JOURNAL OF APPLIED PHYSICS 98, 024508 共2005兲

A porous silicon diode as a source of low-energy free electrons at milli-Kelvin temperatures S. Pilla,a兲 B. Naberhuis, and J. Goodkind Department of Physics, University of California, San Diego, California 92093

共Received 12 October 2004; accepted 6 June 2005; published online 25 July 2005兲 We have developed a porous silicon 共PS兲 diode that yields free-electron currents with energies ⬍0.1 eV below 77 K. The power dissipated during emission is low so that pulses of electrons can be produced below 100 mK without raising the temperature of the system. Free electrons were generated in liquid 4He and 3He as well. The device was developed as a source of electrons for a quantum computing system using electrons on the surface of a dielectric film. The results suggest that a Poole-Frenkel type of mechanism accounts for the observed electric-field-enhanced conduction but the electron emission mechanism is not well understood in the present models of PS. © 2005 American Institute of Physics. 关DOI: 10.1063/1.1988972兴 I. INTRODUCTION

For more than a decade there has been interest in the electrical and optical properties of porous silicon 共PS兲 since it can provide efficient photoluminescence in the visible region, above the band gap of c-Si.1,2 PS is produced by electrochemical etching of crystalline, doped Si in a hydrofluoric acid 共HF兲 electrolyte. The resulting material is an interconnected fractal network of small crystallites with typical size of 3–5 nm.1 The fractal structure is characterized by a typical length scale of ⬃10–100 nm. Efficient photoluminescence in PS is closely linked to quantum confinement of carriers inside the small crystallites, which results in an increased band gap and reduced concentration of thermally activated carriers. In addition, a high density of surface states, e.g., dangling bonds, has been observed due to the large internal surface area of the PS 共⬃500 m2 / cm3兲. This results in a relatively large density of states close to the Fermi level 关N共EF兲 = 1019 eV−1 cm−3兴 in the, otherwise, forbidden gap of the bulk crystallites.3 In the previous dielectric relaxation and transport measurements4 it was concluded that the presence of the two length scales described above were responsible for the observed behavior of the complex dielectric function and conductivity of PS in the 200–400-K tmperature range. At high temperatures and low frequencies the conductivity is attributed to the random walk of charge carriers along the fractal network, for which ␴共␻兲 ⬀ ␻⬃0.5, while at high frequencies the conductivity, ␴共␻兲 ⬀ ␻, is due to activated hopping between neighboring crystallites 共the average distance between crystallites is also 3–5 nm兲.3 The band-gap model adopted in these papers also includes, at high temperatures, carriers activated to extended states above a mobility edge at ⬃0.45 eV.5 This activation energy was identified with the reciprocal of the energy-level density at the Fermi surface N共EF兲 共Ref. 3兲 and several experiments find the same value. Many of the results published so far can be understood in a comprehensive one-dimensional energy-band diagram of a兲

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metal/ PS/ Si structure4,5 but no detailed model of the system appears to explain all of the experimental observations. In all of this work, there was limited effort to study either the mechanism behind the low-energy free-electron emission, observed along with efficient photoluminescence in thin layers of PS, or the electrical transport at low temperatures. There were no studies to verify the applicability of the present models down to mK temperatures. It has been proposed that electron emission for dc bias at room temperature in thick 共3–10 ␮m兲, modulated, and graded 共density dependent on depth兲 PS layers is quasiballistic, i.e., the energy of the emitted electrons scales with the applied voltage.6 However, for ungraded or thin layers 共⬍0.5 ␮m兲 this model does not explain the data and the data available in the literature are not adequate to propose a model for electron emission. In the present work we discuss the electrical transport properties in the free-electron emission regime over three orders in temperature and frequency. We show that a PS diode can be used as a reliable source of free electrons at temperatures down to the mK range. Our interest in developing this source of low-energy electrons was for its application to a system of quantum logic gates using electrons on a helium film,7–9 where the kinetic energy of the electrons sprayed on the liquid surface must be ⬃1 eV so that they will not penetrate the film. II. EXPERIMENT

