Carrier transport and energy band diagram

When the incident particle irradiates the Al_xGa_1-xAs/GaAs p-i-n detector, electron-hole pairs (carriers) are generated in the Al_xGa_1-xAs/GaAs p-i-n detector owing to the ionization effect. The transport process of carriers in the detector is complicated and mainly includes thermal, field, and thermal field emissions. A band diagram is the most suitable form of expression to clearly describe the carrier transport process. The energy band diagram of the Al_xGa_1-xAs/GaAs p-i-n detector is shown in Fig. 2. Compared with the general homogeneous p-i-n junction detector, the Al_xGa_1-xAs/GaAs p-i-n detector designed in this study was a heterogeneous p-i-n junction that introduced changes in Al composition and doping concentration in both the p- and n-type AlGaAs layers.

Fig. 2Full-screen View

Band structure of device where E_c is the conduction band minimum, E_v is the valence band peak level, E_vac is the vacuum level, and E_F is the Fermi level.

Because p-AlGaAs and n-AlGaAs exist on both sides of the intrinsic GaAs, the Al content of the p-AlGaAs increased linearly from left to right, and that of the n-AlGaAs increased linearly from right to left.

As shown in Fig. 1(a), the structure of the detector was a heterogeneous p-i-n junction, in which both the p- and n-type AlGaAs layers introduced changes in the Al composition and doping concentration as the thickness increased. Owing to the change in Al composition and doping concentration, the conduction band of the p-type AlGaAs layer bent upward, and the valence band of the n-type AlGaAs layer bent downward. Owing to the presence of p-AlGaAs and n-AlGaAs on both sides of the undoped i-GaAs, a gradually changing p-i-n heterojunction was formed inside the device owing to the graded change in the Al composition, and a strong built-in electric field from the n- to p-type was achieved. The electron-hole pairs generated by ionization were collected by the positive and negative electrodes of the device to generate electrical signals. The carriers in the area were easier to collect and improved the CCE of the device providing the detector with a high sensitivity and ability to perform efficient detection. In addition, because the p-AlGaAs and n-AlGaAs concentrations on both sides of the i-GaAs exhibited a trapezoidal change and owing to the influence of the built-in electric field, the actual depletion region of the device was wider than that of the intrinsic region.

Lee et al. used the I-V characteristics of a p-n junction to experimentally verify that electron thermionic emission is the main carrier transport mechanism of an Al_xGa_1-xAs/GaAs heterojunction bipolar transistor [23]. Chen et al. studied the current transport in graded p–n Al_xGa_1-xAs/GaAs heterojunction diodes by employing a thermal diffusion model [24]. Their research results suggested that the injection efficiency of carriers can be significantly improved by inserting a certain thickness of intrinsic layer into a graded Al_xGa_1-xAs/GaAs heterojunction.

Simulation

Abrupt or uniformly doped p–n junctions could not be used to analyze the characteristics of our devices. Therefore, we introduced the P-S model to analyze the electrical characteristics of our devices [25]. This model obtained the built-in potential, depletion region width, and electric field distribution of the device by solving the Laplace equation, which can also be used to analyze the electrical characteristics of a linear graded junction. According to the P-S equation, the depletion region width $W_{\text{D}}$ and built-in potential $V_{\text{bi}}$ of the device are expressed as $W_{\text{D}}=\sqrt{\frac{4\epsilon {\epsilon }_0{V}_{\text{bi}}}{q\pi G}},$ (1) $V_{\text{bi}}=\frac{kT}{q}\ln \frac{{\text{G}}^2{W}_{\text{D}}}{n_i^2},$ (2) where ${\epsilon }_0$ is the vacuum dielectric constant, ${\epsilon }_{\text{s}}$ is GaAs (${\epsilon }_{\text{s}}=13.1$), $q$ is the electron charge， $G$ is the graded constant of the doping concentration, $k$ is Boltzmann's constant, $T$ is the absolute temperature, and $n_i$ is the intrinsic carrier concentration.

