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Profiling the Thermoelectric Power of Semiconductor Junctions with Nanometer Resolution

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Science  06 Feb 2004:
Vol. 303, Issue 5659, pp. 816-818
DOI: 10.1126/science.1091600

Abstract

We have probed the local thermoelectric power of semiconductor nanostructures with the use of ultrahigh-vacuum scanning thermoelectric microscopy. When applied to a p-n junction, this method reveals that the thermoelectric power changes its sign abruptly within 2 nanometers across the junction. Because thermoelectric power correlates with electronic structure, we can profile with nanometer spatial resolution the thermoelectric power, band structures, and carrier concentrations of semiconductor junctions that constitute the building blocks of thermoelectric, electronic, and optoelectronic devices.

Thermoelectric coolers and power sources realize energy conversion between heat and electricity without the use of moving mechanical components or hazardous working fluids. Developing new thermoelectric materials with high figures of merit (ZT) has been a topic of great interest; a ZT larger than 3 will allow thermoelectric coolers to have a coefficient of performance comparable to that of a kitchen refrigerator (13). Until recently, the ZT of the best bulk thermoelectric materials has remained at a value of about 1. The emergence of nanotechnology creates new opportunities to design nanostructured materials for achieving high ZT (4, 5). Recent reports of ZT improvement to values up to 2.4 with the use of quantum well (6) and quantum dot (7) superlattices have stimulated much excitement.

ZT is defined as (S2σ/κ)T, where S is the thermoelectric power or Seebeck coefficient, σ and κ are the electrical and thermal conductivities, respectively, and T is absolute temperature. Understanding the effects of low dimensions and nanoscale structures on S, σ, and κ plays a key role in the rational design of nanostructured thermoelectric materials. The ability to directly measure these thermoelectric properties at the nanoscale should facilitate the development of this field.

We report a direct profiling of S across a semiconductor p-n junction with nanometer resolution with the use of scanning thermoelectric microscopy (SThEM). In addition to the divergence and abrupt sign change of S across the electronic junction, we find a direct correlation between the average interdopant spacing and the minimum length scale at which S can be measured in doped semiconductors. Because S is governed by local carrier statistics, SThEM allows us to profile precise electronic junction locations and local carrier concentrations with nanometer resolution, a prominent characterization issue that has challenged the semiconductor industry for many years (8).

Our experiment uses an ultrahigh-vacuum (UHV) scanning tunneling microscope (STM) with a base pressure of 5 × 10–11 torr. A heater wire attached to the sample holder is used to raise the sample temperature to 5 to 30 K above room temperature. As the room-temperature tip makes a nanoscale contact with the heated sample, a localized temperature gradient is created in the sample near the contact point (Fig. 1A). This temperature gradient generates a thermoelectric voltage that is directly related to the local S. The setup shares some similarities with the scanning chemical potential microscope (9, 10), but there are two critical differences. First, in our measurement of the thermoelectric voltage, the tip and the sample are in direct nanocontact. We find this to be necessary for obtaining a stable measurement of the thermoelectric voltage on a semiconductor sample (Fig. 1B) (11). Second, our measurement is conducted in UHV, avoiding heat conduction through the air gap between the STM tip and the sample. This is crucial for confining the temperature gradient near the tip-sample contact in order to achieve nanometer spatial resolution.

Fig. 1.

(A) Schematic of the SThEM setup showing a nonuniform temperature zone in the sample. (B) Time profiles of the measured voltage and the tip height as the tip approaches the sample, then retracts. (C) Histogram of the measured voltage.

The temperature gradient leads to a thermoelectric voltage, Embedded Image(1) where Tc and T1 are the temperatures of the contact and the back side of the sample, respectively, and S(x, y) is the spatial average within the nonuniform temperature zone localized in the semiconductor sample. The S of the metal tip and the lead wires is ignored because it is much smaller than that of the semiconductor sample.

An STM image is shown across an atomically flat GaAs p-n junction in Fig. 2 (inset). The height contrast in the STM image is reversed as the polarity of the STM bias is reversed. Whereas the boundary between the dark and bright regions roughly corresponds to the junction location, the apparent junction location in the STM images can shift as much as 20 nm, depending on the bias condition. As discussed extensively in previous work (1214), this is due to a tip voltage–induced band-bending effect and is responsible for the uncertainty in locating the precise p-n junction location by means of STM.

Fig. 2.

Measured thermoelectric voltage (circles) and calculated S multiplied by 22 K (line) across a GaAs p-n junction as a function of distance (x). The sample was heated 30 K above the tip (room) temperature. Because of the temperature rise in the tip and in a depletion zone within the nonuniform temperature zone, the value of 22 K yields a better agreement than 30 K between the measurement and the calculation. Inset: STM image of the junction (filled state with a sample bias of –2 V). The bright strip is p-doped with Be at 9 × 1018 cm–3, and the dark strip is n-doped with Si at 1.1 × 1019 cm–3. The dashed line is 150 nm, corresponding to the line where voltage profile is measured.

The S profile across the junction (Fig. 2) calculated from the band structure was obtained using the depletion approximation based on the dopant profile measured by secondary ion mass spectroscopy (SIMS) (11, 15). The calculated S profile exhibits an abrupt polarity inversion near the junction: The separation between the positive peak value and the negative one is only 1.2 nm. The reason for this sudden sign inversion is that, under the assumption of a continuous distribution of dopant atoms, the majority carrier type changes abruptly near the junction because a band bending of a few kBT (where kB is the Boltzmann constant) occurs within 1 nm of the junction.

