Electrical scanning probe microscopy of electronic and photonic devices: connecting internal mechanisms with external measures

3.1 SSRM

Figure 6 shows a typical 2D SSRM spreading resistance image over an area of 5×12 μm² on the uncoated facet of the terahertz QCL (V843), which has a metal-semiconductor-metal ridge waveguide structure. In the SSRM scan, the tip bias is 1 V (DC) and the scan rate is 0.5 Hz. The top metal contact layer, the 10-μm-thick quantum-well active region, and the bottom metal contact layer can be delineated in this rough SSRM scan due to their substantial contrast in material electric conductivity. Nevertheless, individual quantum wells (GaAs) and barrier layers (Al_0.25Ga_0.75As) cannot be resolved because the thickness of each layer (<10 nm) is even smaller than the scan step (12 μm/512=23.4 nm).

Figure 6:

The SSRM image of the transverse cross section of the emission facet of the terahertz QCL device (V843). The DC tip bias is 1.0 V, the scan rate is 0.5 Hz, and the scan area is 5×12 μm².

A high-spatial-resolution SSRM image over an area of 1×0.5 μm² of the active region of the terahertz QCL is shown in Figure 7. Fourteen periodic thin lines are delineated with an even spacing of 35.7 nm, which is very close to the thickness of one cascade module of the device (the 10 μm active region of the device comprises 276 identical cascade modules, 10 μm/276=36.2 nm). The SSRM signal contrast results from the non-uniform doping profile of the active region – each quantum cascade module is δ-doped with Si dopants. As higher doping concentration yields lower spreading resistance, each thin line in the SSRM image reveals the exact location of δ-dopants in one module and can be used as a “ruler” for measuring the thickness of one cascade module. The small discrepancy (35.7 nm vs. 36.2 nm) may be attributed to experimental calibration error in SSRM. Figure 7 demonstrates that SSRM can be used to delineate individual quantum cascade modules; however, individual quantum wells (GaAs) and barrier layers (AlGaAs) in one module cannot be further resolved. This is because the AFM tip radius (~20 nm) imposes a limited spatial resolution, and GaAs and Al_0.25Ga_0.75As (small Al composition) have a low material contrast in SSRM.

Figure 7:

The zoomed-in SSRM image over the active region of V843. The scan area is 1×0.5 μm², and the scan rate is 0.25 Hz. This high-solution image delineates 14 quantum cascade modules, with each individual module thickness of ~36 nm.

The measured spreading resistance at different tip bias (1.0, 1.5, 2.5, and 3.5 V) is plotted as a function of lateral distance from the top metal contact in Figure 8. At higher tip bias, the measured spreading resistance is lower, showing a dependence of the SSRM resistance on the tip bias [10, 12, 16, 50]. The SSRM resistance over the metal layer is the lowest due to its highest electric conductivity. The measured SSRM resistance over the active region varies from 6.1 to 3.2 MΩ for different tip bias voltages because of the low average doping concentration of the active region, which is around 9.0×10¹⁵ cm^-3. A small negative slope is observed in the SSRM curves over the active region that is in close proximity to the metal layer (see Figure 8). This can be attributed to the effect of nearby metal-semiconductor interface on SSRM current spreading distribution, which has been modeled by De Wolf et al. [51]. Figure 8 shows there are periodic dips (downward peaks) in the SSRM resistance curve every 35.7 nm. As mentioned earlier, those dips (lower SSRM resistance) stem from the high contrast of the δ-doped layer (with a sheet density 3.25×10¹⁰ cm^-2) comparing to its surrounding undoped layers. Similar signal contrast due to different doping profile has also been reported in SCM scans between n- and p-type materials [52]. Some of the measured SSRM resistance results are summarized in Table 1, which will be used to quantify the average doping concentration of the active region of the device.

Figure 8:

1D SSRM-measured resistance profile near the top metal-semiconductor active region interface of V843 at different DC tip biases of 1.0, 1.5, 2.5, and 3.5 V.

