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图1为传统透射式GaAs光电阴极的能带图。根据Spicer光电发射“三步模型”理论,首先,光照下能量小于GaAlAs的禁带宽度而大于GaAs禁带宽度的光子被p-GaAs吸收而激发产生光生电子。其次,绝大多数光电子被激发到导带后处于能量较高的热电子状态,之后将通过散射同时向GaAlAs/GaAs界面和GaAs发射层表面(x=d)作扩散运动。最后,到达光电阴极表面的光电子隧穿表面势垒发射到真空中。影响GaAs光电阴极时间响应特性的主要因素为Spicer光电发射模型中第二步的电子扩散迁移行为。光电子通过扩散迁移在光电阴极体内的分布是时间的函数,通过矩阵差分求解GaAs激活层内光电子的连续性方程(公式(1))和一系列边界条件(公式(2)~(4)),可以求得GaAs光电阴极出射光电子流密度方程(公式(5))的数值解曲线,曲线的半峰宽即为透射式GaAlAs/GaAs光电阴极的响应时间。
图 1 传统透射式GaAs光电阴极能带图
Figure 1. Energy band diagram of traditional transmission-mode GaAs photocathode
$$ \frac{{\partial \Delta {{n}}}}{{\partial \tau }} = {{{D}}_n}\frac{{{\partial ^2}\Delta n}}{{\partial {x^2}}} - \frac{{\Delta n}}{{{\tau _n}}} $$ (1) $$ {\left. {\left[ {D{}_n\frac{{\partial \Delta n}}{{\partial x}} - s\Delta n} \right]} \right|_{x = 0}} = 0 $$ (2) $$ \Delta n(d,t) = 0 $$ (3) $$ \Delta n(x,0) = F \cdot {{\rm{e}}^{ - \alpha x}} $$ (4) $$ {\left. {j(t) = - {D_n} \cdot \frac{{\partial \Delta n(x,t)}}{{\partial x}}} \right|_{x = d}} $$ (5) 式中:Δ
n为光生电子的分布;t为时间;Dn为光电子在GaAs界面的扩散系数;x为距离GaAlAs/GaAs界面的距离;τn为光电子在GaAs中的寿命;s为GaAlAs/GaAs界面的复合速率;d为GaAs激活层厚度;F为与GaAs吸收系数α相关的值: $$ F = \eta (1 - R) \cdot \frac{N}{A} \cdot \alpha \cdot \Delta t $$ (6) 式中:R为GaAs光电阴极光照面的反射率;η为光生载流子的产生率;N为入射光子数;A为光阴极面积;α为GaAs的吸收系数;Δt为光源的脉冲宽度。
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从物理模型可以得出,对响应时间造成影响的主要物理参数包括GaAs激活层厚度d、GaAs电子扩散系数Dn和GaAs/GaAlAs界面的后界面复合速率Sv,现对这三种因素对GaAs光电阴极时间响应特性的影响进行系统的理论计算。目前传统GaAs光电阴极的电子扩散系数Dn=50 cm2/s,GaAs/GaAlAs界面的后界面复合速率Sv=105 cm/s,激活层厚度d=1.5 μm,在对其中一个参数进行计算分析时,另外两个参数保持上述值不变。研究中所采用的入射光波长为530 nm。
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图2为不同电子扩散系数下GaAs光电阴极出射光电子流密度随时间的变化曲线。从图中可以明显看出,随GaAs电子扩散系数的增大,GaAs光电阴极响应速率不断加快。电子扩散系数是单位浓度梯度作用下的粒子流密度,可用于表征电子在材料内部浓度梯度下的运动速率,电子扩散系数越大,电子运动速率越快,且电子扩散系数与电子迁移率之间存在Einstein正比关系。因此,随着电子扩散系数的增大,电子迁移率也增大,从而使得响应速率不断加快。
图 2 不同电子扩散系数下GaAs光电阴极出射光电子流密度随时间的变化曲线
Figure 2. Curve of the photoelectron current density with time in GaAs photocathode with different electron diffusion coefficients
表1为GaAs光电阴极响应时间与GaAs电子扩散系数的对应关系表。可以看出,随着电子扩散的不断增大,响应速率增长的速度不断变慢,当电子扩散系数增大到70 cm2/s后,响应速率基本达到饱和,不再随电子扩散系数的增大而增大。这主要是因为电子扩散系数不断增大,电子迁移速率不断加快,在GaAs这种双能谷半导体内,这些高能电子将向有效质量较大的次能谷中跃迁,此时将出现负电阻导致电子迁移率下降。同时,次能谷中的高能电子将与声子发生散射而损失能量,因而使得电子迁移速率达到饱和。
表 1 GaAs光阴极响应时间与电子扩散系数的对应关系表
Table 1. Correspondence table of GaAs photocathode response time and electron diffusion coefficient
Item Value Dn/cm2·s−1 30 40 50 60 70 ΔT/ps 329 249 203 170 148 -
GaAs/GaAlAs后界面复合速率指的是GaAs/GaAlAs界面处单位表面积电子-空穴对的复合数,图3为不同后界面复合速率下GaAs光电阴极出射光电子流密度随时间的变化曲线。从图中可以看出,GaAs光电阴极的响应速率随后界面复合速率的增大而加快。产生这种现象的原因在于界面复合中心浓度的增大导致更多的电子向复合中心补充,阴极内部局部电子聚集区域增多,一方面所形成的电势对电子的扩散迁移运动有一定的加速效果,另一方面所形成的局域电场会对GaAs/GaAlAs界面的能带结构会产生一定的影响,导致界面势垒的降低从而引起GaAs内部电子流密度的增大[13],因此使得GaAs光电阴极的响应速率加快。
图 3 不同后界面复合速率下GaAs光电阴极出射光电子流密度随时间的变化曲线
Figure 3. Curve of the photoelectron current density with time in GaAs photocathode with different rear interface recombination rate
表2为GaAs光电阴极响应时间与GaAs/GaAlAs后界面复合速率的对应关系表。可以看出,在后界面复合速率较小时,其对响应时间的影响较大,随后界面复合速率的增大响应速率快速增大。当其增大到约为106 cm/s时,响应速率达到饱和,不再随后界面复合速率的增大而增大。出现这种现象可能的原因为当后界面复合速率增大到一定值后,光电子的运动速率也增长到一个较大值,因此光电子具备较大的能量而发生能谷跃迁,出现负电阻和声子散射导致电子能量下降,最终电子运动速率达到稳定饱和。
表 2 GaAs光阴极响应时间与后界面复合速率的对应关系表
Table 2. Correspondence table of GaAs photocathode response time and rear interface recombination rate
Item Value Sv/cm·s−1 102 103 104 105 106 ΔT/ps 1354 845 313 203 191 -
