24G15
Development of oxygen plasma source and ZnO sputtering experiment
新型 ZnO プロセス研究用酸素プラズマ源の開発とZnO スパッタリング実験
Yuji Nishioka, Haruhiko Himura, Takashi Okamoto,Kiyonori Hirota, Akio Sanpei and Sadao Masamune
西岡 祐司，比村治彦，岡本崇，廣田聖典，三瓶明希夫，政宗貞男
Department of Electronics, Kyoto Institute of Technology
Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan
京都工芸繊維大学 · 電子システム工学専攻 〒 606-8585 京都市左京区松ヶ崎御所海道町
We consider a new method of fabricating ZnO cluster by use of a trapping technique of nonneutral plasmas called Penning trap (H. Himura et al., 25E08 in this conference). To estimate thegrowth time of clusters in the penning trap, we firstly calculate the time evolution of the particle
number in a unit volume with the Becker-Döring model.

Introduction
Zinc oxide (ZnO) has attractive potential in applications such as ultraviolet or blue light emitting diode, laser, solar cell, and transparent thin films transistor. This is because ZnO has a wide direct band
gap of 3.37 eV, large excitation binding energy of 60
meV at room temperature, and eﬃcient radiation recombination.

ploys no AC E-fields so that no heating is occurred.
This is actually a favor aspect if we intend to grow up
clusters larger than 10.
Density limit in penning trap
The Penning trap shows long confinement time, forinstance, even for several days. On the other hand,
there is an inherent limitation on its density that iscalled Brillouiun density limit Brillouin density limit
expressed in nB = ϵ0 B2 /2m. For N-sized ZnO cluster
ions, which is defined as (ZnO)+N based on the ZnO
unit, The value of nB is shown in Fig. 1.

One of most crucial issues on the ZnO applications
is how the amount of impurities is decreased during
processes. For developing a new process to solve theproblem, We consider promoting particle growth ina non-neutral plasma trap where little impurities orresidual gas exist because of ultra-low vacuum pressure. In fact, this may fabricate even ZnO clusters
that become ZnO quantum dots if they grow up in
the trap.
Regarding the cluster growth in a non-neutral
plasma trap, the growth of hydrogenated silicon clusters in an ion trap was reported[1]. In their experiment, Sin H x (n = 2-10) clusters are confirmed bytrapping the ionized hydrogenated silicon cluster ions
(Si x H+x ). However, in this experiment, the cluster size
was less than 10.
One of possible reasons may be due to heating of
the cluster because of the AC electric field used intheir trap. The Penning trap, on the other hand, em-Fig. 1: Brillouin density limit nB .
1

n1 ∼ 1011 [m−3 ] at B = 1 [T]. Therefore, for theinitial condition of the monomer particle with n1 =1011 [m−3 ], nN (t) is calculated as Fig. 3

Calculating ZnO cluster growth time by BeckerDöring model
Let us estimate the growth time of clusters in thePenning trap. To calculate it, we firstly adopt theBecker-Döring model [2]. The particle number of acluster containing N molecules is written as nN (t).
Assuming that most molecules are monomer withN = 1 and particle numbers increase or decrease only
by either a binary collision or/and coalescences between a cluster and a monomer or the disaggregationof a monomer as shown in Fig. 2, the time evolutions of the particle numbers of N-sized cluster are
expressed as
∂nN (t)= n1 (t)nN−1 (t)σN−1 − n1 (t)nN (t)σN∂t

+ nN+1 (t)λN+1 − nN (t)λN (N ≥ 2)



∞
∑
 ∂n1 (t)2= −2n1 (t) σ1 − n1 (t)nN (t)σN



∂t

N=2


∞
∑




+ 2n2 (t)λ2 +nN (t)λN (N = 1)
Fig. 3: Density distribution in the initial condition ofn1 = 1011 [m−3 ].
As recognized from these results, no clusters bigger than (N = 10) are formed within the calculation
time.
Fig. 4 shows the dependence of cluster numbers to
the initial monomer particle number n1 (t).

N=3, where σN is the product of the cross-section between N-sized cluster and monomer and collisionvelocity, and λN is the rate of disaggregation of a monomer. Thus, time evolutions of the particle number
for diﬀerent sized clusters are calculated by solving
these equations.
Here one notes that in this calculation, the particle velocity is assumed to be the thermal velocity, the (Zn-O bond( distance))2 rZn−O is 0.18 nm, and
1/3
σN = π rZn−O /2 1 + Nvth . The final assumption would be valid because the cross section becomes larger proportion to the superficial area of thecluster.

Fig. 4: The dependence of growth rate to initial monomer particle number.
As seen from the data, values of the growth rate
extend to wide ranges of power. Thus, this suggeststhat the growth of clusters strongly depends on thenumber densities of the monomer particle.
More detailed analysis will be presented.

ReferenceFig. 2: Changes in cluster size.
[1] H. Murakami , T. kanayama, Appl. Phys. Lett. 67(16) (1995)

Results
Figure 1 shows number densities against the confinement time of (ZnO)1 monomer for the case of[2] R. Becker , W. Döring, Ann. Phys. 24 719 (1935)
2