Monte Carlo Simulation of Electron and Radiative Emission from Silicon Diodes

Size: px

Start display at page:

Download "Monte Carlo Simulation of Electron and Radiative Emission from Silicon Diodes"

Shonda Wells
5 years ago
Views:

1 SIMULATION OF SEMICONDUCTOR DEVICES AND PROCESSES Vol. 4 Edited by W. Fihtner, D. Aemmer - Zurih (Switzerland) September 12-14, Hartung-Gorre 521 Monte Carlo Simulation of Eletron and Radiative Emission from Silion Diodes H.M.J. Boots, C.G.C. de Kort, and M.F.II. Shuurmans Philips Researh Laboratories, Postbns 80000, 5600 JA Eindhoven, The Netherlands D. Arnold 1 and J.M. Higman Bekman Institute, University of Illinois at Urbana-Champaign, TJrbana, IL 61801, USA Abstrat Two experimental methods to determine an eletron temperature T e, eletron emission and radiative emission from a silion old athode, ar analyzed by Monte Carlo simulation. It is shown that even within the same energy range, these methods yield different values for the eletron temperature. Monte Carlo values of 1\ appropriate for eletron emission neither agree with experimental ones, nor with T values extrated from the simulated radiative emission. Experiment and simulation show a non-exponential relation between intensity and frequeny of radiative emission; in the simulation re-absorption of light inside the devie is the main origin of the non-exponential behavior. The onept of eletron temperature plays a entral role in most desriptions of hot eletron effets. In hydrodynami simulation models, the eletron temperature is mostly alulated vising a paraboli energy band, an empirial expression for the heat urrent and empirial dependenies of the relaxation times on the loal eletron temperature. Monte Carlo simulation of hot eletrons yields the energy distribution funtion; if this is non-maxwellian, the usual definition of the eletron temperature does not apply. Experimental heks on model preditions for the eletron temperature are generally not available, sine only very few experimental methods probe the eletron energy distribution. Two of these methods have been applied to the same devie: We have measured the radiative amission from a. p-i-n silion old athode whih had been used before in an eletron emission study [1]. In this paper we present emission results of reverse biased p-i-n and p-n-i diodes and analyze them using the Monte Carlo method. The eletron emitting surfae of a p-i-n (or p-n-i) diode is at the n-side (or i-side) of the devie. These devies, like the p-n old athodes studied before experimentally [2] and theoretially [3], are of pratial interest as effiient eletron emitters; the extra, intrinsi layers failitate physial modeling in the following way: - If the intrinsi layer in a p-i-n diode is wide, the eletron energy distribution in that layer will be lose to the distribution in intrinsi bulk silion in a. onstant eletri field. This redues the problems [2] of spatial transients and of the suggested [2] importane of impurity sattering. - We study p-n-i diodes with different intrinsi layer widths to ompare Monte Carlo and experimental values for the mean free path of high-energy eletrons in a field-free region. It will be shown that this omparison fixes the refletion ondition of non-emitted eletrons at the surfae. 'Present address: IBM Researh Center, Yorktown Heights, NY 10598

2 522 1 Monte Carlo Model The Monte Carlo ode is basially the same as the one desribed in refs. [4,3,5]. It employs two energy bands from empirial pseudopotential alulations over the full Brillouin zone and XX,XL and LL phonon sattering proesses, alulated in the non-paraboli band approximation and adjusted to be onsistent with the atual density of states. Impat ionization is treated by the Keldysh formula with empirial parameters [3,5] and the eletron emission probability is taken to be the same as for paraboli bands. For justifiations of the approximations involved, we refer to the original literature. The light intensity is alulated from the distribution funtion by the Kramers formula for Bremsstrahlung [6], amended to apply to the silion band struture. Reabsorption of the light inside the devie and refletion at the surfae have been aounted for. The eletri field is taken in the depletion layer approximation. 2 Eletron emission In fig. 1 the eletron emission effiieny r\ is plotted as a funtion of the work funtion <f>. In the experimentally aessible range of work funtions, j) > 1 ev, the simulated relation between effiieny and work funtion may be desribed by rj = A exp (/>/kbt ee where kg is Boltzmann's onstant and A depends at most weakly on (f>; T ee is an effetive temperature for eletron emission. For a Maxwellian distribution one expets T ee to be equal to the eletron temperature T e. Although there is a substantial satter in the experimental values of T ee, mainly due to limited ontrol on proess variations between different devies, fig. 1 and table I show learly that the experimental value of T ee is systematially lower than the Monte Carlo value. In fig. 2 the deay of the effiieny of a p-n-i devie with the intrinsi layer width is plotted. This deay is haraterized by a mean free path of high-energy eletrons in a field-free region, whih from the simulation is found to be 6 nm. The experimental data are sattered in a zone whih is very well desribed by the same mean free path. A muh slower deay with top layer thikness has been reported in fig. 3 of ref.[3]. There a different refletion ondition was used for eletrons that did not esape at the surfae; the agreement between the present experimental and theoretial results onfirms the model assumption that non-emitted eletrons are absorbed at the surfae ontat rather than refleted. 3 Radiative emission The experimental urves in fig. 3 show the radiative emission spetrum of a p-i-n old athode with an intrinsi layer width of 45 nm and an n-doped layer width of 25 nm. There is no signifiant effet of varying the bias voltage between 6 and 10 V. The same is found for the orresponding simulated spetra and an be traed bak to the insensitivity of the high-energy tail of the distribution funtion to variations in this range of voltages. For a Maxwellian highenergy tail of the distribution funtion, the intensity I is related to the energy E through / o ex.p E/kBT e. The simulated and experimental intensities are lose, but the experimental spetrum has a stronger non-exponential behavior than the simulated one; the non-exponential harater of the simulated spetrum is largely due to the re-absorption and refletion of the radiation inside the struture. In order to make a simple omparison between eletron and radiative emission, we plotted in fig. 4 the Monte Carlo results for an idealized p-i-n devie, onsisting of a 100 nm intrinsi layer of onstant high field, with an infinitely small n-doped layer. It is lear that eletron

