⇦Chinese Physics Letters, 2019, Vol. 36, No. 10, Article code 108501 Numerical and Experimental Study on the Device Geometry Dependence of Performance of Heterjunction Phototransistors * Jin-Lei Lu (鲁金蕾)1,2, Chen Yue (岳琛)1,2, Xuan-Zhang Li (李炫璋)1,2, Wen-Xin Wang (王文新)1,2, Hai-Qiang Jia (贾海强)1,2,3, Hong Chen (陈弘)1,2,3, Lu Wang (王禄)1,2** Affiliations 1Key Laboratory for Renewable Energy, Beijing Key Laboratory for New Energy Materials and Devices, Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 2Center of Materials and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049 3Songshan Lake Materials Laboratory, Dongguan 523808 Received 12 July 2019, online 21 September 2019 *Supported by the National Natural Science Foundation of China under Grant Nos 11574362, 61210014, 11374340 and 11474205, the Innovative Clean-Energy Research and Application Program of Beijing Municipal Science and Technology Commission under Grant No Z151100003515001, and the National Key Technology R&D Program of China under Grant No 2016YFB0400302.
**Corresponding author. Email: lwang@iphy.ac.cn Citation Text: Lu J L, Yue C, Li X Z, Wang W X and Jia H Q et al 2019 Chin. Phys. Lett. 36 108501    Abstract Heterojunction phototransistors (HPTs) with scaling emitters have a higher optical gain compared to HPTs with normal emitters. However, to quantitatively describe the relationship between the emitter-absorber area ratio ($A_{\rm e}/A_{\rm a}$) and the performance of HPTs, and to find the optimum value of $A_{\rm e}/A_{\rm a}$ for the geometric structure design, we develop an analytical model for the optical gain of HPTs. Moreover, five devices with different $A_{\rm e}/A_{\rm a}$ are fabricated to verify the numerical analysis result. As is expected, the measurement result is in good agreement with the analysis model, both of them confirmed that devices with a smaller $A_{\rm e}/A_{\rm a}$ exhibit higher optical gain. The device with area ratio of 0.0625 has the highest optical gain, which is two orders of magnitude larger than that of the device with area ratio of 1 at 3 V. However, the dark current of the device with the area ratio of 0.0625 is forty times higher than that of the device with the area ratio of 1. By calculating the signal-to-noise ratios (SNRs) of the devices, the optimal value of $A_{\rm e}/A_{\rm a}$ can be obtained to be 0.16. The device with the area ratio of 0.16 has the maximum SNR. This result can be used for future design principles for high performance HPTs. DOI:10.1088/0256-307X/36/10/108501 PACS:85.60.Dw, 85.60.Bt, 85.40.Qx © 2019 Chinese Physics Society Article Text Detectors with low noise level and high signal-to-noise ratio (SNR) have been widely used in weak optical signal detection fields, such as telecommunication,[1] remote sensing, astronomical observation,[2] medical imaging,[3] homeland security[4] and non-destructive material evaluation.[5,6] Today, the mainstream detector technologies for weak optical signal detection are still focused on positive-intrinsic-negative photodiodes (PIN-PDs) and avalanche photodetectors (APDs). The PIN-PDs have a high-speed response and ultra-low jitter.[7] However, the equivalent input noise of the read-out integrated circuit (ROIC), which determines the detection limit of the PIN-PDs, has been nearly constant over the past 20 years.[8] Fortunately, detectors with an internal amplification mechanism can reduce the input ROIC noise, such as linear-mode APDs,[9] which can enhance the overall system sensitivity compared to PIN-PDs. However, APDs work at high bias voltage and induce excess avalanche noise in the amplification process. Heterojunction phototransistors (HPTs) are detectors that can provide large internal amplification without avalanche noise and operate in linear mode at low bias voltage, compared to mainstream PIN-PDs and APDs.[10,11] In addition, HPTs have the same layer structure as heterojunction bipolar transistors (HBTs).[12,13] The base-collector region, also known as absorber, is used to absorb the optical signal in HPTs. The intrinsic gain of the transistor can amplify the signal without interconnects. Accordingly, HPTs can be widely used in the detection of weak optical signals and have the potential to overtake PIN-PDs and APDs in certain fields.[14,15] Previously, Fathipour et al. have reported that an electron-injection detector with scaling emitter has been measured, with a higher optical gain compared to a detector with normal emitters.[16–19] Then, they qualitatively explained the reason for the improvement of optical gain.[14] However, there has been very little research focused on quantitatively describing the relationship between the emitter-absorber area ratio ($A_{\rm e} /A_{\rm a}$) and the performance of HPTs so far. Furthermore, there is almost no universal protocol of geometric structure of HPT devices. As is well known, the optical gain and the SNR are two important figures of merit of HPT devices. Thus the effect of device geometry on the gain and SNR of the detector was chosen for study in this work. In this Letter, we develop an analytical model based on heterojunction transistors to quantitatively describe the relationship between the optical gain of HPTs and $A_{\rm e}/A_{\rm a}$. Five devices with different $A_{\rm e}/A_{\rm a}$ are fabricated based on the result to verify the analytical model. Furthermore, the SNRs of devices were calculated to find the optimal value of $A_{\rm e}/A_{\rm a}$ for the structure design geometry of HPTs.