The SThEM measurement result is also plotted in Fig. 2. On either side of the junction, the magnitude of the measured thermoelectric voltage increases toward the junction, continuing until about 4 nm from the junction, where the magnitude decreases because the contribution of the minority carriers cancels that of the majority ones. Furthermore, the voltage changes its sign across the junction as a result of the inversion of the majority carrier type. The sign reversal occurs within 2 nm, whereas the distance between the positive and negative peaks is about 8 nm. The measured thermoelectric voltage profile—in particular, the divergence near the junction and the abrupt sign change across the junction—agrees qualitatively with the calculated S profile. However, the calculated profile shows much sharper transition at the junction.

The discrepancy can be attributed to the breakdown of the continuum assumption for the calculation of S at a length scale comparable to the average interdopant spacing (i.e., 4.6 nm), corresponding to a dopant concentration of about 1019 cm–3. Further, it also reveals the spatial resolution of the measurement, which is limited not only by the contact size (1 nm or less) but also by the size of the nonuniform temperature zone.

We note that the peak-to-peak distance of the measured thermoelectric profile is about twice the average interdopant spacing. To further examine this correlation, we performed experiments on p-n junctions with different doping levels. The thermoelectric voltage profile was measured on another GaAs sample consisting of a p layer sandwiched between two n layers (Fig. 3). Compared to the calculated S profile, the measured profile shows a broadening effect with a distance of ∼20 nm between the positive peak and the negative one. This distance is again roughly twice the 10-nm interdopant spacing in the p layer.

Fig. 3.

Measured thermoelectric voltage (circles) and calculated S multiplied by 5 K (line) of a GaAs sample consisting of a p-type layer, 100 nm thick, sandwiched between two n-type layers. The p-type layer is doped with Be at 1 × 1018 cm–3; the n-type layers to the left and right are doped with Si at 5 × 1018 cm–3 and 1 × 1018 cm–3, respectively. x is measured from the left p-n junction.

This observation suggests that the size of the nonuniform temperature zone is defined by impurity scattering to be about twice the interdopant spacing in the highly doped semiconductor. This idea is supported by an experiment showing that the phonon mean free path (λph) in a doped GaAs sample scales with the average interdopant spacing, measuring 13.3, 6.2, and 2.88 nm for a dopant concentration of 1017, 1018, and 1019 cm–3, respectively (16). Because phonons are the dominant heat carriers in the semiconductor sample, one thus expects that in spherical geometry the temperature rise decays as ΔT ∼ λph/r for r > λph, where r is the distance from the contact. Hence, the size of the nonuniform temperature zone should be about a factor of 2 to 3 greater than λph, or about two to three times the interdopant spacing if the values in (16) are used. Still, the nonuniform temperature zone needs to be larger than the electron-phonon scattering mean free path for electrons and phonons to establish local thermal equilibrium in this zone. In a highly doped semiconductor, one expects that the electron mean free path is comparable to the average interdopant spacing because of scattering with ionized impurities. Although impurity scattering is an elastic process and has no direct impact on the electron-phonon scattering mean free time, it alters the electron trajectory and reduces the effective electron-phonon scattering mean free path to be comparable to the interdopant spacing. Hence, electrons and phonons also establish local thermal equilibrium at the length scale of the interdopant spacing, allowing us to profile local S at a length scale of about two to three times the interdopant spacing. Moreover, this method can potentially be applied to directly probe the local S of individual quantum wells and wires, where the nonuniform temperature zone can be further confined within the nanostructures by interfaces.

Inside the nonuniform temperature zone, the S can be nonuniform because of the presence of a depletion zone from the formation of a tip-sample Schottky junction. However, the depletion width of the nanoscale Schottky junction is much smaller than that of a planar one, and this width is comparable to the interdopant spacing (17, 18). Because λph is also comparable to the interdopant spacing, the temperature rise within much of the depletion zone should be only a small fraction of the total value. Experimentally, neglecting the temperature rise in the tip because of its high thermal conductivity, we find the measurement results to be about 80% of the bulk values. Considering a small temperature rise in the tip, one can expect that the measurement results are rather close to the bulk property. Although our observation suggests that the depletion zone and other effects, such as the suppression of the phonon-drag thermoelectric power at a nanocontact (1921), do not cause large measurement errors, this method allows further investigation of these intriguing nanoscale effects.

In Fig. 4, we directly convert the measured S profile to the band structure and carrier profile (11). The band structure calculated from the SIMS dopant profile and the carrier profile calculated from the band structure by Fermi-Dirac statistics are also shown for comparison. The results from SIMS and SThEM exhibit good agreement, although the match is poor at the edges of the depletion region (likely as a result of the continuum assumption and the depletion approximation invoked for the calculation based on SIMS). An important feature is the ability of SThEM to resolve the location of the electronic junction to within 2 nm. This position corresponds to the location where the majority carrier type changes, resulting in the abrupt sign change of the thermoelectric voltage. Because there is no external electrical bias across the tip-sample junction, the SThEM measurement does not suffer the severe tip voltage–induced bandbending effect that exists in STM or scanning capacitance microscopy, where a very large external electric field (∼109 V/m) exists at the tip-sample gap and shifts the junction location. The resolution shown here for junction delineation shows a significant improvement over most of the characterization techniques available today.

Fig. 4.

Carrier profile across the p-n junction shown in Fig. 2. Solid and dashed lines are electron and hole concentrations, respectively, calculated from the SIMS dopant profile. Solid and open circles are electron and hole concentrations, respectively, calculated from the SThEM results. Inset: Energy diagram of the p-n junction. Solid and open circles are the conduction and valence band edge, respectively, calculated from the SThEM results. Solid and dashed lines are calculated from the SIMS dopant profile.

Supporting Online Material

www.sciencemag.org/cgi/content/full/303/5659/816/DC1

Materials and Methods

References

References and Notes

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