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. 2026 Sep 23. Online ahead of print. doi: 10.1039/d6na00204h

Quantitative analysis of carrier concentration and electric field in non-uniform quantum well infrared photodetectors

Zhen Chen a,b,†, Rui Xin b,c,†, Li Yu b,e, Zhen Deng c,d,f, Shenjun Wang a,b, Yue Cheng b, Hui Xia b,c, Shufan Yao a,b, Tianxin Li a,b,c,✉
PMCID: PMC13599731  PMID: 42781048

Abstract

Semiconductor non-uniform quantum wells (NUQWs) improve long-wavelength infrared detection by resolving the trade-off between dark current and responsivity found in conventional uniform structures. By grading doping and barrier thicknesses, these designs enhance absorption in highly doped areas while strengthening electric fields in low-doped regions to trigger carrier multiplication. However, the actual carrier concentration profile within quantum wells (QWs) has long lacked effective experimental verification. In this work, we employed calibrated scanning spreading resistance microscopy (SSRM) to realize nanoscale quantitative analysis of the carrier distribution within GaAs/AlGaAs quantum well infrared photodetector (QWIP) structures. The non-uniform design successfully led to reduction of dark current by nearly 4 times compared to that of the uniform counterparts, thus elevating the background limited infrared photodetection (BLIP) temperature by 4 K. On the other hand, the responsivity failed to show the expected enhancement. Simulations revealed that the deviation of electron densities in the low-doped QWs induces a weak local electric field of approximately 1.7 kV cm−1, which is significantly below the threshold field to trigger impact ionization. These findings guide the design of an optimized asymmetric gradient-doping structure capable of generating a strong electric field of up to 13.8 kV cm−1 in the collection region, thereby achieving high gain while maintaining low dark current.

Calibrated SSRM quantifies carrier profiles in NUQWIPs and reconstructs internal electric fields, revealing how low-doped wells suppress collector-side fields, reduce dark current, increase BLIP temperature, and limit responsivity enhancement.graphic file with name d6na00204h-ga.webp

Introduction

Quantum well infrared photodetectors (QWIPs) play a vital role in infrared imaging and optical communication. These devices offer broad spectral tunability and mature fabrication technology. Additionally, QWIPs are well-suited for large-format focal plane array integration.1,2 Conventional uniform quantum well (QW) structures can achieve targeted spectral responses by adjusting the well width3 or barrier height.4 However, their fixed internal electric field distributions and carrier transport pathways make it challenging to simultaneously enhance responsivity and the background limited infrared photodetection (BLIP) temperature while maintaining low dark current.1,5 To address this trade-off, strategies enhancing barrier confinement are frequently employed. For instance, the transition scheme can be modified from a bound-to-continuum (B-C) to a bound-to-quasi-bound (B-QB) mode. Although this approach effectively suppresses thermionic emission, the lack of selectivity in inhibiting carrier transport inevitably reduces the escape probability of photo-generated carriers, thereby degrading responsivity. This reveals the inherent limitations of solely relying on barrier engineering for QWIP performance improvement. Non-uniform quantum well infrared photodetector (NUQWIP) designs offer a promising alternative. These structures introduce graded doping concentrations and barrier widths to manipulate space charge distributions. Highly doped regions enhance optical absorption. Meanwhile, low-doped regions induce stronger local electric fields. This strengthens the field to promote impact ionization and improves the collection efficiency of photo-generated carriers. Furthermore, the high dynamic resistance in low-doped regions effectively suppresses thermionic emission. This results in reduced dark current and improved overall photoelectric conversion performance.6,7