cpl-36-10-108501-fig1.png
Fig. 1. (a) Epitaxial structure of the Al$_{0.35}$Ga$_{0.65}$As/GaAs HPT. (b) The structure schematic of HPTs with different $A_{\rm e}/A_{\rm a}$. The inset of (b) are optical micrographs of the fabricated HPT taken from the top.
In the two-terminal HPT (2T-HPT) with a floating base,[20,21] the optical absorption occurs in the depleted collector region and the photo-generated carriers drift towards the base region. Under this condition, the incident light provides a quiescent photocurrent that serves as the bias current for the transistor.[22] Moriizumi et al. have derived the expression of the optical gain of traditional 2T-HPT.[23] Based on their results, two variables, emission area ($A_{\rm e}$) and absorber area ($A_{\rm a}$), are introduced to derive the expression of the optical gain when the emission area is not always equal to the absorber area ($A_{\rm e} \le A_{\rm a}$). The expression of the optical gain of 2T-HPT with scaling emitter is derived in the following. Considering the floating base, the currents flowing into the base region should be equal to the currents flowing out of the base region, that is, $$\begin{align} A_{\rm e}j_{\rm n2e}+A_{\rm a}j_{\rm p1}+A_{\rm a}j_{\rm n2c}+A_{\rm a}j_{\rm p3}=0,~~ \tag {1} \end{align} $$ where $A_{\rm e}$ is the surface area of the emitter region, $A_{\rm a}$ is the surface area of the absorber region, $j_{\rm p1}$ is the hole current density (diffusing into the emitter junction), $j_{\rm n2e}$ is the electron current density (flowing out the emitter), $j_{\rm n2c}$ is the electron current density (flowing to the collector junction), and $j_{\rm p3}$ is hole current density (flowing to the collector junction). In the steady-state condition, the concentration profile of excess carriers can be obtained by solving the usual one-dimensional diffusion equation. Then, by differentiating the concentration of excess carrier, the expressions of $j_{\rm p1}$, $j_{\rm n2e}$, $j_{\rm n2c}$ and $j_{\rm p3}$ can be obtained.[23] The increase in the forward bias $\Delta \{\exp (\frac{qv_{\rm e}}{k_{0}T})\}$ at the emitter junction caused by illumination $F_{1}$ can be calculated by putting $j_{\rm p1}$, $j_{\rm n2e}$, $j_{\rm n2c}$ and $j_{\rm p3}$ into Eq. (1), $$\begin{align} &\Delta \Big\{\exp \Big(\frac{qv_{\rm e}}{k_{0}T}\Big)\Big\}\\ =\,&\frac{F_{1}[ A_{\rm a}g_{1}+{A_{\rm a}g}_{2}(f_{\rm n2e}-f_{\rm n2c})+A_{\rm a}g_{3} ]}{j_{\rm 0n2}A_{\rm e}\{ \cosh (\frac{w_{2}}{l_{2}})-1 \}+A_{\rm a}j_{\rm 0p1}},~~ \tag {2} \end{align} $$ where $g_{1}$, $g_{2}$ and $g_{3}$[23] are the contributions of the optical absorption to the optical gain in the emitter, base and collector region, respectively, $f_{\rm n2e}$, $f_{\rm n2c}$, $j_{\rm 0p1}$, $j_{\rm 0n2}$ are the material parameters of the emitter and collector region,[23] respectively, $F_{1}$ is the incident light flux at the surface of the device, $w_{2}$ is the thickness of the base region, and $l_{2}$ is the diffusion length of minority carrier in the base region. The increase of the total current density $\Delta j_{\rm T}$ caused by illumination is given by $$\begin{alignat}{1} \Delta j_{\rm T}=j_{\rm 0n2}\Delta \Big\{\exp \Big(\frac{qv_{\rm e}}{k_{0}T}\Big)\Big\}+(g_{3}+g_{2}f_{\rm n2c})F_{1}.