Pre-irradiation Characteristics

Figure 1 shows the current-voltage characteristics of the VPE Schottky diode under both forward and reverse bias and demonstrate standard Schottky characteristics for low bias, as shown in figure 1(a). However, at higher bias the reverse current did not saturate and continued to increase until diode breakdown at approximately 180 V.

Figure 1: The current characteristics of a VPE GaAs diode measured at 300 K. The key is: dashed line - forward bias; solid line - reverse bias.

[Low bias] [High bias]

From the forward bias characteristic two methods were used to determine the barrier height[7]. The first found the value of the saturation current ($J_{s}$) from the extrapolation of the current characteristics to zero forward bias, shown in figure 2. Using equation 1 with a Richardson constant ($A^{**}$) of 8 Acm$^{-2}$K$^{-2}$, the barrier height ($\phi_{B}$) was found to be $0.81\pm0.005$ V, where the error was due to the uncertainty of $A^{**}$.

$$J_{s} = A^{**}T^{2} \exp\left( - \frac{q \phi_{B}}{kT}\right)$$ (1)

This method requires the exact dimensions of the contact area ($S_{e}$) to determine the current density. The second method, which utilises the temperature dependence of the forward current, has no such dependence. The current was measured at 0.1 V over the temperature range 293 to 308 K. The forward current may be expressed as:

$$\ln \left(\frac{I}{T^{2}} \right) = \ln {A^{**} S_{e}} - \frac{q}{k T} (\phi_{b} - V)$$ (2)

The barrier height for the VPE diode was found from a plot of $\ln (I/T^{2})$ against $1/T$ to equal $0.85\pm0.01$ V. The error was found from the error in the linear regression fit to the data.

Figure 2: The extrapolation of the forward current to determine $J_{S}$.

Capacitance measurements were performed on the diodes. The C-V curves did not show a significant difference between the measurements made with a test signal frequency of 100 Hz and 100 kHz, therefore the concentration of deep levels with a low emission frequency was assumed to be negligible. A doping density ($N_{D}$) of $2.8\pm0.2\times10^{14}$ cm$^{-3}$ for the VPE layer was determined from the capacitance voltage characteristics of the device over a reverse bias range 0-20 V. Such a high value has implications for the extension of the depletion width of the device under reverse bias and thus the charge collection of the device.

The reverse current characteristic was investigated to determine the cause of non-saturation. Figure 3 shows the current voltage dependence up to a reverse bias of 10 V. Illustrated on the figure is the current that would be expected for an ideal barrier. As can be seen this is considerably less than that measured. The effect on the current due to image force lowering of the barrier height for the measured doping density of the material is shown as the dotted line in the figure. This was insufficient to account for the observed current. The current was assumed to be generation current and a fit of the form:

$$J_{gen} = \frac{q n_{i} w}{2 \tau_{r}} = P(1) (\phi_{b} - V_{n} - kT/q + V_{r})^{P(2)}$$ (3)

was performed to the data, where $P(1)$ and $P(2)$ were free parameters, $n_{i}$ the intrinsic carrier concentration, $w$ the depletion width, and $\tau_{r}$ the lifetime of the free carriers. The value of $V_{n}$ was calculated from:

$$V_{n} = \frac{kT}{q } \ln \left( \frac{N_{C}}{N_{D}}\right)$$ (4)

where $N_{C}$ is the effective density of states in the conduction band.

The values obtained for the parameters were: $P(1) = 0.66\pm0.02$ nA/mm$^{2}$ and $P(2) = 0.53\pm0.02$. For generation current the expected value of $P(2)=0.5$ which corresponds to that found and therefore the current was attributed to generation effects. The activation energy of the current at -10V was found to equal $0.73\pm0.02$ eV which is equal, within errors, to half the bandgap energy. The generation current was not likely to be due to the mid-gap donor EL2, as is the case in LEC material, because the concentration of this deep level was low.

Figure 3: The reverse bias current-voltage characteristic. The key is: solid line - measured data; dot-dashed line - ideal current; dotted line - that due to image force lowering; dashed line - the result of the fit of equation (3).

From the capacitance voltage measurements the depletion width as a function of bias was determined up to a bias of 180V, as shown in figure 4. At 100 V the depletion depth was only 22.3 $\mu$m, increasing to 27.4 $\mu$m at 150 V. The low values were due to the high density of donors in the material.

Figure 4: The depletion width as a function of reverse bias, calculated from the capacitance voltage dependence of the device.

The low depletion depth and the high current resulted in the signal from a high energy beta particle being indistinguishable from the electronic noise of the device. For a 100% cce the signal would equal only 3600 electrons at a bias of 150 V. The cce determined for 60 keV gamma photons was $97\pm17$% at a bias of 200V. The error is due to the spread in the peak due to the high leakage current of the device at this bias. Due to the 450 $\mu$m thick $n^{+}$ layer on the back side of the device the detector was only sensitive to alpha particle illumination from the front surface. Although the range of 4.1 MeV alpha particles in GaAs is only $\sim13\mu$m, due to the comparably small depletion region the detector response was no longer due primarily to one charge carrier. The charge collection efficiency as a function of both bias and depletion depth, calculated from the CV data, are shown in figure 5 for two VPE diodes. The charge collection showed the expected increase with bias due to the increase in depletion width. The maximum cce's for the two detectors were $100\pm$7% and $93\pm$7% at a bias close to 150 V. The cce plateaued for a depletion width between 10 $\mu$m and 15 $\mu$m as expected from the alpha particle range in GaAs. At zero applied bias, however, the depletion width, calculated from the capacitance measurements, was only 2 $\mu$m but a signal of 65% of the full alpha particle signal was obtained. Therefore diffusion or drift of charge into the depletion region must occur.

Figure 5: The charge collection efficiency from front illumination by 4.1 MeV alpha particles as a function of reverse bias and depletion depth for two VPE diodes.

[Function of reverse bias] [Function of depletion width]