We prepare the PS by photoanodization of doped n + Si共100兲 wafer 共0.005–0.02 ⍀ cm兲 in a 48%–50% aqueous HF: ethanol solution with a 1 : 1 concentration, for 20–40 s under a white halogen light source with 8–11-mW/ cm2 intensity near the wafer surface.10 The anodizing current density is 30–35 mA/ cm2. In addition, it is treated by RTO 共rapid thermal oxidation兲 in a turbulence-free flow of dry oxygen at 900 °C for 5–6 min. The diode is formed by evaporating a metal contact 共ohmic兲 on the back of the wafer and 10/ 70 Å of Cr/ Au on top of the PS. We reproduced the previous results by Pavesi et al.2 and Koshida et al.,6 in thick PS diodes at room temperature; however, these did not yield emission electrons at 77 K or lower temperatures. Our de-

98, 024508-1

© 2005 American Institute of Physics

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TABLE I. Parameters from the PF fits for the data in Figs. 1 and 2. 1 / 冑V* vs 1 / T

ln共␴0兲 vs 1 / T T range 共K兲 150–90 150–98 115–80 80–30 30–5 5–1 1–0.15

Intercept 21.3 -5.8 -13.9 -17.6 -14.2 -11.0 -28.1

Slope 共eV兲 -0.442 -0.048 -0.048 -0.018 −7.6⫻ 10−3 −1.96⫻ 10−3 −5.6⫻ 10−5

Intercept -4.85 0.6 1.6 0.45 0.5 1.87

1 / 冑V* vs 1 / ␶

ln共␴0兲 vs 1 / ␶ Curve Fig. 2 FIG. 1. Sample plots of conductivity 共␴兲 vs 冑VPS at 共a兲 153 K, 共b兲 and 共c兲 92 K, 共d兲 114 K, 共e兲 90 K, 共f兲 4.2 K, and 共g兲–共j兲 T ⬍ 1.2 K. The inset shows the schematic of the test setup and the wave form used for obtaining IPS-VPS curves. The pulse duration ␶ is defined in the diagram. For clarity, the weakly temperature-dependent ohmic contribution 共Rohmic ⬎ 100 M⍀兲 is subtracted from the data. All the curves are obtained with Vacc = 20 V and ␶ = 0.01 s. The active surface area of the diode is 0.5 cm2.

vices consist of thin porous layers 共⬍0.5 ␮m兲 and produce emission electrons down to the mK temperature range. Under continuous dc bias conditions at room temperature these devices deteriorate very quickly but, when biased with 1–100-ms pulses at a repetition rate 艋2 Hz, the diodes are robust. III. RESULTS AND DISCUSSION

Figure 1 includes a schematic diagram of the system used to obtain the I-V curves. The data show that at a fixed temperature T, ln共IPS / VPS兲 ⬀ 冑VPS is in agreement with the Poole-Frenkel 共PF兲 mechanism, given by11

␴ = ␴00e−eEA/kTe

冑V/V*

,

冑V* = kT/e冑e/␲⑀0⑀d,

共1兲

where ⑀共⯝10兲 is the effective dielectric constant, d is the PS layer thickness, ␴00 is a temperature-independent prefactor, and EA is the activation energy. According to this onedimensional, thermally activated hopping transport model for dc conductivity, ln共␴0兲 should be linear in 1 / T, where ␴0 = ␴00e−eEA/kT. Figure 1 shows the data for two different samples in the 150–0.15-K temperature range and Table I lists the parameters obtained by fitting PF equation to the data in different temperature ranges. The data demonstrate that for T ⬎ 90 K, the conduction is due to activation to a mobility edge with activation energy of 0.44 eV 共5131 K兲. This value is in good agreement with the previous results.4,5,11 At lower temperatures, the conduction is due to activation to different groups of trap states near the Fermi level which were also identified in other experiments.4 For example, at 92 K 关curves 共b兲 and 共c兲 in Fig. 1兴 conduction results from the carriers activated to the mobility edge as well as to the trap states with activation energy of 0.048 eV 共563.9 K兲. Although our measurements do not use sinusoidal ac voltages, we plot ␴0 in the limit VPS = 0 共Fig. 2兲, as a function of 1 / ␶ so as to compare to the frequency dependence predicted for the two length scales in PS. The linear