In order to estimate the doping concentration from SSRM measurement, the AFM probe has to be calibrated by using a standard semiconductor sample with staircase doping profile under the same condition [10]. Figure 9 shows four calibration curves, showing the measured SSRM resistance as a function of doping concentration at DC tip bias voltages of 1.0, 1.5, 2.5, and 3.5 V, respectively. As expected, the SSRM resistance monotonically decreases as the doping concentration increases over a range of 10¹⁵–10¹⁹ cm^-3. The calibration curves will be used shortly to derive the average doping concentration of the QCL active region.

Figure 9:

Four SSRM calibration curves obtained at different DC tip biases (1.0, 1.5, 2.5, and 3.5 V), correlating the SSRM measured resistance to the doping concentration in a GaAs standard sample with staircase doping profile. The doping concentration of the GaAs standard sample is obtained from second ion mass spectroscopy. The error bars are ±10% and ±5% for x- and y-axis, respectively.

3.2 SCM

The terahertz QCL device (V843) is also examined by using SCM, which introduces less physical damages to the sample surface due to weak force being applied by the AFM probe during the scans. A typical SCM image from V843 is presented in Figure 10. During the open-loop mode scans, the AC bias voltage is 1.0 V and the scan rate is 0.5 Hz. The SCM image can also resolve the metal layers and the 10-μm-thick semiconductor active region, but with a lower spatial resolution comparing to the SSRM image. This lower spatial resolution is attributed to the fact that the lateral distribution of the depletion region in semiconductor underneath the probe contact point introduces a substantial shadow effect to smear the SCM image [12].

Figure 10:

SCM image of the transverse cross section of the emission facet of V843. The AC tip bias is 1.0 V, the scan rate is 0.5 Hz, and the scan area is 5×12 μm².

Figure 11 shows a zoomed-in SCM image over an area of 1×0.5 μm² of the active region with a scan rate of 0.25 Hz and an AC bias of 1.0 V under an open-loop amplitude mode. The δ-doped layers can still be resolved as 14 thin lines in the SCM image, but appear not as sharply as the ones resolved in the SSRM image due to the poorer spatial resolution of SCM. The spacing between the 14 thin lines is measured to be 35.7 nm, which is the same as the one obtained from SSRM scans.

Figure 11:

The zoomed-in SCM image over the active region of V843. The scan area is 1×0.5 μm² and the scan rate is 0.25 Hz. Fourteen quantum cascade modules are delineated.

Even though efforts have been made to attain a direct correlation between the SCM signals and semiconductor doping concentration [53–55], there are no well-established and reliable models or algorithm for directly converting the measured SCM signals to the doping concentration. A standard semiconductor sample with staircase doping profile is used to calibrate the SCM approach, as was done in SSRM. Figure 12 presents the five calibration curves for SCM from the n-type GaAs staircase doping profile sample. Contrary to the SSRM calibration curves, the measured SCM signal (dC/dV) monotonically increases with the increase of the doping concentration over the range of 1×10¹⁵–4×10¹⁸ cm^-3. The SCM calibration curves, together with the measured SCM data from the terahertz QCL, will be used to derive the average doping concentration in the active region of the V843 device.

Figure 12:

Five SCM calibration curves obtained at different AC tip biases (0.5, 0.75, 1.0, 1.25, and 2.0 V), correlating the SCM signal to the doping concentration in the GaAs standard sample with staircase doping profile.

3.3 Calibration results

Combining the SSRM calibration curves, the SCM calibration curves, and the measured data from the terahertz QCL device, the average doping concentration of the 10-μm-thick active region of V843 are derived and summarized in Table 2. Shown together is the nominal doping concentration of the device. The derived doping concentration exhibits a reasonably good agreement with the design value (9.0×10¹⁵ cm^-3), while the SSRM-based values show a larger discrepancy (within 25%) and the SCM-based values are more consistent (within ~10%). The discrepancy between the measured doping concentration and the design value could mainly be attributed to system errors in the scans, the non-linear behavior of the tip-sample Schottky contact, and the non-identical surface condition between the terahertz QCL samples and the calibration GaAs staircase samples [10, 12, 56]. The experimental results demonstrate that SSRM and SCM can delineate 2D semiconductor structures with a high spatial resolution and resolve the doping profiles in semiconductor layers with a certain quantitative accuracy.