~~ \tag {3} \end{alignat} $$ Putting Eq. (2) into Eq. (3), the optical gain $G$ of the phototransistor is obtained as follows: $$\begin{alignat}{1} \!\!\!\!\!\!\!\!G=\,&\frac{\Delta j_{\rm T}}{qF_{1}}\\ =\,&\frac{1}{q}\frac{\gamma [ g_{1}+g_{2}f_{\rm n2e}-g_{2}f_{\rm n2c}+g_{3} ]}{\gamma \{ \frac{A_{\rm e}}{A_{\rm a}}\cosh(\frac{w_{2}}{l_{2}})-1 \}+1}\!+\!(g_{3}\!+\!g_{2}f_{\rm n2c}),~~ \tag {4} \end{alignat} $$ where $$ \gamma =j_{\rm 0n2}/j_{\rm 0p1}. $$ According to Eq. (4), the relationship between the optical gain and $A_{\rm e}/A_{\rm a}$ at 3 V is shown in Fig. 3(a) (solid line). Obviously, the device with smaller $A_{\rm e}/A_{\rm a}$ exhibits a higher optical gain. As shown in Eq. (2), the increase in forward bias $\Delta \{\exp (\frac{qv_{\rm e}}{k_{0}T}) \}$ at the emitter junction is inversely proportional to $A_{\rm e}/A_{\rm a}$ because the reduction of the area of emitter region (the volume of the emitter region decreases at the same time) can increase the hole concentration in the Al$_{0.35}$Ga$_{0.65}$As layer. As the hole concentration increases, the potential barrier drops more pronouncedly in the conductive band.[24] Thus under the same illumination condition, the device with smaller emitters tends to have a larger increase in forward bias compared to the device with normal emitters. However, the decrease of the potential barrier will also increase the dark current of the devices. Furthermore, with the shrinking of the emitter, the exposed surface area of the base region becomes larger, which will lead to a larger surface leakage current.[18] To find the optimal value of $A_{\rm e}/A_{\rm a}$ for the structure design geometry of HPTs, five devices with different $A_{\rm e}/A_{\rm a}$ were fabricated. As shown in Fig. 1(b), the radii of absorber ($r_{\rm a}$) are always 600 µm, whereas the radii of emitter areas ($r_{\rm e}$) are 600 µm (not given in the structure schematic), 400 µm, 300 µm, 200 µm, and 150 µm, respectively. Accordingly, the calculated values of $A_{\rm e}/A_{\rm a}$ are 1, 0.25, 0.16, 0.11 and 0.0625, respectively. In the photo-response measurement, a laser source with a peak emission wavelength at 808 nm and 1.5 mW output power was used to illuminate devices from the top. The photon energy of the laser source is smaller than the band gap of the Al$_{0.35}$Ga$_{0.65}$As layer. Therefore, using this laser source can ensure that the emission region is transparent to the incident light, so that the change of the emitter area will not affect the light absorption of the devices. The laser spot size is smaller than the active region, thus the measured output current and the optical gain are independent of the beam size. The fabricated devices were wire bonded to a chip carrier for further characterization. The electrical properties of the devices were measured by a Keithley 4200-scs semiconductor characterization system.
cpl-36-10-108501-fig2.png
Fig. 2. (a) Output characteristics for HPTs with different $A_{\rm e}/A_{\rm a}$ for input optical power at 1.5 mW. (b) The plots of dark current versus bias voltage ($V_{\rm ce}$) characteristic with different $A_{\rm e}/A_{\rm a}$.