Intercept -22.7

Slope 共V−1/2兲 931.8 107.9 31.6 6.6 2.25 0.04

Slope 0.98

Curve Fig. 2

Intercept 1.47

Slope -0.1

dependence of ␴0 on 1 / ␶ in Fig. 2 implies that the transport at these temperatures is predominantly due to hopping between neighboring crystallites.3 However, the anomaly in 1 / 冑V* at 1 / ␶ ⯝ 170 Hz indicates a departure from the linear dependence for finite voltages. Figure 3 shows the dependence of IE on IPS, as well as the emission efficiency 共IE / IPS兲, and the energy dissipated/ pulse as a function of ␶ at various temperatures. It displays a number of features that cannot be explained by the existing models for PS. The linear dependence of IE on IPS shows that the fraction of electrons which escape the PS crystallites and the gold film is independent of VPS at a given T. This is in contradiction with the results of other workers on a variety of systems at higher temperatures. The peak in efficiency 共as a function of ␶兲 occurs at about the same value of ␶ as the minimum in ␴ 共see anomaly in Fig. 2兲 indicating that these effects may be related. An additional feature of our data is that the emission efficiency increases by two orders of magnitude when cooled from 77 to 1 K and plateaus for T ⬍ 1 K. The PF model is derived by considering only the change in carrier density which depends exponentially on the depth of the trap corrected for the applied electric field. It is assumed that the carrier mobility 共where ␴00 ⬀ ␮兲 is independent of temperature and voltage. However, in recent time-of-

FIG. 2. ln共␴0兲 共open square兲 and 1 / 冑V* 共open circle兲 as a function of 1 / ␶ at T = 4.2 K and Vacc = 20 V for a sample anodized under a 30-mW/ cm2 white light for 30 s with a 30-mA/ cm2 current density, RTO treated for 5 min, and annealed for an additional 0.5 min in dry N2 at 900 °C. The arrow indicates the departure from the linear dependence of 1 / 冑V* at 1 / ␶ ⯝ 170 Hz.

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FIG. 3. 共a兲 Emission current 共IE兲 vs diode current 共IPS兲 and 共b兲 emission efficiency 共IE / IPS兲 共open square, open circle兲 and energy dissipated per pulse 共solid circle兲 at 4.2 K and 共c兲 at 300 mK. The height of the voltage pulse max 兲 is the same for all pulse widths in each plot 共b兲 and 共c兲. The samples 共VPS are the same as in Fig. 1 with the open circles and open squares representing 20 and 30 s of anodization. The efficiency at 77 K is ⯝9.1⫻ 10−7.