4.1 Programing the NVM devices and sample preparation

To prepare the SCM experiments, two 512 KB Texas Instrument NVMs (NOR flash devices) are selected and programmed with the word data “AA”=“10101010” and “CC”=“11001100”, respectively, all over their memory blocks. The static charges are stored at the FG-gate oxide interface in the NVM devices, an approach that modifies the threshold voltage and the channel carrier distribution of the FGT [57]. In the FGT channel, the electron density stored in its FG by capacitance coupling through the gate oxide is actually the coupled image of the hole density [58, 59]. In order to probe the carrier density located on the FGT channels by using SCM, the conductive AFM probe has to scan close enough (<300 nm) to the transistor channels but without discharging the FGs. The samples under test therefore need to be deprocessed in a very definite way. A backside approach is adopted for the sample preparation [57], in which the tunnel oxide is exposed from the backside by deprocessing the sample. Figure 13 schematically shows the main steps of this backside approach. The Si substrate is polished to reduce its thickness from around 15 μm down to 0.5 μm, and then a final polishing is performed to achieve the desired silicon thickness of 30–200 nm. A thinner silicon substrate would yield better SCM scan results, but it may also lead to charge loss due to charge tunneling. The FG potentials can then be measured through this tunnel oxide [58]. It is practically impossible to achieve a uniformly thin silicon layer (with a thickness <200 nm) all over the memory device through polishing. A practically feasible approach is to adopt a bevel configuration with a small slope (~0.15%), where only a small area (≈80 μm² large) is usable for the SCM measurements, as marked by a white box and shown in Figure 14. A diamond-coated AFM probe tip is employed in the SCM scans and both DC and AC voltages are applied to the AFM probe in the contact mode [48, 58–61].

Figure 13:

Schematic diagram of the sample preparation process performed on the NVM devices. (A) Sample is glued to the AFM sample holder using silver epoxy, making it ready for backside deprocessing. (B) Rough polishing on the backside of sample to remove the bulk silicon substrate until a thickness of 0.5 μm. (C) Fine polishing to slowly etch the silicon substrate down to a thickness of 30–200 nm.

Figure 14:

An optical microscope image of the final prepared sample, which is ready for SCM scanning on the backside, showing the thin silicon layer in a bevel pattern.

4.2 Stored charge carriers

The buried charge carriers stored in the FGT channels of the embedded NOR flash memory device can now be detected in SCM scans. The capacitance resonator of the SCM has a high sensitivity of 10^-22 F/√Hz to carriers, allowing probing electric charges as small as a single electron [62]. The SCM signals are measured with 2 V AC and -1.8 V DC bias applied to the AFM tip. Figure 15 shows such SCM images over the deprocessed NOR flash devices. The big yellow-colored regions represent the common sources of the FGs, while the small yellow spots (underneath the source regions, with fading color) are individual drains. The drains appear much dimmer in the SCM images comparing to the source regions because the drains are further away from the AFM probe tip. When the FGs are charged, the drains become invisible in the SCM images because the signal from the stored charge overshadows that of the drains. The gate length is measured to be 0.22 μm from the SCM images.

Figure 15:

Two SCM scan images over a 2.50 μm distance of the embedded NOR flash memory device. The preprogrammed word data (A) “AA”=“1010” in binary form, and (B) “CC”=“1001” in binary form, can be read directly from the SCM images. The stored dynamic charges are identified to be present on FGs for “1b” while absent on the FGs for “0b”.

