Email log file after script completes - Powershell

Hey Experts.  I'd like to add the ability to email the log file once the script has finished running.  Below is the script I'd like to add the email functionality to:

$ServerList = @'
	"Name",			"Path"
	Servers
'@ | ConvertFrom-Csv
$LogFile = "\\w2k12FS01\PUBLIC\Tivoli_Master_Logs\Combined_{0}.log"

$Yesterday = (Get-Date).AddDays(-1)
$Pattern = (Get-Date).AddDays(-1).ToString('MM\/dd\/yyyy') + ' * --- SCHEDULEREC STATUS BEGIN*'
$Timestamp = $Yesterday.ToString('yyyyMMdd')
$in = $false
$ServerList | ForEach-Object {
	$Server = $_
	"========== $($Server.Name) ============================================================"
	Try {
		Switch -Wildcard (Get-Content -Path "\\$($Server.Name)\$($Server.Path.Replace(':', '$'))" -ErrorAction Stop) {
			$Pattern					{$in = $true}
			'*SCHEDULEREC STATUS END*'	{$in = $false}
			default						{If ($in) {$_}}
		}
	} Catch {
		"ERROR accessing '$($Server.Path)': $($_.Exception.Message)"
	}
} | Set-Content -Path $($LogFile -f $TimeStamp)

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I tried adding this at the end of the script but it didn't work because of an error (Tivoli_Master_Logs\Combined_{0}.log value cannot be null).

$EmailFrom = "me"
$EmailTo = "me"
$EmailSubject = "Backup results for $($yesterday)"  
$SMTPServer = "smtp"

$emailattachment = $LogFile

$mailmessage = New-Object system.net.mail.mailmessage 
$mailmessage.from = ($emailfrom) 
$mailmessage.To.add($emailto)
$mailmessage.Subject = $emailsubject
$attachment = New-Object System.Net.Mail.Attachment($emailattachment, 'text/plain')
  $mailmessage.Attachments.Add($attachment)
$mailmessage.Body = ("<br />$('*'*72)<br />" + ((Get-Content -Path $LogFile) -join '<br />') + "<br />$('*'*72)<br />")

$mailmessage.IsBodyHTML = $true
$SMTPClient = New-Object Net.Mail.SmtpClient($SmtpServer, 25)  
#$SMTPClient.Credentials = New-Object System.Net.NetworkCredential("$SMTPAuthUsername", "$SMTPAuthPassword") 
$SMTPClient.Send($mailmessage)

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Thanks experts for your help!