flight 共TOF兲 experiments on nanoporous silicon,12 amorphous Si,13 and other disordered systems14 it has been shown that the drift mobility 共defined as ␮ = d2 / ttrV, where ttr is the carrier transit time兲 is also an activated process 共with activation energies comparable to the PF model兲 and ␮ ⬀ exp共冑V兲 as well.14 The temperature dependence of mobility results from two independent processes. The reduction in mobility with lowering temperature results when carriers are immobilized for an increasingly longer time on a given trap. On the other hand, mobility can increase when the carrier is untrapped and mobile within the pores due to the corresponding decrease in thermal disorder with temperature.12 These two processes are unlikely to cancel each other in PS. The net decrease of ␮, in our samples, may explain the disagreement between our data 共Table I兲 and the PF model 关Eq. 共1兲兴, for which the slope for 1 / 冑V* vs 1 / T is expected to be ⬃393 V−1/2 and independent of T. It may also explain the observed increase in the emission efficiency with decreasing temperature because only the untrapped electrons contribute to the emission current and the probability for escape from the barrier 共top electrode兲 increases with an increase in the kinetic energy of the electron. The vacuum in the pores is imperfect because an electron inside a pore would still be weakly bound to the surrounding dielectric medium via weak image charges. Although we do not have experimental values for the frequency dependence of the dielectric loss of PS in the relevant temperature range, based on the available data,3 the dielectric loss of PS is expected to decrease with temperature. Such a reduction can have a direct bearing on the average kinetic energy of the electrons within the pores. The peak in efficiency at 1 / ␶ ⯝ 170 Hz could then result, first, from the increase in the number of carriers that can reach neighboring trapping sites as ␶ increases. At still longer ␶ partial charging of the porous network seems to reduce further gain in efficiency. Measurement of the energy distribution of emitted electrons, described next, supports this hypothesis.

J. Appl. Phys. 98, 024508 共2005兲

FIG. 4. Radial position r共E兲 on the diode surface vs initial energy E required for the electron to escape from the diode and reach the collector plate 共see inset兲. The family of 18 curves at various Vacc listed above are based on electron trajectory calculations for VPS = 12.5 V and Vg = 0 V. The image forces are accounted from 10 nm away from the diode surface. The inset shows the schematic of the energy analyzer setup for measuring emission currents and energy distribution of the electrons. The base plate of the Cu sample cell is in direct contact with the liquid-nitrogen bath. A 0.5-mm-thick sapphire block with a gold layer thermally evaporated onto the top surface is placed between the PS diode and the base plate. Excellent thermal grounding is achieved when the PS diode with its back Au electrode in electrical contact with the Au layer on the sapphire block is mechanically clamped to the base plate using teflon clamps 共not shown兲.

The inset in Fig. 4 shows the schematic of the experimental setup for measuring the energy distribution of the emission electrons. In the previous setup 共Fig. 1兲, the gap between the diode and the collector plate was held at 1 mm and a constant accelerating field ⬎20 V / mm was applied across the gap. For this accelerating field, IE saturated to its maximum value independent of VPS and T. In addition, IPS and IE were held low 共IPS ⬍ 1 mA mA at 77 K兲 to study the I-V characteristics of the diodes without heating or charging the pore structure. To study the energy distribution, however, we require large emission currents because of the limited sensitivity of the electrometer. This required modification of the experimental setup used to measure the diode characteristics. In the energy analyzer configuration of Fig. 4, the diode is in vacuum but excellent thermal grounding is provided by mechanically clamping the diode to the base plate of the sample cell. The sapphire block provides excellent electrical insulation as well as good thermal conduction at low temperatures. The active surface area of the diode is increased to ⬃1 cm2. Various electrodes are biased as shown in Fig. 4, where VPS is the voltage applied across the diode, Vacc = Vc − Vbias is the net accelerating voltage experienced by the emission electrons, and Vg is the voltage on the guard ring. Under such bias conditions, the emitted electrons experience not only the accelerating field 共from Vacc兲 but also the fringe fields from the diode substrate 共from the portion of the chip not covered by the top electrode兲 and fields from the image charge of the electron in the top electrode. The image field will dominate the behavior of electron trajectories when the electron is only a few nanometers away from the surface. The fringe fields generated by Vacc and VPS on the other hand

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FIG. 5. Emission current IE at 77 K for Vacc in the 0–150-V range. The inset shows the bias voltage VPS across the diode and the corresponding diode current IPS. VPS and IPS remain the same for all traces at different Vacc.

