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Low-noise preamplifier for scanning tunneling microscope

Tang Hai-Tao Mi Zhuang Wang Wen-Yu Tang Xiang-Qian Ye Xia Shan Xin-Yan Lu Xing-Hua

Tang Hai-Tao, Mi Zhuang, Wang Wen-Yu, Tang Xiang-Qian, Ye Xia, Shan Xin-Yan, Lu Xing-Hua. Low-noise preamplifier for scanning tunneling microscope. Acta Phys. Sin., 2024, 73(13): 130702. doi: 10.7498/aps.73.20240560
Citation: Tang Hai-Tao, Mi Zhuang, Wang Wen-Yu, Tang Xiang-Qian, Ye Xia, Shan Xin-Yan, Lu Xing-Hua. Low-noise preamplifier for scanning tunneling microscope. Acta Phys. Sin., 2024, 73(13): 130702. doi: 10.7498/aps.73.20240560

Low-noise preamplifier for scanning tunneling microscope

Tang Hai-Tao, Mi Zhuang, Wang Wen-Yu, Tang Xiang-Qian, Ye Xia, Shan Xin-Yan, Lu Xing-Hua
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  • The current preamplifier is one of the important components of the scanning tunneling microscope (STM), and its performance is crucial to the basic operations of the STM system, as well as for the development of demanding novel functionalities such as autonomous atomic fabrication. In this study, the factors that affect the performance of a current preamplifier, including its noise spectrum density and the bandwidth, are analyzed in depth, and a preamplifier is designed and fabricated specifically for the STM system. By using a carefully selected low-noise op amp chip, the optimized current preamplifier has a noise floor as low as 4 fA/Hz and a bandwidth of 2.3 kHz, at its most sensitive transimpedance gain of 1 GΩ. It has three transimpedance gains, 10 MΩ, 100 MΩ, and 1 GΩ, that can be switched through digital control signals. A two-switch configuration is adopted to minimize the noise floor while maintaining the optimal bandwidth. The current detectable by this three-level preamplifier ranges from pA to μA, satisfying the requirements of most STM operations. Using this preamplifier, the fundamental functions of the STM system are successfully demonstrated, including surface topographic characterization, scanning tunneling spectroscopy, and single atom/molecule manipulation. The measurement of shot noise in tunneling current is also explored, and a linear relationship between shot noise and tunneling current is obtained by carefully analyzing noise. It is illustrated that the Fano factor of the shot noise in a normal metallic tunneling junction is approximately equal to 1, revealing the expected Poisson process for electron tunneling in such a scenario. The results are valuable for the high-resolution characterization of correlation systems in the future.
      PACS:
      07.79.Cz(Scanning tunneling microscopes)
      07.79.-v(Scanning probe microscopes and components)
      73.23.-b(Electronic transport in mesoscopic systems)
      Corresponding author: Shan Xin-Yan, Shanxinyan@iphy.ac.cn ; Lu Xing-Hua, xhlu@iphy.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11727902, 21961142021) and the Natural Science Foundation of Beijing, China (Grant No. 4181003).

    在凝聚态物理和表面物理研究领域, 扫描隧道显微镜(scanning tunneling microscopy, STM)因为其具有原子尺度的空间分辨率而扮演着重要角色. STM能够对样品表面进行形貌表征[1], 获得表面电子态密度[2]等信息. 在STM系统中, 隧穿电流的测量是一个非常重要的环节. 一般而言, 隧穿电流极其微弱, 通常在皮安(pA)至纳安(nA)量级[3], 需要经过前置电流放大器进行放大才能被准确测量. 这种前置电流放大器的噪声水平要足够低, 能够分辨pA量级的隧穿电流变化[4], 同时还应该具有较大的动态范围. 近年来基于STM探针的原子搬运[5,6]及自动化操纵[7]发展迅速且引人注目. 在对单个原子进行搬运时, 隧穿结电阻约为50—500 kΩ[6], 对应隧穿电流可达10—100 nA量级. 自动化原子搬运等实验操作, 要求前置电流放大器能够通过计算机程序远程控制进行增益切换. 前置电流放大器的带宽也是影响STM性能的重要因素, 由于反馈电阻寄生电容的存在, GΩ量级增益的前置电流放大器的带宽通常被限制在几百Hz范围. 考虑到压电陶瓷的响应在10 kHz量级[8], 将电流放大器的带宽优化至对应范围, 将有助于提高STM系统扫描成像等核心功能的运行速度.

