Carrier Lifetime Measurements in Semiconductors through the Microwave Photoconductivity Decay Method

Figure 1 shows a schematic diagram of the μ-PCD apparatus consisting of a 10 GHz microwave frequency, X waveguide band, and a rectangular waveguide. The microwave was focused by the double ridge waveguide and irradiated on the sample. The Gunn diode output power was 50 mW and the phase noise was nearly -80 dBc/Hz.

Figure 3 shows the μ-PCD decay curve of a 100-μm-thick n-type 4H-SiC sample excited on the Si-face by 266 nm in the air; μ-PCD signal (V) scaled logarithmically was the dependent variable and time (μs) was the independent variable. The signal voltage peak was approximately 0.046 V prior to amplification. Moreover, the observed voltage of the direct current (DC) component of the reflected microwave obtained from the oscilloscope DC mode was of the order of several volts. As recombination of excess carriers progressed with time, the sample’s conductivity and microwave reflectance decreased.

Figure 4 shows the normalized μ-PCD decay curve of Figure 3. Normalization enables comparison of the time constants with different peak intensities. Typically, carrier lifetime estimation based on the decay curve is carried out with the 1/e lifetime τ_1/e parameter, indicating that time expended to obtain signal intensity decreases from the peak to 1/e (~0.368). Note that µ-PCD decay was not a single exponential and τ_1/e was influenced by both bulk and surface recombination. However, comparing the time constant of samples having different thickness or surface condition necessitated a reference parameter. Usage of τ_1/e was convenient given the good signal-to-noise ratio at the initial part of the decay curve and the simplicity of the data analysis. To characterize the µ-PCD signal, half-time lives, I₄₀/I_max, and k_D constant also adopted such parameters^22,23,24. In fact, τ_1/e was adopted in the SEMI standard: SEMI MF 1535⁸ as the standard for carrier lifetime measurement of Si. For the decay curve in Figure 4, τ_1/e was approximately 0.34 μs.

In Figure 5, the quartz cell, containing the aqueous solution and with the sample on its wall, was placed on the stand in front of the aperture¹¹. Each intensity of the irradiated microwave and the reflected microwave from the sample, as well as the μ-PCD signal-to-noise ratio, were dependent on the distance between the sample and the aperture, which, ideally, should be as close as possible. In the actual measurement, the distance obtained was as close as possible; measurement using the quartz cell yielded a distance of 0.5 mm, which was of the same as the thickness of the quartz cell glass.

Figure 6 shows μ-PCD decay curves of the n-type 4H-SiC in the air and in aqueous solutions. An excitation light of 266 nm was irradiated to the Si-face of the 4H-SiC. Aqueous solutions used had concentrations, as mentioned previously, as follows: 1 M each of H₂SO₄, HCl, Na₂SO_4, or NaOH, or 1 wt% of HF. The time constant of the decay curves was longer with the sample immersed into the acidic aqueous solutions (i.e., H₂SO₄, HCl, or HF), implying that acidic solutions passivated surface states on the Si-face and reduced surface recombination of the excess carriers.

Figure 7 shows the pH dependence of τ_1/e of the n-type 4H-SiC sample excited on the Si-face at 266 nm of light. The pH was calculated from the molar concentrations of H₂SO₄, HCl, and NaOH. This figure indicated the carrier lifetime dependence on pH aqueous solutions; therefore, lower pH would have more effects on the carrier lifetime.

Surface recombination velocity S was calculated to reproduce the τ_1/e used for the samples. The decay model of excess carriers has been reported in refs. 2 and 3. To obtain the excess carrier concentration Dn(x, t), the following continuity equation was solved. Here, Dn(x, t) was defined as a function of time t and depth x in a semiconductor layer; thus,

,              (6)

where τ_B is bulk lifetime due to the Shockley–Read–Hall (SRH) recombination, D_a is the ambipolar diffusion coefficient, B is the radiation recombination coefficient, and C is the Auger recombination coefficient.

At the excited and other surfaces, boundary conditions were given by Equation 7:

and               (7)

where S₀ and S_W denote the surface recombination velocity of the excited and other surfaces, respectively, and W is the layer thickness.

Moreover, the initial excess carrier concentration profile using light pulse illumination could be expressed using Equation 8: 

                                                      (8)

where g₀ is carrier concentration at x = 0 and a is the absorption coefficient.

Solving Equation 6 by employing the boundary conditions of Equation 7 and the initial condition of Equation 8 provided the excess carrier decay curves. In the process, S was estimated by comparing the τ_1/e obtained from the experiments and from the calculated decay curves. Least squares fitting minimized errors between the experimental τ_1/e in the all conditions and the calculated τ_1/e with parameters S₀, S_w, and τ_B.

