Reduction of carrier mobility in semiconductors caused by charge-charge interactions

Abstract

We investigate the effect of charge-charge interactions on carrier mobility in titanium dioxide ͑TiO 2 ͒ and silicon ͑Si͒ using terahertz spectroscopy. Charge scattering times and plasma frequencies are directly determined as a function of charge density. In Si, a linear increase in scattering rate for densities exceeding 10 21 m −3 is attributed to electron-hole scattering. In contrast, in TiO 2 , charge-charge interactions are suppressed due to dielectric screening, highlighting the vastly different dielectric properties for these two materials. DOI: 10.1103/PhysRevB.75.233202 PACS number͑s͒: 72.40.ϩw, 72.10.Di, 72.20.Dp Charge-charge interactions determine many of the properties of highly doped or photoexcited semiconductors. Carrier-carrier collisions, for instance, can strongly affect the conductivity, and the decrease of electron and hole drift mobilities with increasing charge carrier densities is an important factor in determining the current-voltage characteristics of, for example, semiconductor diodes at increased current densities 1 and solar cells under strong illumination conditions. 2 Charge mobility depends on two quantities: its effective mass and scattering time ͑i.e., the average time in-between momentum-randomizing events, due to, e.g., electronphonon scattering͒. Theory has indicated that both of these quantities can be strongly dependent on the free charge density in semiconductors. [3][4][5] Experimental investigations of carrier-carrier interactions are, however, intrinsically more complex, as most experimental techniques ͑such as optical reflectivity measurements 6,7 ͒ cannot easily distinguish between changes in scattering time and effective mass. Terahertz time-domain spectroscopy ͑THz-TDS͒, with its ability to determine both the real and imaginary components of the complex conductivity, 8 allows us to differentiate between density-dependent changes in effective mass from changes in scattering time.Here, we compare the high-density photoconductivity of single crystal silicon ͑Si͒ and rutile-type titanium dioxide ͑TiO 2 ͒, two technologically relevant materials with low and high dielectric functions, respectively. By photoexciting with intense, femtosecond ultraviolet laser pulses and probing with THz pulses, we can generate and measure high-density plasmas in semiconductors on ultrafast time scales, accessing plasma densities spanning 5 orders of magnitude from 10 21 to 10 26 m −3 . In Si, we find that the scattering rate increases linearly for densities Ͼ10 21 m −3 , an effect characteristic of direct charge-charge scattering. For TiO 2 , the variation of the scattering rate with density is much weaker and is caused by band filling effects. The difference between these two materials is shown to originate from their vastly different dielectric screening properties.The TiO 2 ͑1 mm thick 001 rutile crystal grown commercially by the Verneuil method by Crystal-GmbH͒ and silicon ͑0.5 mm thick undoped Si wafer, grown by the Czochralski method with estimated impurity density Ͻ10 13 cm −3 ,...

Assessment of carrier-multiplication efficiency in bulk PbSe and PbS

“…The changes therein, E(t ), following photo injection of charge carriers using femtosecond laser pulses directly reflect the charge carrier density. Figure 1a shows the complex conductivity σ (ω) for PbS (E gap = 0.42 eV) following excitation at 266 nm (4.66 eV), as inferred from the Fourier transforms of the time-domain fields 27 . We follow previous authors 26,27 and fit the data in Fig.…”

“…Figure 1a shows the complex conductivity σ (ω) for PbS (E gap = 0.42 eV) following excitation at 266 nm (4.66 eV), as inferred from the Fourier transforms of the time-domain fields 27 . We follow previous authors 26,27 and fit the data in Fig. 1a with the Drude model of free carriers,…”

“…Hence, a direct comparison between carrier multiplication in bulk and quantum dots requires assessment of bulk carriermultiplication efficiencies on a similar, ultrafast, timescale (see Supplementary Information). Whereas time-resolved optical and infrared spectroscopies are ideally suited to probe carrier populations in colloidal quantum dots 2,5,7,8,10,11,14,15,[17][18][19][22][23][24] , light of terahertz frequencies interacts strongly with free carriers and allows for the direct characterization of carrier density and mobility [25][26][27] . Here, we quantify carrier multiplication in bulk PbSe and PbS on ultrafast timescales using terahertz time-domain spectroscopy 26 (THz-TDS).…”

“…This technique has been used extensively to determine carrier dynamics in semiconductors, as it provides the frequency-dependent complex conductivity σ (ω) of charge carriers 25,27 . We measure in the time domain the electric field of picosecond terahertz pulses transmitted through the unexcited sample E(t ).…”

“…, where ω p is the plasma frequency, ε 0 is the vacuum permittivity and τ r is the carrier scattering time 27 . The plasma frequency is defined as ω 2 p = (e 2 N )/(ε 0 m * ), where m * is the carrier effective mass and N is the carrier density.…”