    隧穿电流中散粒噪声的测量能够揭示电子输运过程中的相互作用信息, 为凝聚态物理关联电子体系的研究提供重要数据和物理基础, 比如量子霍尔系统中的分数电荷[9,10], 超导体中的库伯对[11,12]以及量子点接触中的输运特性[13,14]等. 利用工作在室温的前置电流放大器直接测量隧穿电流中的散粒噪声无需进行互相关测量[13,15,16]和高频测量[17,18], 具有一定的优势. 但是, 这对前置电流放大器的本底噪声水平和带宽都提出了较高的要求.

    本文详细分析了影响前置电流放大器性能的因素, 设计了一款针对STM系统的前置电流放大器. 该放大器具备低噪声、高带宽以及电控多量程的特点, 可满足STM系统基本功能的需求, 并利用其探索了对隧穿电流中散粒噪声谱密度的测量.

    图1(a)展示了前置电流放大器的基本结构. 运算放大器的正相端接地, 电流通过反馈电阻Rf放大成电压, 其增益G(ω)通常表示为

    图 1 (a)前置电流放大器的电路噪声模型; (b)等效输入电流噪声谱密度示意图\r\nFig. 1. (a) Noise model of current preamplifier; (b) schematic diagram of equivalent input current noise power spectral density.
    图 1  (a)前置电流放大器的电路噪声模型; (b)等效输入电流噪声谱密度示意图
    Fig. 1.  (a) Noise model of current preamplifier; (b) schematic diagram of equivalent input current noise power spectral density.
    G(ω)=VoutIin=Zf1+A1(ω)(1+Zf/Zin), (1)

    其中, Zf为反馈阻抗, Zin为输入阻抗, A(ω)为运算放大器开环增益. 考虑1GΩ反馈电阻, 其寄生电容约0.2 pF, 则增益带宽为f=1/2πRfCf800 Hz. 对于给定的反馈电阻, 寄生电容越大, 放大器带宽越小. 因此, 在设计电路时应尽可能选取寄生电容小的反馈电阻来获得尽量大的带宽. 通常来讲, 金属膜电阻的寄生电容比较小, 可达0.1 pF及以下水平. 实际电路设计时, 还需要注意减小反馈电阻与其他导体(如地线)间的电容.

    前置电流放大器的噪声主要来源于运算放大器的噪声和反馈电阻的热噪声4kTRf. 对于运算放大器而言, 其内部噪声可以等效为输入端的电流噪声in和电压噪声en, 两者互不相关[19]. 根据叠加原理, 可得到总的等效输入电流噪声:

    STIA=|VoutZf|2=i2n+e2n|1Zf+1Zin|2+4kTRf, (2)

    其中第2项的贡献随频率呈平方增大, 在高频区域可作如下近似,

    e2n|1/Zf+1/Zin|2=e2n|1Rf+jω(Cin+Cf)|2(enωCtotal)2, (3)

    式中, Ctotal=Cin+Cf. 该项通常称为enC噪声[20], 在高频区占主导. 在低频区, 等效输入噪声由其他两项主导, 不随频率变化, 噪声谱密度如图1(b)所示. 考虑到1 GΩ反馈电阻对应的噪声水平(4fA/Hz), 运算放大器的等效输入电流噪声在fA/Hz量级即可, 应选择电压噪声en尽量低并尽量降低系统的输入端电容. 需要注意的是, 前置电流放大器的最大可能带宽为fT/(2πRfCin), 与运算放大器增益带宽积fT及输入电容Cin有关. 例如, 若反馈电阻为1 GΩ, 输入端电容为10 pF, 增益带宽积为1 GHz, 则前置电流放大器的最大可能带宽约为130 kHz. 目前, 运算放大器芯片的输入端电压噪声可低至1nV/Hz水平, 输入端电容可在10 pF以下.

    基于以上对前置电流放大电路的噪声模型, 图2(a)比较了多款典型的低噪声运算放大器芯片在1 GΩ增益条件下的等效输入电流噪声谱密度. 由此选取了一款enin分别为2.2 nV/Hz和2fA/Hz的运算放大器芯片(OPA1), 其偏置电流低至4 pA, 增益带宽积达2.7 GHz, 可以较好地满足STM实验需求.

