Deep-level transient spectroscopy

Deep level transient spectroscopy (DLTS) is a powerful characterization tool to de-termine the electronic properties and concentrations of deep level traps. Specifically, DLTS enables determination of the trap signature by isolating the emission of ma-jority carriers. It is the depletion region of a rectifying diode that is used to isolate

3.1 Electrical characterization

the emission process, where minority carrier band interactions are considered negli-gible, and the majority carrier capture is not happening due to the depletion of free carriers.

Figure 3.4: Energy band diagram of a Schottky barrier diode for the biasing conditions during the DLTS measurement.

(a)at reverse bias V =VR in equilibrium.

(b)at pulse voltageV =VP= 0 V.

(c)directly after turning off the pulse voltage at reverse biasV =VR.

The capacity DLTS measurement principle is described here using the example of the generation of DLT-spectra of the majority carrier traps. As a device under test a SBD on an n-type semiconductor is used. The energy band diagram for the biasing conditions during the DLTS measurement is shown in Fig. 3.4. We apply a reverse bias V = V_R, hence the electron traps E_T are not occupied by electrons for 0 ≤ x < LR and are occupied by electrons for x ≥ LR (see Fig. 3.4(a)).

3.1 Electrical characterization

Now, the reverse bias is pulsed to V = V_P = 0 V using a rectangular pulse with a duration t_P (see Fig. 3.4(b)). This pulse is called the majority charge carrier filling pulse. The electron traps in the region L_P < x < L_R capture electrons to get into the thermodynamic equilibrium of semiconductor. If t_P (c_nn)⁻¹ (see section 2.2 for capture coefficientc_n), all electrons will be occupied and we call the pulse a saturation pulse. After the pulse, again the reverse bias V =V_R is applied, but this time the space charge density is reduced by the electrons occupying the electrons traps in the region L_P < x < L_R (see Fig. 3.4(c)). The system now relaxes from the non-stationary state generated by the filling pulse as a result of thermal electron emission from the electron traps in this region into the stationary initial state. This process follows time constant which equals the inverse thermal emission rate of the electron trap as described in equation 2.22 from section 2.2.

The associated change in the space charge is balanced by a simultaneous change in the depletion layer width, which can be measured by measuring the capacitance in capacitance transients: which is proportional to the output voltage of the capacitance meter. Therefore, the signal is analyzed by multiplying it with a correlation functionB(t) and temporally averaging this product for a repetitive measurement cycle with the duration TM. The DLTS-signal can be calculated by:

S = 1 T_M

Z TM

0 [∆C(e_n, t) +r(t)]B(t) dt . (3.16) The actual DLTS measurement is performed by continually applying pulses and measuring the capacitance transients while changing the temperature of the sample.

As the emission rate depends strongly on temperature (see equation 2.19), peaks will appear at the temperatures corresponding to the maximum of the function S=f(e_n(T)), which is called a DLTS-peak. If there is more than one electron trap in the semiconductor, there will be more DLTS-peaks corresponding to the electron traps’ emission ratese_n(T). It is possible that these DLTS-peaks are superimposed.

The DLTS measurement principal is illustrated in Fig. 3.5 with a boxcar analysis as the correlation functionB(t). The boxcar analysis is set to B(t=t₁±∆t) = +1 and

3.1 Electrical characterization

Figure 3.5: The DLTS measurement principal shown for a boxcar analysis.

(a)Capacitance transients at various temperatures after turning off the pulse voltage during the DLTS measurement. The transients depend on the temperature T and the emission rate of the respective electron trapen.

(b)The analysis of the difference in capacitance at two points in time(C(t1)−C(t2)) over the temperature give a temperature dependent signal with which it is possible to determineen.

To extract the significant values for DLTS en(T) and ∆C(t = 0), we have to take a closer look at the boundary conditions in the peak maximum. In the peak, maximum the temperature derivative must be zero:

dS(T)

dT = dS(T) d (tie_n(T))

d (t_ie_n(T))

dT = 0 . (3.18)

For the boxcar analysis of the DLT-spectra the emission rate in the peak maximum is:

e_n,max = (t₁−t₂)⁻¹lnt₁ t₂

. (3.19)

In the research conducted in this thesis deep-level transient Fourier spectroscopy (DLTFS) was applied, which uses Fourier coefficients as the correlation function.[67]

The spectra shown in this thesis are calculated using theb₁(t) Fourier coefficient as the correlation function B(t) = b₁(t) (see Fig. 3.6). The emission rate in the peak maximum for the b₁ Fourier coefficient can be calculated with:

τ_n,max

T_M = 4.388×10⁻¹ → en,max = 2.279

T_M . (3.20)

3.1 Electrical characterization

Figure 3.6: The correlation function of the b1 Fourier coefficient of the DLTFS method.

Using the Arrhenius form of equation 2.19 we get:

lne_n T²

= ln σnaAg₁ g₀

!

− ∆H

kBT , (3.21)

it is possible to extract the enthalpy and the apparent capture cross section of the electron trap. For this equation it was assumed that N_eff^V,C ∝ T³² and hv_n,pi ∝ T¹² (see section 2.2). With ∆H ≈ E_C −E_T we achieve the so-called T² correction of the ionization energies and extrapolated capture cross sections from this Arrhenius plot. All energies determined by DLTS in this thesis are theT² corrected ionization energies. All Arrhenius plots in this thesis are plotted using the emission timeτn(T) as the ordinate, which can be easily transformed to the emission rate by:

e_n(T) = 1

τ_n(T) . (3.22)

The simplest approximation for the determination of the trap concentration is:

N_T = 2N_D∆C(t= 0)

C(t=∞) , (3.23)

which commonly underestimates the trap concentration. This concentration was used for the scaling of the y-axis of the DLT-spectra shown in this thesis. The trap concentration can be corrected by including a correction factor [68]:

N_T = 2N_D∆C(t= 0)

C(t=∞) · W_R²

(W_R−λ)²−(W_P−λ)² , (3.24) which slightly overestimates the trap concentration, but takes into account the lambda layer correction resulting from crossover of the Fermi energy with the trap energy due to the band bending within a SBD laying closer to the diode’s interface than the calculated depletion width, with [68]:

λ =

s2εrε₀

e²N_D (E_F−E_T) . (3.25) Both the simple approximation for the trap concentration and the corrected one assume spatially uniform doping and N_T N_D.

The DLTS spectra in this thesis were measured using cpacitance meter with an AC measurement signal of 1 MHz and an amplitude of 100 mV. The pulses have a