As depicted in Equation 6 carrier recombination is the summation of various decay components, namely, surface, SRH, radiative, and Auger recombinations, the last two having remarkable high carrier density. On the other hand, SRH recombination depends on point defects and dislocations in the bulk of the semiconductor material that form energy levels in the semiconductor band gap. The energy levels act as stepping stones for carrier transition between the valence and conduction bands.

μ-PCD also shows nonlinearity at a high injection condition, and overestimates carrier lifetime^13,25,26. Figure 8 shows the measured μ-PCD under a high excitation condition. Note that the decay curve for an injected photon density of 10¹⁵ cm⁻² became more gradual compared to that for photon density of 10¹⁴ cm⁻², owing to microwave nonlinearity. Furthermore, the measurement examples shown in Figure 3, Figure 4, and Figure 6 were obtained for an injected photon density of 8 x 10¹³ cm⁻² resulting in negligible microwave nonlinearity, and Auger and radiative recombinations but dominant SRH and surface recombinations.

Figure 6 can be taken to exemplify decay curve calculations for the n-type 4H-SiC Si-face excited by 266 nm light, by referring to the dashed lines, where τ_B = 3 μs and S for the Si-face S_Si = 200 cm/s or 700 cm/s. For both S_Si settings, the experimental decay curve measured in neutral pH (air, 1 M Na₂SO₄) and in the acidic condition (1 M H₂SO₄), respectively, were well reproduced, which meant that S_Si for the n-type 4H-SiC significantly reduced from 700 cm/s to 200 cm/s in acidic aqueous solutions as hydrogen passivated the surface states on the Si-face.

Figure 1: Schematic diagram of the μ-PCD device. A part of the laser light is reflected by the half-reflection mirror. The reflected laser is detected by the photodiode, and a signal coming from the photodiode is used as a trigger for the oscilloscope. A microwave is generated from the Gunn diode in the direction bent by the circulator; then, a microwave goes through the aperture and irradiates the sample. The reflected microwave from the sample comes back to the aperture and into the circulator, where it is detected by the Schottky barrier diode. Finally, the signal coming from the Schottky barrier diode is observed by the oscilloscope. Please click here to view a larger version of this figure.

Figure 2: The μ-PCD signal for a failed tuning of E-H tuner. No measurable peak is observed for a failed tuning. Please click here to view a larger version of this figure.

Figure 3: The μ-PCD decay curve for the n-type 4H-SiC sample with excitation on the Si-face by 266 nm in air. The pulsed laser is irradiated at time = 0 s at which the signal intensity is at maximum. This figure has been modified from Ichikawa et al.¹¹ with permissions. Please click here to view a larger version of this figure.

Figure 4: Normalized μ-PCD decay curve for the n-type 4H-SiC sample with excitation on the Si-face by 266 nm in air. The maximum value of the decay curve in Figure 2 is normalized to unity. The value of the dashed line is 1/e, and τ_1/e is approximately 0.34 μs as depicted. This figure has been modified from Ichikawa et al.¹¹ with permissions. Please click here to view a larger version of this figure.

Figure 5: Image of μ-PCD measurement in an aqueous solution in a quartz cell. The quartz cell is placed on the stand in front of the aperture to allow μ-PCD decay curve measurement in an aqueous solution. The cell dimension is 5 mm x 20 mm x 40 mm (length x width x height). Please click here to view a larger version of this figure.

Figure 6: Normalized and calculated μ-PCD decay curves for the n-type 4H-SiC sample with excitation on the Si-face by 266 nm, in air and aqueous solutions. Solid lines represent the μ-PCD experimental result curves for the aqueous solutions of H₂O, H₂SO₄, HCL, Na₂SO₄, NaOH, or HF. The dashed lines are calculated curves with the bulk carrier lifetime in the epilayers, τ_B = 3 μs, and the surface recombination velocity for the Si-face, S_Si = 200 cm/s or 700 cm/s. This figure has been modified from Ichikawa et al.¹¹ with permissions. Please click here to view a larger version of this figure.

Figure 7: The pH dependence of τ_1/e for the n-type 4H-SiC sample with excitation on the Si-face by 266 nm. Carrier lifetime increases as the pH of the aqueous solution decreases. This result indicates that lower pH will have more effects on the carrier lifetime. This figure has been modified from Ichikawa et al.¹¹ with permissions. Please click here to view a larger version of this figure.

Figure 8: The μ-PCD decay curve of n-type 4H-SiC with excitation of injected photon density of 10¹⁴ or 10¹⁵ cm⁻² on the Si-face by 266 nm. Measurement with high excitation at photon density of 10¹⁵ cm⁻² makes a more gradual decay curve than that with lower photon density due to nonlinearity of microwave reflectivity. Please click here to view a larger version of this figure.