    图 2 (a)典型低噪声运算放大器芯片的噪声谱密度模拟; (b)多量程复合电路设计\r\nFig. 2. (a) Simulated input current noise spectrum density of typical low noise operational amplifiers; (b) basic circuit of a composite transimpedance amplifier with multiple gains.
    图 2  (a)典型低噪声运算放大器芯片的噪声谱密度模拟; (b)多量程复合电路设计
    Fig. 2.  (a) Simulated input current noise spectrum density of typical low noise operational amplifiers; (b) basic circuit of a composite transimpedance amplifier with multiple gains.

    为增加整个电路的开环增益, 采用如图2(b)所示的复合放大电路, 其中A1和A2两个运算放大器构成一个复合放大电路, 具有更高的稳定性和直流性能[21]. 考虑到STM实验中隧穿电流可能有跨越多个数量级的变化, 我们设计了三个增益档位, 反馈电阻选择1 GΩ, 100 MΩ和10 MΩ, 对应隧穿电流测量范围分别为±10 nA, ±100 nA和±1 μA, 不同的增益通过开关进行切换.

    有些商业化前置电流放大器采用手动机械式开关来进行量程的切换, 虽然具有串扰电容小的优势, 但在实验过程中手动切换增益易引起振动干扰, 且效率低下. 由于其无法通过程序自动化控制, 无法满足自动化原子搬运等先进功能的研发需求. 通过比较, 我们选择舌簧式继电器作为增益切换元件, 其响应速度快于电磁继电器, 具有较好的电磁屏蔽能力, 断开状态下其电阻达10101012 Ω, 电容小于1 pF[20]. 为优化前置电流放大器性能, 我们尝试了多种量程切换方式.

    测试表明, 在反馈电阻之前和之后各放置一个继电器是最为理想的量程切换方式, 如图3(a)所示. 图3(b)显示了继电器的结构原理及其阻抗模型. 其②, ③引脚间的电磁线圈决定①, ④引脚的断开和闭合, ①, ④引脚和地之间存在一个约2 pF的电容, 两引脚之间还有约0.1 pF的电容. 图3(c), (d)展示了不同继电器状态下1 GΩ增益档的增益曲线和噪声谱密度. 当仅有一个继电器断开时, 电路的增益曲线会明显偏离单极点形式, 如图3(c)中的黑色和红色曲线所示. 当仅有继电器2断开时, 电路的噪声水平还会明显增高, 如图3(d)所示. 这是由于100 MΩ电阻通过2 pF电容与地相连, 在输入端增加了额外的热噪声导致的. 只有两个开关都断开时, 该反馈回路对其他回路的增益和噪声才不会产生干扰.

    图 3 (a)多量程开关控制设计; (b)继电器结构示意图及其电容特征; (c), (d) 3种不同开关状态下1 GΩ档的增益和等效电流噪声谱密度\r\nFig. 3. (a) Switching circuit for multiple gain control; (b) schematic diagram of electromagnetic relay and related typical capacitances; (c), (d) the gain and input current noise spectrum density with 1 GΩ transimpedance gain under three different switch conditions.
    图 3  (a)多量程开关控制设计; (b)继电器结构示意图及其电容特征; (c), (d) 3种不同开关状态下1 GΩ档的增益和等效电流噪声谱密度
    Fig. 3.  (a) Switching circuit for multiple gain control; (b) schematic diagram of electromagnetic relay and related typical capacitances; (c), (d) the gain and input current noise spectrum density with 1 GΩ transimpedance gain under three different switch conditions.