dictate the position-dependent escape energy 共i.e., minimum initial energy E兲 above which the electrons can reach the collector plate. Due to the inherent cylindrical symmetry 共except at the corners of the chip兲, we consider only the radial position r on the diode surface measured from the symmetry axis of the top electrode, guard ring, and circular collector plate. Figure 4 shows a family of r共E兲 vs E curves at different Vacc values. These curves are obtained by computing the electric fields in the energy analyzer for a given set of 兵Vacc , Vg , VPS其 values using finite difference methods.15 Electron trajectories are computed based on these electric fields for a given r, initial distance z from the top electrode, initial angle 共from normal to the diode surface兲 of emission, and initial energy of the electron while taking the image field into account. Here we assume that the initial energy distribution of the emitted electrons is uniform throughout the diode surface. Initial energy is increased until an electron trajectory is terminated only on the collector plate. This minimum energy required increases as r increases because of the fringe fields but decreases as the normal component of the electric field is increased by increasing Vacc. Thus, the emission current 共IE兲 observed at a given Vacc will be IE = a

冕

␲r共E兲2 f共E兲dE,

共2兲

where a is a normalization constant, r共E兲 is the radial distance on the surface of the diode 共Fig. 4兲, and f共E兲 is the emission current density of electrons for a particular initial energy E. By measuring IE at various Vacc values one can invert the above equation to obtain the energy distribution f共E兲. Figure 5 shows IE measured for Vacc in the 0–150-V range. The inset shows the pulse shape for VPS and IPS. During the 20-ms-long forward bias of 12.5 V, IPS is constant at ⬇35 mA. The current through the diode during the remaining time with reverse bias of ⬃−8 V is ⬍50 ␮A. The IE curves shown here fit very well to a second-order exponential decay of the form

FIG. 6. 共IE兲0 vs Vacc plot for the traces in Fig. 5, where 共IE兲0 is given by Eq. 共3兲. The scattered points in the inset show data for Vacc = 30 V while the solid curve is the fit based on Eq. 共2兲, where r共E兲 is from Fig. 4 and f共E兲 is from Fig. 7. The dashed curve in the inset shows the fit when f共E兲 follows a lognormal distribution 共Fig. 7兲, where ␮ = 0 , ␴ = 1.6, and the scale parameter m = 0.14.

IE = 共IE兲0 + A1e−t/t1 + A2e−t/t2 .

共3兲

The time constants t1 and t2 are 2.5⫻ 10−4 and 0.007 s, respectively, for all traces in Fig. 5. The signal with a smaller time constant results from the direct coupling of the voltage pulse VPS through the vacuum feedthroughs to the electrometer lead. The observed time constant is in agreement with the time constant of the electrometer circuit. The slower exponential decay is, however, intrinsic to the diode emission behavior. We attribute it to partial charging of the porous network during the forward conduction of the diode. If the pulse shape for VPS is such that we do not apply any reverse bias either during or after the pulse, we observed continual decrease in emission from pulse to pulse with complete suppression of emission after a few hundred pulses. Although partial recovery of emission is achieved by reverse biasing or electrically grounding both terminals of the diode for a long time 共⬃1 h兲, full recovery is achieved only by thermal recycling to room temperature while keeping both terminals of the diode grounded during the thermal cycle. However, for the particular pulse shape for VPS shown in Fig. 5, the emission current is stable over several hours of continuous pulsing where the delay time between successive pulses can be as short as 0.5 s. Due to strong thermal grounding, no heatinginduced variations in conduction are observed even when the delay between pulses is 0.5 s. Soon after cool down, however, we need to apply a few hundred pulses before the emission current stabilizes to the values shown in Fig. 5. Under these conditions, the emission current is stable to ⬃1% rms deviation for pulse widths up to 40 ms and 0.5–10-s delay between successive pulses. To obtain the energy distribution of the emission electrons, we plotted 共IE兲0 values by fitting Eq. 共3兲 to various traces in Fig. 5. Although both 共IE兲0 and A2 show similar dependence on Vacc, in Fig. 6 only 共IE兲0 values are plotted. The inset in Fig. 6 shows the data for Vacc ⬍ 30 V in greater

