Minority carrier lifetimes in silicon

As semiconductor designers we grew up with the concept of lifetimes of minority carriers in silicon. Our task was to take the process parameters and design rules from the foundry and fashion a chip. However, once we venture beyond this safe boundry and pit our skills against device design from scratch, a number of issues come up with which we are not too familiar with. One such came up for me this weekend. I was trying to calculate minority carrier lifetimes for specific conditions. I found out that this is a very difficult thing to do. Minority carrier lifetimes vary quite broadly and are dependent on a number of factors. Among these are Auger recombination, band to band recombination and Shockley-Read-Hall (SRH)recombination.

The lifetime is a strong function of the doping concentration of the silicon. It is easier to use analytical formulas for lifetime calculation when the concentration is high ( > 1E17).

High resistivity material is harder to handle analytically. The lifetimes in these materials can be a function of the construction of the crystal(CZ versus FZ). In addition various processing steps can have an impact on the lifetime.

Nevertheless analytical formulas do exist for estimation of lifetimes. The one that I am now using is: lifetime = 5E-7/(1.0 + 2.0E-17)N, where N is the doping concentration in cm**3.

Roulston has published a curve that also shows the approximate variation of lifetime with concentration. Both of these techniques are just approximations. I compared calculations of the lifetime for various concentrations using the analytical formula with Roulston’s curve. The fit became very close as the concentrations increased, but was poor at low concentrations (highly resistive silicon).

My conclusions are that if the need is simply to estimate the lifetime to a rough order of magnitude then by all means one can use the analytical formula given above or Roulston’s curve. However, if precise numbers are required then measurements must be made on samples of doped silicon under the conditions of operation. There is no shortcut here for that kind of accuracy!


SPG designs, develops and delivers custom analog and RF/wireless asics and modules.

FPGA Design and development service

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A wideand RF detector ( 40 Mhz to 3 Ghz) -75 dBm to 5 dBm input

A wideband RF detector

A wideband RF detector

Linear detector performance

Linear detector performance curves

A wideband linear RF detector

Price for one unit: $25.00. Lead time for delivery 3 days. 30 Day return policy. Pricing for 100 units or more: $20.00 per unit.  Please contact Signal Processing Group Inc. for details for purchase from Signal Processing Group Inc. Email: spg@signalpro.biz 24/7

Wideband RF detector perforamce , more details

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2 stage 35 dB gain RF amplifier. Front of the module

Full range frequency response

2 stage amplifier deta

Please see details at http://www.signalpro.biz/2rf_amplifier_details.htm    Delivery lead time is 3 days. Return within 30 days for a full refund. Price is $15.00 for one unit and $10.00 per unit in volumes of 100. For higher volumes than 100 please contact Signal Processing group Inc.

miniature LNA module

Mni LNA performance

Delivery lead time is 3 days. Return within 30 days for a full refund. Price is $15.00 for one unit and $12.00 per unit in volumes of 100. For higher volumes than 100 please contact Signal Processing Group Inc. at email: spg@signalpro.biz or call 602-626-0272 for fastest service.

A high frequency divider from 500 Mhz to % Ghz+

The input interface.
The frequency divider has a differential analog interface. The following parameters apply:
The minimum frequency that can be input is 500 Mhz and the maximum frequency is 6.0 Ghz.
The RF input level is 5 dBm to – 5 dBm. For lower frequencies make sure that the slew rate is
greater than 560 V/us. The input is biased by two 500 Ohm resistors connected to a 1.6V DC bias.
Therefore AC coupling is used at the input. These are two 100pF capacitors.
The output interface.
The output is single ended. The output driver is capable of sourcing and sinking 24 mA. The
equivalent output impedance is 50 Ohm. To avoid reflections it is recommended that the divider
work into a 50 Ohm load.
General operation.
The inputs are applied to the input SMA I/O. The product will work with both a differential input as
well as a single ended input. However, a differential input works best. The division ratio is applied
to the N1 and N2 control inputs as follows:
N2 N1 Division ratio
0 0 8
0 1 16
1 0 32
1 1 64
The logic levels are:
Logic level Voltage
1 1.4V minimum
0 0.6V maximum
The supply voltage interface.
The operating supply voltage is 3.3V typical. The quiescent (DC) operating supply current is 2 mA.

A high frequency divider 500 Mhz to 5 Ghz+

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SPDT DC to 3 Ghz RF switch

DC to 3 Ghz RF SPDT switch

RF Switch typical features

Supply voltage = Vcc = 0/+5 Vdc
Operatng temperature = TA = -50° C to 125 Deg C
Operating impedance = 50 Ohm
Input power for 1 dB
compression ( 5.0V system) = 37 dBm ( f = 0.5 to 3 Ghz)
Input third order Intercept = 64 dBm ( 0 to 5.0V system, f = 0.5 to 3 Ghz)
Operating frequency range = DC to 3 Ghz.
Insertion loss DC to 3 Ghz = 0.8 dB
Isolation DC to 3 Ghz = 14 dB minimum
Return loss DC to 3 Ghz = 20 dB
50% contl to 10/90 %
( ON/OFF) = 120 ns

A single stage RF amplifier as a gain block

A single stage RF amplifier summary specifications

Summary Specifications

Gain,  Operating: 19.5 dB
Operating frequency range: 1.0 – 2700 Mhz
OIP3: (Pout = 19.0 dBm),  -8.5 dBm
P1dB: 4.6 dBm
N.F: 4.2 dB
Supply voltage Operating: 3.3  – 5.5 Volts

Price: single unit $7.50, 100 units : $5:50.

Free delivery, shipping lead time 2 days.

30 day return policy, buyer ships.
Supply current Supply = 5.0V,  23.0 mA

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