Figure 2(a) shows the measured photocurrent versus bias voltage characteristics for devices with different $A_{\rm e}/A_{\rm a}$ at 1.5 mW. The photocurrent increases with the bias voltage and remains stable above $\sim 1$ V. As is expected, the device with the area ratio of 0.0625 has the largest output photocurrent, which is 0.1 A at 3 V. The value of the largest output photo current is two orders of magnitude larger than that of devices with the area ratio of 1. As mentioned above, the higher photocurrent of the device with the area ratio of 0.0625 can be attributed to its lower barrier potential in the conduction band at the emitter. Next the dark currents versus bias voltage characteristics of the devices are measured at room temperature, as shown in Fig. 2(b). The measured collector dark currents ($I_{\rm Cdark}$) of devices with area ratio of 0.0625 and 1 are $4.02\times 10^{-5}$ A and $9.65\times 10^{-7}$ A at 3 V, respectively. As previously mentioned, the hole concentration increases in the Al$_{0.35}$Ga$_{0.65}$As layer because of the reduction of emitter region. With the increase of hole concentration, the potential barrier drops pronouncedly in the conductive band. Thus $I_{\rm Cdark}$ of HPTs with smaller area ratio is expected to be larger. In other words, not only the photo-generated current in base-collector is amplified by the transistor action, but also the diffusion current which is the component of dark current in the base-collector is amplified.[18] In addition, the exposed surface area of the base region increases with the shrinking of the emitter. The device with the smallest emitter mesa has the largest exposed surface. Thus the device with the area ratio of 0.0625 shows severe surface leakage current. Above all, the device with the smallest $A_{\rm e} /A_{\rm a}$ has the largest dark current, which is forty times larger than the device with the area ratio of 1 at 3 V.
cpl-36-10-108501-fig3.png
Fig. 3. (a) Optical gain as a function of $A_{\rm e}/A_{\rm a}$ at 3 V bias voltage. Markers show the measured data and the solid line shows the developed analytical model. (b) The calculated SNR of five devices with different $A_{\rm e}/A_{\rm a}$.
The optical gain $G$ of HPT is defined and calculated as follows: $$\begin{align} G=\,&\frac{\Delta I_{\rm cP}h\nu}{qP_{\rm in}},~~ \tag {5} \end{align} $$ $$\begin{align} \Delta I_{\rm cP}=\,&I_{\rm ce}-I_{\rm cdark},~~ \tag {6} \end{align} $$ where $h\nu$, $q$ and $\Delta I_{\rm cP}$ are photon energy, elementary charge, and net collector photocurrent due to input optical power $P_{\rm in}$, respectively. The optical gain of the device can be calculated by putting the measured collector photocurrent $I_{\rm ce}$ and dark current $I_{\rm cdark}$ into Eqs. (5) and (6). The calculated optical gains of devices are shown with markers in Fig. 3(a). The solid line in Fig. 3(a) is the analytical result of optical gain. As shown in Fig. 3(a), the measurement data is in good agreement with the analytical model. The device with area ratio of 0.0625 has the highest gain, which is 122 at 3 V. The optical gain of the device with area ratio of 0.0625 is two orders of magnitude larger than that of the device with the area ratio of 1. To examine the quality of the output signal and find the optimal value of $A_{\rm e}/A_{\rm a}$, the SNR of the HPT is calculated. The expression for the HPT's SNR[25–27] is similar to that for a photodiode, and it is given by $$\begin{align} {\rm SNR}=\,&\frac{I_{\rm ce}^{2}}{I_{s}^{2}+I_{\rm T}^{2}},~~ \tag {7} \end{align} $$ $$\begin{align} I_{\rm ce}^{2}=\,&(\beta RP_{\rm