It can be seen from Eqs. (1) and (2) that after introducing the graded constant G of the doping concentration, the depletion region width $W_{\text{D}}$ and the built-in potential V_bi of the device are related. The depletion region width is proportional to the square root of the built-in voltage, which is not the case for conventional p–n junctions. After determining the depletion region width $W_{\text{D}}$ and the built-in potential $V_{\text{bi}}$, the maximum electric field of the device can be obtained as $E_{\text{max}}=\sqrt{\frac{qG{V}_{\text{bi}}}{\epsilon {\epsilon }_0\pi }}.$ (3)

The built-in potential and depletion region width $W_{\text{D}}$ of the device structure shown in Fig. 1 were calculated using MATLAB. As shown in Fig. 3 (a), the relationship between $V_{\text{bi}}$ and the graded constant $G$ of the doping concentration was linear. The higher the $G$, the greater the $V_{\text{bi}}$. When $G$ was 10¹⁸ cm^-3, $V_{\text{bi}}$ was approximately 1.82 V. However, there was a nonlinear relationship between $W_{\text{D}}$ and $G$. The lower the doping concentration, the larger the width of the depletion region. Because the device structure was a p-i-n type, regardless the doping concentration, the width of the depletion region of the device was always greater than 1 μm. When $G$ was greater than 10¹⁵ cm^-3, the width of the depletion region was greater than 1 μm, but the change was not obvious. As shown in Fig. 3(a), increasing the doping concentration increased the built-in voltage, and the corresponding width of the depletion region was narrowed because the effective carrier concentration changed when the doping concentration increased.

Fig. 3Full-screen View

Theoretical simulation of detector: (a) relationship between depletion region width and built-in voltage and graded constant and (b) relationship between device electric field strength and doping concentration.

Under the action of an electric field, the carriers in the depletion region moved towards both ends of the electrode. The electric field strength determines the mobility and saturation velocity of carriers in a device. Equation (3) shows that the electric field strength is proportional to the square root of a device's total voltage, while the electric field strength of a conventional p–n junction (E = −V / W_D) is proportional to the built-in voltage. The relationship between the device's electric field strength and doping concentration was simulated as shown in Fig. 3 (b). The electric field strength increased with an increase in the graded constant G of the doping concentration. When G was 10¹⁵ cm^-3, the electric field strength of the device reached 1.7 × 10⁵ V/cm. This value was obtained without external bias voltage. Compared with conventional uniformly doped p–n junction diodes, the electric field strength of our device was relatively close to the maximum theoretical electric field of GaAs (~ 5 × 10⁵ V/cm).

The range of 5.48-MeV alpha particles in GaAs was simulated using SRIM. As shown in Fig. 4, the alpha particle of 5.48 MeV had a range of approximately 18.4 μm in GaAs. According to our device structure, the depletion region width was approximately 1 μm. According to our device structure, 325 KeV was absorbed by GaAs for a depletion region of 1.19 μm (from theoretical simulations).

Fig. 4Full-screen View

Range of charged particles in GaAs from SRIM program

Experimental assembly

For semiconductor detectors, the ionization energy of the incident rays in semiconductor materials is much smaller than that of gas detectors (~30 eV). Therefore, semiconductor detectors have a higher energy resolution. The electron-hole pairs generated by incident radiation in the intrinsic region of a detector are collected by the electrodes under the action of an electric field. During measurements, because the energy gap of GaAs is 1.4 eV, external light and various electromagnetic radiations in nature interfere with the detector. To shield the detector from external electromagnetic and light interference, an Ortec 807 vacuum chamber was used. The alpha particles were partially lost in the air before reaching the detector. A mechanical pump was used to evacuate the vacuum chamber to reduce the energy loss of the incident rays in the air. The vacuum pressure in the chamber was less than 1 Pa. The electron-hole pairs generated in the intrinsic region cannot be directly collected by subsequent circuits, and a preamplifier must be added at the back end of the detector. There are three types of preamplifier: current, voltage, and charge. To obtain higher-energy-resolution characteristics, a charge-sensitive preamplifier with lower noise is more suitable for energy-spectrum measurements. This system used an Ortec 142A as the detector rear signal amplifier. Usually, the rise time of an output signal from a 142A amplifier is only a few nanoseconds, and the fall time is very long, approximately several microseconds or even tens of microseconds. Neither the voltage amplitude, pulse rise time, nor output signal from a charge amplifier is sufficient for data acquisition. It is also necessary to shape the pulse and amplify the output signal from a charge-sensitive preamplifier. In this experiment, an Ortec 572A shaping amplifier with adjustable forming time and magnification was used. Data were acquired using an Ortec 927-pulse multichannel analyzer with a 16k ADC. The experimental setup is shown in Figure 5. The²⁴¹Am alpha source (5.48 MeV) used in the measurement was a surface source with a diameter of 30 mm, an effective emission area of 25 mm, and a thickness of 2 mm.

