近年半導体リソグラフィ用ステッパや光分解能光学顕微鏡などにおいて光解像度化、高焦点深度化の目的のために用いる照明光源の光は短波長化されてきている。波長域はUV-B，-Cの領域に入ってきており、屈折光学系のみで色収差を除くためにはスペクトル線の波長幅はサブミクロンのオーダーが必要である。しかし通常のインコヒーレント光源からの光は波長幅の狭小化に伴いその強度が減少する。本報告では狭小な波長幅をもちながら分光放射輝度（強度）の高いスペクトル線を放射するランプはどのような特性を持つべきかを調べた。ランプ中のスペクトル線の光エネルギーの伝達式から分光放射輝度L（λ）－λは波長－はランプ内のアーク温度と注目するスペクトル線の吸収係数の両者の空間分布に強く依存することが明らかになった。高いL（λ）をうるためにはアーク内の最高温度はできうる限り高くすること、温度が空間的に低下するとき注目するスペクトル線の吸光種の密度は急激に低下しなければならない。その様な特性を示す吸光種としていくつか例が挙げられる。その一つは大きな振動子強度をもつイオンの共鳴線の吸光種（基底状態の原始状イオン）である。ここではCd⁺の共鳴線（214.4nm）と比較のためにCdの共鳴線（228.8nm）のL（λ）を計算した。前者は後者に比べ2桁も大きく、10⁴w／m²・nm・srのオーダーに達し、高圧NaランプのD線に比し約10倍も大きいことが示された。また波長幅はCdとバッファガスの密度を適切に選定すると0.5nmあるいはそれ以下になることが確認された。この計算結果はCdとKrを封入したランプでの従来の測定結果と定量的にかなり良い一致が見られた。

1．Introduction

Discharge Lamps have recently been used as a light source in an optical instrument in the wavelength region of UV-B, -C and VUV．It is required that the half-width of a spectral line used is extremely narrow, because of difficulty in designing fully achromatic optical system in this range of wavelength．However, its intensity is required to keep a short exposure time or a large exposure area．

In this report，physical properties of such high-radiance lamps are deduced and some lamps are shown as an example．

2．Physical properties of high-radiance lamps．

From the equation of radiative transfer in LTE, the spectral radiance L_λ and radiance L_T on the surface of a lamp in the normal direction are respectively expressed as Eqs.（1）and（2）,

wher λ, R, r, B_λ, K_λ denote wavelength, the lamp radius, the distance from the lamp axis，Planck function and the absorption coefficient being expressed as,

where λ₀, f, n_ι are the unshifted center wavelength of the line, the oscillator strength and the density of absorbing species respectively. The normalized line profile function is denoted as P（Δλ）．

The physical image of Eq.（1）can be describted as follows：radiation emitted at r reaches the lamp surface with absorption of the factor of exp(－∫^R_rK_λdr’） on the way．Physical properties of high-radiance lamps are deduced as follows: in general, the spectral line used shoul have a large f, and nι should be very high in the arc and steeply decreases with reduction in the temperature in the periphery．High-arc temperatures are required． Moreover, it is better that a buffer gas has a large polarizability and a low ionization energy．

In the case of a line with a limited half-width，nι or k_λ0 should be kept to be an optimum value，and a steep-temperature distribution is required．For the buffer gas a small polarizability and a high ionization energy are required．

3．Examples of high－radiance lamps

• （1）Lamps emitting a line with a large probability of the transition of which lower level is highly excited．E．g., high－pressure or super high－pressure mercury lamps emitting the 436，365nm lines
• （2）High－current Lamps．filled with species of high vapor pressure and low ionization energy，which emit resonance lines of ions^1）．E．g., Cd⁺ lamps operated with high currents，which emit the 214．4nm line．
• （3）Lamps emitting strong atomic lines within the arc and almost all the atoms are in the form of an allotropic molecular gas in the periphery of the arc．E．g., lamps containing S emitting the 181nm line

In the above three types of lamps, self-controled distributions of the density of absorbing species are established inside the lamps．

4．Numerical example

Calculated spectral radiances of the resonance line of Cd⁺ （214.4nm）from a short-arc lamp as well as from long-arc lamps are shown in Fig.1．Both of a parabolic distribution and a constant distribution were assumed for the temperature inside the lamps．The distribution measured by H．Burck et al.^2）was used for a short-arc lamp．This calculation has been done using the quasi-static approximation of line broadening．The ratio of L_T of the long-arc lamp with the parabolic distribution to that of the lamp with the constant temperature is 0．258．which is as large as twice compared with that of NaD lines of HPS lamps filled with Xe gas．The high ratio due to less self-absorption is shown．According to the reference¹⁾ the resonance radiation at 228．8nm of Cd atom in the short-arc lamp is not observed except in the far wing．This is a piece of evidence of high radience of ionic resonance lines from the lamps．

5．Conclusion

It is concluded that even if the spectral width is limited to be very narrow, the spectral line with a large oscillator strength can be of high radiance under the following condition： the lamp is operated at high electrical power densities and one chooses the absorbing Species of which density varies with strongly depending upon the temperature．