However, in non-uniform quantum well structures, the graded doping profiles and variations in barrier width significantly influence carrier distribution and transport characteristics. Direct experimental verification of carrier concentration profiles in these complex structures remains limited. Scanning spreading resistance microscopy (SSRM) is a powerful technique for nanoscale electrical characterization. It can directly reveal the real-space carrier distribution with high spatial resolution. In contrast, traditional methods have clear limitations. Hall effect measurements provide only the macroscopic average carrier concentration and mobility, failing to resolve specific spatial distributions.8 Electrochemical capacitance–voltage (ECV) profiling can map carrier distributions; however, variations in electrochemical etching rates among different materials or doping regions may introduce depth calibration errors and cause interface roughening or damage.9 Secondary ion mass spectrometry (SIMS) primarily detects elemental and dopant distributions,10 often failing to directly reflect the electrically active carrier profiles critical to device performance.11 In contrast, SSRM can characterize the real-space carrier distribution and local conductance variations within QWs at the nanoscale. However, accurate quantitative extraction of carrier concentration from SSRM remains challenging. This challenge becomes more severe in NUQWIPs, where doping gradients and barrier variations strongly influence the built-in electric field. A reliable method for quantitative carrier analysis is therefore a key issue that limits further progress. While our previous work used SSRM combined with a thermionic-emission transport model to estimate electron densities in individual QWs of uniformly doped QWIPs and correlate them with device responsivity and dark current,12 the extraction required device-specific calibration of the equivalent barrier/contact parameters for each sample. Here, we address non-uniform QWIPs, for which the central issue is the carrier-concentration variation among different wells within a single device rather than the average density among separate devices. Using ECV-measured active carrier concentrations from step-doped GaAs reference films, we establish a quantitative SSRM calibration curve (R2 = 0.9982) to extract the carrier profile across the non-uniform QW stack. The extracted profile is then used in self-consistent Poisson–Schrödinger simulations to analyze the actual internal electric-field distribution and to guide the optimized asymmetric gradient-doping design. A combined approach using high-resolution scanning probe techniques and electrical simulations is essential for understanding carrier behavior and electric field distribution in non-uniform QWs.

In this work, we investigate non-uniform GaAs/Al0.27Ga0.73As multi-quantum-well structures and reference uniform structures. A high-precision calibration curve was established by correlating SSRM and ECV results measured from GaAs step-doped epitaxial films. This calibration model was subsequently employed to determine the nanoscale carrier concentration in the QW structures. Furthermore, self-consistent Poisson–Schrödinger simulations were performed to analyze how non-uniform doping modulates the carrier distribution and internal electric field. Performance verification through 45° mesa QWIP devices confirms that the non-uniform structure can suppress dark current and modulate the built-in electric field. The analysis shows that the carrier concentration in the low-doped regions deviates from the nominal design. This deviation weakens the local electric field and reduces responsivity. Based on these findings, we propose an optimized gradient-doping scheme for non-uniform quantum wells. This work provides both experimental support and design guidance for improving high-temperature infrared detection performance.

Methods

The samples investigated in this work were grown on GaAs (100) substrates using molecular beam epitaxy (MBE). The detection wavelength for both conventional and non-uniform QWs corresponds to 8.4 µm. The active region of the conventional structure consists of 30 periods of GaAs/Al0.27Ga0.73As quantum wells (QWs), as illustrated in Fig. 1(a). The barrier width and well width are 50 nm and 4.5 nm, respectively, and Si doping at a concentration of 5 × 1017 cm−3 is introduced at the central 2.5 nm of each well. The active region of the non-uniform structure comprises 30 periods of non-uniform GaAs/Al0.27Ga0.73As QWs, with the doping concentration and barrier width varying as shown in Fig. 1(c). The barrier width decreases linearly from 87.5 nm to 12.5 nm, while the Si doping concentration increases nonlinearly from 5.5 × 1016 cm−3 to 4.85 × 1018 cm−3. For both the conventional and non-uniform structures, the top and bottom contact layers are composed of 800 nm thick GaAs with an Si doping concentration of 2 × 1018 cm−3. To ensure identical optical absorption between the two designs, the total doping dose and the total barrier thickness were kept the same. In the non-uniform design, only the spatial distribution of doping concentration and barrier width is modified to regulate the internal electric field within the QW structure.

Fig. 1. (a) Schematic diagram of a conventional QW structure. (b) Schematic diagram of a non-uniform QW structure. (c) The distributions of doping concentration and barrier width of each QW for the non-uniform structure.

Fig. 1

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The carrier distribution in the quantum wells (QWs) was characterized by scanning spreading resistance microscopy (SSRM) using a Bruker Nanoscope IV system. To ensure measurement accuracy, the samples were carefully prepared prior. The specimens were cleaved along the (110) crystal plane to obtain cross-sections with nanoscale flatness, thereby minimizing surface topography effects on imaging results. A conductive diamond-coated Si probe was used during measurement, with a cantilever spring constant in the range of 21–98 N m−1.13 We used a Nanometrics ECVpro apparatus to perform the ECV measurements. The active carrier concentration as a function of depth in the Si-doped gallium arsenide layers was extracted from the capacitance–voltage characteristics during controlled electrochemical etching, enabling determination of the electrically activated silicon donor concentration.

For performance characterization, both the conventional and non-uniform QW structures were processed into 45° mesa devices with an area of 200 × 200 µm2. The fabrication procedure was as follows: first, photolithography and wet etching techniques were adopted to define the 200 × 200 µm2 mesa structures; subsequently, AuGe/Ni/Au (100/20/300 nm) metal layers were deposited on both the top and bottom surfaces of the samples via electron-beam evaporation and annealed to form ohmic contacts; finally, the samples were mechanically polished to form a 45° beveled facet to facilitate optical coupling, and were mounted onto an oxygen-free copper heat sink using low-temperature adhesive.

