ECE 875: Electronic Devices Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

Lecture 22, 28 Feb 14 Chp. 02: pn junction and Chp 03: metal-semiconductor junction About HW06 problems VM Ayres, ECE875, S14

Pr. 2.04: Assume: Si at 300 K

Remember this sequence in real research: find: Charge Q and charge density r Electric field E Potential y Energy barrier q y from y Depletion region WD or equivalent local region from y C-V to find concentration and ybi I-V to find concentration and energy barrier MODEL MODEL EXPERIMENT

Charge Q and charge density r Electric field E Potential y Pr. 2.04: Charge Q and charge density r Electric field E Potential y Energy barrier q y from y Depletion region WD or equivalent local region from y C-V to find concentration and ybi I-V to find concentration and energy barrier MODEL

: r01 = qND01 = a constant (C/cm3) : r02 = qND02 = another constant (C/cm3) VM Ayres, ECE875, S14

VM Ayres, ECE875, S14

What are the two places that you know any E info for? Answer: E 02 (x = WDn) = 0 E 01 (x = 0.2 mm) = E m-02 VM Ayres, ECE875, S14

Solve for E max-02 VM Ayres, ECE875, S14

E max-01 is in terms of WDn because E max-02 is in terms of WDn . Solve for E max-01 E max-01 is in terms of WDn because E max-02 is in terms of WDn . So need to find WDm (= Wm). VM Ayres, ECE875, S14

Charge Q and charge density r Electric field E Potential y Pr. 2.04: Charge Q and charge density r Electric field E Potential y Energy barrier q y from y Depletion region WD or equivalent local region from y C-V to find concentration and ybi I-V to find concentration and energy barrier MODEL

Find ybi (= potential V). Easiest way is graphically: VM Ayres, ECE875, S14

Find ybi (= potential V). Easiest way is graphically: VM Ayres, ECE875, S14

Find ybi (= potential V). Easiest way is graphically: Now have an expression for ybi in terms of WDn. If you had a value for ybi on the LHS, you could use the expression to solve for WDn. VM Ayres, ECE875, S14

Find value of ybi: VM Ayres, ECE875, S14

Find value of ybi: qy1-2: + = VM Ayres, ECE875, S14

Find value of ybi: qy2-3: = VM Ayres, ECE875, S14

Find value of ybi: qy1-2 - qy2-3 = qybi = VM Ayres, ECE875, S14

Put in value for ybi and solve for WDn: Now have an expression for ybi in terms of WDn. If you had a value for ybi on the LHS, you could use the expression to solve for WDn. VM Ayres, ECE875, S14

Put in value for WDn and solve for E max-01 E max-01 is in terms of WDn because E max-02 is in terms of WDn . So need to find WDm (= Wm). VM Ayres, ECE875, S14

Pr. 3.01: Draw band-diagrams with the following values marked on it: Barrier height on metal side: qfBn0 = 0.8 eV = given Barrier height on semiconductor side: qybi Barrier width W: primarily on n-side: WDn

Pr. 3.08:

W-Si example:

= 2.76 x 1019 cm-3 Too high

Too low

Pr. 3.08: Use: X 1/1010