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Pilla, Naberhuis, and Goodkind

FIG. 7. Energy distribution f共E兲 which satisfies Eq. 共2兲 for the experimental data in Fig. 6. The main plot shows the distribution in log scale 共solid curve兲 while the inset shows the same distribution in linear scale. A lognormal distribution 共dashed curve兲 with ␮ = 0 , ␴ = 1.6, and the scale parameter m = 0.14 is included for comparison.

detail along with a fit based on Eq. 共2兲 using r共E兲 values shown in Fig. 4 and energy distribution f共E兲 shown in Fig. 7. Our observations indicate that the above fit is more sensitive to f共E兲 than to the angular dispersion of the electrons near the surface of the diode. As the electron flux is mostly normal to the diode surface,6 in r共E兲 calculations we assumed angular dispersion of ±5° from the normal. Also, r共E兲 curves in Fig. 4 are obtained while accounting for image forces when the separation between the electrons and the top electrode 共z兲 is 艌10 nm. Thus, f共E兲 shown in Fig. 7 is the distribution of electron energies at a distance z = 10 nm from the top electrode. The lowest escape energy ⬃0.036 eV关共1 / 4␲⑀0兲共e / 4z兲兴 in Fig. 4 results from this assumption. For z = 5 nm the corresponding escape energy is ⬃0.072 eV. If the energy scale is increased by 0.036 eV, f共E兲 at z = 5 nm remained identical to the one shown in Fig. 7. Thus, the energy distribution shown in Fig. 7 represents the energy of all electrons that leave the pores and gain an elevation of 10 nm from the surface without being captured back into the top electrode when the accelerating field is ⬍2 V / mm 共i.e., Vacc 艋 30 V兲. While computing r共E兲 curves in Fig. 4, we assumed that the image field is uniform throughout the ⬃1-cm2 active area of the diode. However, variations in the surface roughness over a large area of the PS can result in variations in the image field. It is estimated that f共E兲 in Fig. 7 may have an error ⬍0.1 eV resulting from a distribution of these image fields. Figure 7 clearly shows that ⬎95% of the electrons are emitted with energy ⬍0.1 eV. For Vacc ⬎ 30 V we will be extracting even lowerenergy electrons in the distribution 共see Fig. 6兲 as IE at Vacc = 150 V is more than three times the value at Vacc = 30 V. The distribution in Fig. 7 is rather unusual. Two features in f共E兲 standout when compared to either lognormal or exponential distributions 共only lognormal is shown兲. For E ⬎ 1 eV, it is similar to the distribution at room temperature obtained by several authors.6,16,17 Based on the shift in the