    前置电流放大器的电路PCB设计图如图4(a)所示, 为了尽量减小反馈电阻的寄生电容, 采用两个阻值为500 MΩ的电阻串联构成1 GΩ反馈回路. PCB设计中元件排布尽可能紧凑, 使反馈回路尽可能短, 每一个继电器的控制元件都放置在外围. 运算放大器芯片的供电电源需进行良好的滤波处理, 放置在PCB板的边缘位置, 远离芯片和反馈回路, 以减小对输入信号的干扰. 另外, 运算放大器芯片的地和周围铺铜充分接触以保证散热效率. 为消除外部电磁环境如50 Hz噪声的干扰, 我们设计制作了铝制屏蔽盒作为法拉第笼, 输出线、电源线和档位切换控制线都采用屏蔽效果很好的Lemo接口, 前置电流放大器外观如图4(b)所示. 两级运放芯片的电源电压分别为±5 V, ±12 V. 经过测试发现, 电源噪声对电路的噪声水平有较大的影响, 需经过较好的滤波处理后再给芯片供电. 电源采用Lemo接口和双绞线连接方式, 以最大程度地减小电磁噪声. 整个前置电流放大器的制作成本(约2000元)也远低于商用前置电流放大器的价格.

    图 4 (a)前置电流放大器PCB设计图; (b)前置电流放大器实物图; (c)不同反馈电阻对应的跨阻增益曲线; (d)不同反馈电阻对应的等效输入电流噪声谱密度\r\nFig. 4. (a) PCB layout of the preamplifier circuit; (b) photo of the current preamplifier; (c) measured transimpedance gain with different feedback resistors; (d) equivalent input current spectrum density of three gains.
    图 4  (a)前置电流放大器PCB设计图; (b)前置电流放大器实物图; (c)不同反馈电阻对应的跨阻增益曲线; (d)不同反馈电阻对应的等效输入电流噪声谱密度
    Fig. 4.  (a) PCB layout of the preamplifier circuit; (b) photo of the current preamplifier; (c) measured transimpedance gain with different feedback resistors; (d) equivalent input current spectrum density of three gains.

    图4(c)展示了前置电流放大器3个量程的增益曲线, 对应的–3 dB带宽分别为2.3 kHz (1 GΩ档), 18 kHz (100 MΩ档)和100 kHz (10 MΩ档). 3个档位的等效输入端电流噪声谱密度如图4(d)所示, 图中低频区噪声为反馈电阻热噪声的贡献, 即4kT/Rf. 对于1 GΩ增益档位, 反馈电阻在室温(300 K)产生的等效输入电流噪声谱密度为16fA2/Hz, 显著大于所选运算放大器芯片的标称电流噪声谱密度(4 fA2/Hz). 放大器在低频区的等效输入电流噪声谱密度主要为两者之和, 即20 fA2/Hz, 在高频区则由enC噪声主导. 测量结果与模拟计算吻合.

    本文还对比了自制的前置电流放大器与3款典型商业化产品的主要性能, 主要包括增益范围、噪声水平、带宽以及量程切换方式, 如表1所示. 3款商业化设备都有着大致相同的增益范围, 能够放大mA—pA量级的电流信号; 在增益控制方面, 有一款商用放大器只有手动切换功能, 另外两款商用放大器则同时支持手动和自动切换. 我们自制的前置电流放大器尽管只设计了3个可自动切换量程, 但是已经能够完全覆盖STM各种应用场景下的隧穿电流测量, 而且每个量程的噪声都很低. 在109 V/A增益条件下, 自制的前置电流放大器具有最低的噪声水平, 并且对应的–3 dB带宽也最高. 需要指出的是, 利用我们的设计, 增加更多反馈回路不会产生额外的噪声, 亦不会影响测量带宽. 由于量程较少, 自制的前置电流放大器在仪器尺寸方面亦有明显优势, 可以方便地与STM超高真空腔体法兰直接连接.

    表 1  自制前置电流放大器与三款商业化产品的主要参数对比
    Table 1.  Main parameters of home-built preamplifier and three commercial products.
    Gain/(V·A–1) Input noise@109 V/A/(fA·Hz–1/2) –3 dB bandwidth@109 V/A Gain control(manual, remote)
    自研放大器 107109 4.0 2.3 kHz R
    商用放大器A 1031011 4.3 1.1 kHz M, R
    商用放大器B 1031011 5.0 1.0 kHz M
    商用放大器C 1031012 10.0 15.0 Hz M, R
    下载: 导出CSV 
    | 显示表格

