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Minding the gap—Semiconductor band engineering In a heterojunction structure involving a piezoelectric semiconductor material, the appearance of piezoelectric polarization will lead to a considerable change of free charge distribution in the piezoelectric material and its adjacent semiconductor or metal contacts. 3 For example, in the p-n junction shown in Fig. 2(a), the original interfacial band structure results from charge redistribution caused by Fermi-level mismatch. Because one of the junction materials is piezoelectric, straining creates immobile piezoelectric charge (σpz) at the piezo-material surface. The free charge concentrations in both junctionforming materials are finite. Therefore, free charges with an opposite sign to σpz (that is, screening charge) are attracted to the interface internally from the piezo-material (σs,in) and externally from the contacting material (σs,ex) (the bottom picture of Fig. 2(a)). The sum of σs,in and σs,ex is typically equal or very close to σpz, and the relative ratio between σs,in and σs,ex is determined by the material’s carrier concentrations and density of states. The net charge gain at the interface (σpz – σs,in) at the piezo-material side, and σs,ex at the nonpiezo side) creates additional potential profile at the interface (top curves of Fig. 2(b)). Figure 2(b) illustrates the effect of Ppz on the p-n junction. The original band structure is shown by blue dashed lines, and the band structure modulated by Ppz is sketched in red solid lines. The left and right diagrams, respectively, illustrate situations of positive and negative σpz at the interface. Superimposing the Ppz-induced potential profile onto the original semiconductor band structures resolves the shifted band structure. The greatest band shifting exists at the interface, whereas the band structure remains unchanged far from the interface. With this modification, the built-in potentials and depletion regions in both materials change. Figure 2(b) demonstrates a situation where the σpz is so large that it completely inverts the band tilting direction at the n-type piezo-semiconductor side (for positive σpz, left picture) (a) (d) (d) (d) (b) (c) Figure 1. The new field of piezotronics couples the piezoelectric and semiconducting properties of materials to engineer strain-induced functionality into a wide range of new and familiar materials. or the p-type non-piezo-semiconductor side (for negative σpz, right picture). Metal–semiconductor (MS) heterojunctions are another large category of solid-state devices. Here, the screening length in metal is negligible compared with the semiconductor. Therefore, the Ppz-induced band shifting occurs only on the semiconductor side. Figure 2(c) illustrates a MS Schottky junction. Positive σpz at the MS interface reduces the Schottky barrier height. If σpz is large enough, the Schottky barrier can become ohmic (left picture in Fig. (Credits: (a) Ma; U. Wisc–Madison; (b) Wolf Technical Services for USAF; (c) Wang; U. Wisc–Madison; (d) Wikipedia.) 2(c)). When negative σpz appears at the MS interface, the barrier height is more pronounced and creates a Schottky diode with higher threshold voltage. The existence of Ppz is a steady-state effect as long as the strain is held, although the screening charges prevent external detection of a piezopotential.4 Therefore, applying strain to a piezosemiconductor constantly influences the band structure as described, and it offers an effective strategy to modulate the performance of practical heterojunction based devices. Figure 2. (a) Schematic charge distribution at semiconductor hetero-interface (top) and Ppz-induced charge redistribution (bottom). (b) and (c) Band structure change as a result of the combination of intrinsic and Ppz-induced charge distributions when the piezo-material is (b) n-type semiconductor and the other material is p-type semiconductor or (c) metal. American Ceramic Society Bulletin, Vol. 92, No. 6 | www.ceramics.org 19


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