图4为不同激活层厚度下GaAs光电阴极出射光电子流密度随时间的变化曲线图,图中对GaAs光电阴极的出射光电子流密度进行了归一化处理。从图中可以明显看出,随着激活层厚度的降低,GaAs光电阴极的响应时间迅速减小,这主要是激活层厚度减小使得电子在向真空发射前在激活层内所需扩散迁移的距离变短,从而电子在阴极内部的扩散迁移时间变短,使得光电阴极的响应速率加快。
图 4 不同激活层厚度下GaAs光电阴极出射光电子流密度随时间的变化曲线
Figure 4. Curve of the photoelectron current density with time in GaAs photocathode with different active layer thickness
表3为GaAs光电阴极响应时间与激活层厚度的对应关系表。可以看出,激活层厚度从2.5 μm降低到0.5 μm,响应时间从533 ps缩短至23 ps,响应速率提升了22倍,可以满足大部分光子、粒子辐射探测系统的快响应需求。
表 3 GaAs光阴极响应时间与激活层厚度对应关系表
Table 3. Correspondence table of GaAs photocathode response time and active layer thickness
Item Value d/μm 2.5 2.0 1.5 1.0 0.5 ΔT/ps 533 360 203 90 23
Study on the time-resolved characteristics of the transmission-mode GaAs photocathode
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摘要: 时间分辨特性是GaAs光电阴极应用于泵浦探测等领域的一种极为重要的性能参量。采用矩阵差分求解光电子扩散模型的方式计算了光电子连续性方程和出射光电子流密度方程,发现影响GaAs光电阴极时间分辨特性的因素包括GaAs/GaAlAs后界面复合速率、GaAs电子扩散系数和GaAs激活层厚度,之后较为系统地研究了这三种物理因素对GaAs光电阴极时间分辨特性的影响。研究结果表明,GaAs电子扩散系数和GaAs/GaAlAs后界面复合速率与光电阴极的响应速率存在非线性正比关系,且随着两者的增大,GaAs光电阴极将出现饱和响应速率。激活层厚度对GaAs光电阴极响应时间的影响最大,通过激活层厚度的适当减薄可以将GaAs光电阴极的响应时间缩短至20 ps,可满足绝大多数光子、粒子探测的快响应需求。该研究为快响应GaAs光电阴极的实验和应用提供了必要的理论支撑。Abstract: Time-resolved characteristics are a very important performance parameter of GaAs photocathodes used in pump detection and other fields. In this paper, the photoelectron continuity equation and the outgoing photoelectron flow density equation are calculated by solving the photoelectron diffusion model by the matrix difference method. The factors affecting the time-resolved characteristics of the GaAs photocathode include the recombination rate of the GaAs/GaAlAs rear interface, GaAs electron diffusion coefficient and GaAs active layer thickness. Then, the effects of these three physical factors on the time-resolved characteristics of the GaAs photocathode are systematically studied. The research results show that the GaAs electron diffusion coefficient and the GaAs/GaAlAs rear interface recombination rate have a nonlinear proportional relationship with the response rate of the photocathode, and the saturation response rate of the GaAs photocathode will appear as the two increase. The thickness of the GaAs active layer has the greatest impact on the response time of the GaAs photocathode. The response time of the GaAs photocathode can be reduced to 20 ps by appropriately thinning the thickness of the active layer, which can meet the fast response requirements for most photon and particle detection. This study provides necessary theoretical support for the experiment and application of a fast-response GaAs photocathode.
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Key words:
- response time /
- GaAs photocathode /
- photoelectron diffusion model
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表 1 GaAs光阴极响应时间与电子扩散系数的对应关系表
Table 1. Correspondence table of GaAs photocathode response time and electron diffusion coefficient
Item Value Dn/cm2·s−1 30 40 50 60 70 ΔT/ps 329 249 203 170 148 表 2 GaAs光阴极响应时间与后界面复合速率的对应关系表
Table 2. Correspondence table of GaAs photocathode response time and rear interface recombination rate
Item Value Sv/cm·s−1 102 103 104 105 106 ΔT/ps 1354 845 313 203 191 表 3 GaAs光阴极响应时间与激活层厚度对应关系表
Table 3. Correspondence table of GaAs photocathode response time and active layer thickness
Item Value d/μm 2.5 2.0 1.5 1.0 0.5 ΔT/ps 533 360 203 90 23 -
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