In Figure 15, bright blue-colored regions are observed, which signify the stored electric charges on the FGs and represent a “1b” or ON state. The FGs without stored charges appear in pink color, representing a “0b” or OFF state. The ON and OFF states in Figure 15A and B are marked with black and white circles, respectively. In Figure 15A, binary bits of “1010” can be observed in a repeatable pattern throughout the FGTs, corresponding to the NVM devices that are preprogrammed with the word data “AA”. In Figure 15B, binary bits of “1001” can be observed, corresponding to the NVM devices that are preprogrammed with the word data “CC”. The results demonstrate that SCM is capable of reading the stored charge carriers with submicrometer spatial resolution and high accuracy.

It can also be observed that the appearance of the FGs at the ON state is not exactly identical in the SCM images. As the brightness of the blue-colored region quantitatively reflects the density of the charge carriers stored in FGs, the SCM images provide a direct visualization of the 2D stored charge density profile (Figure 15), showing the charge carrier density may vary substantially across the FGs at the ON state, which should nominally be identical to one another. This variation is revealed more clearly in the cross-section analysis, which is shown in Figure 16. The one-dimension dC/dV signal in Figure 16 is obtained by averaging the line scans of the region marked with white dotted lines in Figure 15B. Over the distance range of 0.5–2.0 μm, there are two positive peaks and two negative peaks. The positive peaks correspond to “1b”, indicating accumulation of charge carriers. The negative peaks correspond to “0b”, representing no charge carriers. The data is therefore read as “1001”, correlating well to the preprogrammed word of “CC” in the NOR flash device. As mentioned earlier, the variation in the measured dC/dV signal of the ON states is attributed to the difference in the quantity of the charge carriers stored in the FGs. The signal-to-noise ratio in Figure 16 is estimated to be ~11, sufficiently high for reliably determining the digital bits stored in the FGs.

Figure 16:

SCM cross-section analysis of Figure 15B for the 2.5 μm distance. The positive peaks represent FGs with stored charges, while the negative peaks represent FGs without.

4.3 Repeatability

The stored data in a Texas Instruments 512 KB embedded NOR flash memory devices of 0.22 μm gate length FGTs are successfully read back using the SCM technique. The results show that individual digital bits of “1b” and “0b” can be determined reliably from SCM scans; moreover, SCM images also reveal the different charge carrier densities stored in FGs. The process used for the sample preparation and the SCM reading of the stored data appears to be data non-destructive and repeatable. The DC and AC voltages applied to the tip for charge detection are maintained at a low range ~(-3.0 to -0.1 V) and ~(+1.0 to +3 V), respectively, levels far below from program-erasable high voltages ~(+8 V, +20 V) for the Flash devices. SCM scanning (reading) of sample surfaces are performed for ~4 h continuously in the same area, and no noticeable reduction of charge level is detected [57]. The device is kept in a dark box after the sample preparation in order to retain the programmed charges and minimized charge loss due to external optical illumination [48, 58]. After a long storage time, the SCM readings of the digital bits are still correct and agree well with the programmed data. This demonstrates that the SCM-based read-back process is reliable and data non-destructive.

5.1 Formation and evolution of electric field domain

In a terahertz QCL, each individual quantum cascade module needs to be biased exactly at designed electric field in order to achieve population inversion – a prerequisite for lasing. In many cases, no lasing can be observed because the quantum cascade modules are biased at wrong electric fields potentially due to the formation of electric field domains (EFDs) in the active region – a hypothesis that has long been suspected and could only be verified indirectly from the measurements of active-region photoluminescence spectra or the observation of sawtooth-like current-voltage (I-V) or light-voltage (L-V) curves [63–66]. SVM has been shown to resolve individual semiconductor quantum wells and quantitatively measure voltage distribution across semiconductor layers [17, 19], and is thus used to experimentally explore the formation and evolution of EFDs in operating terahertz QCLs.

