ECE 255 Fall 2019 Purdue University Doped Semiconductors

ECE 255: Fall 2019 Purdue University Doped Semiconductors (Sedra and Smith, 7 th Ed. , Sec. 3. 2) Mark Lundstrom School of ECE Purdue University West Lafayette, IN USA Lundstrom: Fall 2019 1

Doping makes semiconductors useful metal semiconductor insulator “doping” gold (Au) silicon (Si) Lundstrom: Fall 2019 glass (Si. O 2) 2

Doped semiconductors 1) 2) 3) 4) The n 0 p 0 product Doping Carrier concentration vs. doping density Carrier concentration vs. temperature Lundstrom: Fall 2019 3

Quick re-cap Si atom (At. no. 14) energy 4 s 0 3 p 6 Intrinsic Si crystal conduction band • • • 3 s 2 2 p 6 2 s 2 1 s 2 • • • valence band position 4

The equilibrium n 0 p 0 product For intrinsic semiconductors: Silicon T = 300 K ni is typically small at room temperature, but can become large at high temperatures. Lundstrom: Fall 2019 5

Generation and Recombination requires energy to break covalent bonds releases energy In equilibrium: G = R and n 0 = p 0 = ni Lundstrom: Fall 2019 6

Doping a semiconductor Gallium or boron Phosphorus or Arsenic “P-type doping” “N-type” doping Lundstrom: Fall 2019 7

Dopants in Si column IV P-type dopants come from column III N-type dopants come from column V Lundstrom: Fall 2019 8

Donors: N-type doping Weakly bound Easily broken at room temperature Phosphorus or Arsenic Produces an electron in the conduction band. Lundstrom: Fall 2019 9

Ionized donor Concentration of dopants: Concentration of ionized donors: + Concentration of electrons in the conduction band: Ionized donor Lundstrom: Fall 2019 10

Calibration (moderate doping density) This looks like a big number, and it is, but also it’s really quite small. Lundstrom: Fall 2019 11

Carrier concentrations Phosphorous or arsenic doped Si at 300 K Example: extrinsic N-type semiconductor Lundstrom: Fall 2019 12

Carrier concentrations Note that the N-type doping increased n 0, but it decreased p 0. Lundstrom: Fall 2019 13

Be careful about units! We will be working in SI (MKS) units. The carrier concentration should be given per cubic meter, but semiconductor people like to mix their units. It is safest to do the calculations in SI units, and then convert to cubic cm. Lundstrom: Fall 2019 14

Acceptors: P-type doping Missing bond Boron or gallium Lundstrom: Fall 2019 15

Ionized acceptor Concentration of dopants: Concentration of ionized acceptors: _ Ionized acceptor Concentration of “holes” in the valence band: Lundstrom: Fall 2019 16

Carrier concentrations Example: extrinsic P-type semiconductor Lundstrom: Fall 2019 17

Doped semiconductors ✓ 1) ✓ 2) 3) 4) The n 0 p 0 product Doping Carrier concentration vs. doping density Carrier concentration vs. temperature Lundstrom: Fall 2019 18

Space charge density The net charge in this region: bulk, uniform semiconductor Lundstrom: Fall 2019 19

Space charge neutrality “Nature abhors a vacuum. ” Nature also abhors a charge. Mobile charges (electrons and holes) will be attracted to the immobile ionized dopants), so that the net charge is zero. Almost uniform semiconductors will be nearly neutral, but with strong non-uniformities (e. g. PN junctions), there will be a space charge. Lundstrom: Fall 2019 20

Space charge neutrality + np product Always true in equilibrium –even for doped semiconductors. These are two equations in two unknowns –p 0 and n 0. Lundstrom: Fall 2019 21

Solving for the carrier density 1) charge neutrality: 2) eq. np product: 3) result: Lundstrom: Fall 2019 22

N-type extrinsic semiconductors at moderate temps Extrinsic semiconductors: Lundstrom: Fall 2019 23

P-type extrinsic semiconductors at moderate temps Lundstrom: Fall 2019 24

Example 1 Consider Si doped with phosphorus at ND = 2. 00 x 1015 cm-3 The temperature is 300 K. What are n 0 and p 0? Recall that at 300 K in Si, ni = 1. 00 x 1010 cm-3 Assume that the donors are fully ionized. 25

Example 2 Consider Si doped with phosphorus at ND = 2. 00 x 1015 cm-3 and Boron at NA = 1. 00 x 1015 cm-15. The temperature is 300 K. What are n and p? Lundstrom: Fall 2019 26

Summary (room temperature) Fully ionized: Extrinsic: Intrinsic: In between: Lundstrom: Fall 2019 27

Carrier concentration vs. temperature High temperatures: Moderate temperatures: Low temperatures: 28

Carrier concentration vs. temperature freeze out extrinsic intrinsic 1. 0 0 K 300 K Lundstrom: Fall 2019 600 K 29

Summary To dope a semiconductor, we replace a few atoms with atoms from a different column of the periodic table. Ionized dopants produce electrons in the conduction band or holes in the valence band. The carrier concentration vs. temperature characteristic has freeze out, extrinsic, and intrinsic regions. A low temperatures, semiconductors become insulators. A high temperatures, doped semiconductors become intrinsic. Lundstrom: Fall 2019 30

Doped semiconductors 1) 2) 3) 4) The np product Doping Carrier concentration vs. doping density Carrier concentration vs. temperature Lundstrom: Fall 2019 31