J. Appl. Phys. 98, 024508 共2005兲

peak of the energy distribution with bias voltage 共VPS兲 in these room-temperature experiments, it was proposed that the emission is due to quasiballistic transport of carriers within the pores. The sharp rise in f共E兲 for E ⬍ 0.2 eV is unique to our samples operating at T 艋 77 K. We suggested earlier that the increase in the emission efficiency may be due to the increase in mobility of untrapped electrons as T decreases. The behavior of f共E兲 for E ⬍ 0.2 eV strengthens this hypothesis as the basic emission mechanism is kinetic in nature, i.e., untrapped electrons are accelerated by the strong electric fields within the pores and those with sufficiently high kinetic energy can escape the metal barrier. As we have a large pool of electrons with low kinetic energy 共IPS is several milliamperes when compared to IE of several nanoamperes兲, even a small increase in the kinetic energy of electrons can result in the dramatic increase in emission at low E that we observed in Fig. 7. Further work on the temperature dependence of the mobility of electrons in the emission regime is necessary to better understand the results presented so far including charging effects within the pore structure. In the recent room-temperature experiments, a spread in energy distribution was reported with the increase in top electrode film thickness in the 5–40-nm range.17 In our experiments at low temperatures, we observed a rapid drop in the emission current for Cr/ Au film ⬎10 nm while for thickness ⬍5 nm the film was discontinuous. Therefore, in the limited range of film thickness available, we did not explore the relationship between the energy distribution and the film thickness. In other experiments we used the PS diode along with a superconducting transition-edge bolometer operating at 290 mK which has a sufficient sensitivity to detect a single electron with a kinetic energy ⬍10 eV. We detected on average less than a single electron per pulse for VPS = 15 V and ␶ = 4 ms. From the extrapolation of the curve fits in Figs. 1 and 3共a兲, we estimate that ⬃2500 electrons/ pulse are emitted for the above bias conditions at 290 mK. The observed ⬃1 electron detection is consistent with the ratio of the areas of the detector and the diode, assuming a uniform electron flux.6 This is evidence that the emission efficiency is independent of the applied voltage down to very low voltages. We have obtained stable emission even in the presence of liquid 4He and 3He films on the diode surface. In the case of 4He, no change in emission was observed when the temperature is lowered below its superfluid transition temperature of ⬃2.2 K. However, IE in either liquid 4He or 3He is about 5–10 times smaller when compared to emission in vacuum for the same VPS and Vacc values. Increase in the thermal conductivity 共when the pores are filled with liquid He兲 of the porous network and additional barrier of ⬃1 eV in liquid He for the escape of the electrons may be responsible for the observed behavior. Although, the presence of a few Torr of N2 or He gas at T 艋 77 K did not affect the emission, exposure of the diodes to He gas at room temperature completely suppressed it when these samples are cooled. Emission was recovered only after thorough pumping of the diodes at room temperature for several hours or by leaving the samples in dry He-free atmosphere for several weeks. When the samples

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are operated in liquid He, gas was thoroughly pumped out before the sample temperature is raised above 77 K to avoid the He gas poisoning of diodes. IV. CONCLUSIONS

In conclusion, we have demonstrated a robust electron source based on porous silicon that can be operated over a wide temperature range from 100 K to 75 mK. At 77 K, ⬎40 nA/ cm2 of free-electron currents are obtained for a forward bias voltage of 12.5 V. The emission current is stable to ⬃1% rms deviation over several hours of continuous operation when the diode is biased with square pulses up to 40 ms long and 0.5–10-s delay between successive pulses. Also, presence of a few Torr of N2 or He gas did not affect the emission characteristics. The energy distribution of the emitted electrons is unusual with ⬎95% of electrons having ⬍0.1-eV energy near the emitting surface. The PooleFrenkel-type conduction mechanism seems to explain the observed I-V response over the 150-K to 75-mK temperature range studied. Several groups of trap state levels near the Fermi energy that are identified contribute to the hopping transport in different temperature ranges. For T ⬎ 90 K, the conduction was predominantly due to the activation to mobility edge at 0.44 eV, in agreement with results published by other workers. The emission efficiency was observed to be independent of the bias voltage and to increase from ⬃9.1 ⫻ 10−7 at 77 K to ⬃8.1⫻ 10−4 at T ⬍ 1.2 K. The increase in efficiency with decreasing temperature, the unusually high density of emitted electrons with energy ⬍0.1 eV, and a few other anomalies in the temperature dependence of the conductivity are attributed to the carrier mobility when they are untrapped and mobile within pores. Further work on the dielectric loss and carrier mobility in the emission regime are required to verify the hypothesis. We have also obtained stable emission in the presence of liquid 4He and 3He films on the diode surface. In the case of 4He, no change in emis-

sion was observed when the temperature is lowered below its superfluid transition temperature of ⬃2.2 K. We believe the source is ideally suited for several low-temperature applications including a quantum computing scheme using electrons on liquid-He film7–9 and other applications that require stable, ultralow dispersion electron source such as electronbeam lithography and microscopy.18 ACKNOWLEDGMENTS

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