An indirect pumping-based terahertz QCL laser with uncoated cleaved facets and a metal-metal waveguide [29] is used in the SVM scans. Figure 17A shows a typical 2D voltage profile across the device active region. The device is biased at 12 V in pulsed mode at 77 K. As expected, the measured voltage profile discloses a monotonic drop in voltage from the top metals (at 12 V), through the intermediate layers, to the grounded bottom metals (at 0 V). There is a sharp voltage drop of ~0.8 V at the Schottky junction between the top metal and the top n⁺ GaAs contact layer. The SVM image also directly visualizes the formation of two EFDs at this bias – one higher EFD close to the top metal layer (greater slope) and one lower EFD close to the bottom metal layer (smaller slope). The inset is the topology of the scanned cross section, showing that the cleaved emission facet is almost atomically flat.

Figure 17:

SVM results of an operating terahertz QCL (V843), showing the formation and evolution of EFDs in the active region. (A) An SVM-measured 2D voltage profile across V843 at a forward bias of 12 V (pulsed mode, 3.5 μs pulse width, and 100 Hz repetition rate) at 77 K. Two EFDs (F₁ and F₂) across the ~10-μm-thick MQW active region are observed. The inset of the figure shows a 2D topology image over the same area. (B and C) 1D voltage profile across the device active region at different biases (2–25 V). (D) Experimental and simulated electrical and optical characteristics of V843 at 77 K and other temperatures (10, 50, 100, and 130 K). (E) The SVM-measured electric field across individual cascade modules in the active region of operating V843 device as a function of applied device bias. In the bias ranges of 10–17 V and 22–25 V, the active region splits to two EFDs and the electric field in each EFD remains constant. Shown together is the partition number of the cascade modules in each EFD measured from SVM. The number of cascade modules in the higher EFD increases, while the number of cascade modules in the lower EFD decreases with the device bias.

One-dimensional SVM-measured voltage profile curves are also measured at different device biases from 2 to 25 V, and the results are presented in Figure 17B and C. No multiple EFDs are observed at low biases (2–9 V). Beyond 10 V, a higher EFD (denoted by dashed lines) emerges from the active region close to the top metal layer and expands linearly with the increase of the device bias to the bottom metal layer at the expense of the lower EFD (solid lines), until it expand over the whole active region (10 μm thick). At the biases between 18 and 21 V, only one slope is observed. Multiple EFDs appear again in the device bias range of 22–25 V, and similar EFD evolution behaviors are observed. The SVM results thus directly reveal the formation and evolution of the EFDs in an operating terahertz QCL. In addition, the electric field (F) of the observed EFDs are quantitatively measured from the slopes [F=average of (ΔV/Δd)] of the voltage profile curves in Figure 17B and C. Table 3 summarizes the measured electric field as a function device bias. Figure 17D shows the experimental and theoretical light-current density-voltage (L-J-V) characteristics of the device under test. It has been found that the electric field of the EFDs measured from SVM correlates very well to those of the important features observed in the L-J-V curves in Figure 17D, which can be well explained by the alignment and misalignment of the discrete energy levels in the quantum wells of the device active region as well as the competition of various current-carrying channels under different device biases [44].

The number (n_k) of the cascade modules in each EFD section can be calculated by using n_k=l_k/d (k=1, 2), where l_k is the length of each EFD section measured directly from Figure 17B and C, and d is the thickness of one cascade module (d=36.2 nm) [29]. Figure 17E presents the calculated numbers at different device biases, clearly confirming that the boundary of the EFDs linearly shifts from the top to the bottom contact layer as device bias increases over two ranges of 10–17 V and 22–25 V [44].

5.2 High-resolution SVM

By reducing the scan range, the spatial resolution of the SVM scans can be enhanced so that individual quantum cascade modules can be delineated. Figure 18A shows a typical 1D rough SVM scan across the ~10 μm multiple quantum well (MQW) active region at a device bias of 15 V. Figure 18B–D shows high-resolution voltage profiles by zooming in the SVM scans in three 512×512 nm² regions – one close to the top metal-semiconductor interface, one close to the EFD boundary, and one close to the bottom metal-semiconductor interface. A small voltage dip is observed every ~36 nm in the high-resolution SVM curves. The small voltage dip is attributed to the δ-doping profile (η_2D=3.25×10¹⁰ cm^-2) in the injection barrier, which is the boundary layer between two neighboring modules. As a result, the voltage dips can be used as a “ruler” in SVM scans.

