-14 pF and the other at 205 °K with a maximum of ΔC at -5.30×10-13 pF. The two Arrhenius plots for those two peaks resulted in activation energies equal to 260 meV and 428 meV respectively.

The double exponential fitting routine was applied on each main peak separately. For main peak 1, the optimum value found for NT2/NT1 was 0.70 while that for main peak 2 was 0.85. Fig. 2 shows the output of such fitting. As could be seen from figure, main peak 1 is resolved into two peaks. One has a maximum at 145°K, and the other at 156°K. The Arrhenius plots for those two peaks yielded activation energies ΔE = 270 meV for the first and ΔE = 279 meV for the second.

Temp, Kelv

Fig. 1. A DLTS spectrum measured for the n-AlxGa1-xAs sample using the conventional DLTS system

For main peak 2, the resolved peaks appeared at 201°K and 211°K resulting in activation energies of 445 meV and 452 meV. Applying the procedure explained in the previous section, the three shoulders shown in Fig. 1 could be separated into independent peaks and are demonstrated in Fig. 3 for a window of 12.5 and 32.5 msec. The first shoulder has a maximum at 126°K, the second at 185°K and the third at 231°K.

The Arrhenius plots for the three shoulders are shown in Fig. 4. The figure shows how good the fitting is especially for shoulders 2 and 3. For shoulder 1, the fitting was not as good as for the other shoulders because the separated shoulder signal was broader than the others. One possible reason for this broadness is that this shoulder might be the result of more than one defect level. As shown in figure, the calculated

activation energies for the three shoulders are 334 meV, 413 meV and 486 meV respectively.

The measured values for the activation energies are listed in Table 1 along with previously published data for comparison. It could be seen from the table that the measured values for the traps activation energies are within the reported values for activation energies for DX centers found in n-AlxGa1-xAs using various dopants.

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

080 130 180 230 280

dCap

, pF

Temp, Kelv

Fig. 2. Resulting peaks from double exponential fitting routine plotted with the conventional spectrum

-0.2

-0.18

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

080 130 180 230 280

dCap

, pF

Temp, Kelv

Fig. 3. Resulting peaks from applying the new technique on shoulders

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

080 130 180 230 280

dCap

, pF

Shoulder 1

Shoulder 2

Shoulder 3

Main Peak 2

Main Peak 1

-8.00

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00

3.00 4.00 5.00 6.00 7.00 8.00 9.00

LN

(ge/T

2 )

Shoulder 3ΔE=486 meV

Shoulder 2ΔE=413 meV

Shoulder 1ΔE=334 meV

1000/T

Fig. 4. Arrhenius plots for the three shoulders calculated using the new technique

TABLE I. CALCULATED ACTIVATION ENERGIES (ΔE) FOR THE TESTED N-ALXGA1-XAS SAMPLE AS COMPARED TO VALUES PUBLISHED FOR SIMILAR

TRAPS

Material Dopant Trap No. ΔE (meV) Ref.

Al0.29Ga0.71As Se

1 334

This work

2 270 3 279 4 413 5 445 6 452 7 486

Al0.6Ga0.4As Se 1 286

18 2 433

Al0.22Ga0.78As Se 1 300

19 2 530

Al0.3Ga0.7As Si 1 330

20 2 400 3 430

AlxGa1-xAs Si 1 390

21 2 470

Al30Ga70As Si 440 22 Al35Ga65As Te 280

23 Al30Ga70As Se 270 Al25Ga75As Sn 190

Al0.2Ga0.8As Ge 1 300

24 2 500

V. CONCLUSIONS A new method is proposed to separately detect the

activation energies for closely spaced defect levels. This method could analyze shoulders appearing on one side, or both sides, of a DLTS spectrum. The proposed method

uses an easy and straightforward calculation method based on the conventional DLTS technique along with the double exponential fitting routine. The Arrhenius plots for the detected shoulders gave very good fitting results, indicating the correctness of such results. The activation energies obtained lied within the previously reported values for the DX centers found in n-AlxGa1-xAs using various dopants.

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