3 temperatures found from the average slopes of the urves in this figure, differ signifiantly between radiative and eletron emission. 4 Conlusion We have shown that the onept of eletron temperature beomes ill-defined due to the non- Maxwellian nature of the distribution funtion. Effetive values of T e extrated from eletron emission experiment are higher than the values obtained from radiative emission results alulated by the same Monte Carlo ode in the same range of energies. The eletron temperature values obtained from eletron emission experiments are lower than those predited by the ode. Table I. Eletron temperatures T ee and T er, from eletron and radiative emission, as alulated from the Monte Carlo results of fig.4, ompared with values obtained from eletron emission experiments. Fi is the field in the intrinsi layer. \Fi\ (MV/m) Monte Carlo kbt ee kbt ei. (ev) (ev) exp. kstge (ev) Referenes [1] P. A. M. van der Heide, G. G. P. van Gorkom, A. M. E. Hoeberehts, A. A. van Gorkum, and G. F. A. van der Walle, "Silion old athodes based on PIN diodes" Inst. Phys. Conf. Ser, No. 99, Setion 5, p. 141, [2] G. G. P. van Gorkom and A. M. E. Hoeberehts, "An effiient silion old athode for high urrent densities II", Philips J. Res. vol. 41, p. 343, [3] J. M. Higman, K. Kim, K. Hess, T. van Zutphen, and H. M. J. Boots, "Monte Carlo simulation of Si and GaAS avalanhe eletron emitting diodes", J. Appl. Phys. vol. 65, p. 1384,1989. [4] J. Y. Tang and K. Hess, "Impat ionization of eletrons in silion (steady state)", J. Appl. Phys. vol. 54, p. 5139, [5] H. M. J. Boots, M. F. H. Shuurmans, D. Arnold, J. M. Higman, and K. Hess, "Monte Carlo simulation of hot eletrons in silion p-i-n old athodes", Appl. Phys. Lett. vol. 57, p. 2446, [6] T. Figielski and A. Torun, "On the origin of light emitted from reverse biased p-n juntions", Proeedings of the International Conferene on the Physis of Semiondutors, A. Stikland, ed., Institute of Physis, London 1962, p. 863.

4 524 Fig.l Effiieny as a funtion of the work funtion of a p-i-n devie with a p-dope of 8 x m~ 3, a 100 nm intrinsi layer, and a 25 nm top layer 19, with an n-dope of 5 x 10 m the Monte Carlo urve is to be ompared with the experimental data points. o -3, -^ CD O kz LLI Work funtion (ev)» top layer width (nm) Fig.2 Eletron emission effiieny as a funtion of top layer width for p-n-i athodes. Dopes are as in fig. 1. Monte Carlo values obtained with two values of the work funtion <p are ompared with experimental results of many devies.

5 Fig.3 Radiative intensity as a funtion of photon energy for a p-i-n devie with an i-layer of 45nm; other parameters as in fig. 1. Dotted lines are experimental results at 6 V and 10 V reverse bias; Monte Carlo results with (drawn line) and without (dashed urve) absorption and refletion of emitted light are plotted for a 10 V reverse bias. Z5 GO 10" -z, '*** VT*.w* Xs \x X> *\* x T\ t 1 - '! 10-2 i i l 1 1! energy (ev) energy, work funtion (ev) Fig.4 Effiieny as a funtion of the work funtion (dashed) and intensity as a funtion of the energy of the emitted light (drawn) alulated by the same Monte Carlo ode for an idealized p-i-n with a wide (100 nm) i- layer and an infinitesimal n-layer; both fans of urves are plotted for i-layer fields of 2, 1.5, 1, 0.7 and 0.5 MV/m (from top to bottom).

Semiconductor light sources Outline

Semiconductor light sources Outline Light soures Semiondutor light soures Outline Thermal (blakbody) radiation Light / matter interations & LEDs Lasers Robert R. MLeod, University of Colorado Pedrotti 3, Chapter 6 3 Blakbody light Blakbody