After fabrication, the mesa devices were mounted in a vacuum cryogenic Dewar for electrical and optical characterization. The I–V characteristics were measured at different temperatures, and the device responsivity was measured using a 500 K blackbody source.

Results and discussion

To obtain precise carrier concentration information within the QWs, the carrier characteristics of a calibration sample were systematically characterized by SSRM and ECV. The schematic structure of the calibration sample is illustrated in the inset of Fig. 2(b). Fig. 2(a) presents the cross-sectional SSRM image of the sample, where five distinct doping regions and the underlying GaAs buffer layer are clearly resolved. Fig. 2(b) displays the local conductance profile along the growth direction, exhibiting significant variations across the different doping layers. Fig. 2(c) shows the carrier concentration profile along the growth direction obtained via ECV measurements. Five doping peaks are observed, corresponding to carrier concentrations of 7.39 × 1017 cm−3, 1.07 × 1017 cm−3, 2.12 × 1017 cm−3, 7.11 × 1017 cm−3, 1.26 × 1018 cm−3, respectively. This distribution trend correlates well with the conductance variations observed in the SSRM measurements. Based on the Schottky thermionic emission model found in the literature,14 and leveraging the property that local conductance is proportional to current density (J), a continuous curve correlating local conductance with carrier concentration was fitted. The resulting coefficient of determination (R2) reached 0.9982, indicating that the model possesses high explanatory power regarding the correlation between experimental data points and demonstrates an excellent goodness-of-fit. To further assess the absolute accuracy and predictive error of this quantitative calibration curve, the Residual Sum of Squares (RSS), Mean Squared Error (MSE), and Root Mean Square Error (RMSE) were calculated. The results are as follows: RSS = 8.28 × 10−17, MSE = 1.66 × 10−17, RMSE = 4.07 × 10−9. This precise quantitative calibration curve successfully establishes a correlation between the nanoscale local conductance response and macroscopic carrier concentration, providing a solid experimental foundation for the subsequent precise extraction and quantification of carrier distributions within non-uniform QWs using SSRM.

Fig. 2. (a) SSRM image obtained from the cross section of the reference sample. (b) Local conductance profile along the growth direction, with the inset showing the structural schematic of the reference sample. (c) Carrier concentration profile along the growth direction of the reference sample. (d) Fitted relationship between local conductance and carrier concentration.

Fig. 2

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SSRM measures spreading conductance based on a contact model. The measured values are therefore highly sensitive to the tip–sample contact area and surface states.15 To ensure reliable and comparable results, we strictly controlled the surface condition, ambient humidity, sample bias, and applied load force during all measurements. The contact layer of the conventional QW structure (Fig. 3(a)) exhibits a root mean square roughness (Rq) of 2.62 × 10−10 S and an arithmetic mean roughness (Ra) of 2.54 × 10−10 S. The non-uniform QW structure in Fig. 3(c) shows Rq = 1.32 × 10−10 S and Ra = 1.27 × 10−10 S. These values meet stringent experimental control standards, effectively excluding surface artifacts from interfering with measurements of the active region. Fig. 3(b) shows the local conductance profile of the conventional QWs along the growth direction. The profile clearly reveals the high periodicity of the 30 QWs in the active region. The average conductance is about 3 × 10−9 S. This uniformity across the entire active region is fully consistent with the structure's uniform doping and barrier design.

Fig. 3. SSRM images obtained from the cross sections of the conventional QW structure (a) and the non-uniform QW structure (c). Local conductance profiles along the growth direction for the conventional QW structure (b) and the non-uniform QW structure (d).

Fig. 3

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In contrast, the local conductance profile of the non-uniform QWs (Fig. 3(d)) shows a distinct gradient. The overall trend follows the designed stepwise increase in doping concentration. However, the local conductance of the first three QWs near the bottom contact layer exhibits abnormal electrical behavior that deviates from the expected stepwise increase. Instead, it shows a decreasing trend. The first QWs even display a higher conductance than the following low-doped wells. We attribute this anomaly to the background doping memory effect during material growth. The bottom contact layer undergoes heavy n-type doping. Residual n-type dopants in the growth chamber can carry over into the initial low-doped QW. This carryover leads to an unintended increase in dopant concentration and conductance.16,17 A similar phenomenon is also observable in the measured conductance profile of the uniform QW sample.