in})^{2},~~ \tag {8} \end{align} $$ $$\begin{align} I_{\rm S}^{2}=\,&2q\beta^{2}(RP_{\rm in}+I_{\rm d})\Delta f,~~ \tag {9} \end{align} $$ $$\begin{align} I_{\rm T}^{2}=\,&4\frac{k_{_{\rm B}}T}{R_{\rm d}}\Delta f ,~~ \tag {10} \end{align} $$ where $I_{\rm ce}$ is the mean photocurrent, $I_{\rm S}$ and $I_{\rm T}$ are the thermal noise and the shot noise currents, respectively, $\beta$ is the mean magnification of the HPT, $R$ is the responsivity of the base-collection junction of the HPT, $P_{\rm in}$ is the input optical power, $R_{\rm d}$ is the differential resistance of the base-collection junction, $k_{_{\rm B}}$ is Boltzmann's constant, and $\Delta f$ is the bandwidth of the device, which is 10 Hz. The SNR of devices with different $A_{\rm e}/A_{\rm a}$ is calculated. The plot of the SNR versus $A_{\rm e}/A_{\rm a}$ is shown in Fig. 3(b). As mentioned above, the optical gain of the device with smaller $A_{\rm e}/A_{\rm a}$ is expected to be higher. However, the external dark currents of the device with smaller $A_{\rm e}/A_{\rm a}$ become larger at the same time. Thus a maximum is expected on the plot of SNR. As shown in Fig. 3(b), when the value of $A_{\rm e}/A_{\rm a}$ is equal to 0.16, the device has the maximum SNR, which is 14.3 dB (2.1$\times 10^{14})$. The SNR of the optimized device is thirtyfold larger than that of the original device 12.9 dB (7.0$\times 10^{12})$. Thus the optimal value of $A_{\rm e}/A_{\rm a}$ is 0.16, at which the device has the highest quality of the output signal. In conclusion, we have studied the effect of the mesa area ratio $A_{\rm e}/A_{\rm a}$ on the optical gain and SNRs of HPTs. Five devices are fabricated with different mesa areas of emitters. The experimental measurement data and the analytical model both confirm that the optical gain of HPTs is inversely proportional to $A_{\rm e}/A_{\rm a}$. This is affiliated with lower barrier potential caused by the increasing hole concentration in devices with small area ratios of $A_{\rm e}/A_{\rm a}$. However, the dark current of the device with the smallest mesa area ratio (0.0625) is forty times higher than that of the device with the area ratio of 1. This is because the highest optical gain will also enhance the diffusion current of devices. In addition, the device with the smallest emitter mesa has the largest exposed surface, which can lead to a severe surface leakage current. Thus by calculating the SNR of devices with different $A_{\rm e}/A_{\rm a}$, we find the optimal value of emitter-base area ratio (0.16), at which the HPT has the maximum SNR. Although the performance of the devices in this work still needs to be further optimized in other aspects, the conclusions of this work not only quantitatively explain why HPT devices with smaller $A_{\rm e}/A_{\rm a}$ have higher optical gain, but also provide a way for the geometric structure design of HPT devices in the future. References Recent progress in infrared detector technologiesMonitoring dynamic protein interactions with photoquenching FRETOptical properties of porcine skin dermis between 900 nm and 1500 nm15 μm photon-counting optical time-domain reflectometry with a single-photon detector based on upconversion in a periodically poled lithium niobate waveguideSynthesized multiwall MoS 2 nanotube and nanoribbon field-effect transistorsInGaAs pin photodiode fabricated on semi-insulating InP substrate for monolithic integrationGain of a heterojunction bipolar phototransistorA Short-Wave Infrared Nanoinjection Imager With 2500 A/W Responsivity and Low Excess NoiseSmall‐area high‐speed InP/InGaAs