Figure 18:

(A) The 1D SVM voltage curve cross the active region of the V843 device (device bias: 15 V, temperature: 77 K). The inset shows three zoomed-in SVM scans spanning 512 nm each. (B–D) are the corresponding further zoomed-in curves in which the small voltage dips at the δ-doped injection barriers can be clearly observed. The bottom curve in each figure is the first-order derivative (|dV/dx|) of the corresponding voltage profile curve.

Figure 19 shows high-resolution SVM scans [(A) for 2D and (B) for 1D], which zoom in the EFD boundary region. All scans exhibit two distinct voltage slopes, and the small voltage dips denote individual cascade modules. The periodic spacing measured from these high-resolution SVM scans is ~36.1±0.1 nm, agreeing well with the design value of 36.2 nm. It is also revealed that the EFD boundary (at which the two voltage slopes cross) is located at ~12±0.5 nm away from the small voltage dip (the injection barrier) toward the upstream direction of the electron flux (Figure 19B). Figure 19C shows a series of high-resolution SVM scans by changing the device bias from 14.991 to 15.039 V with an incremental step of ~0.01 V. The experimental results show that the EFD boundary does not shift continuously with the gradual increase of the applied device bias, but rather hops discretely. Only when the device bias is increased by ~30 mV or more does the EFD boundary jump by ~36 nm, which is one cascade module thickness. The minimum bias increase that is needed to flip one complete cascade module from the lower EFD (F=8.58 kV/cm) to the higher EFD (16.77 kV/cm) is 30 mV. This one-module-at-a-time progression of the EFD boundary is therefore convincingly confirmed to be the nanoscopic origin of the reported sawtooth-like current-voltage (I-V) characteristics exhibited by QCLs [67].

Figure 19:

High-resolution SVM scans near the boundary of EFDs. (A) The 2D SVM voltage image over a 512×512 nm² scan area at 15 V and 77 K. (B) A 1D zoomed-in voltage curve over three modules in a row, showing the exact location of the EFD boundary (the turning point of the electric field). (C) 1D SVM voltage profile curves at a series of device biases from 14.991 to 15.039 V, showing the hopping behavior of the EFD boundary. All curves (except the one at 15.001 V) are accumulatively shifted by 0.01 V vertically for clarity.

5.3 Simulation results

In order to understand why the EFD boundary is ~12 nm after the injection barrier, the potential profile, electric field, and charge carrier distribution are calculated by self-consistently solving coupled Schrödinger-Poisson equations. The simulation results across the quantum cascade modules in close proximity of the EFD boundary are presented in Figure 20. The input parameters in the simulation include the lower electric field (F₁), the higher electric field (F₂), and the voltage drop across seven modules around the EFD boundary, which are derived from a high-resolution SVM scan at 12 V. The calculated band diagram, the potential profile, and the wave functions of the confined energy states across the modules are presented in the lower part of Figure 20, which shows a clear turning point between the higher EFD and lower EFD. The turning point (the EFD boundary) is located in the widest well of the module, coinciding with the lobe of the wave function of the extraction state, which is ~12.3 nm away from the center of the injection barrier layer, confirming the experimental results from the SVM measurements. The widest quantum well accommodates the electron accumulation that is resulted from the discontinuity of the electric field across the EFD boundary [44].

Figure 20:

Simulated charge carrier density (ρ/q, top section); electric field (F, middle section); and band diagram, electrical potential, and wavefunctions (bottom section) over quantum cascade modules near the EFD boundary. The simulation results confirm that the EFD boundary is ~12.3 nm away from the δ-doped injection barrier in the transitional module. The device bias used in the simulation is 12 V.

