ENERGY LOSS MECHANISM FOR HOT ELECTRONS IN GaAs

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ENERGY LOSS MECHANISM FOR HOT ELECTRONS IN GaAs

D. Neilson, J. Szymanski, De-Xin Lu

To cite this version:

D. Neilson, J. Szymanski, De-Xin Lu. ENERGY LOSS MECHANISM FOR HOT ELECTRONS IN GaAs. Journal de Physique Colloques, 1987, 48 (C5), pp.C5-263-C5-266. �10.1051/jphyscol:1987556�.

�jpa-00226760�

JOURNAL D E PHYSIQUE

Colloque C 5 , suppl6ment au null, Tome 48, novembre 1987

ENERGY LOSS MECHANISM FOR HOT ELECTRONS IN GaAs

D. NEILSON, J. S Z Y M A N S K I ( ~ ) and D E - X I N L U ' ~ '

School of Physics, University of New South Wales, P.O. BOX 1 , Kensington NSW 2033, Australia

RBsumB. Nous avons Ctudik systCmatiquement le mecanisme de la perte d'knergie des Clectrons chauds inject& dans une couche mince dopCe de GaAs. Les Cnergies incidentes sont gardkes en dessous du seuil de diffusion entre-val. On trouve que pour les densitks de porteurs typiques de celles utiliskes dans les appareils de GaAs, les pertes d'Cnergie sont dominCes par les processus d'excitations semblables A pure Clectrons.

A b s t r a c t . We have systematically investigated the energy loss mechanisms for hot electrons injected into a thin doped GaAs layer. Incident energies are kept below the threshold for intervalley scattering. We find for carrier densities typical of those used in many GaAs devices, the energy losses are dominated by pure electron- like excitation processes.

1. I n t r o d u c t i o n

In this paper we investigate the importance of the various different scattering mechanisms on the transport of hot injected electrons in GaAs. Let us consider a typical ballistic hot-electron device, the Planar Doped Barrier (PDB) transistor.[l] Electrons are injected from the emitter into the narrow base layer.

We deal here with the limitations to the performance of such a device due to the scattering of the electrons in the base region leading t o non-baliistic transport. To keep the RC delay time associated with the base emitter capacitance t o less than 1 ps the base region width needs to be

> 1000A, and the dopant concentration

-

10'~cm-~.[2]

A hot electron injected into the base region can (i) excite a coupled optical-phonon

/

^plasmon

mode, (ii) excite an electron-hole pair, or (iii) it can elastically scatter off one of the ionised dopant impurities.

The total dielectric for the system is

where epl(& w ) is the dielectric function for the electrons and eph(w) the optical phonon dielectric function. Even a t n = 1 0 ~ ~ c m - ~ the effective r: value for GaAs is less than unity and epl($ w) is well approximated by the R.P.A. expression. We can write ePh(w) in the form

Figure 1 shows the regions in q', w phase space for the various excitation modes of the system.

The imaginary part of el$, w) is non-zero in the shaded region. This is the single-particle excitation region which is bounded by the parabolas w(q) = q2 f 29 where hw(q) is expressed in units of the Fermi energy

EF,

and hq in units of the Fermi momentum hkF. Outside the shaded region the zeroes in the function E($,w) determine the dispersion curves for the optical phonon/plasmon modes. These are the curves labelled 1-3 in the figure. Because the plasmon frequency wpl and the optical phonon frequency w~ are similar, the modes hybridise. For densities n

>

8 x 10"crn-~, the plasmon frequency wpl

>

WL, and Branch 1 consists of plasmon-like excitations interacting

( l ) ~ e l e c o m Australia Research Laboratories. 770 Blackburn Road, Clayton Vic. 3168. Australia (2'~ermanent address : Physics Department, Nanjing University, China

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987556

C5-264 JOURNAL DE PHYSIQUE

with phonons while those in Branch 3 are phonons screened by the electrons. For densities n <

8 x 10"c1n-~ the roles of Branches 1 and 3 reverse. In both density ranges Branch 2 is LO phonon-like and approximately follows the uncoupled LO phonon mode. It is found only in the small wave-length region of phase space.

2. Calculations

A hot electron of energy

-

300meV injected into the n-doped base region of a PDB transistor encounters an electron gas typically with Fermi energy EF m 40meV. The incident momentum hpo is much greater than the Fermi momentum hkF so that the Born approximation for the scattering probability will be valid.[3]

Figure 1: Excitation modes of the electron gas which is confined in the n-type base region. The plasmon and optical phonon modes hybridise into the Branches wl(q) and ws(q) as shown. The shaded region is the permitted phase space for single-particle excitations. w2(q) is the nearly pure LO phonon mode which occurs for large q.

