Field emission from structures with quantum wells

Abstract

Computer simulation studies of the properties of some novel types of field emitters have been carried out in the framework of the theory of quantum disc effects. The following cases have been analyzed in detail. (1) Emission from the field surface states (SS) exhibiting both discrete and continuous energy spectra. This case resembles the known effect of the work-function deterioration ΔW∼(Ec−ESS), yet, here, prior to the emission into vacuum, the SS electrons must be excited the conductivity band via the Pool–Frenkel mechanism: ne≂C exp(aEs1/2/kT), or some other. (2) Emission from the δ-doped structures via the internal field ionization of filled states, deposited near to surface in semiconductor or in super-thin insulator layer. (3) Emission from the two-dimensional (2D) quantum well (QW) surface space charge regions. In this case, the bottom of a subsurface c band is shifted by the quantization value E=Ec−Ei with Ei=(ℏ2/2m*)1/3 [3/2πeEs(i+3/4)]2/3∼Es2/3. Here Es=4π/2eNs is the strength of the surface electric field and i stands for the number of a quantum well (or a 2D subband). In contrast with the three-dimensional (3D) case, the electron concentration in the ith 2D degenerate subband is given bt a step function Ns=(m*/πℏ2)kT ln{1+exp[(Ec−Ei)/kT]}. With m*=0.01 me, the difference E=(Ei−Ec) greatly increases in pretty high applied fields (Es∼10 V cm−1) and, thus, may give rise to a pronounced increase of the field emission current. Moreover, with growing Es, subsequent bands are being filed and, due to the steplike dependence of NSS, an additional growth of the emission current may occur, together with emerging collisions on the Fowler–Nordheim differential curve. (4) Emission from very sharp tips containing 2D-conducting layer (QW space charge), when τ tip is comparable to the low thickness of QW layer. Here we have so-called zero-size (zero-dimensional) systems, when the dependence ΔW on ES becomes even sharper. (%) emission from the tips covered by very thin films with quantized conducting electrons. For these, narrow-band or semimetallic materials (such as Bi) with very low effective mass (HgCdTe, InSb, PbSTe, etc.) may be used. Discrete Q levels Ei govern the current oscillations with the increasing Es, when Ei is filled by the applied field. For the transversal current (in the direction of the electron localization) to appear, necessary determine or ionization 2D quasilocalized electron to more high, 3D subbands, or due to different scattering processes (including oscillation in QW).