    我们测试了所研制的前置电流放大器在STM常见功能操作中的应用. 图5(a)为Au(111) 表面的形貌成像, 可看到清晰的herringbone重构结构; 图5(b)为Cu(111)表面的隧穿电流微分电导谱, 可观察到清晰的表面态, 在–0.5 V偏压附近电子态密度的突变对应表面态的带边; 图5(c)为对Cu(111)表面单个CO分子搬运操作前后的表面形貌; 图5(d)展示了形貌表征和原子/分子搬运操作过程中典型的隧穿电流曲线特征. 原子/分子搬运时设定的电流往往在10 nA以上, 比形貌表征所需电流要高一个量级以上. 分子跟随针尖的运动还会在隧穿电流中形成显著增强的噪声, 对该噪声的快速分析可以帮助实时监测原子/分子搬运的状态. 前置电流放大器在进行这两种功能操作时的增益分别设定为1 GΩ和100 MΩ, 两者之间的切换通过控制软件输出的电压信号来实现, 无需手动改变. 这种具有电控增益切换的前置电流放大器为开发STM自动化原子操纵及原子制造功能提供了技术保障.

    图 5 (a) 78 K温度下Au(111)表面的STM形貌表征(V = 0.5 V, I = 0.3 nA); (b) 隧穿电流微分电导谱; (c) 7 K温度条件下原子搬运前后形貌图(V = 0.2 V, I = 1 nA); (d)不同操作功能下的隧穿电流曲线\r\nFig. 5. (a) STM topographic image (V = 0.5 V, I = 0.3 nA) of Au(111) surface at 78 K; (b) tunneling differential conductance spectrum measured on Cu(111) surface; (c) STM topographs (V = 0.2 V, I = 1 nA) before and after atomic manipulation at 7 K; (d) tunneling current under different STM operations.
    图 5  (a) 78 K温度下Au(111)表面的STM形貌表征(V = 0.5 V, I = 0.3 nA); (b) 隧穿电流微分电导谱; (c) 7 K温度条件下原子搬运前后形貌图(V = 0.2 V, I = 1 nA); (d)不同操作功能下的隧穿电流曲线
    Fig. 5.  (a) STM topographic image (V = 0.5 V, I = 0.3 nA) of Au(111) surface at 78 K; (b) tunneling differential conductance spectrum measured on Cu(111) surface; (c) STM topographs (V = 0.2 V, I = 1 nA) before and after atomic manipulation at 7 K; (d) tunneling current under different STM operations.

    此外, 我们还探究了隧穿电流中散粒噪声的测量, 样品为铜单晶Cu(111), 系统温度约10 K. 散粒噪声源于电子在隧穿过程中的离散特性[22,23], 其强度满足公式Sshot=2qIF, 即正比于电荷量q和直流电流I以及法诺因子F. 当电子隧穿满足泊松过程时, F=1. 图6(a)展示了平均电流强度为0 nA (蓝色)及0.28 nA (红色)情况下所测得的电流噪声谱密度, 前置电流放大器增益为1 GΩ, STM反馈关闭, 针尖高度一致. 可以看到, 由于STM系统引入了显著的输入电容, 高频区的enC噪声强度相比图4(c)有所增大. 拟合可得总电容约60 pF, 显著大于前置电流放大器自身的输入端电容11 pF. 在隧穿电流强度不为零的情况下, 在低频区可 观察到显著的1/f2噪声, 该噪声强度与电流大小的平方成正比[24], 通常来源于隧穿结表面缺陷的运动或电子被缺陷随机捕获, 亦被称为调制噪声(modulation noise). 利用低频区的噪声谱密度拟合可得1/f2噪声的系数, α103Hz1. 进一步, 利用以下公式拟合:

    图 6 (a)典型隧穿电流噪声谱密度分析; (b)隧穿电流散粒噪声随电流强度的变化\r\nFig. 6. (a) Typical noise spectrum density of the tunneling current; (b) shot noise in tunneling current, as a function of the current amplitude.
    图 6  (a)典型隧穿电流噪声谱密度分析; (b)隧穿电流散粒噪声随电流强度的变化
    Fig. 6.  (a) Typical noise spectrum density of the tunneling current; (b) shot noise in tunneling current, as a function of the current amplitude.
    Stotal=STIA+αI2f2+Sshot, (4)

    即可获得散粒噪声的强度. 图6(b)给出了散粒噪声强度随隧穿电流变化的结果, 隧穿电流从0.1 nA增大到1 nA. 对于更小的电流, 其散粒噪声强度低于30 fA2/Hz, 容易被前置电流放大器的本底噪声(25 fA2/Hz)所淹没而无法被准确测量到. 图中虚线为散粒噪声理论曲线Spoisson=2qI, 若对实验测量结果进行线性拟合可得法诺因子F约为1.09.