Since the QW width is smaller than the radius of curvature of the probe tip, the measured local conductance is dependent on the contact area. The relationship between the peak local conductance and the contact area is described as follows:12

graphic file with name d6na00204h-t1.webp 1

where S represents the maximum contact area between the probe tip and the sample, J denotes the current density, and VF is the forward bias voltage. The relationship between the tip and the sample is illustrated in Fig. 4. The conductance peak occurs when the contact area between the tip and the QW is maximized; at this point, the contact area is given by:

graphic file with name d6na00204h-t2.webp 2

where R is the tip radius and d is the QW width. When the conductance decreases to half of its peak value, the contact area equals half of the maximum contact area.14 The contact area is given by:

graphic file with name d6na00204h-t3.webp 3

Fig. 4. Relationship between the SSRM signal and the contact area between the tip and the quantum well.

Fig. 4

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Based on eqn (2) and (3), the calculated tip radii for the uniform and non-uniform quantum well samples are 9.8 nm and 10.5 nm, respectively. Based on the calibration results in Fig. 2(d), we extracted the carrier concentrations for different regions. The contact layer of the conventional sample shows a value of 2.16 × 1018 cm−3. The contact layer of the non-uniform sample shows a value of 2.32 × 1018 cm−3. The conventional QWs show a carrier concentration of 6.68 × 1017 cm−3. Fig. 5(a) presents the resulting doping concentration of the non-uniform QWs. In the low-doping regions, the conductivity measured by SSRM is highly reliable. However, in the high-doping regions, the extracted carrier concentration is underestimated to some extent. Nevertheless, despite the reduced absolute values, the relative variation trend of the carrier distribution remains in good agreement with the designed doping profile of the non-uniform QWs. In the highly doped regions, the spreading resistance signal measured by SSRM is no longer strictly confined to the single layer directly beneath the probe tip due to the narrow barrier widths. Current shunting or tunneling may occur across these thin barriers between adjacent wells, and the tip resistance component becomes significant in highly doped areas. Consequently, these effects cause the measured local conductance to exhibit characteristics indicative of coupling with adjacent QWs.18

Fig. 5. (a) Designed doping concentration and actual carrier concentration in non-uniform QWs. Energy band diagrams of non-uniform QWs at 80 K and −1 V calculated using (b) designed doping and (c) actual carrier concentration.

Fig. 5

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The carrier concentration within non-uniform QWs plays a critical role in determining device performance. To investigate this impact, we simulated the band structure and electric field distribution by solving the Poisson–Schrödinger equations self-consistently. Fig. 5(b) and (c) illustrate the band structures calculated at 80 K under a bias of −1 V, based on the nominal design doping concentration and the actual carrier concentration derived from SSRM (as shown in Fig. 5(a)), respectively. The simulation based on the designed doping shows that the expected peak electric field near the collector is 14.194 kV cm−1, which is enough to realize the collision ionization of carriers. The simulation also shows a clear potential dip near the emitter. This effect occurs because the built-in electric field caused by the strong doping gradient exceeds the externally applied field in this region. Since the voltage drop across this region is small, the two fields oppose each other. Their overlap reverses the net electric field and forms the potential dip. However, electric field simulations incorporating the actual carrier concentrations extracted from SSRM reveal that the local electric field near the collector drops to a mere 1.7 kV cm−1. This value is far below the critical field of 13.5 kV cm−1 required to trigger impact ionization.6 This weak electric field severely compromises the collection efficiency of photo-generated carriers, thereby suppressing the overall photoresponse of the device.

The carrier concentration distribution within non-uniform QWs significantly influences the built-in electric field. A weak built-in electric field cannot effectively trigger impact ionization. This limitation directly influences the dark current and the responsivity of the device. As illustrated in Fig. 6(a), both samples exhibit distinct response peaks near ±2 V. The response of the conventional QWIP exhibits asymmetry, which is primarily attributed to dopant segregation along the growth direction during MBE.19 This segregation results in discrepancies in the band structure under forward and reverse biases.20 In contrast, the NUQWIP design forces the electric field to be dominated by the low-doped region under both forward and reverse bias. This feature gives the NUQWIP a much more symmetric photoresponse than the conventional structure. However, the simulated electric field in the low-doped region is only 1.7 kV cm−1 which is too low to trigger impact ionization and results in limited responsivity. At a bias of 2 V, the conventional QWIP reaches a blackbody responsivity of 50.5 mA W−1. Under the same bias, the NUQWIP reaches only 16.5 mA W−1. At 10 K and −2 V, the NUQWIP achieves a responsivity of 21 mA W−1. The conventional device shows a value of 24 mA W−1 under the same conditions. These results indicate that the non-uniform device still exhibits optical absorption and carrier collection efficiencies close to those of the conventional QWIP, even with a weaker electric field in the low-doped collector region.