Fig. 5Full-screen View

Schematic diagram of energy spectrum measurement used in experiment

Before the measurement, a mechanical pump was used to evacuate the alpha source and detector to less than 1 Pa. A collimator was not used between the ²⁴¹Am alpha source and detector. The distance between the 241Am alpha source and detector was 3 mm.

I-V measurement

The current expression for an ideal p–n junction diode is [26] $I=I_{\text{S}}\text{exp}\left(\frac{q(V_{\text{bi}}+V)}{\kappa T}\right)-1,$ (4) $I_{\text{S}}=\frac{q{D}_{\text{p}}{p}_{\text{n}0}}{L_{\text{p}}}+\frac{q{D}_{\text{n}}{n}_{\text{p}0}}{L_{\text{n}}},$ (5) where $I_{\text{S}}$ is the reverse saturation current, V is the detector applied bias voltage, D_n and D_p are the minority electron and minority hole diffusion coefficients, respectively, n_p0 and p_n0 are the minority electron and minority hole densities in thermal equilibrium, respectively, and L_n and L_p are the diffusion lengths of minority electrons and minority holes, respectively.

The p-i-n structure is a special case of the p–n structure; therefore, the device current of a p-i-n structure can also be calculated using Eq. (3). Compared with a conventional p–n junction, the reverse leakage current of a p-i-n type device structure is smaller. For nuclear radiation detectors, the bias voltage applied to both ends of a detector is negative; that is, the detector operates in the reverse bias mode. The reverse leakage current of a device was mainly formed by the diffusion movement of minority carriers.

Current vs. forward and reverse voltage measurements for the p-i-n Al_xGa_1-xAs/GaAs detector were performed at room temperature using a Keithley Model 4200-SCS semiconductor characterization system. As shown in Fig. 6 (a), the forward I-V characteristic of the detector exhibited a threshold voltage of 0.95 V (forward current: 1 mA), which indicates good p–n junction I-V characteristics. When the forward and reverse biases were 1 V, the currents were 0.185 mA and 0.3 nA, respectively. The current ratio of the forward and reverse biases was 1.62 × 10⁶ at 1 V, indicating the high quality of the diodes. The high built-in voltage and high current ratio observed for the p-i-n Al_xGa_1-xAs/GaAs detector structure indicated that tunneling through the narrow triangular barriers was an effective transport mechanism for carriers in the space charge region of the graded composition and grade-doped p-i-n layer.

Fig. 6Full-screen View

Electrical characteristics of detector: (a) I–V characteristics of detector with 1-mm detection diameter under forward and reverse biases and (b) C–V characteristics and depletion width vs reverse bias voltage relationship.

C-V measurement

Based on the relationship between the reverse bias voltage and space charge region width, the C–V method can be used to calculate the width of the depletion region of the device. The expression for the junction capacitance and voltage of the device is $\text{C}=- \frac{\text{d}{Q}_S}{\text{d}V}=qA\frac{\text{d}}{\text{d}V}\underset{0}{\overset{W_{\text{D}}}{{\displaystyle \int }}}{N}_{\text{A}}\left(W_{\text{D}}\right)\frac{\text{d}{W}_{\text{D}}}{\text{d}V},$ (6) where $\text{d}{Q}_{\text{S}}$ is the charge increment of the semiconductor and $N_{\text{A}}$ is the carrier concentration.

The plate capacitor is related to the plate area A, insulating medium, and plate distance d ($C=\frac{\epsilon {\epsilon }_{0}A}{d}$）. The p-i-n device can be approximated as a plate capacitor, and the relationship between the depletion region width and junction capacitance is ${\text{W}}_{\text{D}}=\frac{\epsilon {\epsilon }_{0}A}{C}.$ (7)

According to Eqs. (6) and (7), the depletion region width of the detector can be calculated by measuring the C-V characteristics of the device.