6.1 Voltage profile inside operating ICLs

It has been postulated that the electron density and hole density are not balanced in the active region in an operating ICL, which substantially degrades device performance. By heavily n-doping the electron injection layers, the performance of ICLs has been significantly improved, which was attributed to the rebalancing of electrons and holes [39]. In this section, we present direct experimental evidences obtained from SVM measurements, confirming the rebalancing of electrons and holes in an actively biased ICL with a heavy n-doping profile. The experimental results also show that the charge carrier density in a lasing ICL at low temperatures is pinned above the threshold.

Figure 21A is a 2D voltage profile over a transverse cross-section area (3×3 μm²) on the front emission facet of the ICL (R090) under a forward bias of 3 V. The top metal layer, the top separate confinement layer (SCL, undoped InAs), the interband cascade region (eight cascade modules), and the top SCL layer can be resolved in Figure 21A due to their contrast in electric potential. Most of the voltage drop is observed over the interband cascade region (386 nm in thickness). Figure 21B presents 1D voltage profile curves at different device biases from 0.5 to 5.0 V. The slope of the voltage profile is uniform over the interband cascade region, and it increases proportionally with the increase of device bias. A slight voltage drop is observed at the top contact layer-top SCL layer interface, which is under a local reverse bias even though the device is globally forward biased.

Figure 21:

(A) An SVM 2D voltage profile image of an ICL (device bias: 3.0 V, temperature: 77 K). (B) 1D section analysis of the SVM voltage profiles at different device biases from 0.5 to 5.0 V. It shows that the voltage drop mainly occurs across the interband cascade active region of the device.

6.2 Electric field profile and carrier density profile

High-resolution SVM scans are achieved by reducing the scan range to delineate individual cascade modules. Figure 22A shows such a high-resolution voltage image over a small area (512×512 nm²), in which eight pairs of voltage dips (denoted by dashed lines) appear with a spacing of ~48 nm over the 386-nm-thick interband cascade region, corresponding well to the eight cascade modules in R090. Calculating the first-order derivative of measured voltage profile against distance (F=-dV/dx) yields the internal electric field (F) inside the MQW active region, which is plotted in Figure 22B. The average electric field in the MQW active region is F=8.64 V/μm (86.4 kV/cm) at a device bias of 3.5 V. Two peaks and two valleys are observed in the electric field curve over each of the voltage dip pair regions. This non-uniform electric field profile is attributed to spatial segregation of electrons and holes, which is expected due to the unique type-II quantum wells of this ICL device. The identical electric field distribution profile among the eight cascade modules (Figure 22B) reflects uniform carrier injection and distribution in each of the modules, ensured by the series connection of the modules in the structure [38, 68]. The measured voltage dip pairs and the derived electric field peaks and valleys are more perceivable in a zoomed-in plot (see Figure 22C). By comparing to the band diagram of the ICL (Figure 22D), it is found that the voltage dips exactly overlap with the InAs-GaInSb MQW active section of the corresponding modules.

Figure 22:

(A) A zoomed-in 2D voltage profile across the interband cascade region (scan area: 512×512 nm, temperature: 77 K, and applied bias: 3.0 V). (B) A 1D voltage profile over a distance of 512 nm, together with corresponding electric field (-dV/dx) distribution across the region. (C) A zoomed-in voltage profile over a distance of 63 nm (temperature: 77 K, device bias: 3.5 V), showing two pairs of voltage dips every ~48 nm. The bottom curve shows the corresponding electric field curve. (D) The zoomed-in profile (-d²V/dx²) at 3.5 V, numerically derived from the electric field curve (C). The top curve is the zero-bias band diagram of the MQWs in the active region.