The probability per unit time that the hot electron will couple t o one of the excitation modes of the electron gas, transferring momentum hq and energy hw is then given by [3]

4ne2

P(q7 w) = -2 -1m

e-'(3

w ) . q2

The corresponding differential energy loss rate with distance is

where the energy transfer is hw = (efi

-

e f i - q ) .

We can also define the rate of Ioss of p l , the component of the momentum ~erpendicular to the barrier.

1 d ~ l

- -

--- - ,

PO dz

2

^{PO d z}

.,

I f i - 4 > k r ldP"]

where ~ ~ ' ( d p ~ / d z ) , ~ is the rate of loss arising from elastic scattering off ionised donor atoms (Rutherford scattering).

3. R e s u l t s

In Eq. (1) there are contributions to Im W ) from the three coupled optical phonon/

plasmon normal mode excitations [4] and also from single electron excitations. In Tables l ( a ) and 2(b) we show the separate contributions to ~ i ' ( d ~ ~ / d z ) and P~l(dpl/dz) for an electron of incident energy Eo = 3OOmeV injected into the base region. The electron densities in the base region range from 10" to 3 x 1 0 ' ~ c m - ~ . Table l(a) shows clearly that the two dominant scattering mechanisms for E ~ ' ( d ~ ~ / d z ) are the plasmon-phonon coupled mode i = 1 and the single-electron excitations. In Table l(b) we see that for p;'(dpl/dz) all the modes and, as well, the elastic scattering off the dopant impurities can make a significant contributioq.

Table 1: Contributions t o (a) energy loss rate ~ i ' ( d ~ ~ / d z ) and (b) loss rate of perpendicular momentum pol(dpl/dz) for a fixed incident energy ofEo = 3OOmeV. The dominant energy loss mechanisms are the i = l mode and the single-particle mode over the entire range of densities shown.

In Figures 2(a) and 2(b) we plot the significant contributions to ~ ; l ( d E o / d z ) and p,'(dp~/dz)

as a function of the incident electron energy. The base electron density here is fixed a t l ~ ~ ~ c r n - ~ . At this density mode i = 1 is predominantly plasmon-like, so the energy loss mechanisms are completely electron dominated. At a much lower density such as n

-

10"cm-~ the single-electron excitations are insignificant. The dominant mode for energy loss is still i=l, but this is now pre- dominantly phonon-like. Phonon excitations thus dominate a t this density, and improved response times could be expected by using a non-polar semiconductor.

We may use our results for p;'(dpl/dz) to deduce the broadening of a pulse of current traversing the barrier. For a thin barrier this estimation is straightforward. Table 2 gives the width of a &function pulse of 3OOmeV electrons crossing a 1000Abarrier for different electron densities in the base region.

Density ( ~ m - ~

1

1 x

lo'? 1

3 x 1017

1

¹ x 10"

1

3 X 10"

Width (ps)

1

^0.01

^]

^0.02

1

^0.03

1

^0.04

Table 2: Approximate broadening of a 6-function pulse after traversing a base region of thickness

ioook

Acknowledgements. One of us (J.S.) acknowledges the approval of the Director of Research, Telecom Australia Research Laboratories, to publish this paper.

JOURNAL DE _PHYSIQUE

Figure 2: (a) Total energy loss rate EG1(dEo/dz)

,

and contributions to it from the k = 1 mode

~ ~ ~ ( d E ~ / d z ) ~ = ~ and the single-particle mode ~ ; ' ( d E ~ / d z ) , ~ as a function of the incident energy Eo. The density is n = 1 0 ' ~ c m - ~ . (b) Total perpendicular momentum loss rate p,'(dpl/dz) for the same density. Also shown are the contributions from the individual modes and from elastic scattering.

References

1. R. M a l i , T. AuCoin, R. Ross, K. Board, C. Wood and L.Eastman, Electron Lett. 16, (1980) 837.

2. S. Luryi and A. Kastalsky, Physica 134B, (1985) 435.

3. D. Pines and P. Nozieres, The Theory of Quantum Liquids (Benjamin, New York) 1966.

4. S. E. Kumekov and V. I. Perel', Sov. Phys. Semicond. 16, (1983) 1291.