Electronic – PN junction band gap – equal across all devices

semiconductors

With a given material eg silicon, is the band gap constant across devices? For example, at a constant temperature is the band gap of a diode ("diode drop") exactly the same as that of (say) an NPN transistor? If not, what kind of variation would one expect between devices?

Best Answer

For a 100% pure element (no doping) it will be the same.

For a practical diode or transistor, the dopant levels and purity have quite a large effect on both the forward voltage and temperature coefficient.

For pure silicon the tempco is -2.1mV / degree C, but the venerable 2N3904 usually has -2mV / degree C (depends on manufacturer).

If you read the SPICE files for some devices, this can be inferred from ideality factor as seen in the Schockley diode equation.

For a diode, this is N in the model.

For a transistor NF is the forward mode ideality factor and NR is the reverse ideality factor.

A perfect device will have N=1. Here is the model for the MMBD4148 small signal / switching diode

*SRC=MMBD4148;DI_MMBD4148;Diodes;Si; 75.0V 0.250A 4.00ns Diodes Inc. Switching Diode

.MODEL DI_MMBD4148 D ( IS=300n RS=0.422 BV=75.0 IBV=2.50u + CJO=1.99p M=0.333 N=2.77 TT=5.76n )

Here N is 2.77 (the higher this value, the less ideal it is)

Looking at the 2N3904 model

  • Model Generated by MODPEX * Copyright(c) Symmetry Design Systems
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  • Model generated on Aug 7, 01

  • MODEL FORMAT: PSpice

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.MODEL Q2n3904 npn +IS=1.26532e-10 BF=206.302 NF=1.5 VAF=1000 +IKF=0.0272221 ISE=2.30771e-09 NE=3.31052 BR=20.6302 +NR=2.89609 VAR=9.39809 IKR=0.272221 ISC=2.30771e-09 +NC=1.9876 RB=5.8376 IRB=50.3624 RBM=0.634251 +RE=0.0001 RC=2.65711 XTB=0.1 XTI=1 +EG=1.05 CJE=4.64214e-12 VJE=0.4 MJE=0.256227 +TF=4.19578e-10 XTF=0.906167 VTF=8.75418 ITF=0.0105823 +CJC=3.76961e-12 VJC=0.4 MJC=0.238109 XCJC=0.8 +FC=0.512134 CJS=0 VJS=0.75 MJS=0.5 +TR=6.82023e-08 PTF=0 KF=0 AF=1

Here the forward ideality factor is 1.5 (much closer to an ideal diode). This is one of the reasons that temperature sensors often use a diode connected transistor.

So the forward voltage is process dependent (as is reverse leakage).

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