半导体物理 第七章.pdf

半半 导导 体体 物物 理 编写 刘诺副教授编写 刘诺副教授 制作 制作 刘诺副教授刘诺副教授 动画 刘诺 陈洪彬 赵翔 韩劲松动画 刘诺 陈洪彬 赵翔 韩劲松 Email liunuo2002 Email liunuo2002 电子科技大学电子科技大学 微电子与固体电子学院微电子与固体电子学院 微电子科学与工程系微电子科学与工程系 理 第七章第七章第七章第七章 金属和半导体的接触金属和半导体的接触金属和半导体的接触金属和半导体的接触 Contact between Metal and SemiconductorContact between Metal and SemiconductorContact between Metal and SemiconductorContact between Metal and Semiconductor 重点重点 1 阻挡层与反阻挡层的形成 阻挡层与反阻挡层的形成 2 肖特基势垒的定量特性 肖特基势垒的定量特性 3 欧姆接触的特性 欧姆接触的特性 7 1 7 1 金属金属金属金属 半导体接触和能带图半导体接触和能带图半导体接触和能带图半导体接触和能带图 Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram 重点重点重点重点 功函数 电子亲和势 接触电势势垒 阻挡层与反阻挡层 1 1 功函数 功函数W Wm m W Ws s 与电子亲和势与电子亲和势 Ec Ev Wm Ws EFm EFs E0 En 3 0 c EE 电子亲和势 真空电子能级 0 E 1 0 Fmm EEW金属功函数 2 0 Fss EEW半导体功函数 Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram 出体外所需的最小能量半导体导带底的电子逸 Fcn EEE 又 Fs EEW 0 所以 Fcc EEEE 0 n E Ws En E0 Ec EFs Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram 2 2 接触电势差接触电势差 s 假设金属和 m WWn 型半导体相接触且 n E s W m W v E c E Fm E Fs E 0 E Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram 接触势垒 接触势垒 接触势垒 接触势垒 WWm m W W s s q q VVms ms V V s s qVms q WW V sm ms 接触电势差故 导带底电子向金属运动时必须越过的导带底电子向金属运动时必须越过的导带底电子向金属运动时必须越过的导带底电子向金属运动时必须越过的 势垒的高度 势垒的高度 势垒的高度 势垒的高度 qVqVD D W Wm m W W s s 1 1 金属一边的电子运动到半导体一边也需要金属一边的电子运动到半导体一边也需要金属一边的电子运动到半导体一边也需要金属一边的电子运动到半导体一边也需要 越过的势垒高度 越过的势垒高度 越过的势垒高度 越过的势垒高度 2 m m Wq qVD m qEc EF Ev Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram 3 3 阻挡层与反阻挡层 阻挡层与反阻挡层 阻挡层与反阻挡层 阻挡层与反阻挡层 型半导体接触金属n 1 时电子反阻挡层 时电子阻挡层 sm sm WWb WWa 型半导体接触金属p 2 时空穴阻挡层 时空穴反阻挡层 sm sm WWb WWa Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram 1 1 金属 金属 金属 金属 n n型半导体接触型半导体接触型半导体接触型半导体接触 时电子反阻挡层 时电子阻挡层 sm sm WWb WWa Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram a a WWm m W W s s 电子阻挡层电子阻挡层电子阻挡层电子阻挡层 m W s W Fm E Fs E v E c E 0 E Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram FS E F E 金属一边的势垒半导体一边的势垒金属一边的势垒半导体一边的势垒 m q D qV v E D x c E F E smDmm WWqVWq Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram b b WWm m W W s s 电子反阻挡层电子反阻挡层电子反阻挡层电子反阻挡层 Ws Wm Ev Ec E0 EFm EFs Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram msD WWqV F E v E c E D x Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram 2 2 金属 金属 金属 金属 p p型半导体接触型半导体接触型半导体接触型半导体接触 时空穴阻挡层 时空穴反阻挡层 sm sm WWb WWa 1 1 WW s s W Wm m 空穴阻挡层 空穴阻挡层空穴阻挡层空穴阻挡层 EFm EFs Ws Wm Ev Ec E0 Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram 接触后 接触后 接触后 接触后 qVD Ws Wm xD EF Ev Ec msD WWqV 半导体一边的势垒 2 2 WWm m W Ws s 空穴反阻挡层 空穴反阻挡层空穴反阻挡层空穴反阻挡层 Ws Wm EFs EFm Ev Ec E0 Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram 接触后 接触后 接触后 接触后 EF Ec Ev xD Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram 3 3 表面态对接触势垒的影响 表面态对接触势垒的影响 表表表表 面面面面 态 态 态 态 局域在表面附近的新电局域在表面附近的新电局域在表面附近的新电局域在表面附近的新电 子态 子态 子态 子态 表面能级 表面能级 表面能级 表面能级 与表面态相应的能与表面态相应的能与表面态相应的能与表面态相应的能 级称为表面能级 级称为表面能级 级称为表面能级 级称为表面能级 AA 接触前 半导体体内与表面电接触前 半导体体内与表面电接触前 半导体体内与表面电接触前 半导体体内与表面电 子态未交换电子子态未交换电子子态未交换电子子态未交换电子 E0 EFm Wm Ws Wl Ev EFS0 EF0 表面能级表面能级表面能级表面能级 Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram BB 接触前 半导体体内与表面电子态交换电子后接触前 半导体体内与表面电子态交换电子后接触前 半导体体内与表面电子态交换电子后接触前 半导体体内与表面电子态交换电子后 能带弯曲量能带弯曲量qVD EF0 EFs0 与金属的性能无关与金属的性能无关 半导体的功函数则变为 半导体的功函数则变为 EFm Wl qVD En l 0 Fs 0 FsnD 1 s WEEWEqVW qVD EFs Wm Wl E0 Ev n E EF Ec Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram C C 金属与半导体接触后金属与半导体接触后金属与半导体接触后金属与半导体接触后 m q qVD Ec 0 Ec Ev n E Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram 巴丁模型与金属的性能无关 0 FscnDm E0EEqVq Contact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band DiagramContact between Metal and Semiconductor and Band Diagram 实际中 实际中 实际中 实际中 E EFs Fs 0 0 常位于常位于常位于常位于E E v v 以上以上以上以上1 31 3E E g g 处 所以处 所以处 所以处 所以 ggvcm E 3 2 E 3 1 0E0Eq 7 2 7 2 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal 金金金金 半接触整流理论半接触整流理论半接触整流理论半接触整流理论 Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 重点重点重点重点 阻挡层的整流特性和整流理论阻挡层的整流特性和整流理论阻挡层的整流特性和整流理论阻挡层的整流特性和整流理论 欧姆接触欧姆接触欧姆接触欧姆接触 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 1 1 阻挡层的整流特性阻挡层的整流特性阻挡层的整流特性阻挡层的整流特性 外加电压对阻挡层的作外加电压对阻挡层的作外加电压对阻挡层的作外加电压对阻挡层的作 用用用用 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact qVD q Vs 0 ns q 0JJJ smms 净电流 xd Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact qVD1 q VD V qV ns q smms JJ xd n q smms JJJ 正向电流 V ns q qVD1 q VD V n q qV EFEF V xd Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 加上正向电压加上正向电压加上正向电压加上正向电压 金属一边为正金属一边为正金属一边为正金属一边为正 时 时 时 时 加上反向电压 金属一边为负 时 加上反向电压 金属一边为负 时 加上反向电压 金属一边为负 时 加上反向电压 金属一边为负 时 qVD1 q VD V ns q q V mssm JJ xd V mssm JJJ 反向电流 饱和 sm J EF EF ns q qVD1 q VD V q V xd V Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 2 2 整流理论 整流理论 整流理论 整流理论 1 1 扩散理论 扩散理论 扩散理论 扩散理论 x xd d l l n n 时时时时 2 2 热电子发射理论 热电子发射理论 热电子发射理论 热电子发射理论 x xd d l l n n 时 电子通过势垒区将发生时 电子通过势垒区将发生时 电子通过势垒区将发生时 电子通过势垒区将发生 多次碰撞 多次碰撞 多次碰撞 多次碰撞 势垒高度势垒高度势垒高度势垒高度qVqVD D k k 0 0 T T时 时 时 时 势垒区势垒区势垒区势垒区内内内内 的载流子浓度 的载流子浓度 的载流子浓度 的载流子浓度 0 0 耗尽区耗尽区耗尽区耗尽区 1 xx0 xx0qN d dD V TkqV 0 如果 Tk qV eJJ SD 0 时02 V SD JJ TkqV 0 如果 2 2 2 2 热电子发射理论 热电子发射理论 热电子发射理论 热电子发射理论 x xd d 势垒顶部时 电子可以自势垒顶部时 电子可以自势垒顶部时 电子可以自势垒顶部时 电子可以自 由越过势垒进入另一边由越过势垒进入另一边由越过势垒进入另一边由越过势垒进入另一边热电子发射热电子发射热电子发射热电子发射 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 假设假设假设假设qVDqVD k k 0 0T T Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 思路 思路 思路 思路 a Js m b Jm s c J Js m Jms a Ja J s s mm时 时 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact sF qE x ms 1dnqvJ x方向输运假设电子沿 能量范围内的电子数在dEEE dEEfEgdn 2 2 4 00 2 1 3 2 3 dEeEEe h m Tk EE c Tk EE n cFc dEeEE h m Tk EE c n F 0 2 1 3 2 3 2 4 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 3 2 1 2 vmEE nc 利用 4 vdvmdE n Tk EE c Fc eNn 0 0 又 Tk EE n Fc e h Tkm 0 3 2 3 0 2 2 dve Tk m ndn Tk vm n n 0 2 2 2 3 0 0 2 则 5 2 0 222 2 2 3 0 0 zyx Tk vvvm n dvdvdve Tk m n zyxn Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 界面在单位时间内均能到达 的电子中速度为单位体积秒 的体积秒所以单位截面内长为 dNvv v x x 11 1 单位截面秒 11 x vdndN 6 2 0 222 2 2 3 0 0 zyxx Tk vvvm n dvdvdvve Tk m n