    显然, 实验测得的法诺因子F相比理想泊松过程的法诺因子值有10%左右的偏差. 为减小这种误差, 可考虑尽量减小低频区的1/f2噪声和高频区的enC噪声, 使噪声谱密度在中间频段出现一个明显的平台, 从而显著提高拟合结果的准确度. 在更低温度下, 使用更稳定的STM扫描装置, 以及采用更好的振动隔离措施都有可能降低1/f2噪声; 在前置电流放大器与隧穿结之间使用尽可能短的电容更小的导线, 或者采用低温超高真空兼容的前置电流放大器, 则有望显著降低放大器输入电容及enC噪声. 这些工作涉及整个STM系统的改进, 将在后续研究中完善.

    本文详细分析了前置电流放大电路的噪声模型, 以此为依据筛选出来噪声极低的运放芯片, 并结合STM系统的需求自主设计并制作了一款专用于STM的前置电流放大器. 该放大器具有低噪声、高带宽的特点以及远程控制的三档增益, 能够测量pA—μA之间6个数量级的电流. 通过巧妙的电路设计和细致的测试消除了增益切换电路对放大器增益和带宽的影响. 给出了前置电流放大器各档位的增益曲线和噪声谱密度曲线. 利用该前置电流放大器, 可实现STM的各项基本功能, 也为STM自动化原子制造提供了技术保障. 利用该放大器对隧穿电流散粒噪声的测量研究取得了初步合理的结果, 验证了简单隧穿结中的散粒噪声近似满足 Spoisson=2qI, 为表面更高精度的电子关联体系散粒噪声测量指出了努力方向.

    [1]

    Binnig G, Rohrer H, Gerber C, Weibel E 1982 Phys. Rev. Lett. 49 57Google Scholar

    [2]

    Stroscio J A, Feenstra R M, Fein A P 1986 Phys. Rev. Lett. 57 2579Google Scholar

    [3]

    Chen C J 2021 Introduction to Scanning Tunneling Microscopy Third Edition (Vol. 69) (USA: Oxford University Press

    [4]

    Scheiber P, Riss A, Schmid M, Varga P, Diebold U 2010 Phys. Rev. Lett. 105 216101Google Scholar

    [5]

    Eigler D M, Schweizer E K 1990 Nature 344 524Google Scholar

    [6]

    Bartels L, Meyer G, Rieder K H 1997 Phys. Rev. Lett. 79 697Google Scholar

    [7]

    Kalff F E, Rebergen M P, Fahrenfort E, Girovsky J, Toskovic R, Lado J L, Fernandez-Rossier J, Otte A F 2016 Nat. Nanotechnol. 11 926Google Scholar

    [8]

    Štubian M, Bobek J, Setvin M, Diebold U, Schmid M 2020 Rev. Sci. Instrum. 91 074701Google Scholar

    [9]

    de-Picciotto R, Reznikov M, Heiblum M, Umansky V, Bunin G, Mahalu D 1997 Nature 389 162Google Scholar

    [10]

    Saminadayar L, Glattli D C, Jin Y, Etienne B 1997 Phys. Rev. Lett. 79 2526Google Scholar

    [11]

    Jehl X, Sanquer M, Calemczuk R, Mailly D 2000 Nature 405 50Google Scholar

    [12]

    Bastiaans K M, Chatzopoulos D, Ge J F, Cho D, Tromp W O, van Ruitenbeek J M, Fischer M H, de Visser P J, Thoen D J, Driessen E F C, Klapwijk T M, Allan M P 2021 Science 374 608Google Scholar

    [13]

    Kumar A, Saminadayar L, Glattli D C, Jin Y, Etienne B 1996 Phys. Rev. Lett. 76 2778Google Scholar

    [14]

    DiCarlo L, Zhang Y, McClure D T, Reilly D J, Marcus C M, Pfeiffer L N, West K W 2006 Phys. Rev. Lett. 97 036810Google Scholar

    [15]

    Hashisaka M, Ota T, Yamagishi M, Fujisawa T, Muraki K 2014 Rev. Sci. Instrum. 85 054704Google Scholar

    [16]