The depletion width of the detector can also be determined from the experimentally measured capacitance. The C-V characteristics of the p-i-n Al_xGa_1-xAs/GaAs were measured using a Keithley 4200, and the relationship between the device depletion width and reverse bias voltage was derived. As shown in Fig. 6 (b), as the reverse bias voltage increased, the depletion region width increased. The width under reverse bias voltage increased from 1.08 μm at 0 V to 1.6 μm at 30V. The depletion region width under zero bias was slightly larger than 1 μm, indicating that the results from the theoretical calculations and experimental measurements were consistent. The width measured experimentally included the thickness of the i-GaAs layer 1 and the p- or n-GaAs (10¹⁶ cm^-3) layer doped with thinner graded components owing to the built-in potential of the structure as shown in Fig. 1. Thus, the depletion region width was greater than that of i-GaAs under zero bias in the structure of Fig. 1.

Alpha particle response

The 241Am isotope source emitted charged particles with energies of 5.48 MeV and γ-rays with an energy of 59.6 KeV. To demonstrate the insensitivity of our detector to gamma rays, a 1-mm thick aluminum foil was placed between the detector and radioactive source. No pulsed electrical signal was observed at the output of the charge-sensitive preamplifier using an oscilloscope. This may be because the interaction of the 59.6-KeV X-ray with the detector was mainly owing to the photoelectric effect, and the effective thickness of our detector was only 1.05 µm. It is also possible that the signal was drowned in noise. Further optimization schemes are needed for the detection of X-rays, including material quality improvement, low-temperature measurement, and the use of supporting low-noise nuclear electronics.

The single-particle pulse signal observed using the digital oscilloscope is shown in Fig. 7. This electrical signal originated from charged particles emitted by the 241Am isotope source. The electrical signal was connected to the output terminal of the 142A charge-sensitive preamplifier using a BNC coaxial cable. The bias voltage of the detector was 0 V. As shown in Fig. 7, the signal noise was very small at approximately 5 mV, the voltage amplitude of the output signal was approximately 200 mV, and its signal-to-noise ratio was approximately 40. The noise mainly consisted of detector and electronic system noise. According to the 142A datasheet, its equivalent noise was approximately 3.4 KeV. However, the detector noise mainly included thermal, flicker, and shot noises. Thermal noise is mainly caused by the movement of carriers at thermal equilibrium, flicker noise is related to the frequency of the signal and originates from the surface effect of the device, and shot noise is caused by the dispersion of current-forming carriers. Among these three types of noise, shot noise is the main noise of a detector and is related to a detector's saturation current. The smaller the reverse saturation current, the smaller the shot noise; that is, the smaller the detector noise. For p-i-n devices, the junction capacitance is equivalent to the plate capacitance; therefore, the noise of a detector is relatively small. However, noise affects the energy resolution of a detector.

Fig. 7Full-screen View

Electrical output signal of 142A charge-sensitive preamplifier observed by digital oscilloscope after 5.48-MeV charged particles irradiated the detector

Before measuring the spectral response of our detector, a commercial ORTEC Si-passivated implanted planar (Si-PIPS) charged-particle detector was used to calibrate a standard 5.48-MeV 241Am alpha source (certificate number: 14AM4A1007), and the CCE of the detector was assumed to be 100%. Owing to ionization energy, bias voltage, and crystal quality, it is impossible to use uniform parameters to combine the Si-PIPS and Al_xGa_1-xAs/GaAs detector pulse heights in the energy spectrum measurement of AlGaAs detection. Without changing the Ortec main amplifier, the energy-height spectra of the Al_xGa_1-xAs/GaAs and Si-PIPS detectors using a 241 Am source were measured. In the energy spectrum measurements shown in Fig. 8, the FWHM from the electronic system was not considered. The energy spectrum response of the p-i-n Al_xGa_1-xAs/GaAs detector with a 1-mm sensitive diameter to a standard 241Am alpha source was measured using Ortec's nuclear electronics system under various reverse biases from zero to 20 V at room temperature obtained by single-peak Gaussian fitting as shown in Fig. 9 (a). To further analyze the performance of the p-i-n Al_xGa_1-xAs/GaAs detector, the relationship between the reverse bias voltage, peak position, and FWHM is shown in Figure 9 (b).