zyxn Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact VVqvm 2 1 D 2 x n 到达界面的电子的动能 sF qE x ms 1dnqvJ x方向输运假设电子沿 2 min n D x m VVq v 即电子的最小速度 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact sF qE x ms dnqvJ 于是 0 0 222 2 0 0 2 x zyxn v x Tk vvvm xyy n dvevdvdv Tk m qn 7 0 0 2 Tk qV Tk q eeTA ns Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact b b J Jm m s s 是恒定的 所以是恒定的金属一边的势垒 sm ns J q 800 smms JJV时 9 0 2 Tk q ns eTA 0 VJJ mssm 从而 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact c c 总电流密度总电流密度总电流密度总电流密度J J smms JJJ 11 0 2 Tk q ST ns eTAJ 其中 101 0 Tk qV ST eJ 1 0T k qV SD eJJ 1 0T k qV ST eJJ 扩散理论扩散理论扩散理论扩散理论与与与与热电子理论热电子理论热电子理论热电子理论的差异的差异的差异的差异 ST ST J J 对温度的敏感程度不如 随外加电压而变化 2 1 Tk D qV eVVJ D r SD 0 0 D 2qN 其中 对温度很敏感 与外加电压无关 2 1 ST J Tk q ST ns eTAJ 0 2 其中 xd ln 时 xd ln 时 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 3 3 3 3 镜像力和隧道效应的影响 镜像力和隧道效应的影响 镜像力和隧道效应的影响 镜像力和隧道效应的影响 反向特性不饱和反向特性不饱和反向特性不饱和反向特性不饱和 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 势垒受到镜象力的影响 势垒受到镜象力的影响 势垒受到镜象力的影响 势垒受到镜象力的影响 c E c E q ns q ns q m x Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 1 1 镜象力的影响 镜象力的影响 镜象力的影响 镜象力的影响 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 感应电荷对电子产生库仑吸引力感应电荷对电子产生库仑吸引力感应电荷对电子产生库仑吸引力感应电荷对电子产生库仑吸引力 镜象力镜象力镜象力镜象力 1 24 2 2 0 x q f x x q fdx2 16 0 2 产生的电子附加势能为 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 对于金对于金对于金对于金 半接触势垒中的半接触势垒中的半接触势垒中的半接触势垒中的 电子 附加势能为电子 附加势能为电子 附加势能为电子 附加势能为 3 x16 q r0 2 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 取势能零点在取势能零点在取势能零点在取势能零点在E EFm Fm处 考虑 处 考虑处 考虑处 考虑 附加势能后 附加势能后 附加势能后 附加势能后 电子的有效势能电子的有效势能电子的有效势能电子的有效势能为 为 为 为 xqV x q xVq r 016 2 4 2 1qN 16 2 0 D 2 0 nsd r xxxq x q r Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 当电子所受到的电场力当电子所受到的电场力当电子所受到的电场力当电子所受到的电场力 镜像力镜像力镜像力镜像力 时 有时 有时 有时 有VVmax max VV x xm m 5 4 1 2 1 dD m xN x dm r D nsm xx Nq qxVq 0 2 相应地 式代入将45 qxm处的电势降落则在 dm r D xx Nq 0 2 mns xVqq 6 2 4 1 4 3 0 3 2 7 VV Nq D r D 增大降落值 q 高时将导致势垒最高点可见反向偏压和掺杂较 偏离理想增大时 理想减小时 V V qV qV 0 0 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 反向 Jq qqq nsns 度而金属一边有效势垒高 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact D qV效势垒高度相应地半导体一边的有 D Vq q ns q c E c E m x ns q D qV nsns qq DD VqqV Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 镜向力导致反 向特性不饱和 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 2 2 隧道电流的影响 隧道电流的影响 隧道电流的影响 隧道电流的影响 a 隧道效应 隧道效应 c E F E 超薄势垒失去阻挡载流子的功能超薄势垒失去阻挡载流子的功能 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 决定隧道穿透几率的决定隧道穿透几率的决定隧道穿透几率的决定隧道穿透几率的 两个因素 两个因素 两个因素 两个因素 1 1 1 1 势垒高度 势垒高度 势垒高度 势垒高度 2 2 2 2 隧道厚度 隧道厚度 隧道厚度 隧道厚度 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact cns xqVq 度为金属一边的有效势垒高 cd r D ns xx Nq q 0 2 7 2 3 0 3 2 VV Nq xq D r D cns 偏离理想增大时 理想减小时 V V qV qV 0 0 1 势垒高度 1 势垒高度 Rectification Theory of MetalRectification Theory of MetalRectification Theory of MetalRectification Theory of Metal Semiconductor ContactSemiconductor ContactSemiconductor ContactSemiconductor Contact 隧道效应导致反隧道效应导致反 向特性不饱和向特性不饱和