    Henny M, Oberholzer S, Strunk C, Schönenberger C 1999 Phys. Rev. B 59 2871Google Scholar

    [17]

    Chen R, Wheeler P J, Natelson D 2012 Phys. Rev. B 85 235455Google Scholar

    [18]

    Bastiaans K M, Benschop T, Chatzopoulos D, Cho D, Dong Q, Jin Y, Allan M P 2018 Rev. Sci. Instrum. 89 093709Google Scholar

    [19]

    Kay A 2012 Operational Amplifier Noise: Techniques and Tips for Analyzing and Reducing Noise (Elsevier) pp13–14

    [20]

    Horowitz P, Hill W, Robinson I 1989 The art of electronics (Vol. 2) (Cambridge: Cambridge university Press) pp171–184

    [21]

    Mikhael W B, Michael S 1987 IEEE T. Circuits Syst. 34 449Google Scholar

    [22]

    Blanter Y M, Büttiker M 2000 Physics Reports 336 1Google Scholar

    [23]

    Kobayashi K, Hashisaka M 2021 J Phys Soc Jpn 90 102001Google Scholar

    [24]

    Birk H, De Jong M, Schönenberger C 1995 Phys. Rev. Lett. 75 1610Google Scholar

    期刊类型引用(1)

    1. 肖亮,俞洋,黄成,崔渊,王云松. 宽量程精密电流检测电路的设计. 山东工业技术. 2025(01): 17-24 . 百度学术

    其他类型引用(0)

  • 图 1  (a)前置电流放大器的电路噪声模型; (b)等效输入电流噪声谱密度示意图

    Figure 1.  (a) Noise model of current preamplifier; (b) schematic diagram of equivalent input current noise power spectral density.

    图 2  (a)典型低噪声运算放大器芯片的噪声谱密度模拟; (b)多量程复合电路设计

    Figure 2.  (a) Simulated input current noise spectrum density of typical low noise operational amplifiers; (b) basic circuit of a composite transimpedance amplifier with multiple gains.

    图 3  (a)多量程开关控制设计; (b)继电器结构示意图及其电容特征; (c), (d) 3种不同开关状态下1 GΩ档的增益和等效电流噪声谱密度

    Figure 3.  (a) Switching circuit for multiple gain control; (b) schematic diagram of electromagnetic relay and related typical capacitances; (c), (d) the gain and input current noise spectrum density with 1 GΩ transimpedance gain under three different switch conditions.

    图 4  (a)前置电流放大器PCB设计图; (b)前置电流放大器实物图; (c)不同反馈电阻对应的跨阻增益曲线; (d)不同反馈电阻对应的等效输入电流噪声谱密度

    Figure 4.  (a) PCB layout of the preamplifier circuit; (b) photo of the current preamplifier; (c) measured transimpedance gain with different feedback resistors; (d) equivalent input current spectrum density of three gains.

    图 5  (a) 78 K温度下Au(111)表面的STM形貌表征(V = 0.5 V, I = 0.3 nA); (b) 隧穿电流微分电导谱; (c) 7 K温度条件下原子搬运前后形貌图(V = 0.2 V, I = 1 nA); (d)不同操作功能下的隧穿电流曲线

    Figure 5.  (a) STM topographic image (V = 0.5 V, I = 0.3 nA) of Au(111) surface at 78 K; (b) tunneling differential conductance spectrum measured on Cu(111) surface; (c) STM topographs (V = 0.2 V, I = 1 nA) before and after atomic manipulation at 7 K; (d) tunneling current under different STM operations.

    图 6  (a)典型隧穿电流噪声谱密度分析; (b)隧穿电流散粒噪声随电流强度的变化

    Figure 6.  (a) Typical noise spectrum density of the tunneling current; (b) shot noise in tunneling current, as a function of the current amplitude.

    表 1  自制前置电流放大器与三款商业化产品的主要参数对比

    Table 1.  Main parameters of home-built preamplifier and three commercial products.