Fig. 8Full-screen View

Energy spectra of Si-PIPS at −85 V and Al_xGa_1-xAs/GaAs at 0 V measured using a 241Am source

Fig. 9Full-screen View

Spectral response of detector: (a) 241Am alpha particle pulse-height spectra using a 1-mm diameter p-i-n Al_xGa_1-xAs/GaAs detector under various reverse bias voltages at room temperature and (b) peak and FWMH vs. reverse bias voltage. The inset of b) is the CCE of the detector at different bias voltages.

As shown in Fig. 9 (b), as the reverse bias voltage increased, the peak position shifted to the right of the high-energy region from 340 KeV at 0 V to 342 KeV at 20 V. The higher the applied bias voltage, the wider the depletion region. The energy of the particles deposited in the depletion region increased. The peak position only increased by 2 KeV, but the reverse bias increased from 0 to 20 V. However, when the bias voltage was 15 V, the peak position no longer shifted to the right, and the change in the peak position was only 0.5%. The device was completely depleted when the bias voltage was 15 V. In addition, according to our calculations, the FWHM increased as the reverse bias increased. The FWHM increased from 3.04% at 0 V to 3.65% at 10 V. When the reverse bias voltage increased to 20 V, the FWHM increased by 3.76%. The increases in FWHMs at reverse biases of 10 V and 15 V were the same at 3.65% because the increase in the reverse bias voltage across the device increased the thermal noise of the device and caused a larger FWHM instead of a wider depletion layer.

Combining the peak position and FWHM, although the device was completely depleted at a 15-V bias voltage, the electron-hole pairs generated by the alpha particles in the depletion region were partially recombined and changed the FWHM owing to the presence of impurities or defects in the epitaxially grown p-i-n Al_xGa_1-xAs/GaAs. We used SRIM to simulate the depletion region width of 5.48-MeV alpha particles in our detector, and the depletion region width with a peak position of 340 KeV at zero bias was approximately 1 μm. Therefore, as shown by the energy spectrum response in Fig. 9 (b), although the bias voltage increased, the peak shift to the right was not obvious and only changed from 340 KeV to 342 KeV. However, the FWHM decreased from 3.04% to 3.76%. We believe that the graded composition and doped p-i-n Al_xGa_1-xAs/GaAs detector had a sufficiently strong built-in electric field to nearly deplete the 1-μm i-GaAs. Under zero bias, the C-V results were almost consistent with the width of the depletion region obtained from the spectral response. The thickness of the intrinsic region of our detector was thinner, and 5.48-MeV alpha particles deposited less energy into the intrinsic region. The energy deposited in the 1.19-μm thick intrinsic region was approximately 325 KeV from the SRIM simulation. Hence, the energy detected by the detector was far less than the 5.48 MeV energy emitted from the 241Am.

The calculation of CCE is obtained as [27] $\text{CCE}=\frac{CH-a}{\frac{E}{\epsilon }m{G}_{\text{P}}{G}_{\text{A}}},$ (8) where $CH$ is the channel number corresponding to the peak position, a is the voltage correction factor, E is the energy of the incident particle, ε is the average energy required to create an electron–hole pair, m is the DAC conversion gain of 972, $G_{\text{P}}$ is the gain of the 142A, and $G_{\text{A}}$ is the gain of the 572A.

According to Figs. 8 and 9b, the CCEs of the detectors were estimated as shown in the inset of Fig. 9(b). The CCE of the detector changed from 92.7% at 0 V to 93% at 20 V. When the bias voltage increased, the CCE did not change significantly, indicating that the detector CCE was nearly saturated. Regardless the increase in the detector bias voltage, the detector CCE could not reach 100%. This was mainly owing to the existence of various defects in the epitaxially grown GaAs, such that the electron-hole pairs generated by the incident particles were partially recombined by the defects and not collected by the electric field at both ends of the electrode. However, if the CCE is calculated based on the energy emitted by the radioactive source and energy received by the detector, the CCE is approximately 6.2%.