Calculating the second-order derivative of V(x) yields the net charge carrier density [n(x)],

where ε₀ is the vacuum permittivity, ε_r the relative permittivity, and q the electron charge. Figure 22D presents the calculated -d²V/dx² results, as well as the band diagram of the active and injection sections at zero bias. It shows two negative peaks and three positives across the InAs-GaInSb active section, which correspond to net negative charge accumulation in the two InAs conductive-band quantum wells and net positive charge in the two GaInSb and the neighboring AlSb valence-band quantum wells. The net charge density is zero in other region. The experimental results based on SVM measurements therefore provide the first-ever direct observation of the electron and hole spatial segregation at nanometer scales in an operating ICL [45].

6.3 Bias dependence and temperature dependence of charge carrier density

By integrating n(x),

one can quantitatively calculate the net charge carrier density (σ_i, i=1, 2, 3, 4, 5) in individual quantum wells (as labeled in Figure 22D). Figure 23A presents the calculated carrier sheet density as a function of the applied bias at 77 K, which shows a quick increase prior to the lasing threshold voltage (3.4 V) and saturation at and above the threshold. The saturation of charge carrier density above the threshold voltage is because the additional injected carriers are completely consumed by stimulated emission [69]. Similar SVM measurements and data analysis are repeated on the same device at room temperature, the results are presented in Figure 23B. The carrier density exhibits monotonic increase over the device bias range from 0 to 4 V. This non-clamping behavior is attributed to the absence of stimulated emission at this temperature (the device’s maximum lasing temperature is 248 K). Table 4 summarizes the derived electric field and sheet carrier density at different device biases. The total hole density (σ_h) and the total electron density (σ_e) are in reasonable agreement with each other (~10%, within experimental uncertainty), confirming the maintaining of charge neutrality.

Figure 23:

(A) The experimental sheet charge carrier densities at different device biases at 77 K. The threshold voltage at 77 K is 3.4 V. (B) The experimental sheet charge carrier densities at different device biases at room temperature. The device does not lase at room temperature. (C) The experimental total electron density (σ₂+σ₄) as a function of the internal average electric field. A linear fitting curve (solid line) based on Eq. (3) is plotted for comparison.

The quasi-equilibrium charge carrier sheet density has been found to be linearly dependent on electric field (F) under certain conditions [68]:

where mr∗ is the reduced effective mass, ℏ the reduced Planck constant, and E_SM the overlap energy. Δd is the center-of-mass distance between the electron and hole wave function distributions across the type II interface. Figure 23C plots the experimental electron density at 77 K as a function of the internal electric field (F), together with a linear fitting curve based on Eq. (3), showing a very good agreement over the electric field range of 2.399×10⁶ V/m (23.99 kV/cm) to 8.133×10⁶ V/m (81.33 kV/cm) (corresponding to applied device biases from 1.0 to 3.3 V). Two fitting parameters are obtained as Δd=7.6 nm and E_i =14.6 meV.

The temperature dependence of the charge carrier sheet density is also investigated by conducting SVM measurements on R090 at a constant bias (3.8) for different temperatures followed by corresponding data analysis. The results are presented in Figure 24. The threshold current increases slowly with temperature from 60 to 170 K, and then rapidly increases till the maximum lasing temperature. The measured total electron sheet density and hole density shows a linear dependence on temperature from 77 to 240 K (increases by only ~15%). At temperatures above the maximum lasing temperature, the total carrier density increases rapidly by ~140% from 240 to 298 K. This fast increase observed in carrier density above maximum lasing temperature is attributed to the absence of stimulated emission. The SVM results have shown that the optical gain (proportional to carrier density) has only modest increase from 77 to 240 K. Nevertheless, the threshold current increases rapidly in that temperature range with a characteristics temperature T₀=~29 K, which is likely attributed to a fast reduction in carrier lifetime due to stronger non-radiative Auger recombination process at elevated temperatures [70, 71].

Figure 24:

The active-region charge carrier sheet densities (σ_h and σ_e) measured at 3.8 V from SVM as a function of temperature; shown together is the experimental threshold current as a function of temperature.