    Gain/(V·A–1) Input noise@109 V/A/(fA·Hz–1/2) –3 dB bandwidth@109 V/A Gain control(manual, remote)
    自研放大器 107109 4.0 2.3 kHz R
    商用放大器A 1031011 4.3 1.1 kHz M, R
    商用放大器B 1031011 5.0 1.0 kHz M
    商用放大器C 1031012 10.0 15.0 Hz M, R
    DownLoad: CSV
  • [1]

    Binnig G, Rohrer H, Gerber C, Weibel E 1982 Phys. Rev. Lett. 49 57Google Scholar

    [2]

    Stroscio J A, Feenstra R M, Fein A P 1986 Phys. Rev. Lett. 57 2579Google Scholar

    [3]

    Chen C J 2021 Introduction to Scanning Tunneling Microscopy Third Edition (Vol. 69) (USA: Oxford University Press

    [4]

    Scheiber P, Riss A, Schmid M, Varga P, Diebold U 2010 Phys. Rev. Lett. 105 216101Google Scholar

    [5]

    Eigler D M, Schweizer E K 1990 Nature 344 524Google Scholar

    [6]

    Bartels L, Meyer G, Rieder K H 1997 Phys. Rev. Lett. 79 697Google Scholar

    [7]

    Kalff F E, Rebergen M P, Fahrenfort E, Girovsky J, Toskovic R, Lado J L, Fernandez-Rossier J, Otte A F 2016 Nat. Nanotechnol. 11 926Google Scholar

    [8]

    Štubian M, Bobek J, Setvin M, Diebold U, Schmid M 2020 Rev. Sci. Instrum. 91 074701Google Scholar

    [9]

    de-Picciotto R, Reznikov M, Heiblum M, Umansky V, Bunin G, Mahalu D 1997 Nature 389 162Google Scholar

    [10]

    Saminadayar L, Glattli D C, Jin Y, Etienne B 1997 Phys. Rev. Lett. 79 2526Google Scholar

    [11]

    Jehl X, Sanquer M, Calemczuk R, Mailly D 2000 Nature 405 50Google Scholar

    [12]

    Bastiaans K M, Chatzopoulos D, Ge J F, Cho D, Tromp W O, van Ruitenbeek J M, Fischer M H, de Visser P J, Thoen D J, Driessen E F C, Klapwijk T M, Allan M P 2021 Science 374 608Google Scholar

    [13]

    Kumar A, Saminadayar L, Glattli D C, Jin Y, Etienne B 1996 Phys. Rev. Lett. 76 2778Google Scholar

    [14]

    DiCarlo L, Zhang Y, McClure D T, Reilly D J, Marcus C M, Pfeiffer L N, West K W 2006 Phys. Rev. Lett. 97 036810Google Scholar

    [15]

    Hashisaka M, Ota T, Yamagishi M, Fujisawa T, Muraki K 2014 Rev. Sci. Instrum. 85 054704Google Scholar

    [16]

    Henny M, Oberholzer S, Strunk C, Schönenberger C 1999 Phys. Rev. B 59 2871Google Scholar

    [17]

    Chen R, Wheeler P J, Natelson D 2012 Phys. Rev. B 85 235455Google Scholar

    [18]

    Bastiaans K M, Benschop T, Chatzopoulos D, Cho D, Dong Q, Jin Y, Allan M P 2018 Rev. Sci. Instrum. 89 093709Google Scholar

    [19]

    Kay A 2012 Operational Amplifier Noise: Techniques and Tips for Analyzing and Reducing Noise (Elsevier) pp13–14

    [20]

    Horowitz P, Hill W, Robinson I 1989 The art of electronics (Vol. 2) (Cambridge: Cambridge university Press) pp171–184

    [21]

    Mikhael W B, Michael S 1987 IEEE T. Circuits Syst. 34 449Google Scholar

    [22]

    Blanter Y M, Büttiker M 2000 Physics Reports 336 1Google Scholar

    [23]

    Kobayashi K, Hashisaka M 2021 J Phys Soc Jpn 90 102001Google Scholar

    [24]

    Birk H, De Jong M, Schönenberger C 1995 Phys. Rev. Lett. 75 1610Google Scholar

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  • 期刊类型引用(1)

    1. 肖亮,俞洋,黄成,崔渊,王云松. 宽量程精密电流检测电路的设计. 山东工业技术. 2025(01): 17-24 . 百度学术

    其他类型引用(0)

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Publishing process
  • Received Date:  23 April 2024
  • Accepted Date:  12 May 2024
  • Available Online:  16 May 2024
  • Published Online:  05 July 2024

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