Fig. 6. (a) Blackbody responsivity comparison between the conventional QWIP and the NUQWIP measured at 10 K. (b) Dark current comparison at different temperatures. (c and d) Dark current (dashed lines) and 300 K background photocurrent (solid lines) at temperatures ranging from 50 K to 100 K for (c) the conventional QWIP and (d) the NUQWIP.

Fig. 6

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Fig. 6(b) compares the dark current characteristics of the conventional QWIP and NUQWIP over a temperature range of 70–120 K. At a given temperature, the dark current of the NUQWIP is significantly reduced to approximately one-quarter of that observed in the conventional structure. This reduction is attributed to the specific doping profile of the non-uniform design, where only five QWs possess a doping concentration exceeding that of the conventional QWIP, while the average doping concentration of the remaining wells is lower. Moreover, under both forward and reverse bias, the low-doped regions show high dynamic resistance. This resistance causes most of the applied voltage to drop across regions with low carrier concentration. Consequently, the dark current of the NUQWIP is significantly suppressed compared to the conventional structure.21

Fig. 6(c) and (d) present the photocurrent and dark current for the conventional QWIP and NUQWIP, respectively, over the temperature range of 50–100 K. Under 300 K background radiation, both devices exhibit nearly the same photocurrent. The BLIP temperature is determined when the photocurrent generated by 300 K background radiation is equal to twice the dark current.22 The effective field of view (FOV) of the measurement system is approximately 45°, which defines the solid angle of background radiation incident on the detector. However, the NUQWIP achieves a higher BLIP temperature because it effectively suppresses the dark current. Specifically, the BLIP temperature of the NUQWIP reaches approximately 108 K, representing an increase of roughly 4 K compared to the conventional structure. This provides compelling evidence of the significant advantages offered by the non-uniform doping design in suppressing thermal noise and elevating the device's operating temperature.

The experimental results show that the carrier concentration on the low-doped side of the QW strongly influences the built-in electric field in the barrier region. This effect explains why the initial non-uniform design failed to improve the responsivity. To solve this problem, we propose a new asymmetric gradient doping structure, as shown in Fig. 7(a). This structure operates in a B-C transition mode. It uses an Al composition of 0.2 and an average carrier concentration of 5 × 1017 cm−3. Numerical simulations indicate that this gradient doping profile induces a strong electric field of up to 13.8 kV cm−1 on the low-doped side. This field strength is sufficient to trigger impact ionization.6 This design therefore ensures efficient photoelectric conversion through the B-C transition mode. At the same time, it introduces an additional gain mechanism through gradient-induced impact ionization. The combined action of these two effects is expected to significantly enhance the device responsivity.

Fig. 7. (a) Distributions of doping concentration and barrier width for each QW in the 35-period NUQWIP. (b) Energy band diagram of the 35-period NUQWIP at 80 K and −1 V.

Fig. 7

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Conclusions

In summary, this work establishes a quantitative experimental framework for accurately characterizing carrier concentration and internal electric field distributions in QWIPs. The study uses step-doped thin-film reference samples as calibration standards and combines them with low-noise, highly reproducible SSRM measurements. This approach enables reliable nanoscale quantification of electron concentration in QWs and overcomes the limitations of conventional macroscopic or chemically invasive techniques.

The method is applied to both uniform and non-uniform QWIP structures to extract realistic carrier concentration profiles. These experimentally obtained profiles serve as direct inputs for self-consistent Poisson–Schrödinger simulations, which reconstruct the actual internal electric field distribution. The results show that deviations in electron concentration, especially in low-doped regions, play a dominant role in determining the electric field strength. These deviations directly influence dark current suppression and responsivity enhancement. This analysis explains the performance gap between designed and fabricated non-uniform structures. It also provides clear guidance for optimizing asymmetric gradient-doping designs. Overall, the framework offers practical design principles for achieving high responsivity and low dark current in advanced non-uniform QWIPs.

Conflicts of interest

There are no conflicts to declare.

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (Grant No. U2241219, T. L.; 12393833, T. L.; 12227901, W. L.; 12174416, L. Y.; 11991063, T. L.), Chinese Academy of Sciences (Grant No. XDB0580000, W. L.; GJ0090406, T. L.), and the Science and Technology Commission of Shanghai Municipality (Grant No. 23JC1404100, B. Y.).

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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