phototransistorHeterojunction phototransistors for long‐wavelength optical receiversAlGaAsSb-InGaAsSb HPTs with high optical gain and wide dynamic rangeOptical Characteristics of Responsivity-Enhanced InGaAs/InP Heterojunction PhototransistorsA photon detector with very high gain at low bias and at room temperatureAnalytical and numerical evaluation of electron-injection detector optimized for SWIR photon detectionImpact of three-dimensional geometry on the performance of isolated electron-injection infrared detectorsIsolated Electron Injection Detectors With High Gain and Record Low Dark Current at Telecom WavelengthPerformance optimization of Pnp InGaAs/InP heterojunction phototransistorsOptical gain and collector current characteristics of resonant-cavity phototransistorsEnhancement of Optical Gain in Floating-Base InGaP–GaAs Heterojunction PhototransistorsTheoretical analysis of heterojunction phototransistorsAnalytical modeling and numerical simulation of the short-wave infrared electron-injection detectorsTheoretical investigation of quantum-dot avalanche photodiodes for mid-infrared applicationsNoise modeling of an InP/InGaAs heterojunction bipolar phototransistorNoise analysis of optimized Ge/Ge_1 - x Sn_x/Ge Ge/Ge_1 - x Sn x / Ge p–n–p heterojunction phototransistors for long-wavelength optical receivers
[1] Rogalski A 2011 Infrared Phys. & Technol. 54 136
[2]Guellec F, Dubois S, Borniol E D, Castelein P, Martin S, Guiguet R, Tchagaspanian M, Rouvié A and Bois P 2012 Proc. SPIE 8298 11
[3] Demarco I A, Periasamy A, Booker C F and Day R N 2006 Nat. Methods 3 519
[4] Du Y, Hu X H, Hu X H, Cariveau M, Ma X, Kalmus G W and Lu J Q 2001 Phys. Med. & Biol. 46 167
[5] Diamanti E, Langrock C, Fejer M M, Yamamoto Y and Takesue H 2006 Opt. Lett. 31 727
[6] Fathipour S, Remskar M, Varlec A, Ajoy A, Yan R, Vishwanath S, Rouvimov S, Hwang W S, Xing H G, Jena D and Seabaugh A 2015 Appl. Phys. Lett. 106 022114
[7] Li K, Rezek E and Law H D 1984 Electron. Lett. 20 196
[8]Joshi A, Stevens J, Kononenko A and Blackwell J 2004 Proc. SPIE 34 938
[9]Maruyama T, Narusawa F, Kudo M, Tanaka M, Saito Y, Yoshida T and Nomura A 2002 Filtration Ind. Analyst. 41 138
[10] Chand N, Houston P A and Robson P N 1985 IEEE Trans. Electron Devices 32 622
[11] Memis O G, Kohoutek J, Wei W, Gelfand R M and Mohseni H 2010 IEEE Photon. J. 2 858
[12] Campbell J C, Burrus C A, Dentai A G and Ogawa K 1981 Appl. Phys. Lett. 39 820
[13] Campbell J C and Ogawa K 1982 J. Appl. Phys. 53 1203
[14] Fathipour V, Bonakdar A, and Mohseni H 2017 Front. Mater. 3 33
[15] Jo Y C, Joe S J, Kim H and Choi P O 2005 Jpn. J. Appl. Phys. 44 2537
[16] Memis O G, Katsnelson A, Kong S C, Mohseni H, Yan M, Shuang Z, Hossain T, Niu J and Adesida I 2007 Appl. Phys. Lett. 91 519
[17] Movassaghi Y, Fathipour V, Fathipour M and Mohseni H 2017 J. Appl. Phys. 121 084501
[18] Fathipour V, Jang S J, Nia I H and Mohseni H 2015 Appl. Phys. Lett. 106 021116
[19] Fathipour V, Memis O G, Jang S J, Brown R L, Nia I H and Mohseni H 2014 IEEE J. Sel. Top. Quantum Electron. 20 65
[20] Chen J and Min Z 2016 Appl. Phys. A 122 1034
[21] Lin C C, Martin W, Harris J S and Sugihwo F 2000 Appl. Phys. Lett. 76 1188
[22] Min S P and Jang J H 2010 IEEE Photon. Technol. Lett. 22 1202
[23] Moriizumi T T K 1972 IEEE Trans. Electron Devices 19 152
[24] Movassaghi Y, Fathipour V, Fathipour M and Mohseni H 2016 Appl. Phys. Lett. 108 121102
[25] Krishna S, Kwon O H and Hayat M M 2005 IEEE J. Quantum Electron. 41 1468
[26] Chakrabarti P, Agrawal N K, Kalra P, Agrawal S and Gupta G 2003 Opt. Eng. 42 939
[27] Basu R and Kumar H 2019 Opt. Quantum Electron. 51 52